UNIVERSIDADE ESTADUAL DE CAMPINAS INSTITUTO DE FILOSOFIA E CIÊNCIAS HUMANAS BRENO ANDRADE ZUPPOLINI ONTOLOGICAL UNDERPINNINGS OF ARISTOTLE'S PHILOSOPHY OF SCIENCE Fundamentos Ontológicos da Filosofia da Ciência de Aristóteles CAMPINAS 2017 BRENO ANDRADE ZUPPOLINI TITLE: ONTOLOGICAL UNDERPINNINGS OF ARISTOTLE'S PHILOSOPHY OF SCIENCE TÍTULO: FUNDAMENTOS ONTOLÓGICOS DA FILOSOFIA DA CIÊNCIA DE ARISTÓTELES Thesis presented to the Institute of Philosophy and Human Sciences of the University of Campinas in partial fulfilment of the requirements for the degree of Doctor in Philosophy Supervisor: LUCAS ANGIONI ESTE EXEMPLAR CORRESPONDE À VERSÃO FINAL DA TESE DEFENDIDA PELO ALUNO BRENO ANDRADE ZUPPOLINI E ORIENTADA PELO PROF. DR. LUCAS ANGIONI. __________________ CAMPINAS 2017 UNIVERSIDADE ESTADUAL DE CAMPINAS INSTITUTO DE FILOSOFIA E CIÊNCIAS HUMANAS A Comissão Julgadora dos trabalhos de Defesa de Tese de Doutorado, composta pelos Professores Doutores a seguir descritos, em sessão pública realizada em DATA, considerou o candidato Breno Andrade Zuppolini aprovado. Prof. Dr. Prof. Dr. Prof. Dr. Prof. Dr. Prof. Dr. A Ata de Defesa, assinada pelos membros da Comissão Examinadora, consta do processo de vida acadêmica do aluno. To my parents, Marta and Alexandre, for their love, patience, and support. ACKNOWLEDGMENTS I would like to thank warmly my supervisor Lucas Angioni. His academic excellence has been an inspiration. His friendship is a privilege for which I am immensely grateful. If this dissertation has any merits, he is the main responsible. During the past years, I had the opportunity to discuss my research with outstanding scholars. I am grateful to David Charles, Alan Code, Kei Chiba, Nathanael Stein, Laura Castelli, Phil Corkum, Marko Malink, Paolo Fait, Barbara Sattler, Vasilis Politis, David Ebrey, Adam Crager, Joseph Karbowsi, R. J. Hankinson, Klaus Corcilius, Sean Kelsey, Jacob Rosen, Philipp Steinkrüger, Ben Morison, Jason Carter, Thomas Ainsworth, Stefan Sienkiewicz, Takashi Oki, Harry Alanen, Philipp Kurbel, Guus Eelink, Giulio di Basilio, Antônio Pedro Mesquita, Ricardo Santos, Nicola Carraro, Roberto Grasso, Manuel Berrón,, Inara Zanuzzi, Vivianne de Castilho Moreira, Priscilla Tesch Spinelli, Nazareno de Almeida, Anderson Borges, João Hobuss, Paulo Fernando Tadeu Ferreira, and many others. I am especially thankful to Michail Peramatzis, David Bronstein, Raphael Zillig, and Rodrigo Guerizoli, for their extraordinary generosity and for many contributions to my work over these years. A great portion of this dissertation is the result of my studies at the University of Oxford, in 2013 and 2016, as a visiting student. Many thanks to David Charles and Michail Peramatzis for accepting to be my supervisors during these visits and for careful and insightful comments on my work. I am extremely grateful to my colleagues and friends, members of the Research Group on Plato and Aristotle of the University of Campinas, organized by Prof. Lucas Angioni: Mateus Ricardo Fernandes Ferreira, Wellington Damasceno de Almeida, Francine Maria Ribeiro, Thiago Silva Freitas Oliveira, Fernando Martins Mendonça, Felipe Weinmann, Gustavo Bianchi Ferreira, Natalia Costa Rugnitz, Angelo Antonio Pires do Oliveira, Davi Heckert Cesar Bastos, Ariane Lindemute, and, more recently (but no less important), Nicola Carraro and Roberto Grasso. My greatest debt is to my parents, Marta and Alexandre, and siblings, Maria Clara and Luca, for their constant support. To my beloved Livia, I am thankful for giving me the happy, complete life I always wanted to have. Finally, I would like to express my gratitude to the São Paulo Research Foundation (FAPESP) for funding my studies both in Campinas and in Oxford. First let me talk with this philosopher. - What is the cause of thunder? William Shakespeare, King Lear III. iv. 138-9 ABSTRACT This dissertation focuses on the ontological underpinnings of Aristotle's philosophy of science. His notion of scientific knowledge is committed to a certain kind of foundationalism, which recognizes essences as ultimate explanatory factors. The philosopher distinguishes between two kinds of essence-bearers: subjects and attributes. Our analysis of this distinction involves a study of Aristotle's doctrine of ontological categories and his theory of predication. In addition, we specify the roles played by the essences of subjects and the essences of attributes in scientific explanations. As a result, Aristotle's foundationalism amounts to the view that reality is composed of finite chains of explanatory connections and entities whose essences are connected to one another in a hierarchical structure. Keywords: Aristotle; science; essence; predication; foundationalism. RESUMO Esta tese dedica-se aos fundamentos ontológicos da filosofia da ciência de Aristóteles. Sua noção de conhecimento científico compromete-se com certo tipo de fundacionismo, que reconhece essências como fatores explanatórios últimos. O filósofo distingue dois tipos de portadores de essência: sujeitos e atributos. Nossa análise dessa distinção envolve um estudo da doutrina das categorias e da teoria da predicação de Aristóteles. Ademais, procuramos especificar os papéis desempenhados pelas essências dos sujeitos e pelas essências dos atributos em explicações científicas. Como resultado, temos que o fundacionismo de Aristóteles consiste na visão de que a realidade é composta de cadeias explanatórias finitas e entes cujas essências estão conectadas umas às outras em uma estrutura hierárquica. Palavras-chave: Aristóteles; ciência; essência; predicação; fundacionismo. ABBREVIATIONS APo = Analytica Posteriora APr = Analytica Priora Cael. = de Caelo Cat. = Categoriae De An. = de Anima EE = Ethica Eudemia EN = Ethica Nicomachea GA = de Generatione Animalium GC = de Generatione et Corruptione HA = Historia Animalium IA = de Incessu Animalium Insomn. = de Insomniis Int. = de Interpretatione Long. = de Longaevitate MA = de Motu Animalium MM = Magna Moralia Metaph. = Metaphysica Mete. = Meteorologica PA = de Partibus Animalium Ph. = Physica Po. = Poetica Pol. = Politica Rh. = Rhetorica SE = Sophistici Elenchi Somn.Vig. = de Somno et Vigilia Top. = Topica TABLE OF CONTENTS INTRODUCTION ................................................................................................................................... 21 CHAPTER 1: ARISTOTLE'S FOUNDATIONALISM ................................................................... 27 1.1 – Scientific Knowledge: Demonstration, Comprehension, and Foundationalism ................ 27 1.2 – A Rationalist Interpretation of Aristotle's Foundationalism ................................................. 31 1.3 – Coming to Know First Principles: A Non-Rationalist Account ........................................... 34 CHAPTER 2: CAUSE, ESSENCE, AND ESSENCE-BEARERS .................................................. 47 2.1 – The Four Objects of Inquiry and Knowledge: Fact, Cause, Existence, and Essence ....... 47 2.2 – Interdependence between Defining and Explaining .............................................................. 51 2.3 – The Essence of Subjects vs. The Essence of Attributes: Two Models of Definition-Based Explanation ............................................................................................................................................ 57 CHAPTER 3: A METAPHYSICAL DEFENCE AGAINST INFINITE REGRESS ................. 65 3.1 – Aristotelian Foundationalism Challenged and a Metaphysically Loaded Response .......... 65 3.2 – The Categories: Inherence and Said-of Relations ...................................................................... 73 3.3 – A Defence against Infinite Regress: The Traditional Interpretation .................................... 78 3.4 – A Defence against Infinite Regress: An Alternative Interpretation ..................................... 81 CHAPTER 4: PER SE BEINGS AND PER SE PREDICATIONS .............................................. 91 4.1 – Kinds of Being and Ontological Priority ................................................................................. 91 4.2 – The four uses of 'per se': Posterior Analytics I 4 .......................................................................... 95 4.3 – Per Se Accidents and Primary Universality: the Debate ....................................................... 102 4.4 – Per Se Accidents and Primary Universality: Remodelling the Natural Solution ................ 109 CHAPTER 5: EXPLANATION, ESSENCE, AND PRIMARY UNIVERSALITY ................. 123 5.1 – Two Problems in Posterior Analytics II 16-17 .......................................................................... 123 5.2 The Uniqueness Requirement .................................................................................................. 124 5.3 Aristotle's Answer and the Two Models of Scientific Explanation .................................... 129 5.4 The appearance of 'multiple causes': 'in-a-kind' and homonymous explananda. ............... 135 5.5 A Conciliatory Solution ............................................................................................................. 139 CHAPTER 6: COMING TO KNOW THE ESSENCE OF SUBJECTS .................................... 143 6.1 – The Essence of Subject-Kinds: An Exception? .................................................................... 143 6.2 – The Hylomorphic Analysis....................................................................................................... 147 6.3 – The Analytics-model in the Metaphysics .................................................................................... 150 CONCLUSION ....................................................................................................................................... 159 BIBLIOGRAPHY ................................................................................................................................... 163 21 INTRODUCTION We do not find anywhere in the corpus aristotelicum a systematic approach to the concept of knowledge in general. Perhaps such a general epistemology can be reconstructed in some way or another by comparing the different kinds of cognition Aristotle recognizes in many of his works.1 It is true that one of his treatises, the APo, focuses on the notion of , commonly translated as 'knowledge'. However, unlike Plato in the Theaetetus, Aristotle, in the APo, is not primarily concerned with knowledge generally speaking, with its conditions of possibility, sceptical challenges, or other topics we classify as typically epistemological.2 Actually, the philosopher is interested in – as defined in APo I 2, 71b 9-12 –, the superior kind of knowledge that is characteristic of expert scientists.3 If the main object of the APo is scientific knowledge, we can affirm that the theory advanced in the treatise is better described as a philosophy of science than as a general epistemology.4 Aristotle recognizes two basic types of scientific knowledge. On one hand, there is 'demonstrative knowledge' ( ), which is provided by an argument called 1 For a useful discussion, see Bronstein (2016a, pp. 16-21). 2 See Taylor (1990, p. 116); Ferejohn (1991, pp. 2-3). However, as we shall see, a sceptical challenge against Aristotle's notion of scientific knowledge (and not knowledge in general) is addressed in APo I 3 and APo I 19-22. 3 See Bronstein (2016a, pp. 18-20). Burnyeat (1981) argues that this use of the expression ' ' corresponds to our notion of 'understanding', rather than the broader notion of 'knowledge.' Although I accept Burnyeat's main claims, I agree with Bronstein that it is important to emphasize that ' ' is a kind of knowledge (the kind of knowledge expert scientists possess). Thus, I prefer to translate ' ' as 'scientific knowledge'. 4 Cf. Ferejohn (1991, p. 2-3), who argues that none of the nomenclatures fully applies to Aristotle's theory. 22 'demonstration' ( ). A demonstration is a deductive reasoning in which the premises present the cause or the explanation ( ) of the fact expressed in the conclusion.5 On the other hand, there is another kind of scientific knowledge called 'comprehension' – in Greek, ' '. is the knowledge that scientists have of fundamental explanations, i.e. indemonstrable principles on which demonstrative knowledge is ultimately based. The existence of two kinds of scientific knowledge is crucial to Aristotle. If every premise in a demonstration were itself known by demonstration, the philosopher would have to admit one of the following two scenarios: (A) The number of propositions in a demonstration is finite. However, if all scientific propositions are demonstrable, demonstrations have to proceed 'in a circle and reciprocally' (APo I 3, 72b 17-18), i.e. the demonstration of p includes among its premises propositions whose demonstration includes p among its premises. (B) There is no such thing as circular demonstrations. However, if all scientific propositions are demonstrable, every demonstration must involve infinitely many premises (APo I 3, 72b 7-10), i.e. p is demonstrated from different and more basic premises, whose demonstrations involve different and even more basic premises, and so on ad infinitum. In APo I 3, Aristotle rejects both of these scenarios. Scenario (A) is denied on the grounds that circular 'demonstrations' are not properly explanatory. For him, the relation '...being explanatory of...' is asymmetrical: if a proposition p1 is explanatory of p2 (and p1 is a premise from which p2 is demonstrated), p2 is not explanatory of p1 (and therefore cannot be a premise from which p1 is demonstrated).6 Scenario (B) is also rejected because an infinite set of premises cannot be surveyed with thought.7 Aristotle avoids circularity, on one hand, and infinite regress, on the other, by rejecting the common assumption underlying (A) and (B), namely, that all scientific propositions are demonstrable. For him, demonstrative knowledge relies on noetic knowledge of indemonstrable premises. Given this picture, it is easy to see how the theory advanced in the APo has been taken as a form of 'foundationalism'.8 In the following chapters, I attempt to clarify the main aspects of Aristotle's theory of demonstration and try to specify in what sense it can be taken as a 5 I shall use the word 'cause' to translate Aristotle's notion of ' ' with the consciousness that we should not conflate the concept Aristotle has in mind with the modern (humean) notion of cause. 6 According to Aristotle, 'an explanation is prior to what it is explanatory of' ( , APo II 16, 98b 17) and priority is an asymmetrical relation (Cat. 12, 14a 29-35; 14b 11-22; Metaph. V 11, 1019a 1-4; VII 10, 1034b 30-32; 1035b 6-7). See also APo I 3, 72b 25-73a 20; APr II 16. 7 APo I 3, 72b 7-15; I 22, 82b 3783a 1; 83b 6-7, 83b 32 84a 6. 8 See Irwin (1988, pp. 130-1); Ferejohn (1991, pp. 4-5; 2009, p. 66); Goldin (2013); Zuppolini (2014b; 2016). 23 foundationalist doctrine. My primary aim is to show how Aristotle's foundationalism is deeply rooted in metaphysical views involving concepts such as cause, essence, and predication. In Chapter 1, I discuss in detail the common view that Aristotle endorses some form of foundationalism. Without disputing the nomenclature, I argue that his 'foundationalism' should not be taken as a rationalist theory of epistemic justification, as if the first principles of science could be known as such independently of their explanatory connections to other propositions. On the contrary, knowing first principles as such involves knowing them as explanatory of demonstrable facts. As a result, we can affirm (or so I shall argue) that noetic and demonstrative knowledge are in a sense interdependent cognitive states. In addition, the relation between and elucidates in which way definitions are first principles for Aristotle. The philosopher distinguishes definitional sentences as mere accounts of meaning (or nominal definitions) from definitions as accounts of essence (or real definitions). Real definitions are 'accounts displaying the reason why' (APo II 10, 93b 39), which, in virtue of their explanatory content, play the role of first principles in demonstrative sciences. In other words, Aristotle's 'foundationalism' consists in recognizing essences as ultimate explanations, which makes his essentialism one of the most important ontological underpinnings of his philosophy of science.9 Chapter 2 focuses on another topic closely related to what is discussed in Chapter 1: the interdependence between defining and explaining. I shall follow part of the secondary literature and argue that defining and explaining are interdependent scientific practices.10 For Aristotle, we cannot know the essence of something independently of the explanatory role it plays in demonstrations. This means that the acquisition of definitions intrinsically involves the act of explaining demonstrable facts. According to Aristotle, real definitions are made clear through demonstrations (APo II 8, 93b 17-18) and are described as demonstrations 'differing in arrangement' (APo II 10, 94a 2). These definitions are isomorphic to demonstrative syllogisms: thunder is defined as a certain noise in the clouds caused by extinction of fire; we acquire this definition by explaining syllogistically that the kind of noise we call 'thunder' (major term) occurs in the clouds (minor term) in virtue of fire being extinguished (middle term). At the end of this chapter, I address a long-standing question, recently revived in the literature.11 In different passages of APo II, Aristotle affirms that the middle term captures the essence (or the causal part of the essence) of the major term12: extinction of fire (middle term) is the causal element in the definition of thunder (major term) and explains why it belongs to the 9 This first chapter is a modified version of Zuppolini (2016) 10 The most prominent defence of this view is in Charles (2000). See also Kung (1977); Charles (2010b, pp. 268-328); Williams & Charles (2013); Peramatzis (2011, pp. 180-188; 2013); Koslicki (2012); Angioni (2014c; 2016). 11 Ferejohn (2013, p. 149-155); Angioni (2014c, pp. 103-107); Bronstein (2015; 2016a, pp.48-50). 12 See APo II 8, 93b 6; 12; II 16, 98b 21-24; II 17 99a 21-22, 25-26. 24 clouds (minor term). However, demonstrable attributes are described by Aristotle as 'per se accidents' ( ), which are defined as predicates belonging to a subject 'in itself' ( ), but not as a part of its 'essence' ( ).13 Many interpreters think that, by characterizing demonstrable attributes as per se accidents, Aristotle wants to stress that science deals with properties that are peculiar to their subjects and belong to them in virtue of the subjects being what they are. In other words, demonstrable attributes are non-essential properties that follow from and are explained by the essence of their subjects. Thus, the reader of the APo is entitled to ask: is the middle term the definition of the major (attribute) or the minor term (subject)? I shall not present my solution to this problem until Chapter 5. The debate about whether the explanation of a demonstrable fact is the essence of the attribute or the essence of the subject requires a fine-grained analysis of the distinction between subjects and attributes. In Chapter 3, I reconstruct a sophisticated and complex proof presented by Aristotle in APo I 19-22. An important part of his proof consists of a theory of predication involving the doctrine of ontological categories. Thus, a close examination of these chapters helps us understand the distinction between subjects and attributes and the constraints it imposes on scientific discourse. But there is a reason to consider the proof in its entirety. Its main purpose is to show how a demonstrative science is protected against the threat of infinite regress if it adopts the syllogistic as its underlying logic and regulates its use with certain ontological-semantical principles. If so, we can take Aristotle's argumentation in APo I 19-22 as a metaphysically loaded defence of his foundationalism. The topic of predication is further examined in Chapter 4, in which I analyse the four senses of ' ' ('in itself' or 'per se') distinguished in APo I 4. Far from being just linguistic relations between terms (as it is usually thought), I argue that the four uses of 'in itself' presuppose a hierarchical organization of the different kinds of entities in a scientific domain, in which the ontological priority of subjects over attributes plays an important role. The first use of 'in itself' (per se1) covers all essential predicates of all kinds of essence-bearers (subjects and attributes). The second (per se2) presupposes the distinction between prior and posterior essence-bearers (subjects and attributes, respectively), the former being defined without mentioning the latter, but not the other way around. The third use (per se3) applies precisely to the primary essence-bearers, which are what they are independently of being predicated of something different. Finally, the fourth sense of 'in itself' (per se4) is used to identify the appropriate subjects of demonstrable attributes from an explanatory point of view. In addition, I discuss some of the most prominent views on the notion 13 Metaph. V 30, 1025a 10-34. 25 of 'per se accident' available in the secondary literature and offer my own interpretation of this concept.14 In Chapter 5, I propose an interpretation of APo II 16-17. In these chapters, Aristotle claims that there cannot be more than one explanans for the same scientific explanandum. However, this seems to be true only for 'primary-universal' ( ) demonstrations, in which the major term belongs to the minor 'in itself' and the middle term is coextensive with the extremes. If so, several explananda we would like to admit as truly scientific would be out of the scope of an Aristotelian science. The secondary literature has identified a second problem in II 16-17, which we previously discuss at the end of our Chapter 2 : the middle term of a demonstration is sometimes taken as the definition of the minor term (the subject), other times as the definition (or the causal part of the definition) of the major (the demonstrable attribute). I shall argue that Aristotle's solution to the first problem involves showing that certain problematic attributes, which appear to admit more than one explanation, actually fall into the privileged scenario of primary-universal demonstrations. In addition, his solution suggests a conciliatory way-out to the second problem (or so I shall argue): the existence of an attribute as a definable unity depends on its subject having the essence it has, which indicates that both the essence of subjects and the essence of demonstrable attributes can play explanatory roles in demonstrations. Finally, in Chapter 6, I argue against the view that the essence of subjects constitutes an exception to the interdependence between defining and explaining. By analysing passages from Metaph. VII 17 and VIII 2-4, I try to show how the model applied to attributes and processes in APo II 8-10 works for subjects as well. The chapter includes a brief discussion of Aristotle's hylomorphism. After all, his theory of form and matter is what allows him to extend to subjectkinds the picture advanced in APo II 8-10. In addition, I shall argue that the interdependence between defining and explaining holds good even for subjects that are not analysable as compounds of form and matter: despite not being isomorphic to a demonstrative syllogism, the essence of an unanalysable subject cannot be known as such if it is not perceived as explanatory of the subject's demonstrable properties. In all these six chapters, we can see Aristotle offering general principles that (he believes) can be used by expert scientists in their specific fields. However, those guidelines should apply to all scientific domains independently of their differences and peculiarities. My aim is to clarify how Aristotle's general metaphysics (which he believes to be true for all domains of reality) helps him to accomplish this task. Therefore, this dissertation can be regarded as an attempt to reconstruct the ontological framework associated with Aristotle's philosophy of science. 14 Some segments of this chapter are modified versions of arguments found in Zuppolini (forthcoming). 26 27 CHAPTER 1 ARISTOTLE'S FOUNDATIONALISM 1.1 – Scientific Knowledge: Demonstration, Comprehension, and Foundationalism Aristotle begins the APo with the following general statement: 'all teaching and all learning of all intellectual kind proceed from pre-existing knowledge' (APo I 1, 71a 1-2).15 The philosopher notes that, when intellectual learning is provided by an argument, either deductive or inductive, we learn the conclusion when we have previous knowledge of the premises (APo I 2, 71a 5-9). In the APo, Aristotle focuses on a preeminent kind of learning which produces what he calls 'demonstrative knowledge' ( ). Such knowledge is acquired by demonstration ( ), a deductive argument in which the premises present the explanatory factor ( ) in virtue of which the conclusion is the case. A full-fledged demonstration provides understanding 'without qualification' ( ), which differs from the mere pretence of knowledge labelled as 'sophistic' ( ) or 'incidental' ( ): [T1] 15 All quotations of the APo come from Barnes (1993). Eventual modifications are indicated. 28 We think we understand something without qualification (and not in the sophistical way, incidentally) when we think we know of the cause because of which something holds that it is its cause, and also that it is not possible for it to be otherwise [APo I 2, 71b 9-12; Barnes 1993, with changes]. Aristotle also affirms that demonstrative knowledge is one of the (apparently two)16 types of 'understanding without qualification' ( ): 'whether there is another type of scientific knowledge we shall say later: here we assert that we do know things through demonstrations' (APo I 2, 71b 16-17). Although Aristotle is primarily concerned with demonstrative knowledge in the APo, the other kind of whose existence is implied in this passage is relevant to assessing the overall picture of his philosophy of science. As a result of intellectual learning, demonstrative knowledge is based on previous knowledge, which means that, if the ordered pair ⟨Π, c⟩ is a demonstration – where Π is a set of premises and c is the conclusion –, the knowledge of c is based on the knowledge of the members of Π, p1, p2, ... , pn. However, if the knowledge of each pi is itself demonstrative, there should be, for each pi, a subset of Π, Π', such that ⟨Π', pi⟩ would the demonstration of pi. In that case, either each pi would never be a member of Π' – that is to say, every premise would be demonstrated from different and more basic premises – or ⟨Π, c⟩ would involve circular explanations. In APo I 3, Aristotle takes both alternatives as problematic. In the first case, the set Π would be infinite and Aristotle believes that a demonstration with an unlimited set of premises is impossible simply because we could not survey it with thought.17 The alternative, however, is not better, since Aristotle does not recognize any demonstrative value in circular proofs (see APo I 3, 72b 25-73a 20; APr II 16). The two horns of this (apparent) dilemma relates to two epistemological views Aristotle rejects in APo I 3. One of them admits the possibility of scientific knowledge by accepting circular explanations as authentic demonstrations. The other view is sceptical about the possibility of demonstrative knowledge on the grounds that demonstrating would be a process that leads to infinite regress. Aristotle believes that both views rely on the false assumption that every type of knowledge is demonstrative and offers a solution that has been described as a form of 'foundationalism.'18 If ⟨Π, c⟩ is a demonstration, the set Π is finite, there being a subset of Π, Π', such that, whereas all the members of Π' are indemonstrable, all the other premises in Π (and consequently c) are directly or indirectly demonstrated from them.19 In APo I 2, Aristotle had already anticipated his solution by affirming that all demonstrations proceed from 'items which are 16 The other kind of knowledge in question is called ' .' For a convincing argument that the definition of in T1 applies to noetic knowledge as well, see Bronstein (2016a, pp. 51-57). See also Bronstein (2012, p. 34). 17 APo I 3, 72b 7-15; I 22, 82b 3783a 1; 83b 6-7, 83b 32 84a 6. 18 See Irwin (1988, pp. 130-1); Ferejohn (1991, pp. 4-5; 2009, p. 66); Goldin (2013); Zuppolini (2014b; 2016). 19 APo I 3, 72b 18-25; I 19, 82a 2-9; I 22, 83b 24-84b 2. 29 true and primitive and immediate and more familiar than and prior to and explanatory of the conclusion' (APo I 2, 71b 19-22). Although these basic premises are indemonstrable (APo I 2, 71b 26-7), we do have knowledge of them 'without qualification' by a cognitive state Aristotle calls 'comprehension' ( , APo II 19, 100b 5-17).20 Therefore, the nature of is twofold not without reason. Working with those two kinds of scientific knowledge (noetic and demonstrative) is what enables Aristotle to sustain his foundationalist project. After these general considerations on the nature of knowledge and demonstration in APo I 1-3, Aristotle moves on to present a an abstract model or paradigm of demonstrative knowledge (with its own ontological framework, semantic principles, and formal features) whose feasibility is meant to show that the foundationalist enterprise is possible and worth pursuing.21 Because it produces knowledge by means of arguments of a certain sort, demonstrative sciences should adopt an appropriate set of rules of inferences to underlie its argumentation. To play the role of underlying logic in his abstract model, Aristotle selects the formal system developed in APr, the Syllogistic.22 Thus, in an Aristotelian demonstration ⟨Π, c⟩, each element of Π and c are phrased – or at least susceptible to being phrased – in one of the four syllogistic categorical sentences: Universal Affirmative: P holds of all S (henceforth, 'PaS') Particular Affirmative: P holds of some S ('PiS') Universal Negative: P holds of no S ('PeS') Particular Negative: P holds not of every S ('PoS') In addition, an Aristotelian demonstration is made of one or more syllogistic inferences, in which a pair of categorical premises sharing a common term (the middle term) entails another categorical sentence with the remaining two terms (the major and the minor extremes); an inference in Barbara, for instance, could be represented as follows: PaM, MaS P holds of all M, M holds of all S PaS P holds of all S 20 It is worth noting that in APo II 19 (and also in I 3, 72b 18-25) the term ' ' refers to a narrower notion that excludes the knowledge of first principles. In these passages, ' ' is described not as ' ' but as ' .' 21 Cf. Ferejohn (2013, p. 81) who describes his overall interpretation of the APo as showing that 'there is a major break between the opening three chapters (A 1-3) – where Aristotle develops a set of general pre-theoretical constraints on the possession of scientific knowledge – and the remainder of the book, beginning in chapter A 4, in which he sets out his own (syllogistic based) theory of demonstration designed specifically to satisfy these constraints.' See also Ferejohn (1991; 2013, p. 65). I would like to point out that I take the constraints formulated in APo I 1-3 as concerning scientific knowledge (and not knowledge generally speaking), with its characteristic explanatory content, understood in the strong and restrictive terms I am going to propose in rest of this chapter. 22 For a defence of the view that the Syllogistic is not a logical theory, but an underlying logic, and that syllogisms are not conditionals, but arguments, see Smiley (1973); Corcoran (1974a; 1974c); Smith (1989); Ribeiro (2011, pp. 14-15); Ferreira (2012, pp. 65-68); Weinmann (2014, pp. 4-5). For the opposite view, see Łukasiewicz (1957); Patzig (1968). 30 Several interpreters objected to the presence of Aristotle's Syllogistic in his theory of demonstration by arguing that the logic of the APr is too limited to apply to actual scientific cases, which would explain why it was ignored by scientists of his time – including, according to some of these interpreters, Aristotle himself.23 One may reply to these critics by pointing out shortcomings either in their interpretations of the Syllogistic or in their understanding of Aristotle's scientific practice.24 However, there is a sense in which these criticisms are clearly out of place. Once we take the Syllogistic as part of a model or a paradigm meant to illustrate the nature of demonstrative knowledge in general, it becomes neither necessary nor desirable to assume that the APo require all scientists to adopt the Syllogistic as their underlying logic, as if knowledge 'without qualification' were not possible without this specific formal apparatus.25 In fact, one may argue that Aristotle had good reasons to select a particular logical system for his model of science. In order to come to know c based on a set of premises Π, we need not only to know that the premises are true, but also to be familiar with the rules of inference that allow us to obtain c from Π. Therefore, elaborating and selecting a particular deductive system would be a helpful way of exemplifying what kind of knowledge and skills are involved in the process of learning 'by demonstration' (APo I 18, 81a39-40). It is far from clear, however, how exactly Aristotle thinks we can acquire knowledge through demonstrations. As we shall see in the next section, depending on how this process of learning is specified, Aristotle's solution to the dilemma of APo I 3 can be seriously misinterpreted, rendering his foundationalist model of science inconsistent and unattractive. 23 See, for instance, Barnes (1981); Leslz (1981); Harari (2004, pp. 87-116); McKirahan (1992, p. 150). I do not intend to deal with the problem of whether Aristotle created the syllogistic before or after the development of the core theses of his theory of demonstration. About the topic, see Solmsen (1929); Ross (1939); Barnes (1981); Smith (1982a); Smith (1982b). 24 See Gotthelf (1987); Lennox (1987, pp. 118-119); Ribeiro (2011, pp. 23-31; 2014); Angioni (2014b); Zuppolini (2014b). 25 See Ferejohn (1991; 2013, p. 65; p. 81). Even though the notion of syllogism is present in APo I 2 (71b 16-18; 72a 15), I believe this chapter is primarily concerned with general requirements on the possession of scientific knowledge, which can be met by sciences that eventually adopt alternative underlying logics. Angioni (2012) argues that the requirements introduced in APo I 2, 71b 20-33 already presuppose the syllogistic structure of demonstrations. Previously, I have myself defended that at least the 'immediacy' criterion brings Aristotle's Syllogistic to the context of 71b 20-33. See my Zuppolini (2014b, pp. 187-188); see also Smith (1986; 2009, p. 53); McKirahan (1992, p. 25); Barnes (1993, p. 94). I no longer think that it is necessary to read the passage in this way, mainly because Aristotle clarifies the notion of 'immediacy' in terms of 'priority' in 72a 7-8, not in terms of absence of syllogistic middle terms. Of course, in Aristotle's model of demonstrative science, 'immediacy' amounts to the absence of an explanatory middle term, which might explain why he uses the expression 'immediate syllogistic principle' in 71a 14. However, this does not mean that, for Aristotle, only sciences that adopt the Syllogistic as their underlying logic can meet the requirements listed in 71b 20-33. Nevertheless, I shall argue in Chapter 5 that the Syllogistic is not a random choice of Aristotle: syllogistic inferences always involve three terms, which makes them adequate to capture causal relations, which Aristotle takes to be triadic – i.e. they involve a cause, an attribute of which it is cause ( ) and a subject for which it is cause ( ). This is what Lucas Angioni calls 'the triadic structure' of scientific explanations. For a systematic discussion of this notion – to which I am very much indebted – see Angioni (2008, pp. 328ff.; 2012; 2013; 2014b; 2014c; 2016). For similar approaches, see Charles (2000, pp. 204-209); Ribeiro (2011, pp. 7-31; 2014). 31 1.2 – A Rationalist Interpretation of Aristotle's Foundationalism According to the common contemporary view, someone learns something through an argument ⟨Π, c⟩ when, without previously knowing c to be true, she finds it to be true by (i) knowing in advance that the premises in Π are true and (ii) realizing that c is a logical consequence of Π. Naturally, this view has been imputed to Aristotle and his theory of demonstration: Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises [Corcoran 2009, p. 1]. In the same vein, some interpreters believed that Aristotle's foundationalism implies that the indemonstrable principles of sciences are self-evident premises whose truth is known by noninferential procedures and from which the scientist infers and therefore learns other propositions not previously known to be true.26 This interpretation of Aristotle's foundationalism might seem congenial to the fact that, in his theory, demonstrations proceed from definitions:27 [T2] Again, the principles of demonstrations are definitions, and it has been proved earlier that there will not be demonstrations of principles – either the principles will be demonstrable and there will be principles of principles, and this will continue ad infinitum, or else the primitives will be indemonstrable definitions [APo II 3, 90b 24-7; Barnes 1993]. Certain definitional statements (usually called 'nominal definitions') are meant to fix the meaning of the terms of scientific discourse. Such statements can be described as analytic and knowable a priori. Hence, their status as first principles would rely primarily on self-evidence. According to this view, the intuitive knowledge we have of propositions of this kind is what Aristotle calls ' ', from which is (deductively) derived. Since these are the only kinds of knowledge 'without qualification', it is easy to understand why Aristotle was once seen as 'the 26 See, for instance, Scholz (1975); Irwin (1988, pp. 130-131); Frede (1996). 27 See also APo I 2, 72a 14-24; I 8, 75b 30-1; I 33, 89a 16-9; II 3, 90b 30-3; APo II 8, 93b 6-7, 12; II 17, 99a 3-5, 21-6. 32 paradigm of an extreme rationalist', who would recognise a posteriori truths as knowable (if at all) 'only in a debased sense of knowledge.'28 However, if this is the process of intellectual learning by which we acquire demonstrative knowledge, Aristotle's foundationalist project seems blatantly inconsistent. As we saw, if ⟨Π, c⟩ is a demonstration, the set of premises Π reveals the appropriate explanation of the conclusion c. However, the philosopher believes we cannot start pursuing the explanans without knowing in advance that the corresponding explanandum is true (see APo II 1-2). Thus, how could a demonstration ⟨Π, c⟩ enable us to learn c in the first place if knowing that c is true is a necessary condition for investigating the very explanation the set Π is expected to display?29 The apparent inadequacy of Aristotle's account seems to lie with his assumption that the explanans is presented by the premises of a demonstration, whereas the explanandum is found in the conclusion. In fact, this seems to violate our modern intuitions about how knowledge of causal or explanatory relations is acquired. For instance, modern philosophers of science such as Charles Peirce distinguish between three kinds of arguments:30 Deduction: All the beans from this bag are white, These beans are from this bag These beans are white Induction: These beans are from this bag, These beans are white All the beans from this bag are white Abduction: All the beans from this bag are white, These beans are white These beans are from this bag In a deductive argument such as the one formulated above, the premises state a general rule (all the beans from this bag are white) and a case under the rule (these beans are from this bag), whereas the conclusion is obtained by applying the general rule to the particular case (these beans are white).31 Inductive arguments, on the other hand, obtain a general rule (all the beans from this bag are white) from a number of cases of which certain facts are simultaneously true (these beans are 28 Frede (1996, pp. 157-158). 29 Barnes (1969, p. 146); Burnyeat (1981, pp. 116-117). For a clarifying exposition of the problem, see Bronstein (2014, p. 13; 2016a, pp. 32-33). 30 See Peirce (Collected Papers; 2. 622-623) 31 See Peirce (Collected Papers; 2. 620). 33 from this bag, these beans are white). Finally, abduction is a kind of reasoning that could be described as 'the process of forming explanatory hypotheses'32 or as 'inference to the best explanation.'33 Suppose we find a handful of white beans on a table next to a bag of beans, knowing, in addition, that all the beans from this bag are white. In that case, we are inclined to infer that the beans lying on the table came from the bag simply because this conclusion, if true, would best explain why these beans are white. Thus, abductive inferences produce causal knowledge insofar as the conclusions are explanatory of one or more of their premises. In the APo, on the other hand, the premises are explanatory of the conclusion and not the other way around, which seems to invert the order in which arguments are supposed to produce knowledge of causal relations. This picture explains why the interpretation advanced by Jonathan Barnes (1969) has been so influential. Barnes argued that the APo are not meant to describe how scientists acquire knowledge, nor does it intend to account for scientific research. Instead, 'the theory of demonstration offers a formal account of how an achieved body of knowledge should be presented and taught' (Barnes 1969, p. 147). This solution is attractive. Without violating our intuitions about how causal knowledge is acquired, it explains why it is possible to learn things 'by demonstration': demonstrative arguments do not reflect the order in which the expert scientist reaches his explanations, but the order in which she imparts these explanations to her pupils. However, if demonstrating were essentially a pedagogic procedure, it would not be good one. Aristotle makes it clear that the premises of a demonstration are more familiar and prior to the conclusion precisely because they are explanatory of it (APo I 2, 71b 31-2). In this context, the explanatory priority of the premises corresponds to what Aristotle describes as priority 'by nature'. However, what is prior and more familiar 'by nature' ( ), says he, is not the same as what is prior and more familiar 'to us' ( , APo I 2, 71b 3372a 5). The premises of a demonstration are not more familiar and prior to the conclusion in the sense of being obviously true and more likely to be accepted by someone who is not yet an expert on the subject in question. They are prior and more familiar 'by nature' insofar as they display the cause of the fact expressed in the conclusion – see ' ' in APo I 2, 71b 31 –, a cause that not even the expert knows from the start, but grasps only after a complex procedure of inquiry. In other words, what counts as an for Aristotle is (causally) prior to the phenomenon it explains independently of the way the phenomenon was discovered in the first place. To some extent, this is a problem of philosophical vocabulary. Foundationalism is usually depicted as a theory of how knowledge and true beliefs are justified, whereas Aristotelian 32 Peirce (Collected Papers; 5.172). 33 Harman (1965). 34 explanations cannot be confounded with mere justification. Mere justifications provide answers to questions such as 'why do I believe that p?'. Aristotelian explanations, on the other hand, are meant to answer the question 'why is it the case that p?'34 In order to justify my belief in a proposition p, all I need is to set out the reasons why I believe in p. On the other hand, for Aristotle, to present the of p is to identify a real-world item that is responsible for p being true (instead of being responsible for my belief that p is true).35 Premises that are explanatory in this strong sense are certainly not self-evident or knowable a priori. Therefore, when interpreted according to the rationalist approach depicted above, Aristotle's foundationalism becomes incompatible with his own concept of explanation. If his solution to the dilemma of APo I 3 is to be labelled as a form of foundationalism at all, it seems preferable to specify what kind of foundationalism it is not in terms of justification, but in terms of causal explanations. 1.3 – Coming to Know First Principles: A Non-Rationalist Account The acquisition of first principles is the topic of the very last chapter of the APo. In II 19, Aristotle identifies 'the state that knows' ( , 99b 18) the principles with , which is characterised as the most 'accurate' of our cognitive states (100b 5-14). One of Aristotle's aims in the chapter is to address the following puzzle: [T3] ... ... I have said earlier that you cannot understand anything through a demonstration unless you know the primitive immediate principles. As for knowledge of the immediates, one might wonder [...] whether the states, not being present in us, come about in us or rather are present in us without being noticed. It is absurd to suppose that we possess such states; for then we should possess pieces of knowledge more accurate than demonstration without its being noticed. But if we get them without possessing them earlier, how could we come to acquire knowledge and to learn except from pre-existing knowledge? This is impossible, as I said in connection with demonstration [APo II 19, 99b 20-30; Barnes 1993, with changes]. 34 See Goldin (2013, p. 200). 35 See my Zuppolini (2014b, pp. 178-179; 2016). On the difference between justification and explanation, see Burnyeat (1981, p. 101); Goldin (2013, p. 200); Salmieri (2014, pp. 2-3). For other interpretations that claim or assume that this is the notion of explanation present in Aristotle's theory of demonstration, see Kosman (1973); Matthen (1981); Taylor (1990, p. 120); McKirahan (1992, pp. 209-31); Lesher (2001, p. 46); Charles (2000); Angioni (2007a; 2012; 2013; 2014b; 2014c; 2016); Bronstein (2012; 2014; 2015; 2016a). 35 Aristotle discusses two alternative hypotheses about the origin of our knowledge of first principles: either (i) it is already present in us without being noticed ( , 99b25-26) or (ii) it 'comes about' ( , 99b 25) in us somehow. It is worth stressing that Aristotle does not consider the possibility of first principles being available to us from the beginning, as if they were self-evident propositions we could know without any heuristic procedure being required. On the contrary, if they are known to us at all – as in alternative (i) – we are not completely aware of them (along the lines of Plato's theory of recollection).36 Aristotle rejects alternative (i) on the grounds that such an 'accurate' cognitive state – even more accurate than demonstrative knowledge (99b 27) – could not be present in us without us noticing them. As stated in hypothesis (ii), comprehension ( ) must 'come about' in us, which in this context implies that first principles are acquired by a process of learning ( , 99b 29). Since there cannot be learning except from pre-existing knowledge (99b 28-30) – as the very first sentence of the APo makes it clear (APo I 1, 71a 1-2) –, 'the state that knows' first principles is not a fundamental cognitive state in the sense of not being based on previous knowledge of any kind. This pre-existing knowledge, however, cannot be 'more valuable (...) in respect of accuracy' (99b 33-340) than , since is the most accurate of all cognitive states. Therefore, the task Aristotle takes on in APo II 19 is to indicate a state or capacity that, despite being less accurate than comprehension or demonstration, can at least initiate the process that leads us towards these superior forms of knowledge.37 Aristotle goes on to claim that this initial state is a 'connate discriminatory capacity' ( ) known as 'perception' ( , 99b 34-35). As an innate capacity, perception does not come from pre-existing knowledge nor is it a result of intellectual learning ( ). Therefore, the principle stated in the opening lines of the APo no longer threatens Aristotle's theory with infinite regress, since it does not apply to the capacity that initiates scientific inquiry. However, a feature common to all animals such as perception (99b 34) is certainly not enough to give rise to a sophisticated form of knowledge such as , which means the acquisition of first principles requires co-operation of other capacities. First, Aristotle recognises 'memory' ( ) as indispensable to the process, since the information gathered by perception must be retained in our souls in some way (100a 3-4). Second, several memories of the same thing 36 Some interpreters take hypothesis (i) as referring to Platonic innatism. See Barnes (1993, p. 261); Bronstein (2012, pp. 38-39; 2016a, p. 234; 2016b). 37 This description of Aristotle's aim in APo II 19 follows in general lines the interpretation advanced by Bronstein (2012; 2016a, pp. 225-247), who argues convincingly that the philosopher does not intend in this chapter to specify all the steps involved in the acquisition of first principles, but to defend that our knowledge of them originates in perception. Cf. Kahn (1981). However, my interpretation is significantly different from his when it comes to the role of induction in the acquisition of first principles, as will become clear soon. 36 must be collected and compared with one another, which is made possible by a capacity Aristotle calls 'experience' ( , 100a 4-6).38 Experience, in turn, allows us to grasp what Aristotle calls 'the entire universal' ( , 100a 6-7).39 At some point, this process ends up with the acquisition of (100b 12-14) – or, as it is called in this passage, a 'principle of knowledge' ( , 100a 8; cf. 100b 12-14). We might think that, by tracing the acquisition of first principles back to perception, Aristotle prevents us from understanding his theory of demonstration along the lines of the rationalist interpretation sketched in the previous section. However, the capacities discussed in 99b34-100b5 can be understood as parts of a process of concept-formation.40 If so, the proponent of the rationalist interpretation might argue that the first principles we grasp by the end of this process are nothing more than propositions specifying the meaning of conceptual terms to be used in scientific discourse. This reasoning is a non sequitur. From the fact that perception, memory and experience might be relevant to concept-formation it does not follow that the first principles of science are a priori self-evident propositions or that is nothing more than an intuitive grasp of the meaning of conceptual terms.41 In this chapter, Aristotle is primarily engaged in the task of identifying an innate capacity that is not based on pre-existing knowledge and therefore can serve as a starting point in our journey towards higher forms of cognition. As has been argued, there might well be further steps between the last stages described in 99b34-100b5 and the noetic knowledge of first principles, a gap Aristotle did not attempt to fill in APo II 19.42 Therefore, it is not safe to conclude, only based on APo II 19, that the grasp of first principles is nothing more than a process of conceptformation. Moreover, Aristotle claims that induction ( ) is the kind of inference underlying the process by which we get from perception to the grasp of 'the entire universal' (100b 4-5; with 100a 6-7). Therefore, it plays an important role in the acquisition of the first principles of science ( , 100b 3-4).43 It is certainly true that inductive reasoning is part of the process of 38 See Metaph. I 1, 980b 28-982a 1. Cf. Ferejohn (2009, p. 69), who characterises experience as 'the ability to classify retained percepts into general kinds.' For a detailed discussion of this notion, see Hasper & Yurdin (2014). 39 I shall set aside the question of whether 'the grasp of the universal' is intrinsic to experience (see Ross 1949, p. 674; Barnes 1993, p. 264) or a further, independent step in the acquisition of first principles (see McKirahan 1992, p. 243; Bronstein 2012, pp. 44-46; 2016a, pp. 237-240). 40 See Barnes (1993, pp. 264-265); Ross (1949, pp. 675-676). Cf. Kahn (1981, pp. 391-395); McKirahan (1992, p. 246); Charles (2000, p. 264, n. 37); Bronstein (2012, p. 58, n. 67; 2016a, p. 246, n. 63 ). 41 Lesher (1973, p. 61). 42 See Kahn (1981, pp. 396-397); Bronstein (2012; 2016a, pp. 225-247). 43 In order to avoid the consequence that induction is all it takes to know the first principles, Bronstein (2012, pp. 5354; 2016a, p. 242) argues that ' ' in 100b 4 denotes something else – in his words, 'first universals' and 'preliminary accounts'. However, in APo II 19, 100b 3-4, the dative ' ' does not necessarily mean that induction is sufficient for coming to know the items Aristotle calls ' .' Therefore, it is possible to interpret ' ' as 37 concept-formation. However, this is not the only, nor the most important role it plays in scientific inquiry.44 Aristotle seems to have recognised this fact in APr II 23, where he offers a sophisticated account of the kinds of reasoning involved in the discovery of scientific explanations. Contrary to expectations, his account is significantly close to the one proposed by contemporary philosophers of science: [T4] Induction, then – that is, a deduction from induction – is deducing one extreme to belong to the middle through the other extreme, for example, if B is the middle for A and C, proving A to belong to B by means of C (for this is how we produce inductions). For instance, let A be long-lived, B stand for not having bile, and C stand for a particular long-lived thing, as a man, a horse, or a mule. Now, A belongs to the whole C (for every C is long-lived); but B (not having bile) belongs to every C. If, then, C converts with B and the middle term does not reach beyond the extreme, then it is necessary for A to belong to B: for it has been proved earlier that if two terms belong to the same thing and the extreme converts with one of them, then the other of the predicates will also belong to the term that converts with it. (But one must understand C as composed of every one of the particulars: for induction is through them all.) [APr II 23, 68b 1529; Smith 1989, with changes]. In this passage, Aristotle is primarily concerned not with 'induction' ( ) properly speaking but with an argument derived from it – here called 'deduction from induction' ( ). Let us examine Aristotle's example. Scientists investigate certain biological phenomena by having perceptual contact with certain animals ( ), retaining images of them ( ) and realizing that these animals instantiate certain properties with regularity ( ). Let us suppose that, in this process, the biologist finds out a co-relation between longevity and absence of bile in animals like humans, referring to the first principles of science without committing Aristotle to the view that induction is sufficient for grasping them. 44 I therefore disagree with Kahn (1981, p. 396) and Bronstein (2012; 2016a, p. 243), who limit the use of inductive inferences to the acquisition of nominal definitions. 38 horses and mules. Eventually, an inductive procedure will indicate that all animals of a certain kind are long-lived whenever their bodies do not contain a significant quantity of bile: Syllogism I:45 Longevity holds of humans, horses etc., Being a K holds of humans, horses etc. Longevity holds of all Ks Syllogism II: Absence of bile holds of humans, horses etc., Being a K holds of humans, horses etc. Absence of bile holds of all Ks Relying on this result, the inquirer proceeds to an inference that could be described as an 'inverted demonstration', where the explanatory term is not the middle, but the major extreme:46 Syllogism III: Longevity holds of all Ks, Being bileless holds of all Ks Longevity holds of all bileless animals In fact, the co-occurrence of longevity and absence of bile made Aristotle believe that, in certain animals, the latter is the explanation of the former.47 Thus, in Syllogism III, the explanans appears in the conclusion while the explanandum occurs in the major premise – an inference a modern reader could classify as abductive. However, while the so-called 'inferences to the best explanation' are non-deductive, Aristotle believes that, if the induction that precedes it is sufficiently comprehensive, we can obtain a deduction to the best explanation. Lines 68b 24-27 refer back to APr II 22, 68a 21-25, where Aristotle has shown that if two terms A and B hold of all C, and C also holds of all B, then A necessarily holds of all B. Therefore, if the induction shows us that all and only the members of the relevant kind are bileless – and perhaps this is what Aristotle means by the enigmatic phrase 'the entire universal' in APo II 19 ( , 100a 6-7) –, we are warranted to convert the previous minor premise and obtain 'a deduction from induction' concluding that all bileless animals are long-lived: Syllogism IV: Longevity holds of all Ks, Being a K holds of all bileless animals Longevity holds of all bileless animals 45 I am calling Syllogism I, II, and III 'syllogisms' just for the sake of exposition. Technically speaking, these arguments are not Aristotelian syllogisms, since Aristotle uses the term ' ' only for valid arguments in syllogistic form. 46 The terms called 'middle' and 'extreme' in T4 do not match the roles they play in the argument discussed in the passage, which means that these expressions are used as rigid designators of the middle term and the extremes of a demonstrative syllogism. See Ross (1949, pp. 484-485). 47 PA IV 2, 676a 30-677b 10. 39 Therefore, the steps involved in the discovery of explanations could be represented by the following scheme, where P is the predicate whose occurrence we seek to explain, M is the putative explanation and S is a universal kind comprising all instances of P, while s1, s2, ..., s n are subspecies of S: Induction: P holds of s1, s2 ... sn, S holds of s1, s2 ... sn P holds of all S M holds of s1, s2 ... sn, S holds of s1, s2 ... sn M holds of all (and only) S Abduction: P holds of all S, M holds of all S P holds of all M Deduction from induction (converting the minor premise): P holds of all S, S holds of all M P holds of all M Thus, in APr II 23, Aristotle offers an account of the acquisition of explanations which is (to a certain extent) close to the one advanced by modern philosophers of science. However, none of the steps discussed in the chapter contain ' ' in the strict sense of the term, in which the explanation occurs as the middle term: Demonstration: P holds of all M, M holds of all S P holds of all S Thus, the chapter leaves us without an answer to the question of how exactly can scientists learn by demonstration. Interpreters such as Kosman (1973, p. 383) and McKirahan (1992, p. 243) distinguish between knowing an explanation and knowing an explanation as such. Based on this distinction, David Bronstein (2014; 2016a, pp. 39-40) has recently argued that there is a sense in which it is possible to learn by demonstration: if p1 is explained by p2, demonstration is the reasoning by which a scientist learns that p2 is actually explanatory of p1 (and not simply that p2 is the case). 48 Let me 48 'Learning by demonstration, I suggest, does not consist in deducing a new conclusion from known premises. Rather, it consists in discovering a previously unknown explanatory connection among facts the scientist already knows but not scientifically. Prior to learning, she knows x and y, where y is the explanation of x and x is explained by y, but she does not know x or y as such. She learns by demonstration when she apprehends y as explanatory of x, or-what is 40 endorse Bronstein's interpretation in the following terms. Inductive and abductive arguments merely make it reasonable to accept their conclusions as true, since what they infer is not a necessary consequence of their premises. On the other hand, the argument Aristotle calls 'deduction from induction', despite having premises that do necessitate the conclusion, does nothing more than establishing that the explanans is true, which is quite different from establishing that it is the adequate explanation of the explanandum in question. Knowing that all bileless animals are long-lived is different from knowing that this is the reason why horses and mules are long-lived. For Aristotle, only the second case is qualified as scientific knowledge and only demonstrations are able to provide it. A true expert scientist not only assents to a set of true propositions, but also organizes it in terms of explanatory priority. When she demonstrates a given proposition taken as explanandum, the scientist not only knows that the correspondent explanans is true, but also (and more importantly) makes scientific discourse reproduce the causal order of reality by choosing as premises propositions that are explanatorily prior to the respective conclusions. Hence, the syllogistic inference that would count as a good explanation would run as follows: Syllogism V: Longevity holds of all bileless animals, Being bileless holds of all Ks Longevity holds of all Ks The question of how exactly we are able to recognize causal connections in the world does not seem to have bothered Aristotle (in the same way as it has bothered Hume, for instance). As a result, he never explains in a clear way (as far as I know) how the scientist realizes that a proposition p1 is explanatory of p2. However, if my interpretation of APr II 23 is correct, we can at least affirm that this recognition occurs at some point between Syllogism IV and Syllogism V. If it happens after Syllogism IV, by the time the scientist recognizes p1 as explanatory of p2, she already knows that p1 and p2 are true. Therefore, what she learns 'by demonstration' cannot be the truthvalue of problematic propositions. One the other hand, if the recognition of causal relations happens before Syllogism V, one might object that demonstration is not the reasoning by which the scientist learns that something is causally prior to another, but just a way of exposing this causal priority in scientific discourse. If so, there is nothing the expert scientist really learns 'by demonstration'. How then are we supposed to understand Aristotle's use of the expression 'learning by demonstration'? Let me suggest the following solution. The term 'demonstration' is ambiguous: in one sense of the term, 'demonstration' is the name of a reasoning (a proof-search procedure, one could say) in which a scientist tries to identify propositions (already known to be the same thing-x as explained by y. As a result of her learning, she now has scientific knowledge of x, which she previously knew only non-scientifically' (Bronstein 2014, p. 14). 41 true) from which a given conclusion (also known to be true) can be deduced and explained; in another sense, 'demonstration' is just the name of the syllogistically structured sequence of sentences that results from this procedure.49 In the first sense, Aristotle could say that expert scientists learn 'by demonstration' without contradicting his claim that knowing that the explanandum is true is a necessary condition for investigating the explanans. The acquisition of demonstrative knowledge involves overcoming the ordo cognoscendi and making scientific discourse reproduce the ordo essendi; to demonstrate (in the first sense of 'demonstration') is to realize that and how this is possible. Finally, it is worth noting that even though Aristotle requires the explanandum to be a logical consequence of the explanans, his theory remains quite different from the deductivenomological models of explanation. For him, what makes a scientific proposition prior to another is something more than their difference in generality or the inferential connections between them (APo I 13, 78a 22-b3; II 16, 98b 16-24). As we can see, demonstrations include as premises the same sentences we would find in abductive arguments or , but the inference goes in the opposite direction. The inferential steps discussed in APr II 23 enable the scientist to grasp a set of true propositions, whereas at the demonstrative stage this body of truths is organized in terms of causal priority – that is, priority 'by nature.' In other words, a demonstration of a conclusion c allows us to know not only (i) that c can be logically derived from a set of true premises Π but also (ii) that Π presents the set of factors responsible for c being true (which are prior to c 'by nature'), instead of the factors which make us believe that c is true (which are prior to c only 'relative to us').50 What about our knowledge of first principles? Some authors have pointed out that to understand first principles – that is, to have of them – is to understand them insofar as they are principles.51 As we have been arguing, first principles are nothing more than ultimate explanations. If inductions or 'deductions from inductions' do not make us know explanations as explanations, the same should apply to first principles as first principles. But what does it mean to know a principle as 49 Bronstein (2016a, p. 41) seems to reply to this objection with a similar distinction between two senses of 'demonstration' – although it is not completely clear to me whether the senses of 'demonstration' he briefly discusses are the same two senses I have tried to discriminate. 50 For the differences between Aristotle's and the 'covering law' theory of scientific explanation, see McKirahan (1992, pp. 230-231). See also Brody (1972) for the advantages of the former over the latter. 51 Kosman (1973, p. 389) argues: '[...] the noetic grasp we have of them [first principles] as principles concerns our ability to use them in explaining and making intelligible the world of phenomena. therefore is a feature of our understanding of all explanatory principles or premises [...] just insofar as we understand them in the act of explaining by them, i.e. just insofar as we understand them qua principles and not qua explicanda [emphasis in original].' See also McKirahan (1992, pp. 243-244). 42 principle? Based on our discussion so far, we can define an Aristotelian first principle in the following terms: Def. (First Principle): p is a first principle iff.: (i) there is an Aristotelian demonstration ⟨Π, c⟩ such that p belongs in Π (ii) there is no set Ψ such that ⟨Ψ, p⟩ is an Aristotelian demonstration of p According to this definition, to know a principle p as a first principle is to know that p satisfies conditions (i) and (ii). Whereas condition (ii) accounts for the indemonstrability of first principles, condition (i) states that a principle is always a principle of something. As we know, in APo I 2, 71b 19-22, Aristotle lists six features of demonstrative principles, of which three are relative to a conclusion: 'more familiar than', 'prior to' and 'explanatory of.'52 Therefore, to grasp a first principle as such is to understand it as an indemonstrable premise from which one or more conclusions are demonstrated. If this account is correct, and can be considered interdependent in a certain way. Demonstrative knowledge in the strict sense involves knowing not only the proximate causes of a given phenomenon, but the ultimate ones as well. In other words, if ⟨Π, c⟩ is a full-fledged demonstration, there must be a subset of Π containing only indemonstrable premises, of which we have not but Therefore, is dependent on insofar as full-fledged demonstrative knowledge is impossible without the comprehension of first principles. Nevertheless, a proposition cannot be considered a first principle of science independently of their explanatory roles in demonstrations. Therefore, if is the knowledge of first principles as first principles, its acquisition depends on figuring out their position in the body of science as a whole, which involves the practice of demonstrating (or attempting to demonstrate) other, less basic propositions from them.53 This 52 See McKirahan (1992, p. 243). Cf. Ross (1949, p. 509); Barnes (1993, p. 93). Ferejohn (2009, pp. 78-79) criticises McKirahan for being 'apparently impressed by Aristotle's use of comparatives in APo I 2, 71b 19-22.' Alternatively, he takes the three 'relational' conditions as reducible to a single 'absolute' condition: 'intelligibility in nature.' However, the notion of 'intelligibility in nature' seems more obscure than the conditions it is supposed to clarify. More significantly, Aristotle explicitly takes the condition 'being explanatory of...' as the fundamental one (APo I 2, 71b 2933). The fact that these three requirements are relational does not imply that 'there are no objective and contextindependent features that make somethings acceptable as principles and other things not.' Since Aristotle is not concerned with mere justification (as Ferejohn supposes), what makes something a principle in his theory is something objective: the causal order of the reality (see Hankinson 1998, p. 161). In other words, the principles are relational in the sense of being prior to other propositions, but objective in the sense of being prior 'in nature' and not 'relative to us.' For an approach that expands this 'relational' aspect of the notion of principle to other requirements in APo I 2, 71b 19-22, and to the concept of 'necessary principle', see Angioni (2012) and Angioni (2016) respectively. 53 Aristotle emphasizes the holistic character of scientific knowledge in APr I 30: 'Consequently, if the facts concerning any subject have been grasped, we are already prepared to bring the demonstrations readily to light. For if nothing that truly belongs to the subjects has been left out of the collection of facts, then concerning every fact, if a demonstration for it exists, we will be able to find that demonstration and demonstrate it, while if it does not naturally have a demonstration, we will be able to make that evident [APr I 30, 46a 22-27; Smith 1989].' 43 result is in accordance with part of the secondary literature, which claims that (both noetic and demonstrative) involves a holistic outlook of a given body of truths. Interpreters such as Kosman (1973) and Myles Burnyeat (1981) have argued that to understand ( ) a proposition pi is to determine its place in a complex web of interrelated propositions p1, p2, ... , pn organized in terms of explanatory priority, either as a first principle (noetic understanding) or as a theorem (demonstrative understanding).54 Along the same lines, McKirahan (1992, pp. 243-244) affirms: 'to grasp something as a principle is to understand how the things of which it is a principle depend on it. [...] Thus, knowing principles entails appropriate knowledge of nonprinciples, and this amounts to possessing the whole demonstrative science.' Let me now address some objections that might be raised against my proposal. I have claimed that to have of first principles is to know them as first principles, which involves understanding them as satisfying all the six requirements mentioned in APo I 2, 71b 19-22, including the relational ones: being 'more familiar than...', 'prior to...' and 'explanatory of...'. David Bronstein (2016a, pp. 62-63) has argued that if this is so, and turn out to be one and the same cognitive state. If ⟨{p1, p2}, c⟩ is a demonstration, having demonstrative knowledge of c is to know c as explained by premises p1 and p2. On the other hand, to know that p1 and p2 satisfy the relational criteria is to know them as explanatory of c. However, 'knowing c as explained by p1 and p2' and 'knowing p1 and p2 as explanatory of c' are, according to him, 'two descriptions of the same cognitive state' (Bronstein 2016a, p. 62). However, my claim is that having of p1 and p2 involves determining their places in a given body of interrelated propositions and realizing that: (i) there are no propositions within it from which p1 or p2 can be demonstrated; (ii) there are one or more propositions that can be demonstrated from p1, as well as there are one or more propositions that can be demonstrated from p2 – leaving it open whether p1 or p2 can be used to demonstrate the same proposition. 55 Thus, depends on there being demonstrative knowledge of one proposition or another. That being said, we can reply to this first objection as follows. If p1 and p2 are the first principles from which c is demonstrated, having demonstrative knowledge of c requires having noetic knowledge of p1 and p2. Nevertheless, although noetic knowledge of p1 and p2 requires a comprehensive 54 Ferejohn (2009, p. 75) objects that interpretations like Kosman's associate Aristotle with coherentism, in opposition to the foundationalist view advanced in the APo. In the same vein, one could say that our interpretation also commits Aristotle to some sort of coherentism. However, we would be ascribing a coherentist doctrine to Aristotle only if we were saying that organizing scientific propositions in a coherent body is the method by which scientists get to know explanatory relations. This is not what I am proposing – and, if I understand his interpretation correctly, neither is Kosman. What requires a holistic understanding of the body of scientific truths is not the recognition of a particular explanatory relation between two propositions, but the recognition of first principles as such – after all, figuring out that p is a principle involves realizing that there is no other proposition from which p can be demonstrated. 55 Certainly, clause (ii) does not require a demonstrative knowledge established previously and independently of . Therefore, my view does not imply that there is one piece of demonstrative knowledge which is prior to in time. 44 understanding of a given body of truths (and the explanatory role of p1 and p2 within it), it does not require knowing p1 and p2 as explanatory of a given conclusion c specifically. Therefore, even if the expressions 'knowing p1 and p2 as explanatory of c' and 'knowing c as explained by p1 and p2' describe the same piece of knowledge – a claim which is by itself controversial – 'knowing p1 and p2 as explanatory of c' in which 'c' stands for a determinate conclusion is not a good description of the kind of holistic cognition Aristotle calls ' .' In fact, if the content of noetic knowledge of p1 and p2 could not be specified without mentioning a specific conclusion such as c, it would be difficult to sustain that an expert scientist could learn by demonstration in the way we agreed she could. After all, if having of p1 and p2 already involves knowing p1 and p2 as explanatory of c, the scientist will learn nothing when she tries to demonstrate c from p1 and p2. 56 On the other hand, if coming to know p1 and p2 as principles involves realizing that there are true propositions that can be demonstrated from them (which are not necessarily c), there is still room for discovering new explananda (possibly c) and trying to trace them back to the first principles. Let us consider, for instance, an expert biologist who discovered (through the inferences and capacities described in APo II 23 and APo II 19) that absence of bile causes animals such as horses, mules and camels to be long-lived. Let us also say that it has already been established that all these species are essentially blooded animals (which involves knowing that some of their properties are explained by their being blooded). If the biologist tries to explain their longevity from first principles, she will eventually find out that absence of bile is the cause of their being long-lived because the liver (of which bile is a residue) is vital and necessary to blooded animals. Thus, she will have learned by demonstration that certain blooded animals are long-lived having previous noetic knowledge that their essence involves their being blooded.57 This example illustrates how an account of scientific knowledge in terms of 'interrelatedness' does not require a scientist to know absolutely all the facts in the domain in order to have . The acquisition of scientific expertise is not an all-or-nothing situation. As long as the scientist knows a set of indemonstrable propositions as such – knowledge that involves recognizing their explanatory connections with at least some demonstrable facts–, there is still room for discovering new facts and explaining them from these immediate principles. However, even if there is a way of distinguishing one cognitive state from the other, a second objection could be raised. In APo II 19, Aristotle claims that is 'more accurate' ( ) than demonstrative knowledge. One might argue that we cannot explain this claim 56 As Bronstein (2016a, p. 65) himself notes. 57 See PA IV 2, 677a-b10. In PA IV 5, 678a 33-34. Aristotle affirms: 'that some animals are blooded while some are bloodless will belong in the account defining their substantial being' (translation by Lennox 2001). If this pattern describes Aristotle in his biological treatises, it might count as further evidence for my interpretation the fact that it is in accordance with his scientific practice. 45 if we take these two cognitive states as interdependent. On the other hand, the rationalist interpretation would take this claim in purely subjective terms: the first principles are self-evident and accepted as true without any justification, whereas the respective conclusions become evident to us only through the evidence of the principles. Thus, the rationalist interpretation is able to explain how the 'accuracy' of demonstrative knowledge depends on the 'accuracy' of but not vice-versa. First, the claim that is the most 'accurate' type of knowledge does not need to be understood in subjective or psychological terms, as if the content of noetic knowledge were somehow 'more evident' than the content of other cognitive states. As we have seen, Aristotle describes the premises of a demonstration as being 'more familiar' or 'more intelligible' ( ) than the conclusion. At first sight, this vocabulary might suggest that our mental attitudes towards these premises are at stake. Nevertheless, the feature of demonstrative premises Aristotle wants to stress is fully objective: by 'more familiar' he means not 'more familiar to us' (a subjective notion) but 'more familiar by nature', which amounts to the objective notion of causal or explanatory priority (APo I 2, 71b 31). Lesher (2010), for instance, has convincingly argued that 'clarity' ( ) is not necessarily a psychological notion, the same being true for the notion of 'accuracy' ( ). He points out that in several contexts Aristotle uses the term ' ' and correlate expressions to refer to 'the attainment of full scientific knowledge.'58 Barnes (1993, p.189) also argues that ' ' can be used to describe whatever is of 'good epistemic quality', not necessarily what is certain or evident. According to Liddell/Scott/Jones, the word is used to qualify what is 'consummate' or 'in perfect condition'. Along the same lines, Zabarella had already noted that ' ' means not only certainty, but completeness or perfection.59 Now, as I have argued, if ⟨{p1, p2}, c⟩ is the demonstration of c, one cannot have demonstrative knowledge of c without having noetic knowledge of p1 and p2. However, having of p1 and p2 does not require demonstrative knowledge of c specifically. Therefore, the content of noetic knowledge (e.g. knowing p1 and p2 as principles) is more comprehensive and complete in comparison with the more specific content of the correspondent piece of demonstrative knowledge (e.g. knowing c as explained by p1 and p2) 60 – and this could be what Aristotle had in mind when he claimed that is the most 'accurate' of all cognitive states. 58 Lesher (2010, pp. 148-156). 59 '[...] akribeiam, quae non solam certitudinem significat, sed cum perfection [Zabarella 1582, 168B].' 60 This use of ' ' corresponds to the second sense of the term discussed by Salmeri (2014, p. 2): '"epistēmē"(and "epistasthai") can refer to a certain estimable cognitive state: the state in which the possessor of a science stands toward each of its theorems, in virtue of a demonstration of the theorem from the appropriate principles.' 46 Thus, we have strong reasons to believe that, for Aristotle, noetic and demonstrative knowledge are, in a way, interdependent cognitive dispositions. This account of the relation between and also helps us elucidate in which way definitions are first principles. In APo II 10, the philosopher distinguishes definitional sentences that are mere accounts of meaning (93b 19-37) – or 'nominal definitions' – from definitions as accounts of essence – or 'real definitions' (93b 38-94a 7). According to Aristotle, a definition of the second kind is 'an account which displays the reason why' ( , 93b 39). We know first principles are not self-evident propositions from which problematic beliefs can be justified, but causal explanations acquired after a complex process of inquiry (involving perception, memory, experience, induction etc.). Therefore, in virtue of their causal or explanatory content, real (and not merely nominal) definitions are the propositions playing the role of first principles in Aristotle's theory. In APo II 8-10, it becomes clear that causal definitions of this sort are not grasped independently of the practice of demonstrating. They are made clear by syllogistic demonstrations ( , APo II 8, 93b 17-18) and described as demonstrations 'differing in arrangement' ( , APo II 10, 94a 2). This interdependence between definition and demonstration is in accordance with our account of the relation between and . As has been claimed, this is not just a peculiarity of Aristotle's methods for explaining phenomena and grasping definitions. The epistemic interdependence between defining and explaining – and between comprehension and demonstrative knowledge – is grounded in a metaphysical interdependence between the notion of essence and the notion of cause (or primary cause).61 In the next chapter, I shall discuss the connections between definition and demonstration, essence and causation. Not only in Chapter 2 but also in the following chapters, I will be particularly concerned with the ontological distinction between subjects and attributes, their differences as essence-bearers, and the influence of this distinction in Aristotle's model of demonstrative science. 61 Kung (1977, pp. 168-172); Charles (2000; 2010b, pp. 268-328); Williams & Charles (2013); Peramatzis (2011, pp. 180-188; 2013); Angioni (2012; 2014b; 2014c; 2016); Koslicki (2012). 47 CHAPTER 2 CAUSE, ESSENCE, AND ESSENCE-BEARERS 2.1 – The Four Objects of Inquiry and Knowledge: Fact, Cause, Existence, and Essence At the beginning of APo II, Aristotle affirms that the things we seek ( ) are equal in number to those we know ( ) (APo II 1, 89b 23-4): (1) 'the fact' ( ) (2) 'the reason why' ( ) (3) 'if something is' ( ) (4) 'what something is' ( ) Each of these four objects of inquiry and knowledge corresponds to one question: [T5] 48 When we seek whether this our that is the case, setting down a plurality of terms (e.g. whether the sun is eclipsed or not), we are seeking the fact. Evidence for this: on finding that it is eclipsed, we stop; and if from the beginning we know that it is eclipsed, we do not seek whether it is. When we know the fact we seek the reason why (e.g. knowing that it is eclipsed or that the earth moves, we seek the reason why it is eclipsed or why it moves). These things we seek in this way; but certain items we seek in another way – e.g. if a centaur or a god is or is not. (I mean if one is or is not 'without qualification' and not if one is white or not.) And having come to know that it is, we seek what it is (e.g.: Then what is a god? or What is a man?) [APo II 1, 89b 25-35; Barnes 1993, with changes]. The philosopher groups these questions into two pairs based on a typical Aristotelian division between subjects and attributes.62 The first couple of questions concern the presence of an attribute in a given subject: (Q1) Does the attribute P belong to the subject S? (Q2) Why does P belong to S? Questions Q1 and Q2 ask whether and why a given subject S is 'something or not something' ( , 90a 3-4), is 'partially' ( , 89b39; 90a2) or is 'one of the items which hold of it in itself or incidentally' ( , 90a 11): 'Is the earth moving?' or 'Why is the sun eclipsed'?'. Aristotle also notes that Q1 is prior to Q2 in the order of inquiry, since we can only ask why S is P when we already know that it is P. On the other hand, the other two questions address the subjects themselves: (Q3) Does S exist? (Q4) What is S? Question Q3 does not ask whether a subject S is or is not something, but whether S is 'without qualification' ( , 89b 39; 90a 4) – i.e. whether it exists63 –, whereas Q4 asks about its nature or essence. Questions Q3 and Q4 no longer concern attributes, but the 'substance' ( , 90a10) and the 'underlying subject' ( 90a 12) to which they belong: 'Is there such a thing as a centaur?' or 'What is a god?'. Question Q3 is also epistemologically prior to Q4: in order to know what a subject S is, says Aristotle, we need to know in advance that S 'is' or 'exists'. As one would expect given the definition of knowledge in T1 (APo I 2, 71b 9-12), Aristotle argues that looking for an answer to these four questions is equivalent to seeking for a 62 This reading is a traditional one, with the support of modern interpreters such as Ross (1949, pp. 609-10), Tredennick (1960, p. 11), Mansion (1976, p. 63), Barnes (1993, pp. 203-4), and Bronstein (2016a, pp. 89-107). 63 For a different account, see Gomez-Lobo (1980). However, the examples 'god' and 'centaur', whose existence is controversial, strongly suggests the existential meaning of the verb 'to' be.' 49 cause (APo II 2, 90a 6-7). However, the 'cause' ( ) is now identified with the 'middle term' ( ): [T6] When we seek the fact or if something is without qualification, we are seeking whether or not there is a middle term for it; and when, having come to know either the fact or if it is – either partially or without qualification –, we seek the reason why or what it is, we are seeking what the middle term is [APo II 2, 89b37-90a1; Barnes 1993, with changes]. The expression ' ' comes from the vocabulary of the APr, which suggests that the four questions listed in APo II 2 are limited to syllogistic propositions – hence, they are formulated within the framework of Aristotle's model of demonstrative science.64 One of Aristotle's claims here is that Q1 and Q3 are reduced to a question about the existence of a middle term: (Q1*/Q3*) Is there a middle term? On the other hand, we answer the questions Q2 and Q4 when we find out what that middle term is: (Q2*/Q4*) What is the middle term? In a context where the is identified with the , asking about the existence of a middle term for a given categorical sentence is asking whether this sentence is likely to be scientifically explained.65 At this point, the inquirer is not looking for a middle term that simply establishes the truth of the conclusion, but 'the actual ground in reality of the fact to be explained.'66 Inquiring into the existence of such ground is to examine whether the phenomenon in question presents the kind of regularity and consistency that suggests the presence of an underlying causal structure.67 Asking what that middle term is, on the other hand, is asking what that actual ground is after all. Therefore, first we have: (Q1*/Q3*) Is there an M such that PaM, MaS ⊦ PaS & M is the reason why PaS?68 64 Barnes (1993, p. 203). 65 Barnes (1993, p. 205). 66 Ross (1949, p. 611). 67 Charles (2000, p. 71). 68 Our formulation of Q1* is motivated by the fact that, according to Aristotle, scientific explanations are preferably structured in Barbara (see APo I 14, 79a 24-29; II 8, 93a 3-9). Still, our interpretation is compatible with other syllogistic moods. 50 Once we know that PaS is scientifically explainable – i.e. once we have an affirmative answer to Q1* –, we are able ask: (Q2*/Q4*) What is M such that PaM, MaS ⊦ PaS & M is the reason why PaS? It is important to note that an affirmative answer to Q1 is compatible with a negative answer to Q1* if 'PaS' is indemonstrable. Therefore, Aristotle is assuming that Q1 and Q2 in APo II 1-2 are restricted to demonstrable propositions, which excludes tautologies and definitions.69 At this juncture, it could be argued that limiting Q3 and Q4 to subjects was an unfortunate move. Apparently, nothing prevents us from asking what an eclipse is or whether there is such a thing as an eclipse, which means Aristotle should have included the following two questions in his account: (Q3.1) Does P exist? (Q4.1) What is P? However, Aristotle does not say that we cannot ask questions of existence and essence about attributes. Actually, his claim is that, for the purpose of scientific investigation, those questions are equivalent to, and in fact better phrased in the form of, Q1 and Q2:70 [T7] In all these cases it is clear that what it is and why it is are the same. What it is an eclipse? Privation of light from the moon by the screening of the earth. Why is there an eclipse? Or Why is the moon eclipsed? Because the light leaves it when the earth screens it [APo II 2, 90a 14-18; Barnes 1993]. According to Aristotle, an attribute is said to 'exist' insofar as it is predicated of a subject. Knowing the existence of the lunar eclipse is the same as knowing that it is predicated of the moon. On the other hand, there is a correspondence between the definition of an attribute and the explanation of its occurrence in the relevant subject. For instance, the lunar eclipse is defined as follows: Def. (Lunar eclipse): Lunar eclipse is(df.)the privation of light from the moon in virtue of it being screened from the sun by the earth. 69 See Barnes (1993, p. 205); Gomez-Lobo (1980, p.73, n.10). 70 This could explain why 'night' ( ) appears as an example of Q3 in APo II 2, 90a 5. 51 On the other hand, we explain why lunar eclipse belongs to the moon through the middle term being screened by the earth (APo II 8, 93a 29-b14): Syllogism VI: Eclipse (or privation of light) holds of earth-screening, Earth-screening holds of the moon Eclipse (or privation of light) holds of the moon71 Such isomorphism between definition and demonstration is what probably made Aristotle think that formulating Q3.1 e Q4.1 in APo II 1-2 was unnecessary, since the following equivalencies hold good: (Q1) Does P holds of S? ≡ (Q3.1) Does P exist? (Q2) Why does P holds of S? ≡ (Q4.1) What is P? One may think that such correspondence is just the result of a successful inquiry. If there is an equivalence between the questions 'why is the moon eclipsed?' and 'what is eclipse?', a successful attempt to define eclipse will have its result somehow corroborated by a successful demonstration of the fact that the moon is eclipsed. For Aristotle, however, the correspondence between definitions and demonstrations should not be taken just as a mutual corroboration between the results of two independent practices. On the contrary, defining and explaining are interdependent scientific tasks, as we shall see in the next section. 2.2 – Interdependence between Defining and Explaining As we have seen, as long as the APo is understood as advancing not a theory on epistemic justification, but a theory on causal explanations (and on how these explanations are grasped and displayed in scientific discourse), Aristotle can be correctly described as a foundationalist philosopher of science. His foundationalism lies in the fact that an Aristotelian demonstration ⟨Π, c⟩ always contains a subset of indemonstrable premises Π' from which all the demonstrable premises in Π (and consequently c) are demonstrated. The set Π' includes definitions, i.e. propositions specifying essences or essential features. Therefore, Aristotle's foundationalism would not be viable if there were demonstrations of the form ⟨Π, c⟩ in which c is a definitional proposition. In other words, definitions should be principles of demonstrations, but not themselves demonstrated. 71 Aristotle uses as the major term sometimes the definiendum (e.g. 'thunder' or 'eclipse'; APo II 8, 93a 35-b6; b8-9), sometimes a brief and preliminary elucidation of what the definiendum is (e.g. 'noise' or 'privation of light', 93b 11-12). 52 Given the importance of the matter, in APo II, Aristotle engages in a long discussion about whether or not definitions can be demonstrated. His final answer is negative. Although it is possible to elaborate sound syllogisms whose conclusions are definitional sentences, such arguments are merely 'logical' ( ), without real explanatory force (APo II 8, 93a 9-15). However, Aristotle raises and discusses several puzzles in APo II 3-7, of which one is of particular interest to us: 'you might puzzle over whether you can know the same thing in the same respect both by a definition and by a demonstration, or whether this is impossible' (APo II 3, 99b 1-3). This puzzle is not solved until APo II 8. According to Aristotle, although real definitions (i.e. accounts of essences) cannot occur as conclusions of demonstrations, they are 'made clear by syllogism and demonstration' ( , APo II 8, 93b 17-18), being similar to demonstrations, but 'differing in arrangement' ( , APo II 10, 94a 2). In the following, I shall spell out how Aristotle reaches this result. After denying that conclusions of demonstrations can be definitional sentences (APo II 8, 93a 9-15), Aristotle announces his aim in APo II 8: 'let us say in what way a demonstration [of what something is] is possible, starting again from the beginning' (93a 15-16). 'Starting again from the beginning' ( ), in this context, refers back to the four questions discussed in APo II 1-2, which Aristotle resumes in APo II 8: [T8] [...] Just as we seek the reason why when we grasp the fact [...], in the same way we plainly cannot grasp what it is to be something without grasping that it exists; for we cannot know what something is when we do not know whether it exists [APo II 8, 93a 16-20; Barnes 1993]. As we know, questions of the form (Q1) Does P belong to S?/(Q3.1) Does P exist? are epistemologically prior to questions of the form (Q2) Why does P belong to S?/(Q4.1) What is P? That is to say, we cannot start investigating what something is before we know that it exists. However, as several interpreters have noted72, the priority of Q3 and Q3.1 over Q4 and Q4.1 gives 72 See Bolton (1976); Ackrill (1981, pp. 364-366); Bayer (1995, p. 246); Charles (2000, p. 76); Bronstein (2010; 2016a, pp. 84-88, pp. 93-94). 53 rise to an epistemological problem close to the one discussed in Plato's dialogue Menon.73 I shall call it the 'Inquiry Problem': The Inquiry Problem: If I do not know that x exists, I cannot start investigating what x is (according to APo II 1-2). On the other hand, if I do not know what x is, how could I inquire whether x exists or not? This question is motivated by the following assumption: if the essence of x is unknown to me, I do not have the means to identify eventual instances of x, and hence cannot investigate whether x exists. In APo II 8, Aristotle offers his solution to the Inquiry Problem by undermining the assumption that motivates it. He writes as follows: [T9] But as to whether it exists, sometimes we grasp this incidentally, and sometimes by grasping something of the object itself – e.g. of thunder, that it is a sort of noise in the clouds; of an eclipse, that it is a sort of privation of light; of man, that he is a sort of animal; of soul, that it is something which moves itself [APo II 8, 93a 21-24; Barnes 1993]. If I intend to know what a lunar eclipse is, I need at least some information with which I could start off my inquiry. In one scenario, what I know about eclipse holds of it 'incidentally' ( ). Here, Aristotle probably has in mind the notion of defined in Top. I 5, 102b 6-7, i.e. a predicate that 'can belong or not belong to one and the same thing.' If everything I know about eclipse is contingently connected to it, I would not be able to recognize its instances with the kind of consistency that scientific investigation requires. At this point, it is worth stressing that, according to the doctrine of APo II 1-2, questions of the form (Q1) Does P belong to S?/(Q3.1) Does P exist? are equivalent to a question about the existence of a cause or middle term: (Q1*/Q3*) Is there an M such that PaM, MaS ⊦ PaS & M is the reason why PaS? Therefore, inquiring whether the lunar eclipse 'exists' is not just a matter of investigating whether or not it happens to the moon, but of realizing that it occurs frequently and regularly enough to 73 'How will you look for it, Socrates, when you do not know at all what it is? How will you aim to search for something you do not know at all? If you should meet with it, how will you know that this is the thing that you did not know?' [Meno, 80de; G.M.A Grube in Cooper 1997]. 54 suggest the presence of an underlying cause – a cause that could be used not only to explain why the moon is regularly eclipsed, but also to formulate a causal definition of eclipse. Therefore, Q2 should be interpreted not as asking whether (e.g.) eclipse exists without further qualification, but whether it exists as a definable unity or a genuine kind.74 If all I know about the lunar eclipse is something that may or may not belong to it, I could always mistake its instances for something else. Even if I eventually recognise as a case of eclipse something that actually happens to be one of its instances, I would not have an answer to Q3.1 'except incidentally' ( , APo II 10, 93b 35). In other words, I would never be able to determine whether all the cases to which I apply the word 'eclipse' are actually instances of the same, unified phenomenon. Our inquiry is more promising, says Aristotle, if we 'grasp something of the object itself' ( ), as when we know of thunder that it is a sort of noise in the clouds, or of eclipse that it is a sort of privation of light from the moon. These vague descriptions seem to be preliminary accounts of the words 'thunder' and 'eclipse' without which no one could use them with linguistic competence. In APo II 10, this step of the inquiry is identified with knowing the meaning of words – i.e. knowing their 'nominal definitions'75 –, without knowing yet that they refer to genuine existing kinds:76 [T10] Since a definition is said to be an account of what something is, it is clear that one type will be an account of what its name, or some other namelike account, means – e.g. what 'triangle' means. When we grasp that this exists, we seek why it is [APo II 10, 93b 29-32; Barnes 1993, with changes]. Based on this passage (and its connection to APo II 8), David Charles (2000, pp. 23-76) argued that, according to Aristotle, the inquiry of essences can be divided into three stages: Stage 1: One knows an account of what a name (or a name-like expression)77 signifies, without knowing whether the name denotes a genuine existing kind. Stage 2: One knows that the thing denoted by the name (or the name-like expression) exists (as a genuine kind). 74 See Upton (1991, pp. 322-323); Charles (2000, pp.40-41; p.203); Bronstein (2010, pp.109-110; p. 112; 2016a, pp. 104-107). 75 See Ross (1949 p. 635); Demoss & Devereux (1988, p. 136); Barnes (1993, p. 222). 76 See Charles (2000, pp. 24-24). For a different view, see Bolton (1976, pp. 522-526). 77 I am following Ross (1949, p. 635) and taking ' as referring to complex nominal phrases to be contrasted with simple names. 55 Stage 3: One knows the essence (i.e. the cause) of the thing denoted by the name (or name-like expression). At stage 1, the scientist has the kind of basic information about (e.g.) eclipses that regulates the (standard) use of the word 'eclipse' in ordinary discourse: if there is such a thing as a lunar eclipse, it will be a certain privation of light from the moon. As Charles (2000, p. 35) puts it, the scientist can use this preliminary information as a sort of 'springboard' to move from Stage 1 to Stage 2. By knowing that (e.g.) thunder is a certain noise in the clouds, one might perform induction-based inferences – like Syllogisms I to IV, discussed in Chapter 1 – to gather more information about the phenomenon: for instance, that it happens under certain meteorological conditions, that it follows lightning, etc. Thus, the indefinite pronouns ' ' and ' ' in APo II 8, 93a 22-24 stand for 'place-holders' to be filled in with the kind of information needed to move from Stage 1 to Stage 2 – i.e. that the phenomenon under investigation presents (in a regular basis) distinguishing features that suggest we are not dealing with a chance event. If so, there must be an underlying cause to be grasped at Stage 3. Aristotle gives a helpful example of how one may move from Stage 1 to Stage 2 without yet knowing the cause (i.e. the essence) of the phenomenon at stake. [T11] When we discover it [i.e. the account of eclipse], we know at the same time the fact and the reason why – if we proceed through immediates.78 Otherwise, we know the fact but not the reason why: moon C, eclipse A, not being able to produce a shadow during full moon although nothing visible is between us and it B. If B, not being able to produce a shadow during full moon although nothing visible is between us and it, holds of C, and A, being eclipsed, holds of B, then it is plain that it is eclipsed but not yet why; and we know that there is an eclipse but we do not know what it is [APo II 8, 93a 35-b2; Barnes 1993, with changes]. Suppose a scientist at Stage 1 knows that eclipse is some sort of loss of light from the moon. As she proceeds with her investigation, she realises that it is not any kind of privation of light from the moon that can be correctly called 'eclipse'. If, in a cloudy night, the moon becomes unable to cast shadows, she will probably take into account that the clouds might be blocking the light from the moon and would avoid concluding that an eclipse is taking place. If, however, a full moon 78 Reading ' ' with Ross (1949) instead of ' ', like most MSS. 56 becomes unable to produce shadows even if there is nothing intermediate that could be blocking its light, the following syllogism could be formulated: Syllogism VII: Eclipse holds of inability to cast shadows etc., Inability to cast shadows etc. holds of the moon Eclipse holds of the moon Syllogism VII establishes that the moon is eclipsed – and establishes it in a way that its conclusion is now seen as a legitimate explanandum. Now, we can investigate why this is the case, and hence move from Stage 2 to Stage 3: [T12] When it is plain that A holds of C, then to seek why it holds is to seek what B is – whether screening or rotation of the moon or extinction. And this is the account of the one extreme, i.e. in this case of A; for an eclipse is a screening by the earth [APo II 8, 93b 3-7; Barnes 1993]. At Stage 3, then, the scientist finally discovers the cause of eclipse, which is signified by the middle term of our Syllogism VI: Syllogism VI: Eclipse (or privation of light) holds of earth-screening, Earth-screening holds of the moon Eclipse (or privation of light) holds of the moon Here, the middle term is said to be the definition of the major term 'eclipse' ( ). Strictly speaking, the middle term is the causal part of the definition, which was missing in the preliminary account used at Stage 1. Thus, a Stage 3-definition of eclipse would be isomorphic to Syllogism VI: Def. (Lunar eclipse): Lunar eclipse is(df.)the privation of light from the moon in virtue of it being screened from the sun by the earth. Even if Syllogism VI is not a demonstration of the definition – in the sense of having the definiendum as the minor term and the definiens as the major –, it displays or reveals the essence of eclipse. Therefore, Aristotle can conclude his reasoning as follows: [T13] 57 We have said how what something is is taken and becomes familiar. Although there are no syllogisms and no demonstrations of what something is, nevertheless what something is is made plain through syllogisms and through demonstrations. Hence without a demonstration you cannot get to know what something is [APo II 8, 93b 15-18; Barnes 1993]. The isomorphism between the definition of eclipse and Syllogism VI is not just a coincidence of results of two independent scientific practices: defining and explaining. On the contrary, we cannot know the essence of something independently of the explanatory role it plays in a demonstration: (93b 19-18). In other words, the way we acquire knowledge of definitions intrinsically involves the act of explaining a phenomenon by demonstration.79 This result is in accordance with the claim we advanced in Chapter 1. is the cognitive state that knows definitions. Since demonstrations are based on definitions, is dependent on . However, if we cannot get to know a definition independently of the act of demonstrating, one cannot have without having . The interdependence of the two kinds of understanding 'without qualification' just mirrors the interdependence between defining and explaining. 2.3 – The Essence of Subjects vs. The Essence of Attributes: Two Models of Definition-Based Explanation Pairing up Q1 and Q2 with Q1* and Q2* seems unproblematic. The presence of an attribute in a subject can easily be phrased in a categorical sentence liable to occur as the conclusion of a syllogistic inference. Thus, it is easy to understand why Aristotle takes questions such as (Q1) Does P belong to S?/(Q3.1) Does P exist? (Q2) Why dos P belong to S?/(Q4.1) What is P? as equivalent to questions about a middle term: (Q1*) Is there an M such that PaM, MaS ⊦ PaS & M is the reason why PaS? (Q2*) What is M such that PaM, MaS ⊦ PaS & M is the reason why PaS? However, Aristotle makes it clear that a middle term is sought not only in questions about attributes, but also in questions about subjects (APo II 2, 89b37-90a5). Therefore, questions like (Q3) Does S exist? 79 See Kung (1977, pp. 168-172); Charles (2000; 2010b, pp. 268-328); Williams & Charles (2013); Peramatzis (2011, pp. 180-188; 2013); Koslicki (2012); Angioni (2014c; 2016). 58 (Q4) What is S? would also be reduced to questions about the existence and identity of middle terms. However, several interpreters have noted that, at first sight, it does not seem natural to talk of middle terms when we are asking whether a given subject is 'without qualification': How can and applied to a substance be supposed to be concerned with a middle term? A substance does not inhere in anything; there are no two terms between which a middle term is to be found. A. [Aristotle] gives no example of what he means by the in such a case, and in this chapter the application of the questions and to substances is overshadowed by its application to attributes and events, which is amply illustrated (90a 15-23) [Ross 1949, pp. 611-2]. It seems clear from Aristotle's first examples that his questions are (1) Is X Y? (2) Why is X Y? (3) Does X exist? What is X? – X being a substance (centaur, god, man). But when he goes on to say that in every case we are looking for a middle term or cause, doubts arise; because it is not obviously true that when we ask whether a substance exists, or what is it, we are inquiring for its cause [Tredennick 1960, p. 11]. Once we know that ( ) C is A, we know that there is a middle term holding the extreme terms together. When we ask why ( ) C is A, we ask what is the . If it is B, then we know that C is A because ( ) C is B and B is A. But how can there be a middle term between a single term and the predicate 'exists'? [Gomez-Lobo 1980, p. 73]. This difficulty comes from the general view that the existence of subjects, unlike that of attributes, cannot be reduced to their presence in a more basic entity. Thus, one could say that Q3 and Q4 cannot be translated into subject-predicate sentences (as Q3.1 and Q4.1 can), which makes it difficult to understand why Aristotle takes them as tantamount to questions about a middle term. After reading APo II 1-2, we have the impression that it would be more congenial to Aristotle's theory if Q3 and Q4 were not answered by means of syllogistic demonstrations, letting subjects and their essences fall exclusively within the competence of . If so, in the case of subjects at least, defining and explaining would not be interdependent practices. One could argue that it makes perfect sense to take Q3 and Q4 as questions about a middle term if we understand existence as a first order predicate. In that case, the existence of a subject would be verified insofar as there would be a middle term proving that the predicable 'existing' belongs to it. The cause signified by this middle term, on the other hand, would be the essence of the subject, providing in this way an answer to Q4. However, a few considerations about Aristotle's theory of demonstration shall make it clear that a predicate such as 'being' or 'existing' could hardly occur as the major term in a typical Aristotelian demonstration. 59 Aristotle describes demonstrable attributes as 'per se accidents' ( )80, i.e. as predicates belonging to a subject 'in itself' ( ), but not as a part of its 'essence' ( ).81 Aristotle intends to account for the fact that science is above all concerned with attributes that, unlike existence, are proper to their subjects and hold of them by necessity. Nevertheless, their presence in the relevant subject is not a trivial fact about it, knowable a priori through the analysis of what it is to be that subject. As several interpreters have noted, for Aristotle, necessary predicates are either part of the essence of the subject or follow from its essence.82 Since it is not a part of the essence of its subject, a per se accident is a necessary consequence of and is explained by the subject's essence. It is at least unlikely that this picture could apply to a predicate such as 'existing.' However, this approach not only fails to solve the inconsistency found in APo II 1-2, but also brings into focus another (potential) problem in Aristotle's theory: the philosopher appears to sustain two different (and perhaps incompatible) models of explanation. Since definitions are crucial to Aristotle's foundationalist project, it is mandatory for us to determine what role they play in syllogistic demonstrations. This task involves addressing a long-standing and important question, for many years neglected and recently revived in the secondary literature.83 Definitions are principles of demonstrations insofar as the middle term is the of the extreme and therefore signifies an essence of a certain kind. However, is the middle term the (i.e. the definitional account) of the major or the minor term? The answer depends on whether, for Aristotle, the cause of a subject S being P is the essence of the attribute P or of the subject S. As we have seen, in the second book of the APo, Aristotle is overtly committed to what I shall call the 'A-Model': the reason why 'PaS' is true is the essence (or the causal part of the essence of) of the attribute P.84 In that case, a syllogistic explanation will have the following form: PaDef.(P), Def.(P)aS PaS in which 'Def.(P)' stands for the definition of P (or the causal part of its definition). Let us say, for instance, that the syllogism explaining the occurrence of thunders runs as follows (APo II 8, 93b 714): 80 See APo I 6, 75a 18-19; I 7, 75b 42-b2; I 10, 76b 11-15; Ph. II 2, 193b 22-30; Metaph. III 1, 997a 19-25. For other occurrences of the notion, see Bonitz 713b43-71a3. 81 Metaph. V 30, 1025a 10-34. 82 Loux (1991, p. 73); Barnes (1993, p. 120); Charles (2000, p. 203); Malink (2013, pp. 124-126); Bronstein (2015, pp. 724-725); Shields (2016, pp. 84-85). 83 Ferejohn (2013); Angioni (2016, pp. 103-107); Bronstein (2015; 2016a, 48-50). See also my Zuppolini (2014a, pp. 103-145). 84 APo II 2, 89b 36 90a 14; 90a 31-35; II 8, 93a31-33; APo II 16, 98b 21-24; II 17 99a 21-22, 25-26 60 Syllogism VIII: Thunder (or such-and-such noise) holds of extinction of fire, Extinction of fire holds of clouds Thunder (or such-and-such noise) holds of clouds In that case, the complete (causal) definition of thunder would be isomorphic to Syllogism VIII: Def.(Thunder): Thunder is(df.) noise of fire being extinguished in the clouds (APo II 10, 94 a 5-6). However, according to the traditional account of per se accidents, a demonstrable attribute P is a necessary property of its subject S, which follows from, and is explained by the subject's essence. If so, Aristotle would also be committed to what I shall call the 'S-Model': the reason why a demonstrable proposition 'PaS' is true is the essence of the subject S.85 According to this model, a syllogistic explanation will be structured as follows: PaDef.(S), Def.(S)aS PaS in which 'Def.(S)' stands for the definition of S. Some passages (especially in APo I) can be interpreted as being in accordance with the S-Model. Here is one of them: [T14] We understand something [S being P] non-incidentally when we know it in virtue of that in virtue of which it holds and from what are its principles as such [M]. E.g. we understand that having angles equal to two right angles [P] holds of something [S] when we know it from the principles [M] of that of which it holds in itself [S qua S] [APo I 9, 76a 4-7; Barnes 1993, with changes]. Aristotle might be taken to affirm that an attribute P belongs to a subject S in itself ( ) when S is P in virtue of a cause M that is among the constitutive principles of S as S ( ; ). The jargon used in this passage suggests that being a principle of S is equivalent to being one of its essential features.86 85 The S-Model and the A-Model correspond to David Bronstein's Model 1 and Model 2, respectively (see Bronstein 2016a, pp. 48-50). 86 Although this passage is highly controversial, I think it is useful for introducing this debate given the fact that Aristotle's use of the expression ' ' is usually taken to favour the S-Model, since ' ' refers to the subject of per se predications, as I am going to argue below. For a different understanding, see Angioni (2014c; 2016), who takes the 'in itself' formula and similar expressions to refer to the explanandum as such. For other readings of T14, see Ross (1949, p. 537); Barnes (1993, p. 135); Angioni (2014c; 2016, p. 93). 61 Here, the expression ' ' in 76a 6 is replaced by the well-known formula ' ' in 76a 7. The shift shall not surprise the reader: [T15] To hold of something in itself and to hold of it as such are the same thing: e.g. point and straight hold of line in itself – for they hold of it as line; and two right angles hold of triangle as triangle – for the triangle is in itself equal to two right angles [APo I 4, 73b 28-32; Barnes 1993, with changes]. The passage above shows that, in the formula 'S is P', ' ' refers anaphorically to the subject S. First, the pronoun is in the same gender and number as the subject-terms of the predications cited as examples, ' ' with ' ' and ' ' with ' '. Second, the pronoun ' ' in the expression ' ' is replaced in both cases by the respective subject-terms, ' ' and ' '. Nevertheless, as we can see in the preceding quotation (APo I 9, 76a 4-7), the pronoun ' ' in 'S is P' may refer anaphorically to the subject S, but not tautologically. Rather, we may say that it refers back to S by introducing another item that is, in the relevant way, the 'same as' S ( ) – that is, the essence of S. If this reading is correct, the reason why triangles have 2R is not something different from what it is to be a triangle, i.e. the essence of triangle. Hence, the corresponding demonstration would run as follows: Syllogism IX 2R holds of all three-sided closed plane figures, three-sided closed plane figure holds of all triangles 2R holds of all triangles Other passages in the Analytics favour the S-Model. In APo II 16, 98a35-b4, Aristotle affirms that broad-leaved plants such as vines and fig-trees shed their leaves precisely because they are broadleaved ( ).87 In APr I 35, 48a 33-36, 2R is said to hold of triangle 'in itself' ( ) because anything that has 2R has it 'in virtue of' ( ) triangle, whereas triangle has 2R 'not in virtue of something different' ( ).88 In other passages, the same general idea is formulated with a ' ' or a (explanatory) ' ' instead of ' ' (APo I 5, 74b 2-4; I 24, 85b 5-13).89 Passages from outside the Analytics also suggest something along the lines of the S-Model: 87 See Ferejohn (2013, p. 104). 88 In APr I 35, Aristotle addresses the mistake of taking a primary demonstrandum – in which we have the appropriate subject-term from an explanatory point of view – as an immediate proposition. Although there is not a kind-term that is, in respect of the property 2R, explanatorily prior to 'triangle', a complex expression (maybe the definition of triangle) could be used as a middle term to explain why all triangles have 2R. 89 For an interpretation that also takes the occurrences of ' ' in the first half of APo I 24 as explanatory, see Angioni (2016, pp. 96-100). 62 [T16] For the soul is a sort of first principle of animals. We aim to consider and ascertain its nature and essence, and then its properties, of which some seem to be affections peculiar to the soul itself, while others belong to animals as well because of the soul [De An. I 1, 402a 6-10; Shields 2016]. [T17] The fish do not have distinct limbs, owing to the fact that the nature of fish, according to the account of their essence, is to be able to swim, and since nature makes nothing either superfluous or pointless. And since they are blooded in virtue of their essence, it is on account of being swimmers that they have fins, and on account of not being land-dwellers that they do not have feet [PA IV 13, 695b 17-22; Lennox 2001, with changes]. [T18] They are two-footed of necessity; for the essence of the bird is that of the blooded animals, but at the same time that of the winged animals, and blooded animals do not move by more than four points [PA IV 693b 5-8; Lennox 2001, with changes].90 Therefore, we have textual evidence (from the Analytics and from other works in the corpus) favouring both the A-Model and the S-Model. Thus, a satisfactory account of Aristotle's theory of demonstration must address the question of whether he endorses the A-Model, the S-Model, or a combination of both (if they are compatible in the first place). However, this question cannot be properly answered unless the distinction between subjects and attributes is clearly drawn. Although Aristotle takes this distinction as a datum in APo II 1-2, several issues remain obscure: (A) What are the criteria for distinguishing between subjects and attributes? How does the metaphysical distinction between subjects and attributes relate to the linguistic or logical distinction between subjectand predicate-terms? (B) How do subjects relate to their attributes from a metaphysical point of view? Does this metaphysical relation affect the roles they play in scientific explanations? 90 See also Ph. IV 4, 211a 7-11; PA IV 5, 678a 26-34; IV 6, 682a 35-b32; IV 8, 684a 32-b1. 63 (C) Is there a place for definitions of subjects in demonstrative sciences? Can their definitions be used to explain their demonstrable attributes? Can their definitions be used to explain their existence in syllogistic arguments? In the next chapters, I intend to approach these three topics by analysing some of the metaphysical views that underlie Aristotle's philosophy of science. We shall see that this ontological framework accomplishes three basic tasks: (i) it imposes certain semantic rules for scientific discourse; (ii) it plays a crucial role in Aristotle's conception of causation and scientific explanation; (iii) it provides particular sciences with a set of criteria for linking together and organizing their propositions in terms of explanatory priority. 64 65 CHAPTER 3 A METAPHYSICAL DEFENCE AGAINST INFINITE REGRESS 3.1 – Aristotelian Foundationalism Challenged and a Metaphysically Loaded Response We have seen that the metaphysical distinction between subjects and attributes is a crucial part of Aristotle's model of demonstrative science. However, the philosopher was accused of selecting an underlying logic that overlooks this very distinction. Peter Geach (1972, p. 44) argued: 'Aristotle, like Adam, began right, but soon wandered into a wrong path, with disastrous consequences for his posterity.' In order to promote his Syllogistic, says the author, Aristotle rejected a healthy theory of predication – already sketched by Plato in the Sophist and explored by Aristotle himself in the De interpretatione – which could have anticipated notions and theses that would be achieved only by Frege and Russell.91 Following Plato, Aristotle argued that the simplest propositions available are composed of two basic elements, a 'verb' ( ) and a 'name' ( ). Names and verbs have distinct and mutually exclusive logical roles. A verb is always 'a sign of things said of something else' (Int. 3, 16b 7-8.), like 'thinks' or 'runs', whereas a name, like 'Socrates' or 'Secretariat', refers to the object to which the verb is applied. Together, name and verb compose 91 See also Harari (2004, pp. 81-82). 66 meaningful propositions such as 'Socrates thinks' or 'Secretariat runs', which does not happen when we have a sequence of names ('Socrates Secretariat') or of verbs ('thinks runs'). In addition, Aristotle says that 'there is no difference between saying that a man walks and saying that a man is walking' (Int. 12, 21b 9-10). Thus, the logical asymmetry that holds between subject and predicate is present in sentences with a bipartite syntax of the form 'S Ps' ('Secretariat runs') as well as in sentences with a tripartite structure such as 'S is P' ('Secretariat is running').92 However, at first sight, there seems to be no asymmetry between subject and predicate in the logic of the APr, since all the terms involved in a syllogistic reasoning must be able to play both logical roles. As Geach points out, a combinatory analysis shows us that, in all syllogistic figures, at least one of the three terms (the major, the middle and the minor) must occur as subject in one of the propositions and as predicate in another – in the first figure, the middle term is the subject of the major premise and the predicate of the minor; in the second figure, the major term is the subject of the major premise and the predicate of the conclusion; in the third figure, the minor term is the predicate of the minor premise and the subject of the conclusion. Additionally, the Syllogistic contains a set of conversion rules that change the logical role of the terms of the proposition to which they apply.93 Russell (1961, pp. 195-198) had already criticised the same aspect of Aristotle's Logic, arguing that such shift in the logical role of a term within the same argument makes room for a large-scale production of equivocation fallacies.94 Following Russell's criticisms, Peter Geach (1972, pp.51-54) claimed that abandoning the distinction between name and verb initiated a gradual deterioration of Logic, with harmful consequences for its development. In the same vein, one could claim that Aristotle's model of demonstrative science embraces an underlying logic that is insensitive to the distinction between subjects and attributes, whose importance to his theory is made clear in APo II 1-2, as we have seen. Nevertheless, the APo compensate the loss of logical asymmetry between subject and predicate in syllogistic propositions with a set of (metaphysically loaded) theses on predication. These theses are part of a sophisticated argument presented in APo I 19-22, which we shall analyse in the present chapter.95 In APo I 3, as we have seen in Chapter 1, Aristotle describes a group of sceptics who believe that scientific knowledge is not possible since it would require demonstrations to go on ad 92 Barnes (2007, p.111) notes: 'There is no reason to question the equivalence which Aristotle and his followers proclaim – although it is perhaps worth insisting that the claim does not concern the English continuous present (for which, of course, it would be quite false) but rather a certain Greek paraphrastic idiom. So (the Greek form for) "sang" means the same as (the Greek form for) "was singing"; and in general "VERBs" means the same as "is VERBing".' 93 The conversions are the following: AaB ⊦ BiA; AiB ⊦ BiA; AeB ⊦ BeA. 94 See also Harari (2004, p. 92). 95 I presented a full reconstruction of Aristotle's proof in Zuppolini (2014a), in which some of the claims I advance in this chapter can be found. Nevertheless, the interpretation presented there is significantly different from the one I am proposing now. 67 infinitum. In APo I 19-22, the philosopher presents a very complex argument meant to show that his model of demonstrative science is not vulnerable to this kind of sceptical attack. In other words, the argument is meant to establish that all Aristotelian demonstrations of the form ⟨Π, c⟩ contain a limited number of inferential steps, the set Π being finite.96 Aristotle begins his proof by questioning the possibility of there being infinite series of predications. These series can be of two kinds, the first of them being specified as follows: [T19] Then let C be such that it itself no longer holds of anything else and B holds of it primitively (i.e. there is nothing else between them). Again, let E hold of F in the same way, and F of B. Now must this come to a stop, or is it possible for it to go on ad infinitum? [APo I 19, 81b 30-33; Barnes 1993] Later on, in 81b 39-40, the philosopher describes this series as going 'upwards' ( ): such a series – which I shall call 'U-series' – begins with a 'fixed' subject and the predicate of each categorical sentence occurs as subject in the next predication: Infinite Upwards Series (U-series): M1aS, M2aM1, M3aM2, ... , such that ∀n(Mn+1aMn) The other kind of predicative series runs as follows: [T20] Again, if nothing is predicated of A in itself and A holds of H primitively and of nothing prior in between, and H holds of G and this of B, must this come to a stop, or is it possible for this to go on ad infinitum? [APo I 19, 81b 33-37; Barnes 1993] This second series goes the opposite direction: it starts from a given predicate and the subject of each predication becomes the predicate in the next sentence. In 82a 1-2, Aristotle refers to this sequence of predications as going 'downwards' ( ) – thus, I shall call it 'D-series': Infinite Downwards Series (D-series): PaM1, M1a M2, M2aM3, ... , such that ∀n(MnaMn+1) To these first two questions, Aristotle adds a third one: 96 This has been called Aristotle's 'compactness proof.' See Lear (1980, pp. 15-34), who admits that Aristotle's concern is not exactly the same as the one we understand nowadays as the compactness problem. On this, see Scanlan (1983). 68 [T21] Again, is it possible for the terms in between to be infinite if the extremes are determined? I mean e.g. if the A holds of C, and B is a middle term for them, and for B and A there are different middle terms, and for these others, is it possible or impossible for these to go on ad infinitum? This is the same as to inquire whether demonstrations can proceed ad infinitum and whether there can be demonstrations of everything, or whether terms are bounded by one another [APo I 19, 82a 2-8; Barnes 1993]. At first sight, one might read the first two lines of this passage as referring to the two limits S and P ( ) and the intermediate terms Mis ( ) in Uor D-series. However, what characterises these series seems to be the fact that each of them has only one boundary – an ultimate subject S and an ultimate predicate P respectively. Actually, the occurrence of ' ' in 82a4 suggests that Aristotle has in mind a categorical proposition that requires an infinite number of middle terms in order to be demonstrated. By asking about the possibility of there being infinite middle terms between two (extreme) terms, Aristotle is again addressing the sceptical objection raised in APo I 3. In fact, what he will try to prove in APo 19-22 is precisely that demonstrations cannot be extended ad infinitum. On the other hand, if ' ' and ' ' refer to the terms of the conclusion and to the middle terms of a demonstration, respectively, the connection between this third question and the other two becomes far from obvious. It is worth stressing that the three questions are raised in a context in which the Syllogistic is always present in the background as a fundamental presupposition of Aristotle's argumentation, a point interpreters often neglect. In the first paragraph of APo I 19, 81b 10-29, Aristotle reminds his readers of some of the features of syllogistic reasoning, making comments he would not bother to make if they were not to be taken into account in the next paragraphs. In fact, the first paragraph of APo I 19 and the following chapters make it clear that the first two questions are, more precisely, about whether infinite series of universal affirmative predications can occur in syllogistic demonstrations. Aristotle's point can be illustrated as follows. If a demonstration could go ad infinitum, at least one of its branches would contain infinitely many steps. Thus, the two questions raised in APo I 19 can be taken as exploring two minimum scenarios in which an infinite demonstration would be possible. Suppose, for instance, that an infinite sequence of inferences in Barbara would be necessary to demonstrate a given universal affirmative sentence 'PaS'. In the first minimum scenario, the minor premise of each syllogistic inference in the demonstration would be 69 indemonstrable, which means, in Aristotle's vocabulary, that each predicate of each of these minor premises would belong to their respective subjects 'primitively' – see ' ', ' ' (81b31) and ' ' (81b32). In this situation, a U-series would be generated from the bottom minor term:97 PaMω MωaMω-1 PaMω-1 (...) PaM3 M3aM2 PaM2 M2aM1 PaM1 M1aS PaS In another scenario, the demonstration would proceed ad infinitum through its other branch. In this case, the major premises would be such that the predicate holds of the subject 'primitively' – see again ' ' and ' ' (81b35). Thus, a D-series would emerge from the bottom major term: Mω-1aMω MωaS Mω-1aS (...) M2aM3 M3aS M1aM2 M2aS PaM1 M1aS PaS Of course, Uand D-series do not emerge necessarily from the bottom minor and major terms (the subject and the predicate of the conclusion). The picture we find in these two minimum scenarios can also be found in any other demonstrable premise in the proof, so that these series might well begin with the minor or major term of any of the syllogistic inferences within it. It can be proved that, if at least one of the branches of a demonstration, in any combination of syllogistic moods, contains infinitely many steps, an infinite sequence of universal affirmative sentences will be generated – either a Uor a D-series. Although Aristotle himself does not present a sound argument for it, the chapters APo I 20-21 seem to offer at least a proof sketch that, if properly followed, will make it clear that no demonstrations can be extended ad infinitum without containing infinite series of predications.98 Therefore, with the first paragraph of APo I 19 97 Reading from the bottom (the conclusion) to the top of the deductive tree. 98 It is highly implausible that Aristotle would make the whole argument of APo I 19-22 rely on a premise that is far from trivial without bothering to verify it himself. Lear (1980, pp.25-30) claims that Aristotle's argument is invalid and 70 (81b 10-29) providing the appropriate context, the three questions raised in the chapter can be rephrased in the following terms: I) If ⟨Π, c⟩ is an Aristotelian demonstration, can there be a U-series – let it be Φ – such that Φ Π? (T19, APo I 19, 81b 30-33) II) If ⟨Π, c⟩ is an Aristotelian demonstration, can there be a D-series – let it be Ψ – such that Ψ Π? (T20, APo I 19, 81b 33-37) III) Can there be an Aristotelian demonstration ⟨Π, c⟩ with infinitely many inferential steps, the set Π being infinite? (T21, APo I 19, 82a 2-8) Under these formulations, the connection between the three questions is clear. As we have seen, the possibility of there being an infinite chain of syllogistic inferences in a demonstration entails an affirmative answer to at least one of the first two questions. Thus, Aristotle argues that the answer to both of them is negative, which allows him to give a negative answer to the third question as well. The arguments for negative answers to questions I and II are found in APo I 22. In this chapter, Aristotle formulates a set of constraints limiting the logical roles of certain terms in demonstrative syllogisms. These constraints are at the core of Aristotle's defence of his foundationalist project against the sceptics of APo I 3. On the other hand, they also provide an answer to criticisms (mentioned at the beginning of this chapter) made against the Syllogistic: at least in scientific contexts, the terms involved in syllogistic inferences cannot play the roles of predicate and subject regardless of their semantic contents. These constraints rely on a set of strong metaphysical theses including the doctrine of ontological categories. One could ask why Aristotle's argument follows a metaphysical approach if he intends to deny the occurrence of infinite series of predicative sentences, a purpose that is better described as having a formal or linguistic character. At this point, it is helpful to bring in a distinction, set out in the literature, between 'linguistic' and 'metaphysical' predications.99 What I shall call 'linguistic predication' is an item of a given language and has a syntactical structure of the form 'S is P' – or 'S Ps' or equivalents –, where 'S' and 'P' are called 'subject' and 'predicate' for no other reason than the grammatical roles they perform in the sentence in which they occur. Metaphysical predication, on the other hand, is not a linguistic item, but the state of affairs that determines the truth-value of linguistic predications. The subject of a metaphysical predication S (and not 'S') is offers his own proof of this result. For evidences that Aristotle came up with a sound strategy on his own, see Crager (2013, pp. 38-62; 2015, pp. 100-124). 99 Bogen & McGuire (1985, pp. 1-2); Code (1985); Lewis (1985; 1991). 71 no longer a term or expression, but an object to which a given attribute P (and not 'P') belongs. In the following, I shall call subjects and predicates of linguistic predications 'grammatical subjects' and 'grammatical predicates', whereas the subjects and predicates of metaphysical predications will be called 'metaphysical subjects' and 'metaphysical predicates'. Aristotle's proof is based on the distinction between two kinds of predicative relation. At the very beginning of APo I 22, he discusses essence-specifying sentences, when there is a definitional connection between the (grammatical) subject and the (grammatical) predicate (see APo I 22, 83b 5-8). He argues that there cannot be infinite series of predications of this kind because the essence of a given (metaphysical) subject cannot be composed of infinitely many (metaphysical) predicates: [T22] For items predicated in what something is, the case is plain: if it is possible to define anything, or if what it is to be something can be known, and if you cannot survey infinitely many items, then the items predicated in what something is must be finite [APo I 22, 82b 37-83a 1; Barnes 1993]. After these brief words, Aristotle goes on to examine sentences in which the grammatical predicate is not mentioned in the definition of its grammatical subject; the corresponding metaphysical predicate, in turn, would not be part of the essence of the respective metaphysical subject:100 [T23] You can say truly that the white thing is walking, and that that large thing is a log, and again that the log is large and the man is walking. When you speak in these two ways you make different sorts of statement. When I assert that the white thing is a log, I say that something which is 100 For a similar division of the chapter, see Philoponus (235.10-236.23); Barnes (1993, p. 175); Angioni (2007b, pp. 108-109). Someone may think that ' ' in 83a1 indicates that the rules formulated in 83a1-23 apply both to essential and non-essential predications. Even if this sentence is read as recognizing the need to deal with both kinds of predication (essential and non-essential), this does not entail that one single argument for both kinds must be provided. Neither is it necessary to read ' ' in 83a20-21 as implying the same result, since ' ' may very well be read as meaning 'without containing (non-essential) unnatural predications.' 72 incidentally white is a log, and not that the white thing is the underlying subject for the log. For it is not the case that, being white or just what is some particular white, it came to be a log – hence it is not a log except incidentally. But when I say that the log is white, I do not say that something different is white and that that is incidentally a log, as when I say that the musical thing is white (I am then saying that the man, who is incidentally musical, is white). Rather, the log is the underlying subject which came to be [white] not in virtue of being something different from what is a log or a particular log [APo I 22, 83a 1-14; Barnes 1993, with changes]. Here, Aristotle draws a distinction between two sorts of non-definitional predicative sentences, which I shall call 'natural' and 'unnatural' predications.101 A natural (linguistic) predication like 'the log is white' and 'the man is walking' is such that the grammatical subject denotes the metaphysical subject of the associated metaphysical predication appropriately. On the other hand, unnatural (linguistic) predications such as 'the white thing is walking' and 'that large thing is a log' have as their grammatical subjects terms that fail to refer to the corresponding metaphysical subjects in a proper way. Aristotle makes it clear that we can state truths about the world with unnatural predications. Such sentences are very common in ordinary discourse and, in most cases, they turn out to be perfectly intelligible. Scientific discourse, however, should avoid sentences of this kind and be limited to natural predications (see APo I 22, 83a 20-21). In the sentence 'the log is white', the grammatical subject '(the) log' is an appropriate denoting phrase102 because the corresponding metaphysical subject is white 'without being something different from just what is a log or a particular log' ( , APo I 22, 83a 13-14). Terms that capture just what a given metaphysical subject is ( ) are said to 'signify substance' ( , APo I 22, 83a 24-25). This is congenial to Aristotle's well-known thesis that substances are the metaphysical subjects par excellence, which makes them the primary realities on which everything else ontologically depends.103 Thus, science should avoid unnatural predications because scientific propositions are supposed to describe and explain the world as it is, which involves referring to the basic metaphysical subjects as what they are, namely, substances.104 Therefore, the argument in APo I 22 is underpinned by a metaphysical theory that identifies substances – humans, horses, logs and so on – as the primary subjects based on which 101 See Philoponus 235.17-23; Barnes (1993, pp. 114; 175). 102 We are using the expression 'denoting phrase' as it is defined in Russell (1905). For a comparison between Aristotle's and Russell's theories of descriptions see Williams (1985). 103 We shall discuss in more detail the notion of ontological dependence in Chapter 4. 104 For a similar view, see Barnes (1993, p. 176); Angioni (2006, pp.114-117); Angioni (2007b). Of course, this semantic principle needs to be qualified. As we are going to see below, depending on the science in question, the basic subjects in a scientific domain will not be, strictly speaking, substances, but still have their essence specified independently of mentioning more basic subjects to which they belong. 73 reality is metaphysically structured. In order to understand the claims of the chapter, interpreters usually resort to the Categories. In the next section, we shall analyse the main theses of this treatise before we continue to examine Aristotle's proof in APo I 22. 3.2 – The Categories: Inherence and Said-of Relations We have seen that the argument in APo I 22 relies on the distinction between essential and non-essential predications. In Cat. 2, 1a 20-b9, Aristotle uses a technical vocabulary to draw a similar distinction: linguistic predications of the form 'S is P' are split into two groups depending on the metaphysical relation that holds between the entity introduced by 'S' and the one introduced by 'P'. A sentence like 'Socrates is white' is analysed as expressing, between the (metaphysical) subject Socrates and the (metaphysical) predicate whiteness, a relation Aristotle describes with the expression ' '. We shall call it the 'inherence relation': Inherence Relation: 'Socrates is white' is true iff. whiteness is in the subject Socrates. On the other hand, a sentence like 'Socrates is a man' signifies a predicative connection that Aristotle describes by the phrase ' .' In spite of Aristotle's misleading vocabulary, this kind of predication is metaphysical rather than linguistic.105 We shall call it the 'saidof relation': Said-of Relation: 'Socrates is a man' is true iff. man is said of the subject Socrates. Aristotle does not elaborate clear definitions of these predicative connections, but their basic features are well known. In said-of relations, the (metaphysical) predicate is part of the essence or nature of the (metaphysical) subject, consisting in its species or genus.106 If it signifies a relation of this type, the sentence 'S is P' is a good answer to the question 'what is S?' and should be interpreted as expressing a 'definitional truth' (Ferejohn 1991, p. 82). In inherence relations, on the other hand, the (metaphysical) predicate is not a part of the essence of the (metaphysical) subject, but an 'incidental' attribute ( ). Thus, if it expresses an inherence relation, the (linguistic) predication 'S is P' would not be an answer to the question 'what is S?', but to other questions like 'of what quality is S?', 'of what quantity is S?, 'where is S?' and so on. In Cat. 2, Aristotle classifies 'beings' ( , 1a 20) using as a criterion the roles they play in said-of and inherence relations: 105 See ' ' in 1a 20. See Ackrill (1963, p. 75) and, for another reading, Moravcsick (1967). Cf. Ferejohn (1991, pp. 78-79). On the distinction between inherence and said-of relations, see Chen (1957). 106 See Ackrill (1963, pp.74-75). 74 [T24] ... Of things that are: [1] some are said of a subject but are not in any subject. For example, man is said of a subject, the individual man, but is not in any subject. [2] Some are in a subject but are not said of any subject. [...] For example, the individual knowledge-of-grammar is in a subject, the soul, but is not said of any subject; and the individual white is in a subject, the body (for all colour is in a body), but is not said of any subject. [3] Some are both said of a subject and in a subject. For example, knowledge is in a subject, the soul, and is also said of a subject, knowledge-of-grammar. [4] Some are neither in a subject nor said of a subject, for example the individual man or individual horse – for nothing of this sort is either in a subject or said of a subject [Cat. 2, 1a 20-b9; Ackrill 1963]. The types of being classified in this passage have the following distinctive features: 1Beings that are said of a subject, but are not in a subject. 2Beings that are not said of a subject, but are in a subject. 3Beings that are said of a subject and are in a subject. 4Beings that are not said of a subject, nor are they in a subject. Items of the first type are the genera and species in the category of substance – Aristotle calls them 'secondary substances' ( ) –, which are said of substances without being in them or in any other subject – as man (1a 21) or animal (2a 19) taken universally. Entities of the second type are in certain subjects, but are never said of anything, which means they are never an essential attribute of the subject to which they belong. These are particulars in categories other than substance – for instance, a particular knowledge of grammar (1a 25-6) or a particular white (1a 27). The third type of being includes universals belonging in non-substantial categories – as, for example, knowledge (1b 1), which is in the soul and is said of a particular knowledge of grammar. Finally, entities of the fourth type are individuals in the category of substance – as, for instance, a particular human being (1b 4), like Socrates or Churchill, or a particular horse (1b 4-5), like Bucephalus or Secretariat. These are called 'primary substances' ( ). Although the Categories are not clear about what kind of things can be taken as primary substances, Aristotle's examples made some interpreters describe them as 'concrete individual living things' (Ferejohn 75 1991, p. 81) and 'familiar concrete particulars of common sense' (Loux 1991, p. 23). In any case, the most distinguishable characteristic of primary substances is the fact that they never play the role of predicate in neither of these two predicative relations. It is true that Aristotle does not give us an elaborate account of these four kinds of beings just by identifying their roles in inherence and said-of relations. Nevertheless, the four-fold division in Cat. 2 involves two important principles of Aristotle's ontology. First, primary substances are never the predicate in neither of these predicative relations, while all the other beings occur as predicate in at least one of them. Second, every metaphysical predicate bears a predicative relation with a primary substance (Cat. 5, 2b 3-6). Therefore, beings of the fourth type are taken as the most fundamental realities (i.e. the primary 'beings' or 'substances') because the other entities only take part in reality insofar as they are predicated of them. At least according to the view Aristotle advances in the Categories, what makes entities like courage and whiteness depend on a certain collection of individuals like Socrates and Secretariat is the fact that the former can only be part of reality as long as there are individuals like the latter of which they are (metaphysically) predicated, but which are not themselves (metaphysically) predicated of (and hence are not ontologically dependent on) anything else.107 The dependent items of types 2 and 3 can be classified into further different kinds of being, which, together with substance (types 1 and 4), make up the list of Aristotelian categories: 'of things said without any combination, each signifies substance or quantity or quality or a relative or place or time or being-in-a-position or having or doing or being affected.'108 In a famous passage of his commentary, Ackrill (1963, pp. 78-81) argued that Aristotle might have followed two alternative strategies for arriving at this list. The first strategy consists in distinguishing different kinds of question that can be asked about a given substance x: 'what is x?, 'of what quality is x?', 'where is x?' and so on – in fact, Aristotle uses single-word interrogative pronouns to designate some of the categories ( etc.). We shall then notice that each of these questions admits only a limited range of appropriate answers and therefore corresponds to one of the categories into which beings can be classified (substance, quality, place etc.). Thus, if 'x is in the Lyceum', for instance, is an appropriate answer to the question 'where is x?', then the metaphysical predicate being in the Lyceum belongs in the category of place ( ). It is worth noting that this strategy already presupposes an intuitive way of distinguishing substances (the concrete particulars of common sense) from incidental beings.109 If the object in question is, for instance, a number or 107 At least, this seems to be the kind of ontological dependence that is in question in the Categories. We shall discuss in detail below (see Chapter 4) the problems involved in formulating ontological dependence in these terms and consider other kinds of ontological dependence and their impact in Aristotle's philosophy of science. 108 Cat. 4, 1b 25-27. Ackrill (1963) with changes. 109 Ferejohn (1991, p. 85). 76 a Platonic form, questions like 'where?' and 'when?' would not make sense, which would render the list of categories incomplete. The second method suggested by Ackrill consists not in asking several questions about a given substance, but in asking the 'what is x?' question about any entity whatsoever, a strategy which seems to be operating in Top. I 9: [T25] It is clear at once that an expression signifying the what-it-is will sometimes signify a substance, sometimes a quantity, sometimes a quality, and sometimes one of the other categories. For, supposing the example under consideration is a man, if it says that the example is a human or an animal, then it says what it is and signifies a substance. On the other hand, supposing the example under consideration is a white colour, if it says that the subject is a white or a colour, then it says what it is and signifies a quality. Similarly, supposing that the example under consideration is a foot-long length, if it says that the example is a foot-long length, then it says what it is and signifies a quantity. And likewise with the other categories [Top. I 9, 103b27-35; Smith 1997]. The species or the genus (or higher genus) of Socrates and courage would be appropriate answers to the questions 'what Socrates is?' and 'what is courage?'. If we repeat the same question in respect of the species or genus mentioned in these first answers, and continue thus, we will eventually end up with conceptually simple terms naming one of the categories – substance, quality, quantity etc. –, which would be summa genera to which the 'what is x?' question would not apply. Ackrill (1963, p. 80) argues that, since there is no overlap between the ranges of possible answers to the questions of the first strategy, no item analysed in the second strategy could fall under more than one highest genus if defined by genus and differentia, which explains why these two methods are supposed to produce the same results. It is hard to know whether Aristotle actually adopted these strategies and to which extent they are effective. However, they can still help us understand some important features of inherence and said-of relations. In the first strategy, a set of questions about a given substance is formulated, one of which is answered by a sentence signifying a said-of predication (the 'what is x?' question), whereas all the others are answered by sentences expressing inherence relations. We have also seen that questions corresponding to non-substantial categories are meaningless unless they 77 ask something about an item in the category of substance. All these facts already point to an important metaphysical principle in the Categories: MP 1: if P is in the subject S, then S and P belong in different categories and S is a substance.110 On the other hand, as Ackrill's second strategy and Top. I 9 make it clear, the 'what is x?' question applies not only to substances, but to items in other categories as well. And again, the same being cannot belong in more than one branch of the porphyrian tree, and all the elements in the same branch fall under one and the same summum genus. This gives us another metaphysical principle: MP 2: If P is said of the subject S, then S and P belong in the same category. Something along the lines of MP1 and MP2 seems to underlie Aristotle's argumentation in APo I 22. First, a thesis similar to MP1 underpins the distinction between natural and unnatural predications. For Aristotle, science is supposed to portray reality as it is in a very precise sense: linguistic predications in scientific discourse must correspond to the metaphysical predications they intend to signify. In a non-essential predication between an attribute P and a subject S – that is to say, when P is in the subject S –, S will be an item in the category of substance, whereas P will belong in a non-substantial category. Therefore, the corresponding sentence 'S is P' would be a natural predication only if the grammatical subject 'S' is a substance-term like 'log' or 'man', since otherwise it would not refer to S as what S precisely is. In a linguistic predication like 'the musical [thing] is white' – [ ], 83a10 –, we do not have 'one thing predicated of one thing' ( , APo I 22, 83a 22-23), but a complex sentence with two coincidental attributes (being musical and being white) being predicated of the same underlying subject. As Aristotle points out, what we mean by a sentence like 'the musical [thing] is white' is 'that the man, who is incidentally musical, is white' ( APo I 22, 83a 11-12). Still, items in non-substantial categories can also be subject of metaphysical predication. As long as P is part of the essence of a subject S – that is, P is said of S –, S may well be in a non-substantial category. In that case, according to MP 2, P will belong in the same category as S and none of them will 'signify substance.' In summary: if the sentence 'S is P' signifies a nonessential predication, S is in the category of substance while P is in a non-substantial category. Alternatively, if 'S is P' expresses an essential predication, S is either in the category of substance or in a non-substantial category, the predicate P being, in both cases, in the same category as S. Thus, the distinction between homocategorical and heterocategorical predications in the Categories 110 Furth (1988, p. 14); Ferejohn (1991, p. 82). 78 mirrors Aristotle's strategical distinction between essential and non-essential predicates in APo I 22.111 3.3 – A Defence against Infinite Regress: The Traditional Interpretation Several interpreters believe that the theoretical background of the Categories enables Aristotle to justify negative answers to questions I and II (see T19 and T20 above). In the ontology of the Categories, all kinds of being can occur in metaphysical predications both as subjects and as predicates, with the exception of particular substances (type 4 entities in our analysis of T24) and summa genera (the conceptually simple items that come up at the end of Ackrill's second strategy). Thus, a 'downwards' sequence of predications of the form {PaM0, M0a M1, M1aM2, ... } would always end up with a sentence like 'MiaS' in which 'S' names a particular substance and therefore cannot occur as grammatical predicate in another predication. In conformity with Top. I 9 and Ackrill's second strategy, these interpreters also believe that every 'upwards' sequence like {M0aS, M1aM0, M2aM1, ... } would be interrupted by a predication of the form 'PaMi' in which 'P' signifies a summum genus (substance, quality, quantity etc.) and would not be qualified to occur as subject in another predicative statement.112 Let us call this reading the 'Traditional Interpretation' of APo I 19-22. This interpretation is in accordance with what Aristotle says in APr I 27: [T26] Now of all the things there are, some are such that they cannot be predicated truly and universally of anything else (for instance, Cleon or Calllias, that is, what is individual and perceptible), but other things may be predicated of them (for each of these is both a man and an animal). Some things are themselves predicated of others, but nothing else is prior and predicated of them. And some things are both predicated themselves of others and others of them, as man is predicated of Callias and animal of man [APr I 27, 43a25-32; Striker 2009]. Here, Aristotle divides things into three groups: those that are not predicated of anything else, but of which some things can be predicated; those that are predicated of other things but of which 111 See Philoponus (236.5-8), who believes that Aristotle relies on MP 1 and MP 2 in APo I 22. 112 Philoponus 233.28-29, 244.28-32, 247.17-22; 250.21-251.9; Demos (1944, pp. 257-258); Ross (1949, pp. 578-579); Hamlyn (1961, p.119); Loux (1991, p. 23); Bronstein (2016a, pp. 41-42) 79 nothing can be predicated; and finally those that can be both predicated of other things and other things of them. The first class is exemplified by particular and perceptible objects such as Callias or Socrates (APr I 27, 43a 32-36), while the third class covers intermediary items such as man, which are predicated of things like Callias and of which things like animal are predicated. Aristotle does not give an example of the second class, but just announces that he will argue 'later' ( ) that 'one also comes to a halt if one goes upwards' (APr I 27, 43a 36-37). The occurrence of the phrase ' ' here does suggest that this passage refers to APo I 19-22 and it is easy to see why anyone advocating the Traditional Interpretation of these chapters would like to take the summa genera as examples of the second class listed in T26.113 Indeed, Aristotle seems to accept in his ontology items that function as boundaries in the complex structure of predicative connections of which reality is made. However, there is no reliable evidence that this aspect of his metaphysical theory is crucial (or even relevant) to his argument in APo I 19-22. In addition to the lack of textual evidence, there are also three positive reasons to reject the Tradition Interpretation: (i) First of all, this reading makes names and descriptions of particular substances the basic subject-terms of scientific discourse. However, Aristotle seems hostile to the presence singular terms in demonstrative sciences. In the Categories, a universal kind K is said to be ontologically dependent on its particular members in the sense that it could not exist if there were no individuals of which K could be predicated. Therefore, particular substances are said to be 'primary', while their species and genera only get the status of 'secondary' substances. Nevertheless, the type of dependence between attributes and subjects that demonstrations are supposed to account for is not existential, but explanatory. For Aristotle, the knowledge that the triangle has 2R is in some way prior to the knowledge that 'a given figure in a semi-circle'114 or the isosceles triangle115 have the same property, since 2R belongs to them as triangles. Thus, particular objects x, y, z (...) have the demonstrable properties they have qua members of a universal kind K, i.e. in virtue of being members of K – even if the existence of K depends on the existence of its particular members. As we shall see in the next chapters, one fundamental task of demonstrative sciences is to identify the relevant kinds on which a given property relies from an explanatory point of view. For that reason, the corresponding (universal) kind-terms will be the basic subjects in demonstrative sciences, not names and descriptions of particular substances.116 113 For a careful discussion of T26, and the presence of singular terms and summa genera in Aristotle's syllogistic, see Almeida (2013). 114 APo I 1, 71a 19-21. 115 APo I 4, 73a 28-34; 73b 25 APo I 24, 85b 5-7 APo I 9, 76a 4-9. 116 See my Zuppolini (2014c, pp. 15-17). 80 (ii) On the other hand, being a substance, a quality or a quantity does not seem to be the kind of feature Aristotle would take as a demonstrable attribute. In ideal cases, a demonstrable attribute is peculiar to its subject and belongs to it in virtue of the subject being the specific subject it is.117 This could hardly be the case of highly abstract and generic predicates such as summa genera. Although they are relevant to metaphysical speculation, these concepts seem to be associated with classificatory practices rather than scientific explanation. It is hard to see how a scientist could tell a clear-cut causal story explaining why they are connected to a specific subject and not another – as a geometer is able to explain why 2R belongs to the triangle and no other figure. If there is such causal story to be told, it is certainly not the kind of explanation departmental sciences are supposed to provide. (iii) There is a third and final reason to reject the Traditional Interpretation of APo I 19-22. As we have noted, the aim of Aristotle's argumentation in these chapters is to provide an answer to a group of sceptics described in APo I 3, who believe that scientific knowledge is not possible because demonstrations would proceed ad infinitum. As we know, this sceptical objection relies on the false assumption that every proposition in demonstrative sciences is known by demonstration. Without this assumption, it is possible to insist on a foundationalist solution and hold that every demonstration is ultimately based on propositions which do not need to be demonstrated from explanatorily prior premises in order to be known. However, in addition to the abstract epistemological discussion in APo I 3, Aristotle found it necessary to make sure his own model of demonstrative science was safe from infinite regress, a task he tried to accomplish in APo I 19-22. Since syllogistic demonstrations with an infinite set of premises would contain infinite series of predications, Aristotle believed that showing the impossibility of infinite predicative series was tantamount to proving that no demonstration in his model could proceed ad infinitum. However, the sceptic from APo I 3 might well argue that the connection between infinite chains of predications and infinite regress is a peculiarity of Aristotle's metaphysics and its underlying logic, whereas his challenge concerns the existence of ultimate explanations. Therefore, unless we are able to show a relation between Aristotle's theses on predication and the existence of explanatorily basic premises, the philosopher (at least in APo I 19-22) would have failed to protect his model against infinite regress. Certainly, the Traditional Interpretation does not explain the connection between particular substances and summa genera being boundaries of predicative chains, on one hand, and the existence of ultimate explanations, on the other. 117 See APo I 4 73b32-74a3; I 5, 74a16-b4; I 24, 85b4-15; 85b23-27; 85b38-86a3. This aspect of Aristotle's theory will be clarified in the next chapter. 81 3.4 – A Defence against Infinite Regress: An Alternative Interpretation As I have argued, the three questions raised in APo I 19 concern the occurrence of predicative series within syllogistically structured demonstrations: I) If ⟨Π, c⟩ is an Aristotelian demonstration, can there be a U-series – let it be Φ – such that Φ Π? (T19, APo I 19, 81b 30-33) II) If ⟨Π, c⟩ is an Aristotelian demonstration, can there be a D-series – let it be Ψ – such that Ψ Π? (T20, APo I 19, 81b 33-7) III) Can there be an Aristotelian demonstration ⟨Π, c⟩ with infinitely many inferential steps, the set Π being infinite? (T21, APo I 19, 82a 2-8) Aristotle formulates question III with a typical syllogistic vocabulary: can there be an infinite set of middle terms {M1, M2, M3, ... , Mω} between two extremes P and S? Let us follow the scenario described in T19 and suppose the following sequence of inferences in Barbara, in which the minor premises are 'immediate', whereas the major premises are always demonstrated from more basic propositions: PaMω MωaMω-1 PaMω-1 (...) PaM3 M3aM2 PaM2 M2aM1 PaM1 M1aS PaS In this context, asking whether the demonstration could proceed ad infinitum is equivalent to asking whether a U-series could be formed from the minor term S.118 This question, however, is the same as asking whether there is a middle term Mi which is 'immediately' or 'indemonstrably' connected to P. Here, question III is equivalent to the following question:119 III.1) Is it the case that ∀i∃j((PaMj, MjaMi├ PaMi) & Mj is the reason why PaMi) ? 118 Of course, in a different context, with a different combination of syllogistic moods, a U-series may emerge (e.g.) from the bottom major term instead of the bottom minor term (see the sequence of Camestres in APo I 21, 82b13-21), as well as a D-series may begin with (e.g.) the bottom minor term instead of the bottom major term (see the sequence of Bocardo in 82b 22-28). It is worth noting that the same reasoning applies to all demonstrable premises within the chain, which means a U-series or a D-series may emerge from any minor or major term in the demonstration. 119 See my Zuppolini (2014a, p. 48). Cf. Lear (1980, p. 22). 82 Suppose now a sequence of syllogisms in Barbara in which the minor premises are demonstrable, while the major premises are immediate – like the scenario suggested in T20: Mω-1aMω MωaS Mω-1aS (...) M2aM3 M3aS M1aM2 M2aS PaM1 M1aS PaS Asking whether this demonstration have infinitely many steps is the same as asking whether a Dseries could emerge from the major term P. Such question, however, is equivalent to asking whether there is no middle term Mi to which the bottom minor term S is 'immediately' connected: III.2) Is it the case that ∀i∃j((MiaMj, MjaS├ MiaS) & Mj is the reason why MiaS) ? If this interpretation of APo I 19 is correct, Aristotle is not raising an abstract metaphysical question about the existence of ultimate subjects (such as particular substances) and ultimate predicates (such as summa genera). On the contrary, he is interested in denying that Uor D-series could be part of a demonstration proving the relation between two 'fixed' or 'determined' extremes ( ) – i.e. any major and minor terms in the syllogistic chain, and not necessarily names and descriptions of particular substances or general terms naming ontological categories. But how does Aristotle establish this result? What are the premises of his argument? As we have seen, the ontology of the Categories contains the following metaphysical principles: MP 1: if P is in the subject S, then S and P belong in different categories and S is a substance. MP 2: If P is said of the subject S, then S and P belong in the same category. These two principles (or some close version of them) seem to motivate the distinction between natural and unnatural predications in APo I 22. A categorical sentence 'PaS' – 'every S is P' – is a natural predication when the grammatical subject 'S' refers to the metaphysical subject S by signifying just what S is ( ). In contemporary terms, we would say that 'S' is a sortal or individuative term, whose distinguishing feature is what Quine calls 'divided reference.'120 By specifying what the denoted objects essentially are, such terms provide us with a criterion for counting these objects as discrete entities, which makes them suitable to be attached to 120 Quine (1960, pp. 90-95). 83 quantificational expressions such as 'every S' or 'some S'. In other words, these terms signify 121 (and not etc.), i.e. they specify the essence of the basic subjects of a given domain, which are substances or substance-like entities on which all the other entities in the domain depend.122 Part of Aristotle's argumentation in APo I 22 consists in a discussion of the constraints MP 1 and MP 2 impose on scientific discourse. Let us call 'E-sentences' all essence-specifying predications (i.e. linguistic predications signifying said-of relations), while 'A-sentences' will refer to 'accidental' predications (i.e. linguistic predications signifying inherence relations). Thus, the linguistic correlates of MP 1 and MP 2 could be formulated as follows: LP 1: If 'AaB' is an A-sentence, then 'A' signifies a non-substantial entity & 'B' signifies substance. LP 2: If 'AaB' is an E-sentence, then 'A' and 'B' signify entities in the same category. The fact that a subject-term 'signifies substance' tells us something about the roles it can perform in Uand D-series: [T27] Again, terms which mean substance mean, of what they are predicated of, just what is that thing or just what is a particular sort of it. Terms which do not mean substance but are said of some other underlying subject which is neither just what is that thing nor just what is a particular sort of it, are incidental. E.g. white of a man: a man is neither just what is white nor just what is some particular white – rather, presumably, animal: a man is just what is an animal [APo I 22, 83a 24-30; Barnes 1993, with changes]. The sentence 'every man is musical' is a natural predication because the logical predicate used in the denoting phrase 'every man' specifies what the denoted objects (Socrates, Callias, Coriscus etc.) essentially are ( ). The reason is that 'man' stands for a metaphysical item that is essentially 121 APo I 22, 83a 24-25. See Furth (1988, p. 30); Loux (1991, p. 132) and my Zuppolini (2014c, pp. 30-37). 122 The qualification 'substance-like' is meant to account for basic subjects in mathematical sciences (such as line, surface, figure etc.), which are studied independently of the material elements in which they inhere in the real world. My point is that attributes such as straight is ontologically dependent on lines, even if lines are not substances in the strict sense of the term. What we mean by 'substance-like entities' is what Ross (1949, p. 633) describes as 'entities which are not substances but exist only as attributes of subjects, viz. those which a particular science considers as if they had independent existence and treats as its own subjects' [emphasis in original]. 84 predicated of everything of which it is predicated – like type 1 entities in the four-fold division of Cat. 2 (see T24). Therefore, Aristotle is allowed to use the following premise in his argument: P1: If 'AaB' is an A-sentence & 'BaC' is a scientific predication, 'BaC' is an E-sentence.123 On the other hand, the adjective term 'white', for instance, does not specify what white objects essentially are, which means it is not qualified to occur as subject in A-sentences, but only in Esentences: P2: If 'AaB' is an A-sentence & 'CaA' is a scientific predication, 'CaA' is an E-sentence. A third premise can be obtained from this passage. Aristotle affirms that a term such as 'white' does not 'signify substance' insofar as it fails to specify what (e.g.) a white man essentially is ( ). Here, Aristotle relies on a sort of test to determine whether a word signifies substance or not. If 'white' signified substance, a white man, for instance, would be just what white is ( ), i.e. a colour of a certain kind. Since this is not the case, 'white' does not signify substance. 'Animal', on the other hand, signifies substance insofar as every animal, man included, is just what animal is ( ).124 This test reminds us of what is said in Cat. 3, 1b 10-16, where Aristotle endorses another metaphysical principle: MP 3: If P is said of the subject S & S is said of the subject S', then P is said of the subject S'. If said-of relations are transitive, as stated in MP 3, Aristotle can include the following premise in his argument: P3: If 'AaB' is an E-sentence & 'BaC' is an E-sentence, then 'AaC' is an E-sentence. Finally, as we know, Aristotle repeatedly denies the possibility of one single subject having infinitely many essential predicates.125 If so, he also accepts the following premise: P4: There cannot be infinitely many E-sentences 'A1aB', 'A2aB', ..., 'AnaB.' I shall now argue that the metaphysical framework of the Categories together with P1, P2, P3 and P4 can be used to prove that U-series and D-series cannot occur within syllogistic demonstrations. Unlike the Traditional Interpretation, our proposal does not involve including names and descriptions of particular substances and summa genera in scientific demonstrations. 123 Let us say that 'AaB' is a scientific predication if and only if 'AaB' is true & 'AaB' is not an unnatural predication. 124 See Philoponus (240.14-24); Angioni (2006, pp. 124-125) and my Zuppolini (2014a, p. 96). 125 APo I 22, 82b 37-83a 1; 83b 8; 13-16; 26-27.' 85 Let us first analyse the following predicative series, going 'upwards' from a subject S: Φ = {M1aS, M2aM1, M3aM2, ... , such that ∀n(Mn+1aMn)} The first predication of the series, 'M1aS', is either an E-sentence or an A-sentence, i.e. either M1 is part of the essence of S or not. I shall now analyse each of these two alternatives. Suppose first that 'M1aS' is an E-sentence. Now, we have to ask whether the other predications in the series are also E-sentences or whether an A-sentence comes up at some point. Let us say, for the sake of argument, that all the other predications in Φ are E-sentences as well. If 'M1aS' and 'M2aM1' are E-sentences, 'M2aS' is also an E-sentence (by P3). For the same reason, if 'M2aS' and 'M3aM2' are E-sentences, 'M3aS' is also an E-sentence, the same being true for every Mi in Φ. Thus, if the series Φ were infinite, there would be infinitely many E-sentences, each of which attributing a different essential predicate to S. Φ = {M1aS, M2aM1, M3aM2, ...} M2aS M3aS (...) According to P4, this result is impossible, which means Φ could not be infinite in this way. Therefore, Φ must contain at least one A-sentence. Let us say that the first A-sentence in Φ is 'M2aM1'. In that case, the next sentence 'M3aM2' would have to be an E-sentence, since a predicate in an A-sentence does not 'signify substance' and therefore cannot be itself subject in another Asentence (P2). If 'M3aM2' is an E-sentence, 'M4aM3' would also be an E-sentence, since 'M3', as an essential predicate of 'M2', does not signify substance either (see LP 2), and hence cannot be subject in an A-sentence (see LP 1). Thus, if Φ were infinite, there would be infinitely many E-sentences starting from 'M3aM2', from which infinitely many E-sentences with 'M2' as subject would follow (P3). Since this result is impossible (P4), we must conclude again that Φ is finite. Therefore, if 'M1aS' is an E-sentence, the series of predications Φ cannot be infinite. Even if we assume (alternatively) that 'M1aS' is an A-sentence, Φ could not be infinite either. If 'M1aS' is an A-sentence, the next sentence in the series, 'M2aM1', would have to be an Esentence (P2). In that case, however, the next proposition 'M3aM2' and all the other predications in Φ will also be E-sentences, since none of the Mis would signify substance (LP 2 and P2). If so, 86 there would be infinitely many E-sentences with 'M1' as subject-term (by P3), which is impossible according to P4. Since the first predication in Φ is either an E-sentence or an A-sentence, it follows that U-series cannot occur in syllogistic demonstrations. Therefore, Aristotle has the theoretical resources to justify a negative answer to question I without postulating the presence of summa genera in scientific demonstrations. However, a negative answer to question III requires a negative answer not only to question I but also to question II. In other words, a demonstration ⟨Π, c⟩ could still have infinitely many steps if nothing prevented D-series from occurring in Π. We must then analyse a predicative series going 'downwards' from a predicate P: Ψ = {PaM1, M1a M2, M2aM3, ... , such that ∀n(MnaMn+1)} The first predication of the series, 'PaM1', will be either an E-sentence or an A-sentence. Let us assume first that 'PaM1' is an E-sentence. Suppose, in addition, that all the other predications in Ψ are also E-sentences. Under this supposition, one could think that it is possible to argue as we did in the case of U-series, and use P3 to show that, if Ψ is infinite, there will be infinitely many Esentences with one of the terms in Ψ as subject (which would be impossible according to P4). However, this line of reasoning does not work for D-series: for any Mi in Ψ there will be finitely many sentences from 'Mi-1aMi' back to 'PaM1', as we can see in the following diagram:126 Ψ = {PaM1, M1a M2, M2aM3, ...} M1aM3 PaM3 × Nevertheless, it can be shown that, if Ψ were infinite, there would be infinitely many essential predicates belonging to the same subject, even if this subject is not mentioned in Ψ. If Ψ contains only E-sentences, it would be limited to a single category – either substance or a nonsubstantial category (LP 2). Let us say that every term in Ψ signifies a non-substantial category – e.g. 'sensible quality', 'colour', 'white' etc. According to Aristotle's ontology, each of these terms would be predicated of a type 2 entity (as defined in Cat. 2) – e.g. a particular sort of white. Therefore, if Ψ were infinite, it would be possible to derive from it infinitely many E-sentences 126 Barnes (1993, p. 180) makes a similar point about 84a7-28. 87 with (e.g.) 'seashell white' as subject-term (even if 'seashell white' does not occur in Ψ): 'sensible quality holds of seashell white', 'colour holds of seashell white', 'white holds of seashell white' etc. Similarly, if all terms in Ψ are restricted to the category of substance – e.g. 'living being', 'animal', 'man' etc. –, each of them would be predicated of a type 4 entity – e.g. a particular man. Therefore, infinitely many E-sentences with (e.g.) 'Socrates' as subject-term would follow from Ψ (even if 'Socrates' does not occur in Ψ): 'living being holds of Socrates', 'animal holds of Socrates', 'man holds of Socrates' etc. Since none of these results is possible (by P4), Ψ cannot be infinite if it is composed only of E-sentences. Suppose then that an A-sentence comes up at some point – let it be 'M1a M2'. In that case, the next predication 'M2aM3' is necessarily an E-sentence: as subject of an A-sentence, 'M2' signifies substance and therefore can only be predicate in E-sentences (according to P1). Given LP 2, the same is true for any 'Mi' in Ψ provided that i ≥ 2. Again, if it were infinite, Ψ would contain infinitely many substantial predicates – e.g. 'living being', 'animal', 'man' etc. –, from which infinitely many E-sentences about any particular substance in the domain could be obtained: 'living being holds of Socrates', 'animal holds of Socrates', 'man holds of Socrates' etc. In any case, it follows that Ψ is finite if its first predication is an E-sentence. For similar reasons, the same result follows from the assumption that 'PaM1' is an Asentence. In that case, the next predication 'M1a M2' is necessarily an E-sentence, given P1. In fact, if Ψ begins with an A-sentence, every 'Mi', starting from 'M1', would signify substance. Once again, Ψ would contain infinitely many substantial predicates, all of which are predicated of any of the particular substances in the domain – even if none of them is individually mentioned in Ψ. Since 'PaM1' is either an A-sentence or an E-sentence, Ψ is necessarily finite. Therefore, no demonstration contains D-series, a conclusion which is possible to reach without including names and descriptions of particular substances in scientific demonstrations. We have identified premises from which Aristotle could have justified negative answers to questions I and II. In APo I 22, 83b 17-30, the philosopher not only endorses those premises, but actually obtains from them the conclusion he was trying to prove – albeit in a convoluted and excessively concise way, we must admit. In this passage, Aristotle summarizes his argument and reaffirms at least three of the four premises we formulated above: [T28] We have supposed that one thing is predicated of one thing, and that items are not predicated of themselves when they do not signify what something is. For these are all incidental (though some hold of things in themselves 88 and some in another way), and we say that all of them are predicated of an underlying subject, and that what is incidental is not an underlying subject [APo I 22, 83b 17-22; Barnes 1993, with changes]. [T29] The incidentals are said of items in the substance of each thing, and these latter are not infinite [APo I 22, 83b 26-27; Barnes 1993]. In T28, Aristotle endorses P2: items in non-substantial categories cannot be predicated of one another unless the predicate is part of the 'what-it-is' (the essence) of the subject ( ). In T29, the philosopher reaffirms P1 ( ) and P4 ( ). Probably assuming P3, which had already been stated in 83a 24-30 (quoted above), Aristotle concludes his argument and denies that Uand D-series can occur in scientific demonstrations (83b 24-25; 27-28) – i.e. the answers to questions I and II are negative. If so, no demonstration could have infinitely many steps, which means the answer to question III is also negative. If our interpretation is correct, the two 'determined' extremes Aristotle mentions in T21 (APo I 19, 82a 2-8), the passage in which question III is formulated, are not ultimate subjects and ultimate predicates (particular substances and summa genera in the Traditional Interpretation), but any major and minor term in an extended syllogistic demonstration. Thus, it becomes easier to understand Aristotle's argument in APo I 19-22 as a defence of his foundationalist project. As we have seen, his argument relies heavily on the claim that no subject has infinitely many essential predicates. Aristotle bases this metaphysical claim on an epistemological thesis: essences can be known, and since we cannot 'survey infinitely many items in thought' (83b 6-7), it follows that no subject can have an infinite number of essential attributes.127 As we have seen, essences are the primary causes studied by demonstrative sciences, with the corresponding definitions playing the role of first principles. Thus, it is not surprising that the thesis that every demonstration contains a finite number of steps is ultimately grounded in the belief that essences are knowable. Moreover, as we can see in III.1 and III.2, a negative answer to question III entails that (i) for any major term P in a demonstration ⟨Π, c⟩ there will be a middle term Mi 'immediately' or 'indemonstrably' connected to P, and (ii) for any minor term S in ⟨Π, c⟩ there will be a middle term Mj which is 'immediately' or 'indemonstrably' connected to S. If to be 'immediately' or 'indemonstrably' connected to a term means to be 'definitionally' connected to it, we may have an 127 APo I 22, 82b 37-83a 1; 83b 8. Aristotle defended the metaphysical thesis that no essence is composed of infinitely many predicates based on the epistemological claim that essences are knowable. Nevertheless, he might well have thought that, in reality, the epistemological thesis is grounded in the metaphysical one, and not the other way around. 89 answer to one of the questions we raised in the previous chapter: the A-Model and the S-Model are not mutually exclusive; on the contrary, a combination of both would be part of Aristotle's strategy to defend his model of science against the threat of infinite regress. This result, however, is not final. The ontology of the Categories and the way Aristotle uses some of its theses in APo I 19-22 may give us a preliminary account of the distinction between subjects and attributes and the role their essences play in scientific explanations. However, as we shall see in the next chapter, Aristotle's model includes a much more sophisticated theory of predication, with distinctions that are more fine-grained than the one between 'essential' and 'accidental' attributes. 90 91 CHAPTER 4 PER SE BEINGS AND PER SE PREDICATIONS 4.1 – Kinds of Being and Ontological Priority The Categories gives us a preliminary account of the distinction between (metaphysical) subjects and (metaphysical) predicates. The doctrine of ontological categories helps us understand the semantical constraints imposed on demonstrative discourse: the logical roles a term can play in scientific propositions depend on the category it signifies. Thus, although some critics take Aristotle's Logic to be completely blind to the logical asymmetry between names and verbs, the concrete use of syllogistic inference in demonstrative sciences is limited and governed by a metaphysical distinction between subjects and attributes. In the ontology of the Categories, beings are hierarchically related depending on the roles they can play in predicative connections. An entity like Socrates is ontologically prior to an entity like whiteness insofar as the latter cannot be part of reality unless there are individuals like the former of which it is (metaphysically) predicated, but which are not (metaphysically) predicated of (and hence are not ontologically dependent on) anything else. It is beyond the purpose of the present study to provide a detailed account of the notion of ontological priority or ontological dependence. However, if these notions are specified purely in existential terms, Aristotle's doctrine 92 of ontological categories can become (if not unattractive on its own) inadequate to the task of providing his model of science with satisfying metaphysical underpinnings (or so I shall argue). In Metaph. V 11, Aristotle characterises ontological priority – in his words, priority 'in nature and being' ( ) – in terms of an asymmetrical independence relation: [T30] Besides things called prior and posterior in this way, a thing is prior in nature and being when it is possible for it to be without other things but not them without it. This division was used by Plato [Metaph. V 11, 1019a 1-4; Kirwan 1993, with changes]. The Aristotelian notion of ontological priority has been explained in different manners depending on how the verb 'to be' ( ) is understood. The most usual construal is given in terms of modality and existence. This is, for instance, how contemporary metaphysicians like Kit Fine read T30: Aristotle in the Metaphysics (1019a1-4) takes things to be 'prior and posterior... in respect of nature and substance' when the priors 'can be without the other things, while the others cannot be without them'; and the obvious way to construe him is by reference to the notions of existence and modality [Fine 1995, p. 270]. At first sight, it seems reasonable to read T30 in this way, especially if we have in mind the core theses of the Categories. In the four-fold division of Cat. 2, the distinguishing feature of particular substances – the 'primary substances' or 'primary beings' ( ) – is the fact that they are not predicated of more basic subjects, whereas all the other beings are predicated of them. Thus, secondary substances and non-substantial beings could not exist if there were no particular substances of which they were predicated (see Cat. 5, 2a34-b6). If understood in this way, ontological priority can be defined as follows: Priority in Existence (PIE):128 A is ontologically prior to B iff. 1. A can exist without B 2. B cannot exist without A. The reference to Plato in 1019a 14 might be taken to indicate that the notion of ontological priority in T30 is existential. Gail Fine, for instance, argued that this kind of priority is closely related to one of the senses of 'separation' ( ) in Aristotle, understood as a 'capacity for independent existence'.129 In Metaph. VII 1, 1028a 31-b2, she argues, substance is said to be prior 'in nature' 128 I draw the acronym 'PIE' from Peramatzis (2008; 2011). 129 Fine (2003, p. 256) 93 because it is separate, while the other categories are not. Moreover, Aristotle criticises Plato for having 'separated' the forms130, attributing to him a notion of separation formulated in terms of existence.131 Thus, Gail Fine puts the passages together to conclude that A is separate from B just in case A is 'naturally prior to' B, i.e. 'just in case A can exist without, independently of, B' (Fine 2003, p. 256).132 However, it has been claimed that, if T30 is read in existential terms, particular substances do not fulfil the condition for being ontologically primary entities. Interpreters such as Michail Peramatzis (2008; 2011), Phil Corkum (2008) and Lucas Angioni (2010) argued that individuals in the category of substance do not satisfy PIE in relation to non-substance items. In some cases, PIE.1 is satisfied, but not PIE.2. For instance, Socrates may exist without being courageous, but courage may also exist without Socrates' existing, as long as it is predicated of another substance (e.g. Callias). In other cases, not even PIE.1 is satisfied: Socrates may exist without some of his determinate accidental attributes (e.g. being white or weighing 71kg), but not without the corresponding determinables (e.g. having complexion or having weight). One may think that the issue can be solved by understanding the priority of particular substances collectively: non-substance beings are not ontologically dependent on one specific particular substance or other, but on particular substances in general – e.g. courage may exist without Socrates or Callias, but not without any particular substance whatsoever. However, PIE would not be, properly speaking, an asymmetrical relation if the ontological independence that is affirmed in PIE.1 were not the same one denied in PIE.2. Hence, the relata in PIE must be both understood in the same way, either collectively or individually. However, as we have seen, PIE.1 is false if the relata are understood collectively: particular substances may exist without having one specific accidental attribute or other, but not without any accidental attribute whatsoever. On the other hand, if the relata are taken individually, PIE.2 is not satisfied: in the same way as Socrates can exist without being white, whiteness can also exist without Socrates' existing, provided that there is another particular substance which also happens to be white.133 There might be alternative ways to explain the claim (made in the Categories,) that particular substances are prior to all other beings, including non-substance items and secondary substances. This task, however, is beyond our present concerns.134 However, when it comes to 130 Metaph. XIII 4, 1088b 30-31; XIII 9, 1086a32-b7. 131EE I 8, 1017b 10-15. 132 Fine (2003, p. 256). 133 See Corkum (2008, p. 74) for an elucidating exposition of this problem. 134 For interpretations that avoid understanding the notion of ontological priority in terms of existence, see Corkum (2008); Peramatzis (2008; 2011, pp. 229-248); Angioni (2010). 94 address the metaphysical underpinnings of Aristotle's philosophy of science, the Categories frustrate us at least with respect to the following two topics: (1) As we have seen, a subject like man may exist independently of some determinate accidental feature such as being white, but not independently of the correspondent determinable, such as being coloured. Unlike the determinate features, the corresponding determinables are demonstrable properties and belong necessarily to their subjects135, which explains why they are particularly problematic for the existential construal of the notion of ontological priority. However, the ontology of the Categories focuses on the distinction between essential and accidental predicates. Inherence and said-of relations are the only types of connections into which predications are classified. On the other hand, science deals with a very specific kind of non-essential predicate: the demonstrable attribute, also known as 'per se accident'. As we have seen, per se accidents are significantly different from other (merely contingent) accidental predicates, since they belong to their subjects 'in themselves' and 'by necessity' without being part of their essences. Hence, Aristotle's model of demonstrative science must adopt a theory of predication that elucidates the nature of per se accidents and explains how they differ from non-demonstrable attributes. (2) As we have seen in Chapter 3, one of the problems in reading APo I 19-22 according to the Traditional Interpretation was the fact that singular terms naming particular substances would become the basic subjects in scientific discourse. However, we have argued that in Aristotle's philosophy of science the priority is given to universals. Whatever has a given demonstrable attribute has it in virtue of being a member of a universal kind which is explanatorily connected to the attribute in question. For instance, the property 2R belongs primarily to the triangle, while it belongs to (e.g.) the isosceles or to a given triangle in a semi-circle136 only in a derivative way: the universal triangle is the primary subject for the predicate 2R. In the Categories, however, priority is given to individuals over their species and genera: particular substances, for instance, are said to be 'primary', while their species and genera are only 'secondary' substances. There is no need to assume that there is a conflict between the priority of individuals in the Categories and the priority of universals in the APo. The two treatises were written with very different purposes, and the relevant kind of priority in each of them might be different as well. Still, the APo require a theory of predication that takes into account the explanatory priority of universal expressions over singular terms, a task the theory of predication of the Categories is not able to accomplish. 135 Lowe (2013, p. 197). 136 APo I 1, 71a 19-21; APo I 4, 73a 28-34; 73b 25 APo I 24, 85b 5-7 APo I 9, 76a 4-9. 95 Aristotle's model of demonstrative science adopts an alternative (and, in a way, more sophisticated) theory of predication. This theory can be found in APo I 4, where Aristotle discusses four uses of the expression 'in itself' (per se or ). In Section 4.2 below, I intend to elucidate each of these uses. I shall argue that Aristotle's discussion in APo I 4 assumes the existence of priority relations among the subjects and attributes in a given scientific domain – relations that are different from existential priority and more relevant to his theory of science. In section 4.3, I shall discuss some of the views on per se predications and per se accidents available in the secondary literature. In section 4.4, I shall indicate how the theory of per se predications should be interpreted in order to fill in the two gaps left by the Categories – (1) and (2) discussed above. First, I shall clarify the nature of per se accidents and explain how they fit in APo I 4 (gap 1). In addition, I shall argue that one of Aristotle's aims in APo I 4 is to emphasize that, in order to achieve a full-fledged demonstration, a scientist must identify the relevant kind which is explanatorily connected to the demonstrable attribute (gap 2). 4.2 – The four uses of 'per se': Posterior Analytics I 4 In APo I 4, the first of the four senses of 'in itself' ( ) is introduced as follows: [T31] Some things hold of an item in itself both if they hold of it in what it is – e.g. line of triangles and point of lines (their essence comes from these items, which inhere in the account which says what they are) [APo I 4, 73a 34-37; Barnes 1993, with changes]. As we can see, this first use of ' ' or 'per se' (hereafter, 'per se1') concerns a predicative connection in which the predicate is part of the 'essence' ( or ) of the subject, and hence appears in its definition: Per se1 : P is a per se1 predicate of S iff. P is part of the essence [ of S and P 'inheres in' [ ] the account that shows what S is. Line, for instance, is part of the essence of the triangle, 'inheres in' its definition, and hence is predicated of it in the per se1 manner. 137 137 Zabarella 1582, 23B suggests that we should read the examples sano modo: though line is said to belong in the whatit-is of triangles, Aristotle probably means that something like 'bounded by lines' is predicated of them. For this and other ways of interpreting the examples, see Barnes (1993, p. 112-113). 96 One may ask whether per se1 predications are sentences (or linguistic predications) or real connections between entities (metaphysical predications). On one hand, the per se1 predicate is described as an element in the 'essence' of the subject, which indicates that the connection defined in T31 is a metaphysical predication (like the said-of relation in the Categories). On the other hand, the predicate is also said to 'inhere in' ( ) the subject's definition, which suggests that per se1 connections are linguistic predications (like our E-sentences in Chapter 3). This question can be answered if the meaning of ' ' is properly specified. In 73a 35-37, Aristotle describes per se1 predicates as components of the 'essence' ( ) of their subjects: ' .' Certainly, essences and their components are not linguistic but real-world items. Aristotle's appeal to the notion of ' ' (or 'definition') in 73a 36 is no reason to take the predicative connection described in the passage as linguistic and not metaphysical. First, as an essentialist, Aristotle accepts that not only words have definitions (in the sense of having accounts of their meanings), but also things have definitions (in the sense of having accounts of their essences). Second, the pronoun ' ' in 73a 36 refers back to ' ' in ' ' (73a 34-35). Therefore, if ' ' refers to extra-linguistic items (the components of a given essence), so does ' [...]' in 73a34. However (and this is the crucial point), ' [...]' also introduces the subject of the verb ' ' in ' ' (73a 3637). Therefore, if ' ' and ' [...]' refer to extra-linguistic items (the components of a given essence), the things which 'inhere in the definition' ( ) – that is, the per se1 attributes – are not linguistic, but real-world items. On the other hand, if ' ' stands for a 'real' definition (i.e. an account of essence), both relata of per se1 relations are extra-linguistic items. Therefore, if Aristotle is not committing a use-mention confusion, the text gives us no option but to take the locution ' ' (73a 34-35) (i) as referring to extralinguistic entities and (ii) as introducing the subject of ' ' in 73a37. Since ' ' (73a 36-37) refers to a linguistic item (namely, a given definition), the verb ' ' picks out what we can describe as a 'world-language relation', i.e. a relation of the form 'xRy' in which the variable 'x' ranges over extra-linguistic entities such as objects and attributes, whereas 'y' ranges over items of language such as words or definitions – e.g. the point inhering in the definition of line is a relation of this sort, since point (and not 'point') is a non-linguistic entity, whereas the definition of line is a linguistic one.138 Other examples of world-language relations would be 'x is denoted by y' or 'x has the y' (where ' ' stands for a 'real' definition). On 138 In this sense, 'x ...' is close to 'x is mentioned or referred to ...'. However, we do not translate the verb in this way to avoid the suggestion that, if triangle ' ' in the definition of 2R (and therefore 2R is a per se2 of triangle), the term 'triangle' must be included in the definition of 2R. Since I shall argue that this conditional is false, I prefer the neutral and vague expression 'inhering in'. 97 the other hand, world-world relations would have only extra-linguistic items as values for their variables. As we saw, the text of APo I 4 makes it clear that per se1 connections – in contrast to the inhering in relation that is used to define it – are world-world relations or, to stick to the vocabulary we have been using, metaphysical predications. Let us now analyse Aristotle's characterization of the second kind of 'per se' connection (hereafter, 'per se2'): [T32] And also if the things they hold of themselves inhere in the account which shows what they are – e.g. straight holds of lines and so does curved, and odd and even of numbers, and also prime and composite, and equilateral and oblong [APo I 4, 73a 34-b1; Barnes 1993, with changes]. Per se2 connections are also definition-based. Now, however, it is the definition of the predicate that includes a reference to the subject: Per se2 : P is a per se2 predicate of S iff. S 'inheres in' [ ] in the account that shows what it is to be P. Odd, for instance, is a per se2 attribute of number insofar as number 'inheres in' the definition of what odd is. There is no reason to believe that the verb ' ' works differently in the characterization of per se2 connections. Thus, if the verb picks out a world-language relation in T32 as well, the fact that the subjects of per se2 predications 'inhere in' the of the predicates does not make them linguistic items. Furthermore, since the word ' ' denotes here the definition of an entity (and not of a term), neither the predicates (i.e. the corresponding definienda) are linguistic items. Therefore, per se2 connections are also world-world relations (or metaphysical predications). Per se2 predications play an important role not only in Aristotle's model of demonstrative science but also in his metaphysical theory. As we have seen, in the Categories and the Topics, Aristotle applies the question 'what is x?' indifferently to all categories, overlooking the very hierarchy he is willing to establish (see Top. I 9, 103b28-35). Even when an entity x is a nonsubstantial being, the answer to the question 'what is x?' is a homocategorical predication without a sign of the subject on which x depends. On the other hand, in the APo and the Metaphysics, Aristotle introduces the notion of per se2 predication: definitions of attributes must register their status as dependent entities by referring somehow to the items of which they are predicated: the 98 definition of odd must refer to numbers, the definition of male should mention animals, the definition of white must contain a reference to bodily surfaces etc.139 However, which kind of ontological priority should definitions account for? As we have seen, interpreting the notion of ontological priority in T30 in purely existential terms is problematic. Although we do not intend to offer a definitive interpretation of Aristotle's concept of ontological priority, alternative readings of T30 may shed some light on the metaphysical framework adopted by Aristotle's model of demonstrative science. Some authors tried to preserve an existential construal of the notion of ontological priority by adding important qualifications. According to them, Aristotle understands existence with some sort of essentialism in the background: to be is always to be with regard to a certain nature; to exist for x is to be a member of a certain kind that states what x is.140 Others avoid the existential construal all together. Michail Peramatzis (2008; 2011), for instance, claims that ontological priority can be understood as what he calls 'Priority in Being':141 Priority in Being (PIB): A is ontologically prior to B iff. 1. A can be what it is without B being what it is. 2. B cannot be what it is without A being what it is. Peramatzis argues that, although the claim put forward in T30 'is neutral or open as it can be understood either as PIE or PIB'142, several of Aristotle's metaphysical views inside and outside the context of Metaph. V are successful if ontological priority is understood as PIB, and false or misleading if interpreted in terms of PIE (as we have seen above). With either PIB or an essentialist approach to the concept of existence, ontological priority would be intrinsically connected to the notion of essence. In Aristotle's vocabulary, x's essence is 'what being is for x' ( + noun in the dative + ). The philosopher talks of essence as a way of being 143 – either in the sense of existing as something of a certain kind or in the sense of being what something is. If we follow this approach, we could say that an attribute P (a non-substance entity) is ontologically dependent on the relevant subject S (a substance or substance-like entity) in the sense that P does not have the essence it has (i.e. cannot perform the way of being that distinguishes it as such) independently of S having the essence it has. Thus, a definition of P would fail to describe what it is to be P if it does not refer to S. Bodily surfaces, for instance, are the proper subjects of 139 Metaph. VII 1, 1028a 35-36; VII 5, 1030b 23-24; APo I 4 73a 37-b5; II 2, 90a 14-18; II 10, 93b 38-94a 7. 140 Loux (1991, p. 3-6; pp. 27-28; pp. 34-35); Irwin & Fine (1995, p. 569); Zillig (2010, p. 41). 141 Compare with Corkum (2008) who also avoids reading T30 in terms of asymmetrical existential independence. 142 Peramatzis (2008, p. 191). 143 Loux (1991, p. 85); Peramatzis (2011, pp. 3-4); Charles (2011). 99 colours, with the relevant features that make colours what they are. Therefore, doing science about colours and explaining how they come about involves doing science about bodily surfaces as well, of which colours are per se2 predicates. We can say then that the linguistic correlate of ontological priority (understood as PIB) is what Aristotle calls 'Priority in Definition' (PID):144 Priority in Definition (PID): A is prior in definition to B iff. 1. A is (correctly) defined without mentioning B 2. B is not (correctly) defined without mentioning A. Subjects are 'prior' to their per se2 attributes precisely in the sense formulated in PID. Odd cannot be defined without mentioning numbers, nor can white be defined without mentioning bodily surfaces. Satisfactory accounts of what it is to be odd or white – the kind of account scientists should provide – must somehow refer to the way of being of numbers and surfaces, without which the phenomena of oddness or whiteness could not be properly explained or even identified. A significant number of interpreters argue that only the first two uses of 'per se' are relevant to Aristotle's theory.145 However, there are strong reasons to believe that the other two uses also play significant roles in his model of demonstrative sciences. The third sense of 'per se' (hereafter, 'per se3') is defined as follows: [T33] Again, certain items are not said of some other underlying subject: e.g. whereas what is walking is walking being something different (and similarly for white), substances and whatever signifies this something are not just what they are being something different. Well, items which are not said of an underlying subject I call things in themselves, and those which are said of an underlying subject I call incidental [APo I 4, 73b 5-10; Barnes 1993, with changes]. 144 Again, I am borrowing the acronym 'PID' from Peramatzis (2011, p. 6; p. 23). See Fine's notion of ontological dependence as 'the real counterpart to the nominal notion of one term being definable in terms of another' (Fine 1995, p. 275). 145 For interpretations arguing that the other two senses of 'per se' are totally or partially irrelevant to Aristotle's purposes in the APo, see Ross (1949, p. 519); Sorabji (1981, pp. 210-211); McKirahan (1992, pp. 94-95); Barnes (1993, pp. 1101120; Ebert (1998, p. 154); Porchat Pereira (2001, pp. 142-143); Tierney (2004, p. 5, n.8). For another view, see Code (1986, pp. 350-351); Furth (1988, p. 237); Ferejohn (1991, pp. 123-128; 2013, pp. 90-05); Angioni (2004); Terra (2009; 2014); Ribeiro (2011). 100 T33 is an obscure and controversial passage. Aristotle seems to be distinguishing not predicative relations but things: those that are 'in themselves' from those that are 'incidentally'.146 An entity x is a per se3 being if x is what it essentially is – Aristotle uses the expression ' ' again – without (i.e. independently of) being predicated of a different underlying subject. Substances, which satisfy PIB in relation to all other beings, are what they are (i.e. have the essences they have) independently of being predicated of something else, whereas 'incidental' beings could not be what they are without being predicated of their proper subjects: Per se3 : S is a per se3 being iff. S is what it is (i.e. S has the essence it has) independently of being predicated of another underlying subject. One might think that only particular substances are per se3 beings, since they are the only entities which are not predicated of anything else. In that case, the expressions ' ' and ' ' in 73b 7-8 would refer to their substantiality and particularity, respectively.147 However, Aristotle does not say that per se3 beings are not predicated of anything whatsoever. Actually, what is said in T33 is that they are never predicated of something different ( ), i.e. if x is a per se3 being, there is no y such that x is predicated of y as a non-essential predicate. 148 If so, the secondary substances of the Categories can also be classified as per se3 beings: as we have seen in Chapter 3, for Aristotle, substantial (and substance-like) beings are essential predicates of everything of which they are predicated. If understood in this way, per se3 is certainly connected to the other two uses of 'per se'. The first use (per se1) covers all essential predicates of all kinds of essence-bearers (substances and non-substances). The second (per se2) presupposes the distinction between prior and posterior essence-bearers (as stated in PIB), the former being defined without mentioning the latter, but not the other way around (as stated in PID). Finally, the third use of per se (per se3) applies precisely to the primary essence-bearers, which are what they are independently of being predicated of items which differ from them in essence. 146 Peramatzis (2010) and Ferejohn (2013, pp. 92-93) are exceptions. Ferejohn (2013, pp. 92-93) argues that this third use of 'per se' applies to predications (or, more precisely to what we have called 'natural' predications): 'man is walking' is a per se predication in this sense because 'man' is the proper 'logical' subject of the predicate 'white'. As Barnes (1993, pp. 114-117) has shown, the third use of per se is relevant to the distinction between natural and unnatural predications, since per se beings (substances and substance-like entities) are the proper subjects of 'incidental' beings (nonsubstances); hence, the grammatical subjects of natural predications must be substance-terms. However, the expression ' ' and the formula ' ' indicate that Aristotle's point is that (e.g.) white is not what it is independently of it being predicated of another subject (see Angioni 2006, pp. 112-113). 147 See Ross (1949, p. 519). 148 See Angioni (2007b, pp. 119-122); Zuppolini (2014c, pp. 33-37). 101 There are several reasons to believe that the fourth use of 'per se' (hereafter, per se4) is also relevant to Aristotle's model of demonstrative science. This use is explained in the following passage: [T34] Again, in another way what holds of something because of itself holds of it in itself, and what does not hold because of itself is incidental. E.g. if there was a lightning while he was walking, that was incidental: it was not because of his walking that there was lightning – that, we say, was incidental. But what holds because of itself holds in itself – e.g. if something died while being slaughtered, it died in the sacrifice since it died because of being slaughtered, and it was not incidental that it died while being slaughtered [APo I 4, 73b 10-16; Barnes 1993, with changes]. It has been argued that this kind of per se relation takes place between two events causally linked:149 the event E1 (slaughtering) relates to the event E2 (death) in itself whenever E2 occurs because of E1 itself ( ). Nevertheless, Aristotle would be comfortable with a reduction of events to predications in the following terms:150 an event E1 (slaughtering) would be reducible to a predication of the form 'S is P1' (S undergoes a certain slaughtering procedure), whereas E2 (death) would correspond to a predication 'S is P2' (S dies). Therefore, a per se4 connection is more properly understood not as holding between a predicate and a subject, but between two predicates occurring to the same subject (or subjects): Per se4 : if P1 and P2 are per se4 related, P2 holds of a given S because [ ] P1 holds of S. We are going to argue in more detail in favour of this interpretation in the next section. However, we can say in advance that if every occurrence of P1 (being slaughtered) causes the occurrence of P2 (dying), the causal link between E1 and E2 could be expressed by a universal predicative statement with 'P1' as in the subject-term and 'P2' as the predicate-term: 'every P1 is P2': everything that undergoes a slaughtering procedure dies.151 If this use of 'per se' is interpreted as we propose, it becomes easier to understand its relevance to the theory of the APo. The explanatory character of demonstrations is partially due to the fact that their categorical propositions have subjects and predicates explanatorily connected. Such connection can be understood as a per se4 relation: 'triangle' is the appropriate grammatical subject for the predicate '2R' because the 149 Ross (1949, p. 520). 150 See Barnes (1993, p. 117); Angioni (2004, p. 16); Ferejohn (2013, p. 93) 151 For a similar interpretation of the example, see Ferejohn (2013, p. 93). 102 metaphysical predicates being a triangle and having 2R are per se4-related: if a given figure in a semicircle has 2R, it has 2R because it is a triangle. However, a complete understanding of this aspect of Aristotle's theory depends on a satisfactory account of the notions of per se accident and primary universality. 4.3 – Per Se Accidents and Primary Universality: the Debate As we know, Aristotle describes demonstrable attributes as per se accidents ( ).152 In Metaph. V 30, a per se accident is defined as a predicate that belongs to a subject 'in itself' ( ), but not as a part of its 'essence' ( ): [T35] 'Accident' has also another sense, namely, whatever belongs to each thing in virtue of itself, but is not in its essence; e.g. as having the sum of its angles equal to two right angles belongs to the triangle [Metaph. V 30, 1025a 30-32]. The paradigmatic example is the predicate 2R, i.e. the property of having the sum of internal angles equal to two right angles, a per se accident of triangles. Although in APo I 4 Aristotle discusses several ways in which a predicate holds of a subject 'in itself', he was accused of not having elucidated the crucial notion of per se accident.153 Since Aristotle defines the per se accident as a predicate belonging to its subject 'in itself', but not as an item in its essence, we are apparently prevented from taking it as a per se1 attribute. In the APo, the philosopher speaks as if all scientific propositions signify either a per se1 or a per se2 connection. 154 If so, by elimination, we feel inclined to classify 2R and all per se accidents as per se2 predicates. 155 In addition to the APo, passages from other parts of the corpus substantiate this result. In Ph. I 3, 186b 18-23, for instance, Aristotle divides 'accidents' ( ) attributes into two types, one of which is a predicate that may or may not belong to its subject (which demonstrative sciences do not study) while the other is a 'per se' accident: the per se2 attribute. Certainly, Aristotle secured a place for per se accidents in demonstrative sciences, which precludes any possibility of understanding them as contingent attributes. The most intuitive reaction to this 152 See APo I 6, 75a 18-19; I 7, 75b 42-b2; I 10, 76b 11-15; Ph. II 2, 193b 22-30; Metaph. III 1, 997a 19-25. For other occurrences of the notion, see Bonitz 713b43-714a3. 153 Barnes (1993, p. 114). 154 See APo I 4, 73b 3-4; 73b 16-18; I 6, 74b 5-12; I 22, 84a 11-14. As I shall clarify soon, this does not mean that the other two uses of 'per se' are irrelevant to Aristotle's theory. 155 See, for instance, Ross (1949, p. 580); Wedin (1973); Graham (1975); Mignucci (1975, p. 64); Granger (1981); Sorabji (1980, p. 18); Terra (2009, pp. 55-121; 2014). 103 passage is to understand per se accidents as per se2 predicates. I shall refer to this interpretation as the 'Natural Solution' to the problem of whether and how per se accidents fit in APo I 4. Nevertheless, many commentators feel uncomfortable about classifying per se accidents and especially the 2R-attribute as per se2 predicates. 156 Their reasons are basically two. First, it is hard to see why 'triangle' should be part of the definition of 2R. Second, Aristotle's examples suggest that, if P belongs to S as a per se2 predicate, then P is a member of a pair of opposites (like odd and even, straight and curved, male and female) of which one or the other must belong to S. However, 2R is not a member of a pair of opposites and seems to work more like a proprium ( ), since it is coextensive with 'triangle' and cannot fail to hold of it (see Top. I 5, 102a 18-20).157 Thus, several alternatives to the Natural Solution have been offered in the secondary literature. The first alternative to the Natural Solution I shall consider (hereafter, 'A1') consists in understanding the notion of per se accident according to the first sense of 'per se' defined in APo I 4. A systematic defence of this interpretation comes from Richard Tierney (2001a), who argues that, for Aristotle, a predicate can belong in a subject's 'what-it-is' ( ) without belonging in its 'essence' ( ), which allows him to classify 2R and other demonstrable attributes as per se1 predicates without contradicting Aristotle's statement in T35 (Metaph. V 30, 1025a 30-32).158 It is hard to believe that Aristotle used his vocabulary as rigorously as Tierney's claim requires. In fact, it would be necessary to recognize in Aristotle's texts a distinction even more subtle than the one between ' ' and ' . On one hand, we would have the items 'from which the essence comes' ( ), which are per se1 attributes according to T31 (APo I 4, 73a3437). On the other, there would be items 'in the essence' ( ), which are not per se accidents according to T35. Therefore, if it were a per se1 predicate, 2R would be one of the items the essence of triangles comes from, but not an element in their essence ( ), since otherwise it would not be a per se accident. 156 See Inwood (1979, p. 323); Ferejohn (1991, pp. 123-128); McKirahan (1992, pp. 98-100); Barnes (1993, pp. 113114); Tierney (2001a, pp. 74-78) and even Granger (1981, p. 119, n.2) and Sorabji (1981, p. 189), who nevertheless are willing to classify per se accidents as per se2 predicates. For a detailed discussion of the 2R example, see Tiles (1983). 157 Inwood (1979, p. 323) argues that in APo I 7, 75b1-2 Aristotle recognizes two kinds of explananda: and . According to him, only would be coextensive with their subjects. However, Aristotle does not seem to be distinguishing between two classes of predicates in this passage, but rather using two different expressions to refer to the same class of predicates: the per se accidents, attributes that belong to their subjects in themselves but not as a part of their essences. See also Bronstein (2016a, pp. 46-48), who also distinguishes between two kinds of demonstrable attributes: per se2 predicates and 'in itself incidentals' (or per se accidents). 158 It should be noted that the Tierney classifies as per se1 predicates are demonstrable attributes such as 2R – or, as he calls them, 'logical incidentals' –, which follow demonstratively from the essence of their subjects. These should be distinguished from 'inhering incidentals', which belong to underlying subjects (but are not themselves underlying subjects). 'Inhering incidentals', in turn, are distinguished into two types: 'inseparable inhering incidentals' (per se2 predicates) and 'separable inhering incidentals' (purely 'accidental' or 'contingent' predicates). 104 The difficulties A1 has to face are not only textual but also theoretic. According to Tierney (2001a, pp. 75-76), some per se1 predicates are 'immediate' and therefore belong not only in the what-it-is of the subject, but also in its essence: namely, the proximate genus and the proximate differentia. Since the relation belonging in the what-it-is is transitive – Tierney quotes APo II 4, 91a 921 –, the genera and differentiae of the initial genus and differentia would be also (non-immediate or derivative) per se1 predicates of the subject in question. It is not clear how it follows from these considerations that 2R can be taken as part of the 'what-it-is' of triangles. One may suggest that 2R would be a non-immediate (or a second-level) differentia of one of the immediate (first-level) differentiae of the triangle – see the discussion on 'intermediate' differentiae in Tierney (2001b, pp. 157-158).159 Relying on Ph. II 9, 200a 16-17, for instance, we could think that the first-level differentia in question here is being a figure bounded by straight lines, of which 2R would be some sort of second-level differentia (see Tierney 2001a, pp. 77-78). However, if this is how A1 is underpinned, other objections can be raised. A differentia seems to specify a determinate way of being a member of the corresponding genus. Although being a rectilinear closed figure entails having internal angles equal to a certain amount or another, having 2R is not a specific way of being a rectilinear figure in the same manner as being three-sided, for instance, is.160 Aristotle seems concerned with this distinction in the Parts of Animals: [T36] One ought to divide by features in a thing's substantial being, and not by its per se accidents, as would happen if someone were to divide figures on the ground that some have angles equal to two right angles, while others have angles equal to more; for having angles equal to two right angles is a sort of accident of the triangle [PA I 3, 643a 27-31; Lennox 2001, with changes]. James Lennox comments on the passage: Within that context, Aristotle is probably thinking of the error of dividing a general difference by sub-differences that are only incidentally related to it. For example, if figures are divided into those enclosed by straight lines and those enclosed by curved lines, then dividing rectilinear figures based on the equivalence or non-equivalence of the interior angles to two right angles will be incidental. In essence, it is to begin a new division, based on angle-sum equivalencies rather than the nature of lines [Lennox 2001, p. 163]. 159 See also McKirahan (1992, pp. 169-171) for an interpretation along the same lines. He argues that such implicit definitional predicates are part of what he calls a 'fat definition'. 160 See Ferejohn (2013, pp. 175-176). 105 If Lennox is right about T36, Tierney's arguments in favour of A1 are not convincing. Another passage challenges Tierney's interpretation more directly. In APr I 27, 43b 6-11, Aristotle distinguishes the predicates in the what-it-is ( ) from the so called 'propria' ( ). This passage is particularly troublesome for A1 since it draws a distinction between the propria and the items in the ' ' – and not items in the ' ' as in T35 and T36. Therefore, Tierney needs either to reject the plausible view that 2R is an of the triangle or to postulate that in APr I 27 the clause ' ' is used in a stronger sense than the one we find in APo I 4. There is a further objection to consider. Tierney believes that the transitivity of the relation belonging in the what-it-is is what enables us to know, by demonstration, that a subject has a certain derivative essential attribute (a per se accident) by means of another and more basic essential predicate occurring as the middle term. However, the passages Tierney quotes in support of the demonstrative status of such a deduction are clearly diaporematic (APo II 4, 91a 18-21 and II 6, 92b 2-13). In fact, Aristotle's final word is that such deduction would be nothing more than a nondemonstrative (see APo II 8, 93a 9-15) – even though the relation belonging in the what-it-is remains transitive. A second alternative to the Natural Solution (hereafter, A2) is an interpretation which argues that per se accidents are covered by the fourth sense of 'per se' defined in APo I 4.161 The proponents of A2 take per se4 connections to take place between a subject and a predicate (and not between two predicates belonging to the same subject, as we have argued). In APo I 4, 73b 3-5, Aristotle says that predicates that are not per se1 or per se2 are 'accidents' ( ). If so, they argue that the other kind of per se connection discussed in the chapter (per se4) should be understood as occurring between a given subject and one of its 'accidents', one that nevertheless belongs to it 'in itself'.162 More precisely, the per se4 connection would take place between a subject and a predicate that are explanatorily linked in a certain way: Per se4 (according to A2): P is a per se4 predicate of S iff. P holds of S because [ ] S is what it is. Dying (P) happens to an animal that has been slaughtered (S) precisely because it has been slaughtered ( ). Interpreters who advocate A2 argue that this is the relation that obtains between triangle and 2R. The triangle has 2R because it is what it is, namely, a triangle. Given that per se accidents belong by necessity to their subjects, but are not part of their essences, it seems reasonable to understand them as something that necessarily follows from their subjects being what they are. 161 See Code (1986, pp. 350-351); Furth (1988, p. 237); Ferejohn (1991, pp. 123-128; 2013, pp. 91-94) and, less empathically, Tiles (1983, p. 13). 162 See Code (1986, p. 350); Furth (1988, p. 237). 106 Although A2 seems promising, anyone willing to accept it must overcome two crucial difficulties. The first one regards lines 73b3-4, in which Aristotle says that every item that is not predicated of something as a per se1 or a per se2 predicate is an 'accident'. We can infer that per se4 predicates are 'accidents' in the same sense which occurs in 73b4 only if we take the four senses of 'per se' to introduce heterogeneous classes of predicative sentences with no intersection between them.163 However, sentences expressing a per se4 connection could not take part in science unless they signify in addition a per se1 or a per se2 connection. Some passages deserve our attention: [T37] Thus, with respect to what is knowable without qualification, whatever is said to hold of things in themselves (in the sense of inhering in what is predicated or of being inhered in) is also said to hold of them because of themselves and from necessity [APo I 4, 73b 16-18; Barnes 1993, with changes]. [T38] If demonstrative understanding proceeds from necessary principles (since what you understand cannot be otherwise), and if whatever holds of an object in itself is necessary (since either it holds in what it is, or else the object holds of what is predicated of it in what it is and the predicate are opposites one of which necessarily holds), then it is clear that demonstrative deductions will proceed from certain items of this sort; for everything holds either in this way or incidentally, and what is incidental is not necessary [APo I 6, 74b 5-12; Barnes 1993]. [T39] Demonstration applies to what holds of the objects in themselves – in themselves in two ways: both items which hold of the objects and inhere in what they are, and also the items for which the objects of which they hold inhere in what they are [APo I 22, 84a 11-14; Barnes 1993]. In T37 and T38, Aristotle affirms that scientific knowledge concerns predicative connections in which either the predicate inheres in the definition of the subject or the subject 163 See Terra (2014, p. 42), who argues that per se1 and per se2 connections are also per se4, which would be a more general kind of per se relation (a solution I reject). This is quite different from saying that a single sentence can signify a per se2 and per se4 connection at the same time, as I shall argue. 107 inheres in the definition of the predicate. Aristotle's words seem to imply that all scientific propositions express either a per se1 or a per se2 connection. Tiles (1983, pp. 11-12) conjectured that T37 and T38 might be only about the axioms or primary principles of science, so that nothing would commit us to classify the corresponding conclusions (or theorems) as per se1 or per se2 predications. Although viable for T37 and T38, such a hypothesis would not work for T39. As we have seen in Chapter 3, Aristotle intends to deny the possibility of there being infinite chains of proofs in demonstrative sciences, in which all premises would be themselves demonstrated from more basic premises and so on ad infinitum. In the paragraph in which T39 belongs, 84a 7-28, Aristotle argues that a demonstrative chain could not proceed ad infinitum insofar as it would contain infinite series of per se1 or per se2 predications, which is impossible according to him. The argument implies that only the premises that interrupt the sequence are indemonstrable, whereas the other premises would occur also as conclusions at some point of the chain. Therefore, Aristotle does not limit per se1 and per se2 connections to indemonstrable propositions. 164 If all scientific propositions must signify either a per se1 or a per se2 connection, it seems more convenient to read ' ' in 73b4 as referring to contingent predicates, in respect of which there is no demonstrative knowledge (see APo I 6, 75a18-22). In fact, the examples we find in 73b 5 (musical and white said of animal) are predicates of this kind, and not per se accidents as readers sympathetic to A2 would expect.165 Furthermore, in T37, Aristotle states that, when we have knowledge 'without qualification' ( ), per se1 and per se2 predicates hold of their subjects also 'because of themselves'. Here, the philosopher uses again the same formula ' ( )' we find in the characterization of per se4 connections in T37. Thus, there seems to be some sort of overlap between these types of relations, which should prevent us from inferring that per se4 items are ' ' in the same sense in which the word is used in 73b4.166 164 One could think that, in relying on T39, we are committed to at least some demonstrable per se1 connections. However, a demonstrative chain can proceed ad infinitum if at least one of its branches contains infinitely many demonstrable propositions (even if the other branch contains only indemonstrable premises). Therefore, a sequence of syllogisms in Barbara, for instance, would go on ad infinitum if all the major premises within it were demonstrable, even if all the minor premises were 'immediate' or indemonstrable. Aristotle seems take essence-specifying propositions (that is to say, per se1 predications) as indemonstrable (see, for instance, APo II 3, 90b 24-7; II 8; 93a 9-15). Therefore, if the minor premises in our example signify per se1 connections, our (infinite) syllogistic chain would contain infinitely many sentences signifying per se1 connections, even though these connections are indemonstrable. Since the argument assumes that all sentences involved in demonstrative chains signify either per se1 or per se2 connections, we can conclude that at least per se2 predications are not limited to first principles of science. Furthermore, as we have seen, while we have textual evidence for taking per se1 connections as indemonstrable, the same does not apply to per se2 connections. 165 One could accept a version of A2 that takes per se accidents as per se2 and a per se4 predicates at the same time. However, as I shall argue, the per se4 connection is not a predicative relation between an object and an attribute (as a per se2 connection is), but a causal or explanatory relation between two attributes occurring to the same object (or objects). 166 I shall clarify what kind of overlap this is. As I shall argue, the fact that all scientific propositions must signify either a per se1 or a per se2 predication does not mean that per se4 connections are out of the scope of science. 108 The other difficulty that interpreters advocating A2 have to face is conceptual rather than textual. According to them, if a per se accident is an attribute that simply follows from its subject being what it is, there is a way in which the per se accidents of a genus are also per se accidents of its species; in other words, if P is a per se accident of (the genus) S and S is a per se1 predicate of (the species) S', then P is a per se accident of (the species) S' (see Code 1986, p. 351). Therefore, if 2R is a per se accident of the triangle, it must be a per se accident of the isosceles as well. Identifying per se accidents with per se4 predicates, as A2 suggests, we have that, if P is a per se4 predicate of (the genus) S and S is per se1 predicate of (the species) S', then P would be a per se4 predicate of (the species) S'. For instance, if 2R is a per se4 predicate of the triangle, it would be a per se4 predicate of the isosceles as well. At first sight, this seems to be a welcome result. After all, the sentence 'every isosceles (triangle) has 2R' seems to be under the scope of science and therefore must signify a per se connection in one way or another.167 However, according to Aristotle, someone who knows that the members of the genus triangle have 2R is in possession of a prior and more basic knowledge than someone else who knows only that the members of the species isosceles have the same attribute. Triangle, and not isosceles, is the relevant universal type – the primary universal ( ) – that comprises all the instances of the property 2R.168 Therefore, Aristotle says that the equilateral or the isosceles has 2R only 'incidentally' ( , Top. II 3, 110b 22-25). In the same vein, he affirms that a demonstration applies universally to the triangle 'in itself', whereas it applies to the equilateral or the isosceles 'in a certain way not in itself' (' ', APo I 4, 74a 2). It would be inappropriate to say that 2R belongs to isosceles triangles ' ' in the same way in which a contingent predicate is said to be a ' '. After all, 2R is a demonstrable attribute (that is, a per se accident) of triangles in general, including isosceles triangles. If so, there is a sense of ' ' (namely, that of ' ') according to which 2R is a of the (species) isosceles in the same way as it is a of the (genus) triangle. However, Aristotle's point in Top. II 3, 110b 22-25, is that there is still another sense of ' ' according to which 2R belongs to the (species) isosceles ' ', but not to the (genus) triangle. If there is a sense of ' ' contrasting this other sense of ' ', we can think that a similar point is made in APo I 4, 73b38-74a3: there is a use of ' ' according to which 2R belongs to the (genus) triangle ' ', but not to the (species) isosceles. Thus, we have to face a pressing question: when Aristotle affirms that a demonstration of the 2R-theorem applies to the isosceles ' ' (APo I 4, 74a 2), which kind of 167 Sentences like 'every isosceles triangle has 2R' are demonstrated by what Lennox's 'type A' syllogisms (see Lennox 1987) and McKirahan calls 'application arguments' (see McKirahan 1992, pp. 177-187). 168 See APo I 4 73b32-74a3; I 5, 74a16-b4; I 24, 85b4-15; 85b23-27; 85b38-86a3. 109 connection is he denying? If we follow A2, the only way we can consider 2R a per se predicate (either of isosceles or of triangles in general) is by appealing to the notion of per se4 connection. However, such interpretation leaves us with no grasp of the meaning of 'in itself' according to which 2R belongs to the triangle 'in itself', but to the isosceles 'not in itself'. Therefore, at least in the terms it was proposed, A2 is not completely satisfactory. The three interpretations we have considered so far present disappointing results. Interpreters who advocate the Natural Solution fail to explain how the paradigmatic example of per se accidents (2R predicated of triangles) could match the characterization and examples of per se2 predications in APo I 4. Interpretation A1 seems to violate Aristotle's claim that essential predications (in which the predicate is part of the of the subject) are not demonstrable in the strict sense. Interpretation A2, in turn, overlooks the passages in which Aristotle takes per se1 and per se2 predications to cover all scientific propositions; moreover, A2 is unable to explain in which sense of 'in itself' 2R belongs to the triangle 'in itself', but to the isosceles 'not in itself'. Thus, understanding the concept of per se accident and its role in the APo involves addressing three basic difficulties: (A) Does the 2R-example satisfy the definition of per se2 predication? If it does, is there a pattern in all of Aristotle's examples of per se2 predicates (including 2R)? (B) What does Aristotle mean when he says that per se1 and per se2 connections cover all scientific propositions? Would not this make his theory excessively restricted? (C) In which sense of 'per se' is 2R per se-related to triangle, but not to isosceles? 4.4 – Per Se Accidents and Primary Universality: Remodelling the Natural Solution The discussion about the nature of demonstrable attributes is crucial for understanding Aristotle's model of scientific explanation. A successful account of the relation between a subject and its per se accidents would help us determine whether Aristotelian demonstrations follow the SModel, the A-Model or a combination of both.169 For instance, each of the three interpretations discussed in the last section is associated with one of these models of essence-based explanation. The Natural Solution takes per se accidents to be per se2 predicates. As we have seen, P is a per se2 predicate of a subject S if the definition of P somehow refers to S. Here, what grounds the per se relation between S and P would be the essence of the predicate P, as we have in the A-Model. However, demonstrable attributes are predicated of their subjects by necessity, which makes several 169 For a similar point, see Bronstein (2016a, pp. 46-50). 110 interpreters think that per se accidents are somehow attached to the essence of the items to which they belong, along the lines of the S-Model.170 In the same vein, alternatives to the Natural Solution take the per se accident to be either part of the essence of the subject (A1) or a consequence of the subject being what it is (A2). In this section, I shall defend the Natural Solution. Nevertheless, in my analysis of the concept of primary universality, I shall preserve some of the intuitions underpinning interpretation A2. As a result, our account will once again suggest that the S-Model and the A-Model are both part of Aristotle's doctrine. As we have noted, the Natural Solution to the problem of per se accidents has met with resistance from interpreters of Aristotle. I believe that such resistance is due to a confusion between two levels of analysis in which this discussion should take place: the level of extra-linguistic connections between objects and their attributes (metaphysical predications), on one hand, and the level of sentences expressing these connections (linguistic predications), on the other. As we have argued, per se connections are metaphysical predications. Therefore, the proponents or opponents of the Natural Solution must address two distinct questions: The Metaphysical Question: What characterizes a per se2 connection? The Linguistic Question: What kinds of sentences (or linguistic predications) express per se2 connections? Despite being interconnected, the Metaphysical and the Linguistic Question are substantially different from each other and must be addressed separately. In the following, we shall first address the Metaphysical Question, which involves identifying the kinds of entities that participate in per se2 connections and understanding the role these connections play in Aristotle's metaphysical theory as a whole. It has been said that the subjects of per se predications are always universal (Sorabji 1980, pp. 189-191). Aristotle affirms – in Metaph. VII 15, for instance – that it is impossible to give a definition of individuals, whereas per se1 and per se2 predications are such that subject and predicate maintain a definitional link in one direction or the other. However, the fact that definitions are only of universals does not entail that particulars cannot be subjects of per se1 predications, as it might seem at first sight. The impossibility of giving a definition of Socrates, for instance, probably means that there is not a definition exclusive to Socrates, with the proper name 'Socrates' as the definiendum. Nevertheless, according to 73a 36-37 in T31, in order to be a per se1 predicate of a given subject S, an attribute P only needs to inhere in 'the account that says what S is', which is not necessarily a 170 See, for instance, Loux (1991, p. 73); Barnes (1993, p. 120); Charles (2000, p. 203); Malink (2013, pp. 124-126); Bronstein (2015, pp. 724-725); Shields (2016, pp. 84-85). 111 definitional statement with 'S' occurring as the subject-term. If S is an individual, the account displaying what S is will be the definition of the species of which S is a member. As Aristotle himself admits, animal is a per se1 predicate of Callias insofar as animal is mentioned in the definition of the species man, of which Callias is a member (see Metaph. V 18, 1022a 27-29). Moreover, the argument that there is no definition of individuals (and therefore the subjects must be universals) is inconsequential in the case of per se2 predications. After all, it is the definition of the predicate (and not of the subject) that occurs in the characterization of this kind of per se connection. In a series of articles, Richard Tierney (2001a; 2001b; 2004) argued that particular substances – and also substance-like entities such as numbers and surfaces – are subjects of per se predications. According to his view, odd would be a per se2 predicate of numbers like 5 or 7, whereas male would be a per se2 predicate of animals such as Socrates or Secretariat. Without accepting all the reasons Tierney sets out in favour of his interpretation, I would like to subscribe to his understanding of per se2 connections in the following terms. 171 The possibility of individuals being subjects of per se predications is congenial to Aristotle's Categories, according to which the subjects of predication par excellence are particular substances, on which other beings are ontologically dependent. As we have seen, the ontological priority of substances over incidental beings (PIB) has a definitional priority (PID) as its linguistic correlate: definitions of non-substantial entities must somehow register their dependent status by containing a reference to their proper subjects. However, since an attribute can be instantiated in a plurality of individuals, it would be unreasonable to require its definition to provide us with a complete list of the particular objects to which it belongs. For that reason, all Aristotle expects is the presence of a kind-term that picks out the subjects to which the definiendum attribute belongs as a per se2 predicate (Metaph. VII 5, 1030 b 23-24).172 Animals are the sort of things that are either male or female and therefore the definition of male must contain the kind-term 'animal'. In that case, we could say, following Tierney, that animals satisfying the relevant criteria (such as Socrates or Secretariat) are subjects to which male belongs as a per se2 predicate. Similarly, (bodily) surfaces are the sort of things that have colours. For that reason, the term 'surface' should be part of the definition of white, which makes it a per se2 attribute of surfaces of a given kind (see Metaph. V 18, 1022a 29-31; VII 4, 1029b 16-18). However, since the subjects of a given predicate can be described in many ways, it is not immediately clear which kind-term should be part of its definition. As Tiles (1983, p. 10) points 171 Yet, as we saw in the last section, Tierney would not allow us to infer from his thesis that the term 'triangle' does not need to occur in the definition of 2R if 2R is a per se2 predicate of triangles (as I shall argue). 172 See Goldin (1996), who argues that per se accidents are things such as eclipse, thunder or deciduousness, whose subjects, on which their being depends, are mentioned in their definitions. 112 out, Aristotle seems to believe that definitions of attributes should determine their range of significance. In other words, what is expected is a sortal expression – which can be either a substance term, such as 'animal', or a substance-like term, such as 'number' or 'surface' – that refers to the objects it applies to as countable discrete wholes, establishing thereby a homogeneous domain of application for the attribute in question. For that reason, white is a of some men (in the sense of being a contingent predicate of them) and nevertheless is a per se2 predicate of the surfaces that are part of their bodies.173 Surfaces are the primary (proximate) subjects in which colours are naturally found ( , Metaph. V 18, 1022a16), which means that the property of being a (bodily) surface or being composed of a (bodily) surface is what unifies very dissimilar objects (such as a pale man, a painting by Barnett Newman or a snowball) in a cohesive domain. Therefore, doing science about colours and explaining how they come about involves doing science about bodily surfaces as well, since they are the proper subjects of colours with the relevant features that make colours what they are. The fact that particular objects can be subjects of per se2 predications (provided that the relevant kind is mentioned in the predicate's definition) gives us a preliminary answer to the Metaphysical Question. However, this picture still needs to turn out consistent with a plausible answer to the Linguistic Question. Naturally, the Metaphysical Question takes precedence over the Linguistic one, since, in order to evaluate whether a given sentence expresses a certain fact or state of affairs appropriately, we need to know previously – at least, in general lines – what this fact or state of affairs is. However, without bothering to give a precise answer to the Metaphysical Question, several interpreters have assumed, for instance, that all categorical statements expressing a metaphysical predication in which odd occurs as a per se2 predicate must have the term 'number' as their grammatical subject. Under this assumption, the options available would be the following: (i) 'Every number is odd.' (ii) 'Every number is odd or even.'174 (iii) 'Some numbers are odd.'175 Option (i) should be rejected as false. Option (ii), on the other hand, can hardly be extracted from the texts – especially from Metaph. VII 5, 1030b 18-26 – and sounds too eccentric for the important 173 Tierney (2004, p. 14) notes that the kind-term appearing in the definition of an attribute applies to its 'immediate subjects' (surfaces in the case of white) rather than its 'ultimate subjects' (a particular pale man). Mignucci (1975, p. 63), speaks in terms of 'condizione prossima' and 'condizione remota': '... mentre numero è condizione prossima di pari o dispari, uomo è solo condizione remota (in quanto ha superficie) di bianco.' 174 See Ross (1949, pp. 59-62; pp. 521-522); Wedin (1974, p. 34); Mignucci (1975, p. 63); Granger (1981, p. 120). 175 See Ferejohn (1991, p. 99-108). 113 role Aristotle ascribes to per se2 connections in his theory of demonstrative science. 176 Particular statements like (iii), in turn, also do not get support from the text and conflict with Aristotle's preference for universal propositions in scientific demonstrations (see Barnes 1993, p. 114). However, there is no textual evidence forcing us to assume that, if P is a per se2 predicate of S, the term 'S' must be part of the definition of what P is. Indeed, this would be the case only if the verb ' ' signified what we could describe as a language-language relation – that is, a relation assuming only linguistic items as values. Actually, we cannot take ' ' as a relation of this kind without committing Aristotle to a theory that is based on use-mention confusions, as we have seen. On the other hand, if we take 'inhering in' as a world-language relation, the number of sentences that can be interpreted as signifying per se2 connections is considerably higher than it is usually thought. Consequently, the important place Aristotle reserves for them in his theory of science becomes much easier to understand. Let us clarify this point. The characterization of per se2 connections in T32 is the following: ' ' (73a 37-38). Answering the Metaphysical Question requires identifying the referent of the pronoun ' , the grammatical subject of ' . In Metaph. V 18, 1022a 29-31, Aristotle describes white as a per se2 predicate of the surface, using a definite article ( ). One could say that the definite article introduces the word 'surface' as the (grammatical) subject of a linguistic predication. However, we have already ruled out this option by reading ' ' as picking out a world-language relation. Another option would be to take the article to introduce a universal entity (the surface), as when we say, for instance, that 'the elephant is a mammal.' However, this use of the article seems to imply a universal quantification (all elephants are mammals), which is not compatible with the surface/white case (since not all surfaces are white). A third and more viable option would be to take the article to introduce a particular object. When we say, for example, that 'the chair is made of wood', the referring expression 'the chair' denotes a particular chair. In the same vein, in sentences like 'the surface is white' or 'white is a per se2 predicate of the surface', the expression 'the surface' would refer to a particular surface. Therefore, not only Aristotle's example of per se1, but also his example of per se2 connections in Metaph. V 18 indicates that particular objects can be taken as subjects of per se predications.177 A similar reasoning applies to the use of the definite articles ' ' and ' ' in APo I 4, 73b29-30. 176 Although sentences of this form may appear in arguments that are relevant to scientific inquiry (such as reductio ad absurdum or arguments relying on platonic division), they do not seem to fit Aristotle's characterizations of (full-fledged) demonstrations. Barnes (1993, p. 113) correctly points out that, for Aristotle, such propositions are 'likely to be, at best, rare in the sciences'. 177 Of course, this does not imply that universals cannot be subjects of per se predications. 114 Well, if the definite article in Aristotle's example is interpreted as implying that white can be taken as a per se2 predicate of some particular (bodily) surfaces, these surfaces must somehow 'inhere in' the definition of white. For the same reason, if male is a per se2 predicate of animals such as Socrates and Secretariat, Socrates and Secretariat must somehow 'inhere in' the definition of male. Certainly, this does not mean that 'Socrates' and 'Secretariat' need to be present in the definitional locution specifying what male is. Indeed, this absurdity comes out only for those who take 'inhering in' as introducing a language-language relation, as several interpreters seem to do. On the other hand, those who take 'inhering in' as introducing a world-language relation find themselves able to explore the following exegetical hypothesis: a subject S 'inheres in' ( ) the definition of a predicate P if the relevant kind-term 'K' applying to S appears in the definition of P.178 If this hypothesis is correct, we could say that insofar as 'animal' is part of the definition of male, some of the members of the kind animal (like Socrates and Secretariat) are subjects to which male belongs in the per se2 way. Similarly, the definition of straight contains the kind-term 'line', which makes straight a per se2 predicate not of the kind line itself – after all, not all lines are straight –, but of the members of the kind that satisfy the relevant criteria for being considered a straight line.179 With this background in mind, we are able to address the reasons set out by those who oppose the Natural Solution and resist classifying per se accidents (especially the property 2R) as per se2 predicates. The first of these reasons states that there is no good motivation to include the term 'triangle' in the definition of 2R.180 Consequently, the attribute 2R would not satisfy the most basic requirement to be considered a per se2 predicate of triangles. This objection to the Natural Solution relies on the assumption we have just undermined; namely, that if P is a per se2 predicate of S, the term 'S' must be part of the definition of what P is. As we saw, the kind-terms 'number' and 'animal' appearing in the definitions of odd and male are responsible for marking off their ranges of significance. Thus, those kind-terms do not apply exclusively to the actual instances of these attributes, but to all the items to which 'odd' and 'male' apply meaningfully. Similarly, there is no 178 Perhaps, in some special cases, the proper name of S itself will be in the definition of the predicate. For instance, 'Moon' is part of the definition of the lunar eclipse and not a generic term applying to the Moon (APo II 2, 90a 15). 179 The interpretation that Socrates, Callias and all male animals 'inhere in' the definition of male (in the precise way I have defined the 'inhering in' relation) – and similarly for the other examples – is also reinforced by the irregular combination of a neuter plural and a plural verb in 73a37-38. As has been noted, the plural verb may be used 'when variety is emphasized (distributive plural)' (Gildersleeve 1980, p. 48, §102) and 'when stress is laid on the fact that the neuter plural subject is composed of persons or of several parts' (Smyth 1920, p. 264, §959). See De An. II 3, 415a5-6; II 8, 420b9-10, II 9, 421b10-11; Plato, Laches, 180e; Laws, 856d-e. For other references, see Gildersleeve (1980, pp. 4849). 180 One could argue that, for Aristotle, there is indeed good reason to include the term 'triangle' in the definition of 2R because 2R and triangle have a relation of primary universality. However, Aristotle never says that if there is a relation of primary universality between S and P then 'S' should be part of the definition of P. In addition, it would be hard to unify Aristotle's examples in a single pattern – and hence to answer our question (A) – if one pursues this solution. 115 need to have the term 'triangle' as a part of the definition of 2R in order to classify 2R as a per se2 predicate of triangles. What is required of the definition of a predicate is no more than a reference to the objects to which the predicate applies with meaning, not necessarily with truth. Therefore, as 'number' in the case of odd or 'animal' in the case of male, the kind-term that needs to be present in the definition of 2R shall be something like 'rectilinear closed figure'181, since only rectilinear closed figures can have internal angles equal to a certain amount or another. In that case, we could say that triangles 'inhere in' ( ) the definition of 2R insofar as this definition contains a kind-term applying to them: 'rectilinear closed figure'. Thus, just as odd is a per se2 predicate of certain numbers and male is a per se2 predicate of certain animals, 2R is a per se2 predicate of certain rectilinear figures, namely, triangles. We must also not overestimate the impact of a second objection raised against the Natural Solution, according to which all per se accidents (2R included) should be members of a pair of opposite attributes in order to be classified as per se2 predicates. As some scholars have noted, Aristotle is not concerned with pairs of opposites when he defines and exemplifies the per se2 connection, but at most to a limited range of mutually exclusive attributes – otherwise, it would be hard to see why Aristotle takes white as an example of per se2 predicate in Metaph. V 18. 182 Although 2R is a not a member of a pair of opposites, it is indeed a member of a set of incompatible attributes, which is given, as Tiles (1983, p. 7) puts it, by the values of the function 'having internal angles equal to X'. All rectilinear closed figures – i.e. all items in the domain of application of the predicate 2R – must present one or another of the values of this function as a necessary and demonstrable property. Our answer to the Metaphysical Question allows us to answer the Linguistic Question in such a way that, although per se2 predicates belong to a range of mutually exclusive attributes, the predicate-terms that signify them may be coextensive with a given subject-term depending on the statements in which they occur. Let us consider the following sentences: (iv) '5 is odd' (v) 'this rectilinear figure in the semi-circle has 2R' (vi) 'every prime number other than 2 is odd' (vii) 'every triangle has 2R' At first sight, Tierney's interpretation suggests that sentences like (iv) and (v) are the most likely candidates to be interpreted as signifying per se2 connections, but this cannot be the whole story. 181 For more accurate options, see Tiles (1983, p. 10). 182 See Wedin (1973, p. 34, n. 9); Granger (1981, p. 120); McKirahan (1992, pp. 89-90); Tierney (2004, p. 11, n. 38). 116 Odd is a per se2 predicate of certain numbers and therefore a universal affirmative sentence such as (vi) could be interpreted as expressing, in a distributive reading, several per se2 connections between odd and all prime numbers other than 2. Similarly, 2R is a per se2 predicate of certain rectilinear figures, namely, triangles. Therefore, we can say that sentence (vii) signifies (distributively) several per se2 connections between 2R and each particular triangle. In this case, nothing prevents statements with coextensive subjectand predicate-terms from signifying per se2 connections. This entire debate opposes two different exegetical hypotheses. Most interpreters assume that P being a per se2 predicate of S entails that the term 'S' appears in the definition of P and is the subject-term of all sentences expressing a per se2 connection between S and P. Not only the opponents of the Natural Solution but even some of its proponents make this assumption, which explains why they were unable to show how the 2R-example fits Aristotle's characterization of per se2 connections. 183 We, on the other hand, suggested that P will be a per se2 predicate of S if S is a member of a kind K and the corresponding kind-term 'K' appears in the definition of P (determining thereby its range of significance). This second hypothesis is preferable on its own insofar as it interprets the verb ' ' in a way that does not commit Aristotle to use-mention confusions. In addition, it allows particular objects to be subjects of per se predications, being therefore in tune with the examples and the use of definite articles in Metaph. V 18 and APo I 4. Moreover, our interpretation provides solutions to problems (A) and (B) raised at the end of section 4.3: first, it enables us to understand passages in which per se accidents seem to be taken as equivalent to per se2 predicates and at the same time explain how the paradigmatic example of 2R fits the description of per se2 connections in APo I 4 (problem A); second, a larger number of sentences can now be interpreted as expressing per se2 connections, which allows us to explain the passages where Aristotle takes per se1 and per se2 connections to cover all scientific propositions without limiting his theory to sentences like (i), (ii) and (iii) (problem B). 183 Ross (1949, pp. 59-62) and Granger (1981, p. 120), who accept the Natural Solution, assume that a disjunction of exclusive attributes should appear in the predicate position, as we have in sentence (ii) above. This seems to be an awkward and ad hoc way out, which is unnecessary in our interpretation. Certainly, sentences with coextensive subjectand predicate-terms are not the only ones to express per se2 connections. For that reason, it would be wrong to claim that the class of propria coincides with the class of per se accidents (see Barnes 1970, pp. 139-140). Wedin (1973) adopts the disjunctive reading but argues that each member of the disjunction is a per se accident and not the disjunction as a whole, taken as a single attribute. He believes that per se accidents are always disjunctive and, therefore, cannot be propria. Graham (1975) has a more inclusivist view and argues that propria and per se2 attributes are subtypes of per se accidents. However, he assumes that per se2 attributes, unlike propria, are not counterpredicable (i.e. coextensive) with their subjects. As we have argued, this assumption conflates linguistic and extra-linguistic levels in which we can speak of predications. For a way of interpreting the necessity of per se2 predications that does not require the disjunctive reading, see Tierney (2007). 117 What about question (C)? According to the interpretative schema we are advancing, a sentence like (viii) 'every isosceles triangle has 2R' also expresses (distributively) per se2 connections between 2R and each isosceles triangle. Insofar as it signifies a per se connection, (viii) is under the scope of demonstrative science, as we would expect (since 2R is not a contingent attribute of isosceles triangles). However, Aristotle believes that sentence (vii) takes precedence over (viii) because (as it is usually phrased) 2R belongs to isosceles triangles not qua isosceles, but qua triangles. But what does this mean exactly? In other words, in which sense of ' ' does 2R belong to the isosceles (or equilateral) ' ' (Top. II 3, 110b 23-25)? When Aristotle says that the demonstration of the 2R-theorem applies to the isosceles ' ' (APo I 4, 74a 2), to which sense of ' ' does the expression ' ' refer?184 The concept of primary universality seems to be related to the fact that, for Aristotle, the subject-term of demonstrable propositions should somehow be explanatorily related to the predicate. If this is the case, the per se connection that characterizes primary universality must hold between a demonstrable property and another feature (expressed by the subject-term) in virtue of which all the objects that have such property happen to have it (see Kosman 1973, pp. 374-375). As we have seen, Aristotle characterizes the per se4 connection as an explanatory relation, as the proponents of A2 would accept. However, these interpreters do not seem to capture the relevant kind of explanatory relation Aristotle has in mind. According to them, P being per se4related to S means that P merely follows from S being what it is. Thus, they assume that a per se4 predicate (in their view, a per se accident) of a genus would be a per se4 predicate (that is, a per se accident) of its species as well – since being a member of the species entails being a member of the genus. This result, however, leaves us with no sense of 'per se' in which 2R is per se-related to triangle, but not to isosceles, equilateral or scalene. Consequently, A2 is unable to identify the kind of per se connection that characterises primary universality (APo I 4, 73b26-28). We can avoid this unpleasant outcome if we reinterpret the per se4 connection as follows. First, in T34, Aristotle does not seem to describe the per se4 connection as holding between a subject and a predicate (as the proponents of A2 assume it to be). At first, the connection in question seems to take place between events causally linked: a slaughtering procedure and the 184 On the equivalence between the ' ' in Top. II 3 and the ' ' in APo I 4, 74a 2, 110b 23-25, see section 4.3 above. In my view, 2R is a per se accident (that is, a per se2 predicate) of all triangles, which implies that sentences like (vii) –'every triangle has 2R' – and (viii) – 'every isosceles triangle has 2R' – express relations between certain objects and one of their per se accidents. However, as I shall now argue, sentence (vii) signifies a kind of per se connection that (viii) does not (namely, a per se4 connection). 118 death of an animal, for instance. However, we have seen that the kind of relation between events Aristotle has in mind consists in an explanatory connection between two predicates occurring to the same subject (or subjects): being slaughtered and dying: Per se4 : if P1 and P2 are per se4 related, P2 holds of a given S because [ ] P1 holds of S. This characterization of per se4 connections might be compatible with the one advanced by A2. However, the presence of the concept of primary universality in the context in which this connection is introduced forces us to take the per se4 connection as a very precise kind of explanatory relation, which is stronger than the mere 'following from' relation that A2 suggests. That this is so becomes clear once we realize that in APo I 4 Aristotle intends not only to classify the meanings of the expression 'in itself', but also to hierarchize demonstrable propositions. Suppose a geometer, for instance, discovers that all isosceles triangles have 2R and starts looking for an explanation for that fact. Her investigation is likely to end up with a demonstration concerning only the cases examined, viz. the occurrences of 2R in isosceles triangles.185 Even if the geometer includes in his agenda finding explanations for the presence of 2R in scalene and equilateral triangles as well without unifying them in a single kind, the knowledge acquired in this way would be nothing more, in Aristotle's words, than a sophistic ( ) understanding of the 2R-theorem (see APo I 5, 74a 25-32; I 2, 71b 9-10).186 In order to have scientific knowledge without qualification, it is not enough to figure out the range of significance of the attribute in question, not even the whole domain of its actual instances: the appropriate extension cannot be grasped only 'in number' (74a 31). There is an appropriate intension to be considered, which consists in a property or cluster of properties explanatorily related to the attribute whose occurrence we seek to demonstrate. For example, whatever has the attribute 2R has it independently of having two, three or none of their sides equal to each other (i.e. independently of being an equilateral, an isosceles or a scalene figure), but ultimately because it is, by definition, a three-sided rectilinear closed figure, that is, a triangle.187 The vocabulary used in passages where 2R is said to be per se-related to triangle, but not to isosceles, is close to the vocabulary used in the discussion of per se4 connections in APo I 4. As we have seen, Aristotle affirms that 2R belongs to triangle 'in itself' in the sense that whatever has the property 185 Smith (2009, p. 60) gives a helpful example: 'it can be proved that every isosceles triangle has 2R as follows: bisect the triangle's base and connect this to its opposite vertex, producing two congruent triangles. Invert one of these halves and join it to the other, producing a rectangle. It is then evident that the angles of the two triangles add up to four right angles, so the angles of each add up to two. From Aristotle's perspective, this is not really a demonstration since it cannot explain why all triangles have 2R, even though all triangles do have 2R.' 186 Of course, just failing to capture the appropriate kind-term (from an explanatory point of view) is not enough to classify an explanation as 'sophistic'. What makes an explanation sophistic is the intention of producing a false appearance of knowledge and wisdom. On this, see Hasper (2006); Angioni (2016). 187 For similar views, see Lennox (1987, p. 91); Kosman (1973, p. 375); Hasper (2006); Angioni (2007a; 2014b, pp. 9798; 2014c; 2016). 119 2R has it 'in virtue of' ( ) triangle, whereas triangle has 2R 'not in virtue of something different' ( ).188 If this is the kind of explanatory relation underlying Aristotle's characterization of the per se4 connection, we can say that 2R is per se4-related to triangle, but not to its subspecies: for any S that has 2R, S has 2R in virtue of being a triangle and independently of being an isosceles, equilateral or scalene figure. As we have seen, Aristotle argues that demonstrable propositions like (vii) – 'every triangle has 2R' – are prior to sentences like (viii) – 'every isosceles triangle has 2R'. The reason is that, for every demonstrable attribute, there is one subject-term which is the most qualified to occur in the corresponding (demonstrable) proposition. The per se4 connection, if understood as we propose, can be used to explain this aspect of Aristotle's theory. If a per se4 connection holds between two predicates P1 and P2, whatever is P2 is so in virtue of being P1, and hence must fall under denoting phrases such as 'the P1' or 'every P1'. Thus, if a sentence expresses a per se4 connection, its grammatical subject must be a denoting phrase that is explanatorily related to the predicate in question in the precise way we have described. As we have argued, per se accidents such as 2R are per se2 predicates of the objects of which they are predicated. For instance, sentence (viii) – 'every isosceles triangle has 2R' – is demonstrable insofar as it expresses per se2 connections between 2R and every isosceles triangle. However, only propositions that also exhibit a per se4 connection can be considered the primary demonstranda of science, since they have as their grammatical subject a denoting phrase that not only comprises all (and only) the actual instances of the predicate, but also stands for a set of features that are explanatorily linked to it. This is the case of sentence (vii), which, in virtue of having the denoting phrase 'every triangle' as its grammatical subject, not only expresses per se2 connections between 2R and all the figures to which 2R belongs (i.e. all triangles), but simultaneously signifies a per se4 connection between being a triangle and having 2R. If our interpretation of the nature of per se4 connections is correct, the corollary of alternative A2 does not follow. In fact, it would be false to say that if P is per se4-related to S and S is per se1-related to S', then P would be per se4-related to S'. There is a per se4 connection between being a triangle and having 2R. However, although being a triangle is a per se1 predicate of isosceles triangles, there is not a per se4 relation between having 2R and being isosceles. Therefore, we have our solution to problem (C): when Aristotle affirms that 2R is per se-related to triangle but not to isosceles or equilateral, he has a per se4 connection in mind, which is the kind of per se relation that enables him to take sentences like (vii) – and not (viii) – as primary demonstranda. 188 See APr I 35, 48a 33-36. 120 The most natural reaction to texts like Ph. I 3, 186b 18-23, and our T37, T38 and T39 is to take per se accidents to be per se2 predicates, as several interpreters have done. However, Aristotle's paradigmatic example of a per se accident in T35 (2R predicated of triangles) seemed to challenge this view. We advanced an interpretation that maintains the natural reading of those passages and explains how 2R could be taken as a per se2 predicate of triangles. In our interpretation, the number of sentences that can be interpreted as expressing per se2 connections is significantly larger than alternative interpretations would be able to admit, rendering Aristotle's theory richer and more likely to apply to actual scientific cases. In addition, it is perfectly possible to make sense of T37, T38 and T39 without excluding per se4 connections from the scope of science: sentences like (vii) – 'every triangle has 2R' – express per se2 connections between 2R and triangles and a per se4 connection between the predicates being a triangle and having 2R. The per se4 connection is not only relevant, but crucial to Aristotle's theory, since it enables him to distinguish between primary and secondary demonstrable propositions. In fact, it seems Aristotle tried to make this point explicit in T37: 'with respect to what is knowable without qualification, whatever is said to hold of things in themselves (in the sense of inhering in what is predicated or of being inhered in) is also said to hold of them because of themselves [ ]' (APo I 4, 73b 16-18).189 Sentences like '5 is odd' and 'every isosceles has 2R' are under the scope of science, but only propositions like 'every triangle has 2R', which signify both per se2 and per se4 connections, are scientific 'without qualification.' This picture helps us determine which model of essence-based explanation Aristotle endorses. As we have said, the Natural Solution to the problem of per se accidents is in accordance with the A-Model. The definitions of per se accidents, understood as a per se2 predicates, contain a reference to their proper subjects. If so, we can affirm that the relation between a subject and a demonstrable attribute is part of the essence of the attribute. Interpretations A1 and A2 are more sympathetic to the S-Model: per se accidents would either be part of the essence (A1) or follow from the essence (A2) of the subject. Since we have argued in favour of the Natural Solution, we are committed to the view that the relation between a subject and a demonstrable attribute is somehow part of the way of being of the attribute, which is why the subject is mentioned in the attribute's definition.190 If our interpretation is correct, in addition to significant textual evidence from APo II, the notion of per se accident in APo I also corroborates the A-Model. 189 Passage T37 seems to imply that sentences expressing per se1 connections can also signify per se4 connections, if they are knowable 'without qualification'. Aristotle's words in T37 seem to make sense: lines have points precisely in virtue of their being lines (the same seems to be true of other per se1 predicates). Of course, in our interpretation, per se1 predications are first principles of science, and hence knowable not by demonstration. On the other hand, sentences expressing per se2 connections are knowable by demonstration. If, in addition, they also signify a per se4 connection, they are knowable by demonstration and 'without qualification' (i.e. as a primary demonstrandum). 190 See Bronstein (2016a, pp. 46-50). 121 Nevertheless, we have also seen that if a (linguistic) predication is a primary demonstrandum, it has as its (grammatical) subject a denoting phrase (e.g. 'every triangle') containing a predicate that is explanatorily connected to the demonstrable attribute in question (e.g. '2R') in a precise way: the corresponding (metaphysical) predicates (e.g. being a triangle and having 2R) are per se4-related. If triangles have 2R in virtue of being triangles, there is a sense in which the S-Model is also part of this picture. Although the essence of 2R involves its being predicated of rectilinear figures of a certain sort (namely, triangles), the occurrence of 2R in those figures is also grounded in their essence: if they were not essentially three-sided rectilinear closed figures, 2R would not be predicated of them as a demonstrable attribute. If we are right, Aristotle endorsed both the Aand the S-Model. However, several questions must be raised: Are these patterns of explanation incompatible or complementary? Could there be two (or even more) alternative and independent explanations of the same phenomenon? Or can the essences of subjects and attributes be parts of the same coherent causal story? 122 123 CHAPTER 5 EXPLANATION, ESSENCE, AND PRIMARY UNIVERSALITY 5.1 – Two Problems in Posterior Analytics II 16-17 Few chapters of the APo are as elucidating as II 16-17. Aristotle spells out, with helpful examples, what kind of syllogism can be taken as a full-fledged demonstration – i.e. a demonstration of the 'primary universal' – and what kind of explanatory role definitions play in demonstrative arguments. However, these chapters also present us with at least two major difficulties. (1) In APo II 16, Aristotle raises the question of whether a scientific explanandum always entails and is explained by the same explanans (98a 35-98b 2). As we shall see below, the philosopher discusses two hypothetical scenarios, each of which leads to different answers to this question (98b 25-28). In the first of them, different middle terms play the role of explanans depending on the subjects of which the explanandum attribute is predicated. Thus, the answer to the question raised in APo II 16 would be negative. In the second scenario, the demonstration is of the 'primary universal': the major and minor terms of a syllogism are coextensive, which entails that the major (explanandum) and the middle term (explanans) also counterpredicate (since demonstrations of this kind are in Barbara). In APo II 17, the philosopher goes on to argue that in proper scientific contexts – in which we demonstrate something 'in itself' ( ) – there cannot be several explanantia of the same explanandum. Hence, only instances of the second scenario, in which the three terms of the syllogistic demonstration are coextensive, would be properly scientific. If so, Aristotelian 124 demonstrations seem to be restricted to very specific kinds of phenomena, while certain explananda we would like to admit as truly scientific – some of which considered by Aristotle himself in APo II 17 – would be out of the scope of science. (2) It has been argued that in APo II 16-17 Aristotle advances two different (and potentially incompatible) models of scientific explanation, which correspond to what we have been calling the 'S-Model' and the 'A-Model.' Michael Ferejohn (2013), for instance, claims that these chapters present 'two alternative ways of explaining' the fact that certain plants shed their leaves.191 According to Ferejohn (2013, p. 104), lines 98a35-b4 favour the S-Model: broad-leaved plants are deciduous precisely because they 'have broad leaves' ( ). This is, Ferejohn argues, Aristotle's 'canonical' model of scientific explanation: the demonstrable attributes of a given subject are explained by the subject's essence. However, lines 98b 36-8 and 99a 23-29 support the A-Model, which Ferejohn would describe as a 'non-canonical' pattern of explanation: the explanans (coagulation of sap) is the essence (or rather the causal or explanatory part of the essence) of the explanandum attribute (deciduousness). In the following, I shall argue that Aristotle's solution to the first problem involves showing that certain problematic attributes, which appear to admit more than one explanation, actually fall into the privileged scenario of primary-universal demonstrations. In addition, his solution suggests a conciliatory way-out to our second problem (or so I shall argue): both the essence of subjects and the essence of demonstrable attributes can play explanatory roles in demonstrations. I shall indicate how these results are underpinned by two of Aristotle's views on essence and causation: (i) causal or explanatory connections have a three-fold configuration, which means that one cannot evaluate whether a feature x is the primary explanation of a feature y unless the relevant domain of objects for the occurrences of x and y is properly specified; (ii) the existence of a demonstrable attribute as a unified phenomenon (i.e. as having such and such essence) depends on its subject having the essence it has. 5.2 The Uniqueness Requirement Aristotle begins APo II 16 interested in knowing whether every 'occurrence' of an attribute – the verb used is ' ' – that can be scientifically explained involves the occurrence of its putative explanatory factor (APo II 16, 98a 35-36). In other words, does the explanandum always entails its explanans? We can formalize the question in the following way: Q1: ∀x∀y((x is explanatory of y) → (y occurs → x occurs)) [?] 191 Ferejohn (2013, p. 149). 125 In APo II 16, 98b 2-4, a second question, apparently less controversial, is added. It concerns sufficient causality as it is usually conceived: given a certain cause, does its effect follow? Q2: ∀x∀y((x is explanatory of y) → (x occurs → y occurs)) [?] If affirmative answers are given to both of these questions, there will be a mutual entailment between explanans and explanandum: given a certain cause, its effect follows (affirmative answer to Q2) and, given a certain effect, its putative explanation occurs as well (affirmative answer to Q1).192 The use of ' ' without a dative in 98a35-b4 may suggest that, for Aristotle, causation (or 'being explanatory of') is a relation that takes place between events or processes. However, the next lines make it clear that 'x is explanatory of y' is short for 'x is explanatory of y for z'193 – that is to say, we have to consider not only the 'cause' ( ) and 'that of which it is cause' ( ) or 'the thing caused' ( ), but also the subject or subjects 'for which it is cause' ( ).194 In the same vein, an expression such as 'x/y occurs' ( ) is short for 'x/y holds of z' or 'x/y is predicated of z' ( plus dative). In fact, the introduction of a third item in the analysis of causal relations is a crucial part of Aristotle's solution to the problems addressed in APo II 16-17. In 98a35-b24, for instance, the philosopher is concerned with the following difficulty: do affirmative answers to Q1 and Q2 entail that 'being explanatory of' is a symmetrical relation? His tripartite analysis of causation allows him to approach the problem in syllogistic terms. If x and y entail each other, one can prove syllogistically that 'x holds of z' from the premise 'y holds of z' and vice-versa (98b 4-5). Let us say, for instance, that being a broad-leaved plant is the reason why vines are deciduous. If Q1 and Q2 are answered affirmatively, one could formulate the following two syllogisms (98b 5-16): Syllogism X: Deciduousness holds of all broad-leaved trees, Being a broad-leaved tree holds of all vines Deciduousness holds of all vines Syllogism XI: Being a broad-leaved tree holds of all deciduousness trees, Deciduousness holds of all vines Being a broad-leaved tree holds of all vines In this passage, Aristotle addresses the mistake of taking both X and XI as demonstrative syllogisms. In demonstrations, the middle term explains why the major term is predicated of the minor. Hence, if X and XI were both demonstrative syllogisms (in the strict sense of the term), the 192 Barnes (1993, p. 252) notes that, in APo II 16, Aristotle is not interested in temporal relations between explanans and explanandum (like in APo II 12), but in logical relations. 193 See Barnes (1993, p. 252). 194 Angioni describes this as 'the triadic structure' of scientific explanations. See n. 25. 126 attributes deciduousness and being a broad-leaved tree would be 'mutually explanatory' ( , 98b 17). However, says Aristotle, 'an explanation is prior to what it is explanatory of' ( , 98b 17). Since priority is an asymmetrical relation195, the relation 'being explanatory of' is also asymmetrical. By arguing that explanatory relations are asymmetric, Aristotle points out that, in demonstrations, the priority of the premises over the conclusion goes beyond mere inferential connections between them: although the properties being a broad-leaved tree and being deciduous entail each other, the former is explanatory of the latter, but not the other way around, which means that only Syllogism X is of 'the reason why' ( ς, APo I 13, 78a 28-b4; II 16, 98b 19-21). As has been noted, in APo II 16-17, Aristotle takes Q2 as uncontroversial.196 From 98b 25, the focus is on Q1 or, more specifically, on a different (and in a certain way more relevant) problem related to it. Let us say that, in a given context c1, x is the putative explanans of the explanandum y. If there is a context c2 in which y occurs without x occurring, there must be a different item z which is explanatory of y in c2. Thus, if Q1 is answered negatively, it follows that an explanandum can be explained by different explanantia. This motivates Aristotle to address the following requirement: Uniqueness Requirement (UR): ∀x∀y((x is explanatory of y) → ∀z(z is explanatory of y → z = x)) Of course, Aristotle recognizes that a demonstration may be composed of several syllogistic inferences, which happens when one or more of the premises that contribute to explain the conclusion are themselves demonstrable.197 If so, all middle terms of such a syllogistic chain may be said to be 'explanatory of' the conclusion in a certain sense. However, in II 16-17, as well as in other key passages of the APo, Aristotle has a stronger explanatory connection in mind, in which the explanans is not something that merely contributes to explain the explanandum, but the determinant causal factor in virtue of which the explanandum is the case – or the 'primary middle term' ( , 99a 25).198 In the rest of APo II 16-17, the philosopher argues that every phenomenon susceptible to scientific explanation has a 'primary middle term' satisfying UR.199 Let us now examine Aristotle's strategy. 195 See Cat. 12, 14a 29-35; 14b 11-22; Metaph. V 11, 1019a 1-4; VII 10, 1034b 30-32; 1035b 6-7. 196 See Barnes (1993, p. 252). 197 APr I 23, 41b 18-20; APr II 18, 66a 17-18; APo I 19-22. 198 What Aristotle calls the 'primary middle term' is probably the one which produces – as defined in APo I 2, 71b 9-12 – by apprehending the primary of a given . 199 It is worth saying that UR is compatible with APo I 29, where Aristotle claims that 'it is possible for there to be several demonstrations of the same thing' (87b 5). As Barnes (1993, p. 191) argues, Aristotle shows, at best, that there 127 In the last part of APo II 16, Aristotle discusses UR in two hypothetical scenarios (98b 25-28). In the first of them, the same explanandum attribute belongs to distinct subjects, each of which relates to distinct explanantia (APo II 16, 98b 25-29). Let us call it the 'multiple causes' scenario or 'MC-scenario.' For instance, if a single attribute A is predicated of distinct subjects D and E, nothing prevents us from elaborating two demonstrative syllogisms with also distinct middle terms, B and C respectively: AaB, BaD AaC, CaE AaD AaE If C and B are incompatible but equally adequate explanations for the major term A, UR is not satisfied. Later on, in APo II 17 99b 5-7, Aristotle seems to exemplify the MC-scenario: 'the explanation of longevity for quadrupeds is their not having bile, while for birds it is their being dry (or something else):' Syllogism XII: Longevity holds of absence of bile, absence of bile holds of quadrupeds Longevity holds of quadrupeds Syllogism XIII: Longevity holds of having dry bodies, having dry bodies holds of birds Longevity holds of birds The longevity of quadrupeds cannot be explained by the same item used to explain the longevity of birds.200 Therefore, at least at first sight, none of the explanations of longevity satisfies UR. Next Aristotle discusses a second scenario in which the explanandum entails the occurrence of the same explanans – I shall call it the 'one-cause scenario' or 'OC-scenario': 'or if problems are universal, then must the explanation be some whole and what it is explanatory of be universal?' (APo II 16, 98b 32-33).201 Aristotle brings up here the notion of 'universal problem.' 'Problem' translates the Greek ' probably in its technical sense of APo II 14, i.e. the conclusion of a demonstrative syllogism whose premises provide its adequate explanation. The meaning of 'universal' ( ), on the other hand, is not as clear. However, a case can be made can be several valid arguments for the same conclusion, which suggests that the term ' ' is being used in a weaker sense. 200 I shall take for granted, as the intelligibility of the example requires, that the minor 'quadrupeds' denotes all the objects for which longevity is a consequence of the absence of bile. The example is problematic. First, this explanation would work only for some quadrupeds – perhaps blooded quadrupeds (see PA IV, 677a 30-b10) or quadrupeds without gall bladders (see Ferejohn 2013, pp. 104-105). Second, in PA IV 2, 677a 30-35, Aristotle recognizes that also among dolphins longevity is caused by absence of bile. We should not assume that the examples express Aristotle's own scientific views. In one of his best-known examples of scientific explanation, thunder is said to be caused by fire being extinguished in the clouds, which is not the view he advances in Mete. II 9, 369a 14-369b 4. At any rate, the inadequacy of the example does not affect Aristotle's philosophical point. 201 Barnes' (1993) translation with changes. 128 for the following interpretation: the example – deciduousness predicated of broad-leaved plants (APo II 16, 98b 32-33) – suggests that 'universal' refers to the concept introduced in APo I 4, 73b 25-27. As we have argued, the notion in question is more properly called ' ' or 'primary universal' (see APo I 5, 74a 4-6; II 17, 99a 33-35) – although Aristotle himself is flexible with his vocabulary.202 What is particularly relevant in the context of APo II 16-17 is that, among other intensional features, the attribute is coextensive with the subject it belongs to (see APo I 4, 73b 32-39; II 17, 99a 33-35). In fact, the role played by the concept of primary universality is, among other things, to require scientific explanations to cover all instances of the attribute taken as explanandum. Suppose that distinct subjects D and E are both members of a kind F and that A belongs not only to D and E, but to all Fs and nothing more. Thus, it is reasonable to seek for a single middle term explaining why all Fs are A. If there is such a term (let it be G), D and E would be A insofar as they are F or, put in Aristotelian terms, A would not belong 'primarily' to D and E (see ' ' in 98b 27) but 'primarily' to their common kind F.203 In this case, the demonstranda 'AaD' and 'AaE' would not fall into our MC-scenario, since a syllogistic proof of greater explanatory power would be available: AaG, GaF AaF Primary-universal demonstrations explain all occurrences of the explanandum attribute in a single syllogistic argument. If all its occurrences can be explained at once, there must be a single cause for all them. In this scenario, a simple syllogistic deduction can establish a mutual entailment between explanans and explanandum. In Barbara, the sole syllogistic mood that proves universal affirmative sentences, co-extensiveness between major and minor terms entails co-extensiveness between the major and the middle (see APr II 5). Thus, in a demonstration with a primary-universal conclusion, in which major and minor terms counterpredicate, the major (explanandum) and the middle (explanans) counterpredicate as well. In APo II 16, Aristotle's example of such syllogism runs as follows: Syllogism XIV: Deciduousness holds of coagulation of sap, coagulation of sap holds of all broad-leaved trees Deciduousness holds of all broad-leaved trees 202 See APo I 4, 73b 25-74a 3; I 24. 203 I am following Barnes (1993) in translating these occurrences of ' ' with adverbial locutions – 'primarily', where Barnes has 'primitively' – for the sake of the clarity and fluency. However, it might be useful to have in mind that ' ' qualifies the subject-term of categorical sentences occurring in demonstrations, and is being used here to specify the relation that the major term has with the middle and the minor terms. 129 The conclusion of the syllogism states a primary-universal predication, i.e. the phenomenon of deciduousness is considered in all its instances (i.e. all broad-leaved trees), not only in vines or figtrees (APo II 16, 98b 5-10; II 17 99a 23-26). In this case, the explanation is 'some whole' ( , 98b 32) or, as Ross (1949, p. 667) puts it, 'the whole and sole cause of the effect.' That is to say, the middle term (coagulation of sap at the connection of the seed) holds of and (more importantly) explains all instances of the major. Predicates such as '2R' and 'deciduousness' are, in Aristotle's words, 'determined to some whole' ( , 98b 33), i.e. they are restricted to a domain of objects that can be grasped by a single kind-term (the item), which clears the way for a single, unifying explanation (the ). As we have seen, Aristotle addresses Q1 and UR introducing a third item ( ) in his analysis of causal connections: the subject (or subjects) to which the -attribute belongs primarily ( ). At first sight, it seems that UR is satisfied or not depending on how the -term (minor) relates to the other two, the (middle) and the (major). When the demonstration is of the – and minor ( ) and major terms ( ) are coextensive –, there is a single middle term ( ) which not only is coextensive with the major, but also (and more importantly) explains all its instances. On the other hand, when the relation between the major ( ) and the minor term ( ) is not one of primary-universality, nothing seems to prevent us from demonstrating the same explanandum/major term with two syllogisms with distinct middle terms as explanantia. 5.3 Aristotle's Answer and the Two Models of Scientific Explanation In APo II 17, Aristotle goes on to state the conditions under which UR is satisfied. [T40] Can it or can it not be the case that what is explanatory of some feature is not the same for every item but different? If the conclusions have been demonstrated in themselves, and not in virtue of a sign or incidentally, then perhaps the explanations cannot be different (for the middle term is the account of the extreme); but if they have not been demonstrated in this way, perhaps they can be different [APo II 17, 99a 1-4; Barnes 1993, with changes]. An answer to the question raised in 99a 1-2 depends on the way the explanandum attribute is demonstrated to belong to its subject. Can there be different explanations of the same item? If the conclusion is proved in itself ( ), the answer is negative. If it is demonstrated in virtue of a sign 130 ( ) or incidentally ( ), nothing prevents the existence of several explanantia for the same attribute. As we know, Aristotle uses the expression ' ' to refer to authentic demonstrative knowledge, in opposition to the mere pretence of knowledge labelled as ' '.204 Is Aristotle claiming that only phenomena falling into the OC-scenario are scientifically explainable? Would not it be possible to admit explananda such as longevity as properly scientific by arguing that, in those cases, there is a single explanans for them in restricted domains (quadrupeds in one case, birds in the other)? Could not we understand the minor terms as imposing a domain restriction in Syllogisms XII and XIII? After all, what is being sought is an explanation for longevity in quadrupeds in one case and in birds in the other. If there is a single item explaining longevity in each of those domains (not having bile and being dry respectively), would not be too demanding to say that here 'something else will be explanatory' (APo II 16, 98b 1-2)? Answering these questions requires identifying what Aristotle takes to be the most determinant feature of authentic demonstrative knowledge. When the conclusion of a syllogism is demonstrated ' ', says he, the middle term is the definition ( ) of the extreme (99a 34). Again, is the middle the of the major or of the minor term? Is the cause ( ) the essence of the attribute of which it is cause ( ) or of the subject for which it is cause ( )? Michael Ferejohn (2013) has argued that Aristotle does not answer this question consistently in the APo. According to the author, lines 98a35-b4 favour the S-Model: broad-leaved plants such as vines and fig-trees shed their leaves precisely because they are broad-leaved ( ). Thus, the would be the essence of the subject and the middle term, the definition of the minor term: Syllogism XV: Deciduousness holds of Def(broad-leaved tree), Def(broad-leaved tree) holds of all broad-leaved trees Deciduousness holds of all broad-leaved trees However, as we have seen, what predominates in book II of the APo is what Ferejohn claims to be a 'non-canonical' model of scientific explanation:205 the is the essence (or the 204 APo I 2, 71b 9-12; I 4, 74a 1-3; I 5, 74a 25-32. Proofs 'in virtue of a sign' are not properly explanatory, since they establish the truth of its probandum through one of its consequences (one that is more easily perceived than the probandum itself). See APr II 27. Ross (1949, p. 669) also quotes APo II 8, 93a37-b3 as providing an example of such a proof. I will not discuss in detail the use of the expression ' ', since it is usually absent from Aristotle's most relevant accounts of scientific knowledge, while the concept of ' ' is often characterized in opposition to that of ' .' For more accurate accounts of this opposition, see Hasper (2006) and Angioni (2016). 205 Ferejohn (2013, pp. 131-155). 131 causal part of the essence) of the -attribute.206 Chapter II 17 is no exception to this pattern. The following passage is particularly eloquent: [T41] The middle term is an account of the first extreme (which is why all sciences come about through definitions). Shedding leaves both follows vine and exceeds it, and it follows fig and exceeds it – but it does not exceed all of them: rather, it is equal to them. If you take the primary middle term, it is an account of deciduousness. For there will be first a middle term in the one direction (that all are such-and-such); and then a middle term for this (that the sap coagulates, or something of the sort). What is deciduousness? – The coagulation of the sap at the connection of the seed [APo II 17, 99a 21-29; Barnes 1993, with changes]. Aristotle not only affirms that the middle term is the of the major term ( ), but claims that this is the reason why 'all sciences come about through definitions' ( , 99a 22-23). Quite emphatically, Aristotle seems to endorse the view that our Syllogism XIV (rather than Syllogism XV) is the one providing the primary explanation – the 'primary middle term' ( ) – of the fact that all broad-leaved trees shed their leaves: Syllogism XIV: Deciduousness holds of coagulation of sap, coagulation of sap holds of all broad-leaved trees Deciduousness holds of all broad-leaved trees An important thesis of APo II corroborates the A-model. As we have seen in Chapter 2, there is an isomorphism between the definition of an attribute and the explanation of its occurrence in the relevant subject. For instance, thunder is defined as a noise in the clouds caused by fire being extinguished. On the other hand, we explain why the noise we call 'thunder' is predicated of clouds through the middle term 'extinction of fire' (APo II 8, 93a 7-b14). This is our Syllogism VIII: Syllogism VIII: Thunder (or such-and-such noise) holds of extinction of fire, Extinction of fire holds of clouds Thunder (or such-and-such noise) holds of clouds 206 APo II 2, 89b 36 90a 14; 90a 31-35; II 8, 93a31-33; APo II 16, 98b 21-24; II 17 99a 21-22, 25-26. 132 The definition of thunder, in turn, is isomorphic to Syllogism VIII: Def. (Thunder): Thunder is(df.) noise of fire being extinguished in the clouds (APo II 10, 94 a 5-6). If this pattern is followed also in the case of deciduousness, its whole definition would be isomorphic to Syllogism XIV: Def. (Deciduousness): Deciduousness is(df.) the loss of leaves in broad-leaved trees caused by coagulation of sap. As we can see, the that plays the role of middle term in Syllogisms VIII and XIV is not the entire definition of the major term, but the causal or explanatory element in it. Still, the middle term is a specification of the attribute's essence – in fact, of the most determinant element of its essence.207 Therefore, the A-Model is definitionor essence-based no less than the S-Model.208 Still in favour of the A-model, one could argue that there is no textual evidence for us to assume that Aristotle is committed to the S-model in APo II 16. When in 98a 35-b4 Aristotle presents 'having broad leaves' ( ) as the of deciduousness, he probably has in mind our Syllogism X, formulated in 98b 5-10 – and not Syllogism XV as Ferejohn (2013, p. 104) supposes. Syllogism X: Deciduousness holds of all broad-leaved trees, Being a broad-leaved tree holds of all vines Deciduousness holds of all vines Syllogisms of this sort have been called 'application arguments.'209 One way of approaching these arguments is to take them not as properly explanatory, but as mere classificatory inferences meant to 'upgrade' non primary-universal problems into primary-universal ones. The deciduousness example is an instance of the OC-scenario. Since a problem with coextensive terms such as 'deciduousness holds of all broad-leaved plants' is available, sentences like 'deciduousness holds of all vines' or 'deciduousness holds of all fig-trees' are not 'primary demonstranda' – i.e. sentences in which the predicate belongs primarily ( ) to the subject. In APo II 18, Aristotle generalises a rule that was already implied in T41: it would be wrong to demonstrate a non-primary-universal conclusion such as 'deciduousness holds of all vines' with the of deciduousness as the middle term. Aristotle begins the chapter affirming that not all scientific problems are explainable directly 207 Williams & Charles (2013, pp. 122-124). 208 Cf. Ferejohn (2013, p. 155), who seems to assume that only the 'canonical' model is essence-based or definitionbased, whereas the 'non-canonical' or 'causal' model would at best 'generate definitions.' 209 See McKirahan (1992, pp. 177-187); Ferejohn (2013, pp. 122-131). Application arguments are called 'type A' syllogisms by Lennox (1987). 133 by 'atomic' (i.e. immediate) premises ( , 99b 7). As we know, demonstrations may be composed of several syllogistic inferences and contain premises that are themselves demonstrable. Therefore, in the deciduousness example, the first deductive step of the demonstration ( 99a 26) – 'first' in the 'analytic' or 'proof-search' order, i.e. from the conclusion to the premises –, subsumes 'vine' under the wider kind 'broad-leaved tree' ( , 99a 26-27). Hence, the major premise of this first inference would state a primary-universal demonstrandum ('deciduousness holds of all broad-leaved plants') and only then ( , 99a 27) the 'primary middle term' ( , 99a 25) – the of deciduousness – becomes part of the demonstration: (Extended) Syllogism (X + XIV) Deciduousness holds of coagulation of sap, coagulation of sap holds of all broad-leaved trees Deciduousness holds of all broad-leaved trees Deciduousness holds of all broad-leaved trees, Being broad-leaved holds of vines Deciduousness holds of all vines Not only is the presence of the S-Model in APo II 16-17 questionable, but also the Amodel appears to serve the purpose of these chapters more successfully. From APo II 8, it is clear that Aristotle takes the definiendum and the causal part of its definiens as coextensive.210 Thus, if the explanans is the causal element in the definiens of the explanandum attribute, affirmative answers to Q1 and Q2 are mere corollaries of this definitional tie. Moreover, the A-model is part of Aristotle's reply to those willing to take coextensive middle and major terms as reciprocally explanatory (see APo II 16, 98b 4-16): if x is part of the definition of y (and if the definition of y avoids circularity), x and y cannot be mutually explanatory, x being used to clarify what y is, but not vice-versa (see APo II 16, 98b 21-24). Therefore, at first sight, our problem (2) does not seem to be that challenging (see Section 5.1). At least in APo II 16-17 – letting aside the question of whether this is the case in respect of the APo as a whole –, Aristotle seems to be committed not to two alternative models of explanation, but only to the A-model. However, this is just an apparent solution. Even if an 'application argument' such as Syllogism X is implied in 98a 35-b4, Ferejohn is right in recognising 210 Or at least within a restricted domain, determined by the minor term. See Barnes (1993, p. 253). The major premises in syllogisms such as XIV and VIII and the corresponding definitions yield this result: every deciduous plant undergoes coagulation of sap (from the definition of deciduousness) and every plant that suffers coagulation of sap is deciduous (major premise of Syllogism XIV). 134 the presence of the S-Model in the passage (or, at least, some modified version of it). Let us spell this out. The question of whether or not a predicate holds primarily of a given subject ( ) cannot be decided in purely extensional terms. If the scientist arbitrarily selects a term that counterpredicates with the -term, the demonstrandum does not immediately qualify as a problem. In APo I 5, 74a 25-32, Aristotle argues that the mere extensions of the terms involved in a demonstrative syllogism are not enough to warrant its scientific status. Let us say, for instance, that 2R is predicated of two different subjects: a simple one ('triangle') and a disjunctive complex one ('everything that is either equilateral or isosceles or scalene'). The extension of the subject 'everything that is either equilateral or isosceles or scalene' would cover all instances of 2R only 'in number' ( , APo I 5, 74a 31): although the disjunction exhausts the desired extension (extensional grasp), the objects it denotes are not described as members of a cohesive kind (intensional grasp), e.g. being a triangle.211 This intensional requirement becomes perfectly understandable if we assume that something along the lines of the S-Model underlies the notion of primary-universality. The reason why 'triangle' – and not some other coextensive term – is the proper subject-term for the predicate '2R' may lie with the fact that the definition of triangle plays an important role in explaining the 2R-theorem. Whatever has the attribute 2R has it independently of having two, three or none of its sides equal to one another (i.e. independently of being an equilateral, an isosceles or a scalene figure): a given figure may have the property 2R without being an isosceles (negative answer to Q1), which means that something else in this case must be explanatory.212 Rather, the demonstration of the 2R-theorem is meant to show how 2R is explanatorily related to a specific property (or cluster of properties) common to all objects that have 2R: being a three-sided rectilinear closed figure, i.e. being a triangle. If being a triangle is actually explanatory of certain figures having 2R, application arguments are not meant to promote minor classificatory adjustments. In fact, Aristotle's vocabulary makes it clear that the kind of upgrade accomplished by arguments such as Syllogism X are truly explanatory rather than merely taxonomic. If, as Aristotle affirms, the triangle has 2R 'not in virtue of something different' ( )213, one may argue that the reason why ( ) triangles have 2R is not something different from what it is to be a triangle, i.e. the essence of triangle. If this account is correct, we can say that the S-Model is viable after all. Additionally, a serious objection can be formulated against the A-Model. If the middle term of demonstrative 211 Lennox (1987, p. 91). 212 See Kosman (1973, p. 375); Hasper (2006); Angioni (2014b, pp. 97-98; 2014c; 2016). 213 APr I 35, 48a 33-36. 135 syllogisms is always the of the major term, a phenomenon such as longevity does not seem to be scientifically explainable, or even properly definable. When it occurs in quadrupeds, longevity is explained by absence of bile, whereas its presence in birds is explained by their bodies being dry or something similar. Since one and the same item cannot have two alternative and incompatible definitions, attributes such as longevity would not be scientifically definable or explainable. However, why would Aristotle – who devoted a whole treatise to the topic: De Longevitate et Brevitate Vitae – exclude an attribute such as longevity from the scope of science? This question brings us back to our problem (1), raised in Section 5.1. As Aristotle's solution to it sheds some light on (2) as well, I shall first concentrate on (1), which is the topic of our next section. 5.4 The appearance of 'multiple causes': 'in-a-kind' and homonymous explananda. In order to understand Aristotle's solution to our problem (1), it is worth mentioning some of the views set out in APo II. As we have seen in Chapter 2, Aristotle claims that a question of the form 'does P holds of S?' (Q1) is equivalent to 'does P exist?' (Q3.1), whereas a question like 'why does P holds of S?' (Q2) is equivalent to 'what is P?' (Q4.1). We have also seen that Aristotle believes that questions Q1 and Q3.1 are reducible to a question about the existence of a middle term: (Q1*/Q3*) Is there an M such that PaM, MaS ⊦ PaS & M is the reason why PaS? On the other hand, we answer questions Q2 and Q4.1 by finding out what that middle term is: (Q2*/Q4*) What is M such that PaM, MaS ⊦ PaS & M is the reason why PaS? We have argued that, for Aristotle, asking question Q3.1 – 'Does P exist?' – is equivalent to asking whether there is a middle term M which could be used not only to explain why P belongs to its subject S, but also to formulate a unifying, causal definition of P. Hence, it would be wrong to take question Q3.1 as concerning the mere existence of an attribute. Actually, what is a stake is its existence as a definable unity or a genuine kind. That being said, let us analyse the solution Aristotle offers to our problem (1): [T42] . You can inquire incidentally both about what is explanatory of and about what is explanatory for – but such things are not thought to count as problems. Otherwise, the middle term will have a similar character – if the items are homonymous, the middle terms will be homonymous; and if 136 they are in a kind, the middle terms will have a similar character [APo II 17, 99a 4-8; Barnes 1993, with changes]. At least in this context, to investigate something 'incidentally' ( , 99a 5) is to approach a scientific problem inappropriately, as if it were a case of the MC-scenario. If, on the other hand, the scientist investigates something 'non-incidentally', ( , 99a 6), 'the middle term will have a similar character' ( ).214 In order to clarify the point, let us consider two syllogisms with non-coextensive extreme terms: AaB, BaD AaC, CaE AaD AaE Aristotle's examples suggest that the obscure phrase ' ' refers to two types of apparent (but not real) cases of the MC-scenario – and therefore two apparent (but not real) counterexamples to the validity of UR (99a 7-15).215 If A holds of D and E in a kind ( ), so A holds of B and C in a kind. If A holds of D and E as homonymous ( ), so A holds of B and C as homonymous. The first of these two situations is exemplified by the following problem: 'why do proportionals alternate?' (99a 8).216 Someone may commit the mistake of thinking that the explanation depends on the subjects considered: proportional numbers and proportional lines 'alternate' for different reasons (see APo I 5, 74a 17-24; I 14, 85a 36-b1). Aristotle believes, however, that a single explanation could be reached if numbers and lines were treated as members of a common kind ( ), i.e. not qua numbers or qua lines, but qua items having such-and-such ratio ( , 99a 10). The mistake consists in 'investigating the incidentally': minor terms D and E were mistaken for subjects to which A belongs 'primarily' ( ), when in fact D and E are A not in themselves, but as members of a wider-kind F, which is A 'not in virtue of something different' ( ).217 If so, the conclusions 'AaD' and 'AaE' can be upgraded, by application arguments, into a single demonstrandum with coextensive terms: 'AaF.' Moreover, if two subjects D and E are A 'in a kind', the respective middle terms B and C can also be replaced by a unifying 214 I here follow Ross (1949, p. 669), who argues, against most commentators, that ' ' in 99a 6 means 'if we study not the or the .' I take the future ' ' as consequential: a scientist who is dealing with an apparent case of the MC-scenario infers that the middle term has 'a similar character' as soon as she starts investigating the problem 'non-incidentally.' For a defence of the common reading, see Hasper (2006, p. 268). 215 In APo II 17, 99a 4-8, Aristotle also mentions a third case: explanations 'by analogy' ( ). Analogical explanations are neither about one attribute predicated of two subjects of the same kind, nor about two different attributes called by the same name (see Ross 1949, p. 670). The terms 'bone' and 'fish-spine' refer to quite different things, which nonetheless play the same function in the animals in which they are found (APo II 14, 98a 20-23). These explananda do not threat the validity of UR as homonymous explananda do, which explains why Aristotle mentions them very briefly without a proper discussion. See APo II 14, 98a 20-23. 216 That is to say: 'why is the case that if W is to X as Y is to Z, then W is to Y as X is to Z?' See Ross (1949, p. 525). 217 APo I 5, 74a 25-32; cf. I 2, 71b 9-12 137 middle term G: . For instance, deciduousness belongs to vines and fig-trees 'in kind' ( ). Hence, we should obtain a primary-universal demonstrandum in the major premise of an application argument such as Syllogism X before trying to propose a unifying explanation for the major term 'deciduousness.' Thus, any causal story about vines being deciduous that does not work for fig-trees as well can and should be improved by a wider explanation covering all instances of deciduousness (i.e. all broad-leaved trees), like in Syllogism XIV. Therefore, the violation of UR is merely apparent. However, not only the but also the term can be investigated incidentally' ( , 99a 5). In this case, a scientist may falsely believe that the conclusions 'AaD' and 'AaE' fall into the MC-scenario not because she did not realize that D and E are subspecies of a common kind F, but because D and E appear to be subjects of the same attribute, whereas in fact 'A' is an ambiguous term and holds of D and E homonymously. In the Categories, Aristotle defines homonymy as follows: 'when things have only a name in common and the definition of being which corresponds to the name is different, they are called homonymous' (Cat. I 1, 1a 1-2).218 Aristotle's notion of homonymy is not that of equivocality or ambiguity, though the former may be derived from the latter. Homonymy is a property of things in relation to a certain expression, while equivocality (or ambiguity) is a feature of the expressions themselves.219 Two subjects D and E are homonymous in relation to a certain expression 'A' when 'A' applies to both of them but each application is associated with different definitions of 'A'. Consequently, 'A' must be an ambiguous word if it applies homonymously to D and E. However, homonymy can obtain at different levels.220 In cases of what has been called 'strong homonymy', the expression 'A' has associated with it totally unrelated definitions, as when we apply the word 'bank' to disparate types of thing such as a riverbank and a financial institution.221 On the other hand, 'weak homonymy' occurs when the distinction between the different definitions of 'A' is more subtle. In this case, the two homonymous items D and E may share a property in virtue of which they are both called 'A' and consequently the corresponding definitions may also have something in common – though the complete definitions must obviously remain distinct if weak homonymy is to be case of homonymy at all.222 Aristotle's example in APo II 17 suggests that he has in mind this second and weaker kind of homonymy: 'similar' signifies different things when applied to figures and colours (APo II 17, 99a 11-15). Between figures, similarity means 'having proportional sides and equal angles' (99a 13-14), while between colours it means 'the fact 218 Ackrill's translation (1963). 219 See Ackrill (1963, pp. 71-72). 220 For a systematic discussion of those different levels, see Shields (1999). 221 See Wedin (2000, p. 13). 222 See Wedin (2000, pp. 13-14). See Zingano (2013), for a detailed discussion of what he calls 'attenuated homonymy'. 138 that perception of them is one and the same' (99a 14-15). Hence, figures and colours are homonymous in relation to the expression 'similar' and hence 'similar' is an equivocal term. However, there is no equivocality at the level of ordinary parlance, since the word currently means, regardless the items it applies to, a likeness or resemblance of a certain sort. Therefore, similarity is a case of weak homonymy. Scientific definitions are explanatory and involve more than a brief account of the current meaning of the definiendum term. At a scientific level of analysis, similarity in figures and in colours relates to very different sets of truth-conditions and explanatory factors. Thus, part of the process of defining something in contexts of weak homonymy is to realize that there is no single attribute to be defined (similarity without qualification), with two (or more) competing explanatory accounts, but actually two (or more) different attributes (similarity in figures and similarity in colours) with their own definitions and explanations. Apparently, the same diagnosis applies to the case of longevity.223 Aristotle believed that the phenomenon of longevity is realized in very different manners depending on the group of living-beings considered, in such a way that it becomes impossible for us to come up with a single explanation for all its instances.224 Being long-lived for a quadruped is so different from what being long-lived is for birds that we have different middle terms for the major 'longevity' in each case: 'absence of bile' and 'being dry' respectively. If the middle term is the causal part of the definition of the major, the term 'longevity' gets one definition when predicated of quadrupeds and another when predicated of birds. Therefore, longevity holds of quadrupeds and birds homonymously. Consequently, the respective middle terms 'absence of bile' and 'being dry', as long as they refer to very distinct ways of being long-lived, also have 'longevity' predicated of them in the respective major premises homonymously: . Again, this reasoning does not entail that 'longevity' is equivocal at the level of ordinary language. Rather, homonymy comes up only when we find out that there is no such thing as longevity without qualification that could be object of scientific definition. Rather, what can be defined in a scientific way are quite distinct attributes: longevity-for-quadrupeds (or Q-longevity) and longevity-for-birds (or B-longevity): Q-longevity is(df.) quadrupeds living long because of absence of bile. B-longevity is(df.) birds living long because of their bodies being dry. 225 223 I am indebted to Lucas Angioni and David Bronstein on this point. 224 See Long. 1, 464b 22-464b 25; 4, 466a1466a 8. 225 These definitions avoid circularity precisely because the definienda are specific kinds of longevity, 'living long' being an expression that accounts for what Q-longevity and B-longevity have in common (since this is not a case of strong homonymy). 139 If this interpretation is correct, longevity is not an explanandum that fails to satisfy UR. What appears to be a single explanandum attribute at the level of ordinary language gives way to two different attributes (Q-longevity and B-longevity), each of which holds of its subject (quadrupeds and birds) primarily ( ) and relates to one single item as its proper explanation (absence of bile and dryness respectively). If so, what appears to fall into the MC-scenario is actually an instance of the OC-scenario. Once we restrict the domains of the demonstrations in order to disambiguate the major term, what appeared to exemplify the MC-scenario turns out to be a case of the OC-scenario and no longer threatens the validity of UR. In other words, longevity (without any disambiguation) does not exist as a definable unity or a genuine kind, but Q-longevity and B-longevity do. As Aristotle makes it clear since the beginning of APo II, when a scientist attempts to define an attribute such as longevity, she does not seek for a vague and abstract account of the term 'longevity' covering its (standard) uses in ordinary speech. Rather, she is interested in knowing whether these uses refer to a single homogenous phenomenon, i.e. whether they are all associated with one and the same underlying cause. If not, it is possible to look for unifying causes in more restricted domains than the one assumed in ordinary language. In this case, either there will not be restricted domains in which UR is satisfied (and the phenomenon is not scientifically explainable) or the scientist will find herself dealing with several scientific explananda – instead of just one as everyday discourse makes it appear. Now, I shall explain how this picture invites us to pursue a conciliatory solution to our problem (2). 5.5 A Conciliatory Solution As we have seen in APo II 16, 98b 21-24, the priority of the explanans over the explanadum is illustrated in terms of an asymmetric relation of definitional dependence: thunder (the explanandum attribute) cannot be defined without mentioning extinction of fire (explanans), whereas extinction of fire can be defined without mentioning thunder.226 However, definitions of attributes contain reference not only to its explanans (e.g. extinction of fire), but also to its proper subject (e.g. clouds). Thunder cannot be defined without mentioning clouds, but clouds can be defined without reference to thunder. Can this definitional priority of subjects tell us something about the role their essences play (if any) in Aristotelian demonstrations? In Chapter 4, we have seen that, for Aristotle, definitions of attributes (i.e. nonsubstantial beings) must somehow account for their status as dependent entities.227 That is to say, 226 The example in the passage is the lunar eclipse, but the two cases are strictly parallel. 227 Metaph. VII 1, 1028a 35-36; VII 5, 1030b 23-24; APo I 4 73a 37-b5; II 2, 90a 14-18; II 10, 93b 38-94a 7. 140 ontological priority of subjects over their attributes would have definitional priority as its linguistic counterpart. We have also argued, following Peramatzis (2011), that the 'real' or 'metaphysical' correlate of definitional priority (PID) should be understood as PIB. An attribute P (a nonsubstance entity) is ontologically dependent on the relevant subject S (per se3 being, i.e. a substance or substance-like entity) in the sense that P does not have the essence it has (i.e. cannot perform the way of being that distinguishes it as such) independently of S having the essence it has. The way Aristotle deals with problem (1) corroborates this approach. After all, his solution involves arguing that a single term 'A' may stand for two (or more) different attributes, with different causal definitions, depending on the subjects of which it is predicated. In other words, attributes are not what they are and do not get the definitions they get independently of the subjects to which they belong primarily. Their identity is partially fixed by these subjects, on which their status as definable unities ultimately depends. For that reason, the definitions of Q-longevity, Blongevity and deciduousness should mention quadrupeds, birds and trees respectively. If quadrupeds were not the sort of animals they are, their longevity would not have absence of bile as its primary explanation (and, consequently, as the causal part of its definition). Similarly, if broad-leaved plants had not the essences they have, they would not undergo coagulation of sap, which is the process that makes deciduousness the unified phenomenon it is. Therefore, given that the essence of subjects is prior to the essence of attributes, guaranteeing a place for the definitions of attributes in demonstrative sciences and denying one for the definitions of their proper subjects seems, at best, uncongenial to Aristotle's philosophy. In fact, the structure of demonstrations allows definitions of subjects (as much as definitions of attributes) to play the role of explanatory middle term. As we have seen in our analysis of APo II 17, 99a 16-9, a complete demonstration may have the form of an extended argument with several syllogistic inferences. Moreover, the passage is also clear that it is not in every deductive step that the middle term is the of the major term. The demonstration may involve (as it does when it contains application arguments) further syllogistic steps in which the middle term is not definitionally connected to the major. In Syllogism XIV, for instance, the definitional connection between coagulation of sap and deciduousness makes the major premise 'immediate'.228 Nevertheless, the relation between coagulation of sap and broad-leaved tree in the minor premise remains demonstrable. Therefore, in a complete demonstration, this branch of the demonstration would go on until it reaches a middle term 'immediately' connected to broad-leaved tree, i.e. the of broad-leaved tree. Otherwise, the demonstration would proceed ad infinitum, since it would always 228 This result follow if we apply to the deciduous example what Aristotle says about the syllogism of the lunar eclipse in APo II 8, 93a 35-36. 141 contain at least one demonstrable premise (as we have seen in Chapter 3). If this is how a complete demonstration of the phenomenon of deciduousness should be, the pieces of textual evidence in favour of the Aand the S-Model are not incompatible, but complementary.229 The same pattern holds true mutatis mutandis for other examples. In the major premise of Syllogism VIII, thunder is said to follow the causal part of its definition, namely, extinction of fire. The minor premise, in turn, introduces a new demonstrandum: why do clouds undergo extinction of fire? Extinction of fire is what explains why thunder holds of clouds 'non-incidentally', i.e. why there is a regular connection between thunder and clouds. However, this could hardly be the case if extinction of fire were 'incidentally' connected to clouds. Thus, it would not be surprising if the nature of clouds were what directly or indirectly explains why, under certain conditions, fire is regularly extinguished in them. In other of Aristotle's favourite examples, the occurrence of the lunar eclipse in the moon is explained by the middle term earth screening (see APo II 8, 93b 3-7). Whereas the connection between eclipse and earth screening (the causal part of its definition) is 'immediate' (93a 35-36), the link between earth screening and moon, on the other hand, requires further explanation. According to Aristotle's cosmology, having the earth interposed between it and the sun is due to the location of the moon in the system of celestial spheres combined with its natural movement, which the philosopher would probably take either as essential to the moon or as features following from its essence. Finally, a combination of the Aand the S-Model is especially attractive in contexts of weak homonymy. In the major premise of Syllogism XII, for instance, the middle term absence of bile and the major longevity (which here stands for Q-longevity) are definitionally connected, whereas the connection between absence of bile and quadrupeds requires further premises in order to be fully understood. According to Aristotle, bile is a residue of impure blood that affects the conditions of the liver, which is a vital organ to quadrupeds in virtue of their being essentially blooded animals.230 Therefore, in an extended version of Syllogism XII, absence of bile in quadrupeds may be explained, directly or indirectly, by one or more of their essential features. This new perspective also corroborates our analysis of the intensional aspect of primary-universality. As we have seen, a disjunction of all deciduous trees ('everything that is vine or fig trees or oak ....'), despite covering (extensionally) the desired domain, would not work (intensionally) as a minor term in a primary-universal demonstration. The reason is the following: the essence or way of being on which the essence of deciduousness depends is the one picked up by the definition of broad-leaved tree. In other words, what ultimately explains why coagulation of the sap 229 This solution has been recently defended, with different arguments, by David Bronstein (2016a, pp. 48-51). 230 PA IV 2, 677a 30-677b 10. In this passage, Aristotle mentions very specific kinds of quadrupeds (and also dolphins). On the inadequacy of Aristotle's example, see n. 200 above. Nevertheless, we believe the philosophical point we attribute to him remains solid. 142 occurs to all deciduous trees is the essence displayed by a definition whose definiendum is neither 'vine' nor an exhausting disjunctive term, but 'broad-leaved tree'. For the same reason, we cannot explain why 'all isosceles triangles have 2R' with the definition of 2R as the middle term without first subsuming 'isosceles triangle' to the wider term 'triangle.' 'Triangle' is the sole term apt to occur as subject in the primary-universal demonstrandum because what is part of the demonstration of the 2R-theorem is the definition of triangle, not the definition of any of its subspecies. Ferejohn (2013, p. 151) rejects this kind of conciliatory solution on the grounds that it does not get support from Aristotle's texts. He argues that the philosopher never combines Syllogisms XIV and XV to formulate a complete demonstration, and this is what we would expect him to do if the S-Model and the A-Model were complementary to each other. However, Aristotle's aim in APo II 16-17 is to deal with problem (1), whose formulation and solution is under the influence of what can be taken as the main topic of APo II: the isomorphism between definitions and syllogistic demonstrations. Aristotle's favourite examples of this phenomenon are attributes or processes such as thunder, eclipse, and deciduousness. For that reason, the essence of attributes is under the spotlight, which explains why the A-Model stands out in comparison to the S-Model. Problem (2), on the other hand, does not seem to bother Aristotle, which suggests he endorsed both models as parts of the same coherent doctrine. We have tried to show how his own solution to problem (1) leads to the same result. 143 CHAPTER 6 COMING TO KNOW THE ESSENCE OF SUBJECTS 6.1 – The Essence of Subject-Kinds: An Exception? The different aspects of Aristotle's theory we have discussed in Chapters 3, 4, and 5 point to the same result: the S-Model and the A-Model are not antagonistic patterns of explanation; actually, the philosopher seems to endorse both of them as parts of the same coherent doctrine. The 'primary middle term' of P belonging to S – let it be 'M' – is the causal part of the definition of P (following the A-Model). However, the causal-definitional relation between M and P does not take place independently of S being what it is, since the identity of demonstrable attributes is partially fixed by their proper subjects – as becomes clear once we examine, for instance, cases of homonymy. The consistency and regularity that make P a demonstrable attribute of S (and, therefore, a genuine kind) depends on there being a more or less close connection between M (the causal part of the definition of P) and the essence of S, which will appear as a middle term at some point of the demonstration (in accordance with the S-Model). Consequently, a scientist does not have scientific knowledge of S being P – at least, not in the full sense of the term – if she does not know the essence of S. But how do scientists come to know the essence of subjects? It is time for us to address a problem we raised in Chapter 2. As we have seen, according to APo II 1-2, scientists investigate four kinds of question: 144 (Q1) Does P belong to S? (Q2) Why does P belong to S? (Q3) Does S exist? (Q4) What is S? Questions Q1 and Q2 concern the occurrence of an attribute in a given subject, whereas questions Q3 and Q4 concern the existence and essence of subject-kinds. In the order of inquiry, Q1 and Q3 are prior to Q2 and Q4, respectively. We cannot investigate why S is P (Q2) unless we already know that S is P (Q1). Similarly, it is not possible to determine what S is (Q4) without knowing in advance that S exists (Q3). We have argued that the distinction between subjects and attributes in APo II 1-2 should not make us think that questions about existence (like Q3) and essence (like Q4) are exclusive to subjects. Actually, the existence of an attribute P can be analysed as a predicative relation between P and its subject S. The essence of P, in turn, can be identified with the reason why S is P – as we can see in our T7, APo II 2, 90a 14-18. In addition, answering the question about the existence of P, understood as a question about its presence in a subject S, is the same as determining whether there is a middle term M explaining why P belongs to S. Finding out what P is, on the other hand, is the same as identifying M: (Q1) Does P holds of S? ≡ (Q3.1) Does P exist? ≡ (Q1*) Is there an M such that PaM, MaS ⊦ PaS & M is the reason why PaS? (Q2) Why does P holds of S? ≡ (Q4.1) What is P? ≡ (Q2*) What is M such that PaM, MaS ⊦ PaS & M is the reason why PaS? These equivalencies reflect two correlate theses we have attributed to Aristotle. The first of them is the interdependence between noetic and demonstrative knowledge, as argued in Chapter 1. Full-fledged demonstrative knowledge of a conclusion c requires noetic knowledge of the immediate premises p1 ... pn from which c is demonstrated. On the other hand, acquiring noetic knowledge itself requires some demonstrative practice: to know a first principle pi as such involves realizing (i) that there are propositions (such as c) that can be demonstrated from pi and (ii) that there are no propositions from which pi can be demonstrated. The second thesis is closely related to the first: the interdependence between defining and explaining, as discussed in Chapter 145 2. Definitions (objects of noetic knowledge) become known as such insofar as they are seen as explanatory of demonstrable propositions (objects of demonstrative knowledge). After all, definitions are 'revealed' by demonstrations (APo II 8, 93b 17-18) and in fact are described by Aristotle as demonstrative syllogisms 'differing in arrangement' (APo II 10, 94a 2). The interdependence between noetic and demonstrative knowledge, defining and explaining, helps us understand the equivalencies between Q1, Q3.1, and Q1*, on one hand, and Q2, Q4.1, and Q2*, on the other. Acquiring noetic knowledge of the essence of P requires the ability to explain, in a demonstrative syllogism, why P belongs to its subject S. For instance, we grasp the complete definition of thunder – thunder is(df.) noise of fire being extinguished in the clouds (APo II 10, 94 a 5-6) – when we discover a middle term that can be used to explain why the noise we call 'thunder' is predicated of clouds. To know that there is such a middle term (Q1*) is to know that 'thunder holds of clouds' is a demonstrable proposition (Q1) and that thunder exists as a genuine kind (Q3.1) – i.e. that it happens with the kind of regularity that implies an underlying causal factor. When we find out what that causal factor is (Q2*), we grasp at once the reason why thunder occurs to the clouds (Q2) and the essence of thunder (Q4.1). What about subjects? How should scientists investigate Q3 and Q4? One reaction to this question is to affirm that subjects and their essences constitute an exception to the interdependence between defining and explaining. The following passage may suggest that Aristotle himself admits such an exception: [T43] Of some things there is something else which is their explanation, of others there is not. Hence it is plain that in some cases what something is is immediate and a principle in relation to which we must assume or make clear in some other way both that the thing exists and what it is. (Arithmeticians do this: they suppose both what a unit is and that there are units.) But in cases where there is a middle term and something else is explanatory of its being, you can – as we have said – show what something is through a demonstration without demonstrating what it is [APo II 9, 93b 21-28; Barnes 1993, with changes].231 Here Aristotle affirms that only the essence of things 'whose cause is something else' is made clear through demonstrations. Some interpreters claim that T43 is meant to show that the 231 Deleting Ross' comma in 93b 22, which implies that only definitions of things 'whose cause is not something else' are immediate and principles. 146 interdependence between defining and explaining holds good for the essence of processes and attributes such as thunder and eclipse, but not the essence of substances such as human beings or broad-leaved plants.232 David Bronstein, for instance, argues that the essence of attributes are 'causally complex', having a structure of the form 'A holds of C because of B' – e.g. the being of thunder can be reduced to a predicative relation between two items (noise and clouds) caused by a middle term (extinction of fire).233 Because of their causally complex structure, the essences of attributes are isomorphic to syllogistic demonstrations. On the other hand, claims the author, the essences of subjects are 'causally simple'. Their structure is a combination of genus plus differentiae, which can be known by division and induction independently of explanatory connections between the elements in the definiens.234 I believe this interpretation, although attractive, is mistaken for the following reasons. First, T43 is not conclusive on the issue. It is far from clear that Aristotle is interested in the distinction between subjects and attributes in this passage. Strictly speaking, the distinction is between items whose definition is isomorphic to a demonstration, because their cause is 'something else', and items whose definitions are 'assumed' (the verb in 93b 23 is ' ') or 'made clear in some other way'. It is not clear what it means to say that an item has 'something else' as its cause. But it is even less clear that Aristotle's intention is to affirm that attributes have 'something else' as their causes, while substances do not. As Ross (1949, p. 633) notes, the example of something whose cause is not 'something else' – the unit ( ) – is not strictly speaking a substance. Moreover, we do not have an example of something whose cause is 'something else' in APo II 9. Even if we take the main examples from the previous chapter (thunder and eclipse) as beings whose cause is 'something else' (which I think is correct), nothing in the text suggests that this class of things does not include substances. Quite on the contrary, if we are allowed to take the examples from APo II 8 into account, we must notice that 'human' and 'soul' are also examples found in the chapter (93a 22-24), which suggests that the isomorphism between definition and demonstration applies to substances as well.235 However, the main reason to reject the view that the essence of subjects constitute an exception to the interdependence between defining and explaining comes from APo II 2. As we have seen in Chapter 2, Aristotle affirms that Q3 – Does S exist? – and Q4 – What is S? – are also answered by investigating a middle term (APo II 2, 89b 37-90a5). What does it mean if not that the 232 Ross (1949, p. 633); Bronstein (2016a, pp. 131-143). 233 See Bronstein (2016a), Chapter 7, 9, and 10. 234 See Bronstein (2016a), Chapter 9 and 12. Nevertheless, Bronstein claims that the knowledge of a definition, if acquired only by induction and division, is 'non-noetic'. According to the author, we acquire noetic knowledge of the definition of a subject-kind when we are able to use its definition to explain its demonstrable attributes. 235 See Peramatzis (2011, p. 11). In addition, I shall argue that even in the case of items whose cause is not something else (e.g. unit) there is a sense in which defining and explaining remain interdependent practices. 147 essence of subjects are somehow revealed by demonstrations? Nevertheless, as we have discussed, one could argue that Aristotle's own theory gives him reasons to exclude subjects from the picture advanced in APo II 2: the existence of subjects cannot be reduced to their presence in a more basic entity; if the existence of S cannot be spelled out in terms of a predication in which S occurs as an attribute, it would not make sense to seek for a middle term when the essence of S is being investigated. However, this is not Aristotle's view. In Metaph. VII 17 and VIII 2-4, the philosopher explicitly claims that the model presented in the APo also works for subject-kinds. Before we see how Aristotle applies his model to substances as well, let us address the theoretical resource that allowed him to do so: the hylomorphic analysis. 6.2 – The Hylomorphic Analysis In the Categories, Aristotle affirms that one of the most distinctive features of particular substances is their capacity to receive contraries while remaining numerically one: one and the same man can be pale at one time and dark at another, and hot and cold, and good and bad etc. (Cat. 5, 4a 10-22). Already here we can have a rough idea of how Aristotle thinks change should be described: a subject x which is not-F (at instant t1) becomes F (at instant t2). However, the issue receives the careful discussion it deserves only in Ph. I 6-8. Aristotle affirms that the process of an unmusical man becoming musical can be described in the following ways (Ph. I 7, 189b 35-190a 1): 1. The man comes to be musical. 2. The unmusical comes to be musical. 3. The unmusical man comes to be a musical man. The three sentences contain one subjectand one predicate-term. In sentence 1, the subject-term refers to the subject of change, whereas in 2 and 3 it denotes the terminus a quo, the state of the subject before the process begins. In all of them, the predicate-term captures the terminus ad quem, the final result of the process.236 The distinction between these three sentence-patterns relies on the use of 'simple' terms ( ), such as 'man' and 'musical', or 'compound' ( ) expressions, such as 'musical man'.237 The fact that each of them contains one subject- (simple or complex) and one predicate-term (simple or complex) should not let us think that there are only two items involved in the process. In this context, the expressions 'the man' and 'the unmusical' should not be interpreted as definite descriptions refereeing to one single being. Actually, these expressions designate two different entities: a substance (the man) and what has been described as 236 For this vocabulary and its use in this context, see Charlton (1992); Angioni (2007c, pp. 58-64; 2009). 237 Ph. I 7, 189b 33; 190a 1-5. See Angioni (2009, pp. 145-16). 148 an 'accidental compound' (man plus unmusicality).238 Although 'numerically one', these entities are different 'in form' (190a 16). In other words, 'the being of man is not the same as the being of the unmusical' (190a 17), which means they have different essences and are therefore defined in different ways (Ph. I 7, 190a 15-16).239 Thus, the man and the unmusical (the latter being understood as accidental compound) are the same only 'by accident': even if, in a particular context such as the initial state of the change, we cannot count them as two discrete wholes (which makes them, in a sense, 'numerically one'), they do not share all properties in all contexts.240 In fact, Aristotle wants to stress one specific difference between them: the man persists through the change, while the unmusical do not – i.e. by the time the man becomes musical, the accidental compound man-plusunmusicality ceases to exist.241 As a result, three elements are involved in the process: the man, the musical and the unmusical. In fact, this is the main outcome of Aristotle's discussion in Ph. I: any change involves a subject that persists through the process and a pair of contrary attributes, these three items being the 'principles' ( ) of nature and natural change. Although the example discussed in the first half of in Ph. I 7 is a case of what Aristotle calls 'alteration' ( ), the philosopher makes it clear that this formula captures what is common to all kinds of change (Ph. I 7, 189b 30-32). However, substances cannot play the role of subject in all of them. Suppose we are interested in describing a particular substance coming into being or going out of existence. In that case, the underlying subject x cannot be the substance itself, nor can the contraries F and not-F be the substance's existence and nonexistence, for the underlying subject must persist through the process (see Lewis 2009, p. 163). In the second half of Ph. I 7 (190b 1 ff.), Aristotle addresses the issue by comparing natural substances to products of craft. When a bronze statue is produced, the bronze – which is present at the beginning of the process, persists through it, and constitutes its product – is called 'matter' ( ); the final arrangement that makes the statue what it is is the 'form' ( ); at last, there is the 'absence of form' ( ), the 'shapelessness' ( ) and 'disarray' ( ) found in the bronze before the process begins (Ph. I 7, 190b 13-17). 238 For a detailed defence of this reading, see Lewis (1982). While Lewis argues that this is Aristotle's canonical use of expressions such as 'the unmusical [thing]', I prefer to restrict my claim to the context of Ph. I 7 – although I recognize that this is not the only place where these expressions refer to an accidental compound (substance plus accident). 239 Cf. Lewis (1982, pp. 15-18). 240 See Top. I 7, 103a 23-32. For a comparison between accidental sameness and sameness 'in essence' and 'being', see SE I 24, 179a 37-39; Ph. III 3, 202b 14-16. See Code (1976, p. 364), who argues that 'to say that the man and the unmusical are one in number at any given time is that the latter is a spatio-temporal segment of the former and they are taking up the same space right now – or to use Aristotle's phrase (190b 18-19, 26-27, 192a 31-32), the one coincides in the other.' 241 See Ph. I 7, 190a 9-21. Aristotle affirms that both the accidental compound and the contrary attribute (unmusicality) go out of existence (190a 11-13, 18-20). 149 One may think that this picture does not apply to natural substances as easily as we may think at first sight. We know the form is the factor that, once instantiated in a given portion of matter, makes the resulting hylomorphic compound what it is. However, Charlton (1992, p. 76) points out that we can describe a dog coming into being either (i) as a seed (matter) being fertilized in a certain way (form) or (ii) as flesh, bones, etc. (matter) being animated or having a certain kind of life (form). In both cases, the matter does not seem to persist through the process.242 If we follow the first alternative, the seed is not a constituent element of the final product.243 In the second alternative, flesh, bones and organs are not given at the beginning of the process. Therefore, the matter cannot be at the same time the item from which and of which the compound is made. However, in Ph. I 7, 190a 5-13, Aristotle says that a natural way to rephrase sentence 2 – 'the unmusical comes to be musical' – is the following: 2*. The musical comes to be from ( ) the unmusical. On the other hand, sentence 1 – 'the man comes to be musical' – cannot be translated as: 1*. The musical comes to be from ( ) the man. In other words, the preposition ' ' should be reserved for the non-persisting element, i.e. the unmusical (Ph. I 7, 190a 7-13). Nevertheless, in Ph. I 7, 190a 21-30, Aristotle admits that in some changes the product is said to come from the persisting element. That is, in natural language, we can say things such as: 4. The statue comes to be from ( ) bronze. Commenting on the passage, Alan Code (1976, pp. 359-362) persuasively argues that Aristotle wants to avoid the following confusion: because the statue is said to come from the bronze in the same way as the musical is said to come from the unmusical, we may think that the bronze, like the unmusical, does not persist through the process.244 Aristotle explains that sentences like 4 are acceptable in natural language only because, in these cases, the non-persisting element is 'nameless' – e.g. there is no name for the configuration of the bronze before it receives the form of a statue (see Metaph. VII 7, 1033a 5-23). However, we should avoid using these sentences 'without qualification'245 precisely because they give the wrong impression that the matter does not persist through the process described. Therefore, when Aristotle says that an animal comes to be from ( ) 242 For this and other related difficulties, see Ackrill (1997, pp. 169-178). See also Angioni (2007c, pp. 64-67). 243 See GA II 3, 736a 24 ff. 244 See Furth (1988, p. 217); Angioni (2009, pp. 151-155). 245 Metaph. VII 7, 1033a 19-22. The 'qualification' required, explains Code (1976, p. 363), is that the sense of 'from' used in 4 does not imply that the item 'from which' the final product comes perishes in the process. 150 the seed (Ph. I 7, 190b 4-5), he must be using the preposition in the canonical sense. If so, we can rule out Charlton's option (i): even if the seed initiates the process of a man coming into being, we cannot say that the seed is the man's 'matter', and hence we should not expect it to be one of his constituent elements.246 On the other hand, how could we say that flesh, bones, organs etc. are the man's 'matter' – Charlton's option (ii) – if they are not given before the process begins? Interpreters solve this difficulty by unpacking the steps involved. Alan Code summarizes Aristotle's account of the generation of human beings: What a man is made of is flesh and bones since the primary nutrient (the menstrual fluid) is converted into flesh upon fertilization, the flesh is converted into a heart, and then through the successive stages of development and growth explained in the second book of the Generation of Animals a human being finally comes to be [Code 1976, p. 364].247 Since the generation of a man is complex, we should not expect all his material constituents to be present at the very first stage of the process. Nevertheless, the account of change proposed at Ph. I 7 remains solid. At each step, it is possible to identify a pair of contrary attributes and an underlying matter that persists through it. However, as Angioni (2007c, pp. 68-87) points out, one thing is to be an underlying matter at some point of the process, and another is to be the 'proper' matter of the final product.248 All the different portions of matter that suffer alterations during the generation of a man should be taken into account when the process itself is the explanandum. However, only the matter that underlies its final stage and remains as a constituent element of its product is useful to explain the basic properties of the generated human being. After all, as we shall see in the next section, to find out the cause in virtue of which this 'proper' matter constitute a human being is the same as discovering the essence of human beings. 6.3 – The Analytics-model in the Metaphysics In this section, we shall analyse how Aristotle, in the Metaphysics, applies to subjectkinds the model developed in the Analytics. However, before we start, a couple of comments on our strategy might be required. One could object that the idea that sensible substances can be analysed as compounds of form and matter is not present in the APo and was developed in later treatises such as the Physics and the Metaphysics. If so, we should not rely on Aristotle's 246 Code (1976, pp. 364-366) quotes GA I 18, 724a36 ff. to argue that when Aristotle says that a man comes to be from semen or an embryo (see Ph. I 7, 190b 4-5), he means that this is his efficient cause. See also Metaph. VIII 4, 1044a 35. 247 See also Furth (1988, pp. 111-113). 248 'Not fire or earth, but the matter proper to the thing' (Metaph. VII 4, 1044b 1-2). 151 hylomorphism to sustain that the essence of substances are also known through demonstrations.249 However, why should we think that the only reason Aristotle had for not presenting his hylomorphism in detail in the APo is that his theory was not completely developed by the time the treatise was written? The theses advanced in the APo are meant to apply to all sciences independently of their particular domains. Hence, the peculiarities of physical objects should not affect Aristotle's main claims in the treatise. Of course, that does not mean Aristotle is never interested in topics that are characteristic of natural sciences. In APo II 11, for instance, he discusses one of the best-known doctrines of his philosophy of nature: there are four canonical types of explanation in the natural world, the material, the formal, the efficient, and the final.250 All this shows that even if Aristotle is not primarily concerned with physical phenomena in the APo – which explains why we do not find there a detailed defence of his hylomorphism –, there is no reason to doubt that he already had consolidated views on the metaphysical structure of the natural world. More importantly, there is a simpler reason to believe that at least some aspects of Aristotle's hylomorphism are assumed in the APo: such a hypothesis has a greater explanatory power than its alternative. As explicitly stated in APo II 2, the essence of subjects is discovered when a middle term is identified. In addition, as we have seen, two of the examples provided in APo II 8 are substances (93a 22-24), which suggests that defining and explaining are interdependent practices even for subject-kinds. If it was not for all that, one could say that the reappearance of the 'interdependence' thesis in Metaph. VII 17 and VIII 2-4 should be ignored by interpreters of the APo. However, given this scenario, the fact that Aristotle actually uses the Analytics-model in the Metaphysics provides further corroboration for our strategy instead of undermining it. That being said, we can turn to Metaph. VII 17. As we have seen, to ask whether the kind thunder exists is the same as asking whether a certain noise occurs in the clouds. However, this question should not be interpreted as concerning an episodic event. Rather, what is being sought is the existence of a middle term: does this sound occur in the clouds with the kind of regularity that implies the agency of the same underlying cause? Thus, when a scientist investigates the existence of thunder, she is not interested in whether 'thunder' is an empty term or not. Actually, what is at stake is whether the kind of noise we call 'thunder' can be treated as a genuine, definable kind. If the scientist finds what that middle term is, she will have found the factor that makes the thunder the kind of thing it is. Could we ask the same question about subject-kinds? 249 See, for instance, Bronstein (2016a, p. 101) 250 See Ph. II 3; II 7; Metaph. I 3; V 2. The only kind of explanation listed in APo II 11 which is not clearly identified with one of the four causes is the first one (94a 24-35), although the natural candidate is the material cause. See Ross (1949, pp. 638-639). 152 Does it makes sense to ask why a man is what he is? According to Aristotle, it depends on how we formulate the problem: [T44] [...] When one asks why, one is always asking why one thing belongs to another. For to ask why a musical man is a musical man is either, as we have just said, to ask why a man is musical, or it is something else. But to ask why a thing is itself is to ask nothing at all. [...] However, one could ask why a man is such a kind of animal. It is clear that this is not to ask why one who is a man is a man. So what one asks is why it is that one thing belongs to another. (It must be evident that it does belong, otherwise nothing is being asked at all.) Thus one may ask why it thunders, for this is to ask why a noise is produced in the clouds, and in this way what is sought is one thing predicated of another. And one may ask why these things here (e.g. bricks and stones) are a house [Metaph. VII 17, 1041a 1027 Bostock 1994, with changes]. Aristotle's point is the following. At first sight, it might seem useless to ask questions such as: (i) Why is the musical musical? (1041a 17-18) (ii) Why is this man a man? (1041a 18) These questions may be interpreted as expressing trivialities, which would make them illegitimate explananda (see Lewis 1985, p. 69). One may think that the issue can be solved by appealing to the semantic rules Aristotle formulates in APo I 22, discussed in Chapter 3. According to these rules, question (i) is ill-formed. The referring expression 'the musical' does not describe the denoted object appropriately. For Aristotle, the grammatical subject must signify just what the metaphysical subject is ( ), and whatever is musical is not essentially musical. Thus, what we want to ask is why (e.g.) a certain (musical) man is musical (1041a 12). If we comply with Aristotle's rules, a non-trivial version of question (i) can be provided (1041a 13-14), one which asks 'why one thing belongs to another' (1041a 11; 25-26): (i*) Why is this man musical? (1041a 13-14) Although effective for question (i), this analysis would not work for question (ii), since the grammatical subject 'this man' captures just what the metaphysical subject is. In T44, Aristotle 153 is probably suggesting the same strategy for reinterpreting both questions. If so, there must be another way of finding a non-trivial version of question (i), one which also works for question (ii). As we have argued in the previous section, in some contexts – especially when notions like form and matter are at stake – an expression such as 'the musical' refers not to a particular substance which happens to be musical, but to an accidental compound, i.e. the combination of a subject (man) and an attribute (musicality). Therefore, if we want to know why a musical man is as he is (namely, a musical man), we just need to disarticulate its constituent parts and ask why they are connected as they are. If 'cloak' is the name given to the accidental compound man-plusmusicality251, to ask why a cloak is a cloak – i.e. why the musical (man) is (a) musical (man), like in question (i) – is the same as asking why the man is musical – as we have in question (i*).252 Since the hylomorphic analysis allows Aristotle to treat man as a compound of form and matter, he can reinterpret question (ii) as follows: (ii*) Why is this body with this feature a man? (1041b 6-7) Let us discuss Aristotle's argument in detail. At the end of T44, the philosopher applies his strategy to processes and artefacts. To investigate why the musical (man) is musical is the same as asking why the components of the complex man-plus-musicality are connected. Likewise, we can investigate why thunder is what it is by seeking the cause in virtue of which its constituent elements (noise and clouds) are related as they are.253 Here, Aristotle is reaffirming the isomorphism between demonstrations and definitions, as argued in the APo. As we have seen, the essence of thunder is revealed by our Syllogism VIII, which is isomorphic to the definition of thunder: Syllogism VIII: Noise holds of fire being extinguished, fire being extinguished holds of clouds Noise holds of clouds Def. (Thunder): Thunder is(df.) noise of fire being extinguished in the clouds (APo II 10, 94 a 5-6). Similarly, a house can be described as a connection between a set of materials (bricks, stones etc.) and a certain structure. Thus, if we want to investigate why a house is a house, what we seek is the reason why these bricks, stones etc. are arranged in this way (Metaph. VII 17, 1041a 2627; b5-6). The example of an artefact is not introduced without reason. What fixes the identity of 251 As Aristotle does with 'pale man' in Metaph. VII 4, 1029b 22-1030a 17. 252 In general lines, I am following the interpretation proposed by Angioni (2008, p. 333). 253 See the examples of eclipse and sleep in Metaph. VIII 4, 1044b 8-20. 154 processes such as thunder and eclipse is an efficient cause, whereas what makes a house or a bed what they are is a final cause (Metaph. VII 7, 1041a 27-30). What makes something a house is its being structured so as to protect human beings, their belongings etc. (Metaph. VIII 2, 1043a 14-18). If so, the syllogism and the definition that display the essence of a house would run as follows:254 Syllogism XVI: This structure holds of protecting etc., protecting etc. holds of these bricks and stones This structure holds of these bricks and stones Def. (House): House is(df.) a structure made of bricks, stones etc. for the sake of protecting human beings, their belongings etc. As the reader of Metaph. VII 17 can expect at this stage of the argument, the essence of human beings can be grasped through the same explanatory practice that reveals the essence of process-types and artefacts: [T45] One is particularly liable not to recognize what is being sought in things not predicated one of another, as when it is asked what a man is, because the question is simply put and does not distinguish these things as being that. But we must articulate our question before we ask it, otherwise there would be something common between investigating something and nothing. And since the existence of the thing must already be given it is clear that the question may be 'Why are these things here a house?' (and the answer is 'because what being is for a house belongs to them'), or it may be 'Why is this thing here a man?', or 'Why is this body with this feature a man?' So what is sought is the cause by which the matter is soand-so, i.e. the form [Metaph. VII 17, 1041a 32-b8; Bostock 1994, with changes]. For Aristotle, the essence of natural substances is, like the essence of artefacts, specified in teleological terms. The parts of the human body and its structure as a whole are for the sake of a certain kind of life, a soul of a certain type. To spell out what that soul is is the same as specifying what it is to be ( ) a human being (Metaph. VII 10, 1035b 14-22). Since the interdependence 254 See Charles (2000, pp. 286-290); Peramatzis (2013, p. 303). 155 between defining and explaining holds good for substance-kinds, we can determine the essence of human beings by specifying (syllogistically) the reason why the human body is structured as it is: Syllogism XVII: This arrangement holds of being rational soul, being a rational soul holds of this type of body This arrangement holds of this type of body. Correspondingly, the definition of human being would run as follows: Def. (Human Being): Human being is(df.) a body arranged in such-and-such way for the sake of being a rational soul. 255 If at least part of the ideas spelled out in Metaph. VII 17 and VIII 2-4 are implied in APo II, it becomes easier to understand why Aristotle affirms that the essence of a subject S is discovered when the cause of S's being is identified. However, according to T43, the essence of S can be revealed by a demonstration only if 'its cause is something else' ( ). Therefore, if the essence of natural substances becomes known through demonstrations, their 'cause' must be something distinct from them. But what does this mean? We can surely affirm that the cause that makes the thunder what it is is not the same thing as the thunder itself. A thunder is a certain kind of noise whereas its 'cause' is fire being extinguished in the clouds. The distinction between thunder and the cause of its 'being' is what enables us to decompose its essence in three basic elements and articulate them in a syllogistic structure: a certain noise (major term) belongs to the clouds (minor term) in virtue of fire being extinguished (middle term). Similarly, composite substances are not identical to the cause of their 'being' (namely, their form). Human beings are compounds of body and soul, not souls. However, in Metaph. VIII 3, Aristotle warns us that we may not realize this fact due to a linguistic phenomenon: [T46] One must bear in mind that sometimes it is not clear whether a word signifies the compound substance or the actuality and shape; for instance whether 'house' is a sign for the compound, a shelter made from bricks and stones placed thus, or for the actuality and form, a shelter, and similarly whether 'line' means duality in length or just duality, whether 'animal' means a soul in a body or just a soul (for the soul is the substance 255 See Charles (2000; 2010b, pp. 268-328); Peramatzis (2011, pp. 180-200; 2013, pp. 303-305). 156 and actuality of a certain kind of body) [Metaph. VIII 3, 1043a 29-36; Bostock 1994, with changes]. The fact that a word designating a natural substance may also be used to refer to its soul should not prevent us from distinguishing the two things. Actually, Aristotle explicitly distinguishes one thing from the other few lines after T46: 'a man', he says, 'is not the same as what-being-is-for-aman, unless the soul too is to be called man' (Metaph. VIII 3, 1043b 3-4). In some contexts, the philosopher uses the locution 'what being is for S' ( + noun in the dative + ) to refer the most basic component of S's essence, namely, its form. In T45, for instance, Aristotle affirms that bricks, stones etc. become a house when 'what being is for a house belongs to them' ( ), i.e. when the form of a house inheres in its material constituents (minor premise in Syllogism XVI). Similarly, in 1043b 3-4, what-being-is-for-a-man is identified with the human soul. Thus, to distinguish the man from what-being-is-for-a-man is the same as distinguishing the hylomorphic compound from its form. Again, nothing in T43 should make us think that the essence of substances are not discovered through demonstrations.256 The passage does not affirm or imply that the 'cause' of natural substances being what they are is identical to them. Actually, as we have just seen, the Metaphysics provides us with evidence to the contrary. In the absence of proof that Aristotle changed his mind, we have good reason to believe that the essence of subject-kinds become known through the explanatory practices described in APo II 8 and reaffirmed in Metaph. VII-VIII. The example of an 'item whose cause is not something else' offered in T43 is 'unit', which suggests that the exceptions to the method proposed in APo II 8 are conceptually simple notions, and not hylomorphic compounds. However, there is a sense in which the interdependence between defining and explaining remains solid even for definienda such as 'unit'. Even if the definition of unit is not isomorphic to a demonstrative syllogism, its status as a first principle depends on its being used to explain arithmetic theorems. This conclusion can be drawn from a famous passage in De An. I 1: [T47] ... ... 256 Of course, that does not mean that other methods like induction and division are not useful for investigating the essence of subjects (or even the essence of attributes). Perhaps, these practices reveal part of their essences (namely, the one appearing in nominal definitions, based on which the scientist starts its inquiry). For another view, see Bronstein (2016a, pp. 189-222). 157 It seems that not only is ascertaining what a thing is useful for considering the causes of the properties of substances [...], but also, conversely, that ascertaining the properties of a substance plays a great part in knowing what a thing is. [...] For the principle of every demonstration is what a thing is, so that those definitions which do not lead us to ascertain the properties of a substance, or at least to know them in a ready sort of way, will clearly and in every case be dialectical and vacuous [De An. I 1, 402b 16-403a 2; Shields 2016, with changes]. In this passage, Aristotle is relying on the claim that what characterizes the essence of a substance – in comparison to other necessary (but non-essential) properties – is its being explanatorily basic, i.e. their presence in the substance explains the substance's having other derivative properties, but is not explained by any other property the substance may have. Thus, to know the essence of a substance as the essence of that substance involves realizing that it explains the substance's demonstrable attributes. Similarly, to recognize propositions as an authentic definitions – and not merely 'dialectical and vacuous' – involves realizing that certain phenomena can be demonstrated from them. This result is in accordance with our account of the relation between demonstrative knowledge and . is the cognitive state that knows definitions. Since demonstrations are based on definitions, demonstrative knowledge is dependent on . However, if we cannot get to know a definition independently of the act of demonstrating, it is impossible to have without having demonstrative knowledge. Again, the interdependence of these two kinds of knowledge just mirrors the interdependence between defining and explaining. 158 159 CONCLUSION Knowledge 'without qualification', the kind of knowledge expert scientists have, consists in grasping stable connections between subjects and attributes in the world and explaining them from 'appropriate principles', i.e. indemonstrable premises that are true, primitive, immediate, more familiar than, prior to, and explanatory of the conclusion (APo I 2, 71b 19-22). The possibility of relying on indemonstrable principles is what allows scientists to explain phenomena without producing circular demonstrations or running the risk of infinite regress. Given this scenario, it is understandable that Aristotle has been classified as a foundationalist. However, his foundationalism should not be understood as a rationalist theory of epistemic justification, as if the indemonstrable principles of science were self-evident propositions acquired by non-inferential procedures. First, Aristotelian explanations are not justifications, i.e. they answer questions of the form 'why is it the case that p?' and not questions such as 'why do I believe that p?' Second, his acknowledgement of indemonstrable principles amounts to the recognition of essences, understood as ultimate explanations. Essences do not become known as such independently of their being used to explain scientific problems. Noetic knowledge of indemonstrable principles and demonstrative knowledge of explainable facts are therefore interdependent cognitive states in the same way as defining and explaining are interdependent scientific practices. 160 Aristotle's philosophy of science cannot be fully understood unless its ontological underpinnings are properly specified. For him, essences are primary explanatory factors. However, in every scientific domain, we can distinguish two basic kinds of essence-bearers: subjects and demonstrable attributes. Subjects are defined without mentioning a more basic subject in the domain, since there is not another being of which they could be predicated that differs in essence from them. On the other hand, demonstrable attributes (or per se accidents) cannot be defined without specifying the kind of objects in which they inhere. With the distinction between subjects and attributes in mind, Aristotle imposes a set of semantical rules on scientific discourse as a way of guaranteeing that linguistic predications will capture the corresponding metaphysical predications appropriately. These semantical rules are also part of Aristotle's foundationalist project, since they prevent a syllogistic chain of demonstrations from proceeding ad infinitum. Notwithstanding the differences between the essence of subjects and the essence of attributes, there is room for both of them in demonstrative sciences. The 'primary' middle term explaining why an attribute belongs to a subject is the causal part of the attribute's essence. In other words, the final and crucial step in a demonstration follows the A-Model. However, if there is a stable, regular connection between attribute and subject, the attribute's essence and the subject must be connected in a similar way – after all, the attribute's 'way of being' involves its being predicated of that subject. If the demonstrandum is a primary-universal problem, the attribute counterpredicates with the subject and belongs to it in virtue of the subject being what it is. That is to say, the subject's essence partially explains why it possess its demonstrable attributes. Thus, it is not without reason that Aristotle seems to endorse something along the lines of the S-Model as well. As it is clear from the examples used in APo II, the essence of attributes are discovered through demonstrations. It is not possible to know their essences without having the corresponding explanatory syllogism, which turns out to be isomorphic to the attribute's definition. As we have argued, the essence of subjects does not constitute an exception to the 'interdependence' principle. In the Metaphysics, Aristotle explicitly applies the model developed in APo II to substance-kinds – in fact, examples of substances are already mentioned, although not fully explored, in APo II 8. In addition, we argued that subjects that cannot be analysed as compounds of form and matter also have their essences revealed by explanatory practices. The essence of an unanalysable subject cannot be recognized as the essence of that subject without its being used to explain the subject's demonstrable attributes. It is not exactly surprising that Aristotle uses some of his ontological theses in his attempt to formulate general principles about how should be pursued and 161 expressed. Certainly, other aspects of the relation between Aristotle's metaphysics and his philosophy of science remain to be clarified and further explored. However, we hope we have offered a relatively comprehensive reconstruction of the ontological framework associated with his theory of demonstration. We should be particularly satisfied if our reader is convinced, among other things, that, for Aristotle, the intelligibility of reality depends on there being finite chains of explanatory connections in the world and entities whose 'ways of being' are associated with one another in a hierarchical structure. 162 163 BIBLIOGRAPHY Aristotle's works: ACKRILL, J. (1963) Categories and De interpretatione: translation and notes. Oxford: Clarendon. ANGIONI, L. (2002) Aristóteles Segundos Analíticos, livro II. (tradução) Clássicos da Filosofia: Cadernos de Tradução no 4. Campinas: IFCH/UNICAMP. ____. (2004) Aristóteles Segundos Analíticos, livro I (tradução). Clássicos da Filosofia: Cadernos de Tradução no 7. Campinas: IFCH/UNICAMP. ____. (2005). Aristóteles Metafísica, livros VII e VIII. 2nd ed. Campinas: Instituto de Filosofia e Ciências Humanas da Unicamp, col. Clássicos da Filosofia: Cadernos de Tradução n.11. ____. (2009). Aristóteles: Física I-II. Campinas: Editora Unicamp. BARNES, J. (1975). Aristotle: Posterior Analytics. 1st edition. Oxford: Clarendon Press. ____. (ed.) (1984) The complete works of Aristotle. Volumes 1 e 2. Princeton: Princeton University Press. ____. (1993) Aristotle: Posterior Analytics. 2nd edition. Oxford: Clarendon Press. BEKKER, I. (1961) Aristotelis Opera. Berlin: Walter De Gruyter. BODEÜS, R. (2002) Aristote: Catégories. Paris: Les Belles Lettres. BONITZ, H. (1961) Index Aristotelicus. Aristotelis Opera vol. V. Berlin: De Gruyter. BOSTOCK, D. (1994). Aristotle Metaphysics Books Z and H. Oxford: Clarendon Press. BRUNSCHWIG, J. (1967) Les Topiques I-IV. Paris: Les Belles Lettres. CHARLTON, W. (1992) Aristotle's Physics: Books I and II. Oxford: Clarendon Press. KIRWAN, C. Aristotle's Metaphysics: Books Gamma, Delta, and Epsilon. Translated with notes. 2nd edition. Oxford: Clarendon Press. LENNOX, J.G. (2001) Aristotle: On the Parts of Animals I-IV. Translation, introduction and commentary. Oxford. Clarendon Press. MINIO-PALUELLO, L. (1949) Categoriae et Liber De Interpretatione. Oxford: Clarendon Press. PELLEGRIN, P. (2005) Aristote Seconds Analytiques. Présentation, traduction et notes. Paris: Flammarion. ROSS, D. (1924) Aristotle's Metaphysics: A Revised Text with Introduction and Commentary. 2 volumes. Oxford: Clarendon Press. 164 ____. (1949) Aristotle's Prior and Posterior Analytics: A Revised Text with Introduction and Commentary. Oxford: Clarendon Press. ____. (1950) Aristotle's Physica: A Revised Text with Introduction and Commentary. Oxford: Oxford University Press. ____. (1958) Aristoteles: Topica et Sophistici Elenchi. Oxford: Clarendon Press. ____. (1961) Aristotle De Anima. Oxford: Clarendon Press. SHIELDS, C. (2016) Aristotle: De Anima. Oxford: Oxford University Press. SMITH, R. (1989). Aristotle Prior Analytics, Cambridge: Hackett Publishing Company. ____. (1997) Aristotle: Topics, Books I and VIII. Oxford: Clarendon Press. STRIKER, G. (2009) Aristotle: Prior Analytics Book I. Translated with an introduction and commentary. Oxford: Clarendon Press. TREDENNICK, H. (1960) Aristotle: Posterior Analytics. Loeb Classical Library, Harvard University Press, Cambridge, Mass. WAITZ, T. (1844-6) Aristotelis Organon Graece. 2 vols. Leipzig: Hahn. Secondary Literature: ACKRILL, J. (1972). "Aristotle's Definition of Psuche". Proceedings of the Aristotelian Society 73: 119133. Reprinted in: ACKRILL, J. Essays on Plato and Aristotle (pp. 163-179). Oxford: Clarendon Press. ____. (1981) "Aristotle's Theory of Definition: some questions on Posterior Analytics II 8-10" In: Berti, E. Aristotle on Science: The Posterior Analytics, Proceedings of the Eighth Symposium Aristotelicum (359384). Padova: Editrice Antenore. Reprinted in: ACKRILL, J. Essays on Plato and Aristotle (pp. 110130). Oxford: Clarendon Press. ____. (1997). Essays on Plato and Aristotle. Oxford: Clarendon Press. ALMEIDA, W. D. (2013) "Termos Singulares, Transcategoriais e Summa Genera na Lógica de Aristóteles". Manuscrito 36 (1): 5-48. ANGIONI, L. (2004) "Relações causais entre eventos na ciência aristotélica: uma discussão crítica de Ciência e Dialética em Aristóteles, de Oswaldo Porchat" Analytica 8 (1): 13-27. ____. (2006) Introdução à Teoria da Predicação em Aristóteles. Campinas: Editora Unicamp. ____. (2007a) "Conhecimento Científico no Livro I dos Segundos Analíticos de Aristóteles" Journal of Ancient Philosophy 1 (2). ____. (2007b) "Aristóteles e a noção de sujeito de predicação (Segundos Analíticos I 22, 83a 1-14)". Philosophos 12 (2): 107-129. 165 ____. (2007c) "A noção aristotélica da matéria". Cadernos de História e Filosofia da Ciência 17(1): 4790. ____. (2008) As noções aristotélicas de substância e essência. Campinas: Editora Unicamp. ____. (2010) "Prioridade e Substância na metafísica de Aristóteles." Dois Pontos 7 (3): 75-106. ____. (2012) "Os seis requisitos das premissas da demonstração científica em aristóteles (Segundos Analíticos I 2)" Manuscrito 35: 7-60. ____. (2013) "Knowledge and Opinion about the same thing in APo A-33." Dois Pontos 10: 255290. ____. (ed.) (2014a) Lógica e Ciência em Aristóteles. 1st edition. Campinas: PHI. ____. (2014b) "Demonstração, silogismo e causalidade." In: Angioni, L. (Org.). Lógica e Ciência em Aristóteles. (pp. 61-120) Campinas: PHI. ____. (2014c) "Aristotle on Necessary Principles and on Explaining X through X's essence". Studia Philosophica Estonica 7(2): 88-112. ____. (2016) "Aristotle's definition of scientific knowledge (APo71b9-12)". Logical Analysis and History of Philosophy 19: 79-105. BARNES, J. (1969) "The Aristotle's Theory of demonstration". Phronesis 14 (2): 123-152. ____. (1970) "Property in Aristotle's Topics". Archiv für Geschichte der Philosophie 52: 136–55. ____. (1981) "Proof and Syllogism". In: Berti, E. Aristotle on Science: The Posterior Analytics, Proceedings of the Eighth Symposium Aristotelicum (pp. 17-59). Padova: Editrice Antenore. ____. (2007) Truth, Etc.: Six Lectures on Ancient Logic. Oxford: Oxford University Press. BAYER, G. (1995) "Definition through Demonstration: the Two Types of Syllogisms in Posterior Analytics II-8". Phronesis 40(3): 241-264. BOGEN, J. & McGUIRE, J. (eds.) (1985) How things are: Studies in predication and the history of philosophy and science. Dordrecht: Reidel. BOLTON, R. (1976) "Essentialism and Semantic Theory in Aristotle: Posterior Analytics, II, 7-10". Philosophical Review 85 (4): 514-544. BRODY, B. A (1972) "Towards an Aristotelian Theory of Scientific Explanation". Philosophy of Science 39: 20-31. BRONSTEIN, D. (2010) "Investigação e Paradoxo do Mênon: Aristóteles, Segundos Analíticos II 8". Dois Pontos 7 (3): 107-130 ____. (2012) "The Origin and Aim of Posterior Analytics II 19". Phronesis 57(1): 29-62. ____. (2014) "Aristotle's theory of demonstration revisited". Metascience 23: 1–35. 166 ____. (2015) "Essence, Necessity, and Demonstration in Aristotle." Philosophy and Phenomenological Research XC (3): 724-732. ____. (2016a) Aristotle on Aristotle on Knowledge and Learning: The Posterior Analytics. Oxford University Press. ____. (2016b) "Aristotle's critique of Plato's theory of innate knowledge". Logical Analysis and History of Philosophy 19: 126-139. BURNYEAT, M. (1981) "Aristotle on Understanding Knowledge". In: Berti, E. Aristotle on Science: The Posterior Analytics, Proceedings of the Eighth Symposium Aristotelicum (pp. 97-139). Padova: Editrice Antenore. CHARLES, D. (2000) Aristotle on Meaning and Essence. Oxford: Clarendon Press. ____. (ed.) (2010a) Definition in Greek Philosophy. Oxford: Oxford University Press. ____. (2010b) "Definition and Explanation in the Posterior Analytics and Metaphysics" In: Charles, D. (ed.) Definition in Greek Philosophy. Oxford: Oxford University Press. ____. (2011) "Remarks on substance and essence in Aristotle's Metaphysics Z.6" In: Morison, B. & Ierodiakonou, K. (2011) Episteme, Etc.: Essays in Honour of Jonathan Barnes (pp. 151-171). Oxford: Oxford University Press. CHEN, C.H. (1957) "On Aristotle's two expressions: and : their meaning in Cat. 2, 1a20-b9 and the extension of this Meaning". Phronesis 2 (2): 148-159. CODE, A. (1976) "The Persistence of Aristotelian Matter". Philosophical Studies 29 (6): 357-367. ____. (1985) "On the origins of some Aristotelian theses about predication". In: Bogen, J. & McGuire, J. (eds.) How things are: Studies in predication and the history of philosophy and Science (pp. 101131). Dordrecht: Reidel. ____. (1986) "Aristotle's Investigation of a Basic Logical Principle: Which Science Investigates the Principle of Non-Contradiction?" Canadian Journal of Philosophy 16 (3): 341 357. CORCORAN, J. (ed.) (1974a) Ancient Logic and its Modern Interpretations. Dordrecht: D. Reidel. ____. (1974b) "Aristotle's Natural Deduction System". In: Corcoran, J. (ed.) Ancient Logic and its Modern Interpretations (pp. 85-131). Dordrecht: D. Reidel. ____. (1974c) "Aristotelian syllogisms: Valid arguments or True Universalized Conditionals?" Mind, New Series 83 (30): 278-281. ____. (2009) "Aristotle's Demonstrative Logic". History and Philosophy of Logic 30(1): 1-20. COOPER, J. (ed.) (1997) Plato: Complete Works. Indianapolis, Ind.: Hackett. CORKUM, P. (2008) "Aristotle on Ontological Dependence". Phronesis 53 (1): 65-92. 167 CRAGER, A. (2013) The infinite in Aristotle's logical epistemology. Master of Logic Thesis. Institute for Logic, Language and Computation. University of Amsterdam. ____. (2015) Meta-logic in Aristotle's Epistemology. Doctoral Dissertation. Philosophy Department. Princeton University. DEMOS, R. (1944) "The structure of substance according to Aristotle". Philosophy and Phenomenological 5 (2): 255-268. DEMOSS, D. & DEVEREUX D. (1988). "Essence, Existence and Nominal Definition in Aristotle's Post. Analytics II 8-10". Phronesis 33 (2): 133-154. EBERT, T. (1998) "Aristotelian Accidents". Oxford Studies in Ancient Philosophy 16: 133-156. FEREJOHN, M. (1991) The origins of Aristotelian science. New Haven: Yale University Press. ____. (2009) "Empiricism and First Principles in Aristotle". In: Anagnostopoulos, G. (ed.) A Companion to Aristotle (pp. 66-80). Chichester: Wiley-Blackwell. ____. (2013) Formal Causes: Definition, Explanation, and Primacy in Socratic and Aristotelian Thought. Oxford: Oxford University Press. FERREIRA, M. R. F. (2012) A Lógica de Aristoteles: problemas interpretativos e abordagens contemporaneas dos Primeiros Analíticos. Tese de doutorado em História da Filosofia Antiga, Instituto de Filosofia e Ciências Humanas, Universidade Estadual de Campinas, Campinas. FINE, G. (2003) "Separation". In: Fine, G. (ed.) Plato on Knowledge and Forms: Selected Essays. Oxford: Oxford University Press. First published as Fine, G. (1984) "Separation". Oxford Studies in Ancient Philosophy 2: 31-87. FINE, K. (1995) "Ontological Dependence". Proceedings of the Aristotelian Society 95: 269-290. FREDE, M. (1996). "Aristotle's Rationalism". In Frede, M. & Striker, G. (eds.) Rationality in Greek Thought. Oxford: Clarendon Press. FURTH, M. (1988) Substance, Form and Psyche: An Aristotelian Metaphysics. Cambridge: Cambridge University Press. GEACH, P. (1972) Logic Matters. Berkeley: University of California. GILDERSLEEVE, B. L. (1980) Syntax of Classical Greek from Homer to Demosthenes. First Part. New York: American Book Company. GILL, M. L. (1989). Aristotle on Substance: the Paradox of Unity. Princeton: Princeton University Press. GOLDIN, O. (1996) Explaining an Eclipse: Aristotle's Posterior Analytics 2.1-10. Ann Arbor: University of Michigan Press. ____. (2013) "Circular justification and explanation in Aristotle". Phronesis 58: 195-214. 168 GOMEZ-LOBO, A. (1977) "Aristotle's Hypotheses and the Euclidean Postulates." Review of Metaphysics 30: 430-39. ____. (1980) "The So-Called Question of Existence in Aristotle, An. Post. 2. 1-2". Review of Metaphysics 34: 71-89. GOTTHELF, A. (1987) "First Principles in Aristotle's Parts of Animals" In: Gotthelf, A. & Lennox, J.G. (eds.) Philosophical Issues in Aristotle's Biology (pp. 167-198). Cambridge: Cambridge University Press. GOTTHELF, A. & LENNOX, J. G. (eds.) (1987) Philosophical Issues in Aristotle's Biology. Cambridge: Cambridge University Press. GRAHAM, W. (1975) "Counterpredicability and Per Se Accidents". Archiv für Geschichte der Philosophie 57 (2): 182-187. GRANGER, H. (1981) "The differentia and per se accident in Aristotle". Archiv fur Geschichte der Philosophie, 63 (2): 118-129. HAMLYN, D.W. (1961) "Aristotle on Predication". Phronesis 6 (2): 110-126 HANKINSON, R. J. (1998) Cause and Explanation in Ancient Greek Thought. Oxford: Clarendon Press. HARARI, O. (2004) Knowledge and Demonstration: Aristotle's Posterior Analytics. Dordrecht: Kluwer Academic Publishers. HARMAN, G. H. (1965). "The Inference to the Best Explanation". Philosophical Review 74 (1): 8895. HASPER, P. S. (2006) "Sources of Delusion in Analytica Posteriora I.5" Phronesis 51: 252-284. HASPER, P. S. & YURDIN, J. (2014) "Between Perception and Scientific Knowledge: Aristotle's Account of Experience". Oxford Studies in Ancient Philosophy 47: 119-150. HINTIKKA, J. (1972) "On the Ingredients of an Aristotelian Science". Noûs 6 (1): 55-69. IRWIN, T. (1988) Aristotle's First Principles. Oxford: The Clarendon Press. IRWIN, T. & FINE, G. (1995) Aristotle: selections. Translated with introduction, notes and glossary. Indianopolis: Hackett. INWOOD, B. (1979) "A Note on Commensurate Universals in the Posterior Analytics". Phronesis 24 (3): 320-9. KAHN, C. (1981) "The Role of Nous in the Cognition of First Principles in Posterior Analytics II 19" In: Berti, E. (ed.) Aristotle on Science: The Posterior Analytics, Proceedings of the Eighth Symposium Aristotelicum (pp. 385-414). Padova: Editrice Antenore. KOSLICKI, K. (2012). "Essence, necessity, and explanation." In: Tahko, T. (ed.) Contemporary Aristotelian Metaphysics (pp. 187-206) Cambridge: Cambridge University Press. 169 KOSMAN, L. (1973) "Understanding, Explanation, and Insight in the Posterior Analytics". In: Lee, E.N. Mourelatos, A.P.D. & Rorty, R.M. (eds.) Exegesis and Argument, Studies in Greek Philosophy presented to Gregory Vlastos. New York: Humanities Press. KUNG, J. (1977) "Aristotle on Essence and Explanation". Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 31 (6): 361-383. LEAR, J. (1979) "Aristotle's Compactness Proof". Journal of Philosophy 76 (4): 198-215. ____. (1980) Aristotle and Logical Theory. Cambridge: Cambridge University Press. LENNOX, J. G. (1987) "Divide and Explain: The Posterior Analytics in Practice". In: Gotthelf, A. & Lennox, J.G. (eds.) Philosophical Issues in Aristotle's Biology (pp. 90-119). Cambridge: Cambridge University Press. LESHER, J.H. (1973) "The Meaning of Nous in the Posterior Analytics". Phronesis 18: 4468. ____. (2001) "Aristotle on as understanding." Ancient Philosophy 21: 45-55. ____. (2010) "Saphêneia in Aristotle: 'Clarity', 'Precision', and 'Knowledge' ". Apeiron 43 (4): 143156 LESZL, W. (1981) "Mathematics, Axiomatization and the Hypotheses". In: Berti, E. (ed.) Aristotle on Science: The Posterior Analytics, Proceedings of the Eighth Symposium Aristotelicum (pp. 141-156). Padova, Itália: Editrice Antenore. LEWIS, F. (1982) "Accidental Sameness in Aristotle". Philosophical Studies 42 (1): 1-36. ____. (1985) "Form and Predication in Aristotle's Metaphysics". In: Bogen, J. & McGuire, J. (eds.) How things are: Studies in predication and the history of philosophy and Science (pp. 59-83). Dordrecht: Reidel. ____. (1991) Substance and Predication in Aristotle. Cambridge: Cambridge University Press. ____. (2009) "Form and Matter". In: Anagnostopoulos, G. (ed.) A Companion to Aristotle (pp. 6680). Chichester: Wiley-Blackwell. LOWE, E. J. (2013) "Neo-aristotelian metaphysics: A brief exposition and Defense". In: Feser, E. (ed.) Aristotle on Method and Metaphysics (pp. 196-205). New York: Palgrave Macmillan. LOUX, M. (1991) Primary Ousia: An Essay on Aristotle's Metaphysics Z and H. Ithaca: Cornell University Press. ŁUKASIEWICZ, J. (1957) Aristotle' Syllogistic from the Standpoint of Modern Formal Logic. 2nd edition. Oxford: Oxford Clarendon Press. MALINK, M. (2013) Aristotle's Modal Syllogistic. Cambridge, MA: Harvard University Press. MANSION, S. (1976) Le jugement d'éxistence chez Aristote. Louvain: Inst. Superieur de Philosophie. MATTHEN, M. (1981) "The Structure of Aristotelian Science." In: Matthen, M. (ed.). Aristotle Today: Essays on Aristotle's ideal of science. (pp. 1-23) Edmonton: Academic Printing & Publishing. 170 McKIRAHAN, R. (1992) Principles and Proofs. Princeton: Princeton University Press. MIGNUCCI, M. (1975) L'Argomentazione Dimostrativa in Aristotele – Commento agli Analitici Secondi. Padova: Editrice Antenore. MORAVCSICK, J.M.E. (1967) "Aristotle on Predication". Philosophical Review 76:1: 80-96. PATZIG, G. (1968) Aristotle's Theory of the Syllogism: A logico-philological study of Book A of the Prior Analytics. Translated by J. Barnes. Dordrecht: D. Reidel Publishing Company. PORCHAT PEREIRA, O. (2001) Ciência e dialética em Aristóteles. São Paulo: Editora Unesp. PEIRCE, C. S. (1974) Collected papers. Vols. 1-6 edited by C. Hartshorne and P.Weiss; Cambridge: Belknap Press of Harvard University Press. PERAMATZIS, M. (2008) "Aristotle's Notion of Priority in Nature and Substance". Oxford Studies in Ancient Philosophy 35: 187-247. ____. (2010) "Essence and Per Se Predication in Aristotle's Metaphysics Z.4". Oxford Studies in Ancient Philosophy, 39: 121-182. ____. (2011) Priority in Aristotle's Metaphysics. Oxford: Oxford University Press. ____. (2013) "Science and Metaphysics in Aristotle's philosophy". Metascience 22 (2): 303-315. PHILOPONUS. "In Aristotelis Analytica Posteriora Commentaria." In: Wallies, M. (ed.) (1909) Commentaria in Aristotelem Graeca. Voluminis XIII. Pars III Ioannis Philoponi in Aristotelis analytica posteriora commentaria cum anonymo in librum II. Berlin: G. Reimer. QUINE, W.V.O. (1960) Word and object. Cambridge, MA: MIT Press RIBEIRO, F. M. (2011) O conhecimento científico nos Segundos Analíticos de Aristóteles: causa e necessidade na demonstração. Dissertação de Mestrado em História da Filosofia Antiga, Instituto de Filosofia e Ciências Humanas, Universidade Estadual de Campinas, Campinas. ____. (2014) "Silogismo e demonstração na concepção de conhecimento científico dos Analíticos de Aristóteles". In: Angioni, L. (Org.). Lógica e Ciência em Aristóteles (pp. 121-160). Campinas: PHI. ROSS, D. (1939) "The discovery of the syllogism". The Philosophical Review. 48 (3): 251-272. RUSSELL, B. (1905) "On Denoting". Mind. New Series 14 (56): 479-493. ____. (1961) History of western philosophy: and its connection with political and social circumstances from the earliest times to the present day. London: Allen and Unwin. SMYTH, H.W. (1920) Greek Grammar. Cambridge, Mass.: Harvard University Press. SALMIERI, G. (2014) "Aristotelian epistêmê and the relation between knowledge and understanding". Metascience 23: 1-9. 171 SCANLAN, M. (1983) "On finding compactness in Aristotle". History and Philosophy of Logic 4 (1&2): 1-8. SCHOLZ, H. (1975) "The Ancient Axiomatic Theory", In: Barnes, J.; Schofield, M.; Sorabji, R. (eds.) Articles on Aristotle, Vol.1: Science. (pp.50-64). London: Duckworth. SMILEY, T.J. (1973) "What is a syllogism?" Journal of Philosophical Logic 2: 136-154. SMITH, R. (1982a) "The Relationship of Aristotle's Two Analytics". The Classical Quarterly, New Series 32 (2): 327-335. ____. (1982b) "The syllogism in Posterior Analytics I". Archiv Für Geschichte der Philosophie 64: 113-27. ____. (1986) "Immediate Propositions and Aristotle's Proof Theory" Ancient Philosophy 6: 4768. ____. (2009) "Aristotle's Theory of Demonstration". In: Anagnostopoulos, G. (ed.) A Companion to Aristotle (pp. 51-65). Chichester: Wiley-Blackwell. SOLMSEN, F. (1929) Die Entwicklung der Aristotelischen Logik und Rhetorik. Berlin: Berlin: Weidmannsche Buchhandlung. SORABJI, R. (1980) Necessity, cause, and blame: perspectives on Aristotle's Theory. London: Duckworth. TAYLOR, C. C. (1990) "Aristotle's Epistemology". In: Everson, S. (ed.) (1990). Epistemology: Companions to Ancient Thought (Vol. I, pp. 116-142). Cambridge: Cambridge University Press. TERRA, C. A. (2009) Conhecimento Prévio e Conhecimento Científico em Aristóteles. Tese de Doutorado em História da Filosofia Antiga, Instituto de Filosofia e Ciências Humanas, Universidade Estadual de Campinas, Campinas. ____. (2014) "Os predicados per se em Aristóteles." In: Angioni, L. (ed.) Lógica e Ciência em Aristóteles (pp. 23-60) Campinas: Editora PHI. TIERNEY, R. (2001a) "On the Senses of 'Sumbebekos' in Aristotle". Oxford Studies in Ancient Philosophy 21: 61-82. ____. (2001b) "Aristotle's Scientific Demonstrations as Expositions of Essence". Oxford Studies in Ancient Philosophy 20: 149-170. ____. (2004) "The Scope of Aristotle's Essentialism in the Posterior Analytics". Journal of the History of Philosophy 42 (1):1-20. ____. (2007) "Aristotle on the Necessity of Opposites in Posterior Analytics 1.4" Oxford Studies in Ancient Philosophy. 32: 139-167. TILES, J.E. (1983) "Why the triangle has two right angles kath'hauto". Phronesis 28: 1-16. UPTON, T. (1991). "The If-It-Is Question in Aristotle". Ancient Philosophy 11: 15-330. WEDIN, M. (2000) Aristotle's Theory of Substance. Oxford: Oxford University Press. 172 WEDIN, V.E. (1973) "A Remark on Per Se Accidents and Properties". Archiv für Geschichte der Philosophie 55 (1): 30-35 WEINMANN, F. (2014) A Cláusula Final da Definição Geral do Silogismo e suas funções na silogística e nos Primeiros Analíticos I de Aristóteles. Dissertação de Mestrado em História da Filosofia Antiga, Instituto de Filosofia e Ciências Humanas, Universidade Estadual de Campinas, Campinas. WILLIAMS, C. (1985) "Aristotle's Theory of Descriptions". The Philosophical Review 94 (1): 63-80. WILLIAMS, S. & CHARLES, D. (2013) "Essence, modality and the master craftsman." In: Feser, E. (ed.) Aristotle on Method and Metaphysics. (pp. 121-145). New York: Palgrave Macmillan. ZABARELLA, J. (1582) In duos Aristotelis libros Posteriores Analytici Commentarii. Venice: Paulus Meietus. ZILLIG, R. (2010) "A substância e o ser dos itens não-substanciais em Z1". Dois Pontos 7 (3): 3751. ZINGANO, M. A. A. (2013) "Unidade do gênero e outras unidades em Aristóteles: significação focal, relação de consecução, semelhança, analogia". Analytica 17: 393-430 ZUPPOLINI, B.A. (2014a) Aspectos Formais e Ontológicos da Filosofia da Ciência de Aristóteles. Dissertação de Mestrado em História da Filosofia Antiga, Instituto de Filosofia e Ciências Humanas. Campinas: Universidade Estadual de Campinas. ____. (2014b) "Fundacionalismo e Silogística". In: Angioni, L. (Org.). Lógica e Ciência em Aristóteles (pp. 161-201). Campinas: PHI. ____. (2014c) "Forma Lógica das Proposições Científicas e Ontologia da Predicação: um falso dilema nos Segundos Analíticos de Aristóteles." Philósophos, 19 (2): 11-45. ____. (2016) "Aristotle's Foundationalism." Dissertatio (UFPel) 44: 187-211. ____. (forthcoming) "Aristotle on Per se Accidents." Ancient Philosophy.