This is an introductory handbook for some of the main themes around the notion of predication in Aristotle. It does not aim at being exhaustive, but only sketches some important lines about the subject; it contains an introductory essay, besides the translation (into Portuguese) and commentary of basic texts (such as Posterior Analytics I-22, Categories 1-5, Interpretation 1-6 etc.).

Translation of Aristotle's Posterior Analytics II into Portuguese, with a few notes, experimental glossary and introduction. The translation, which was made at 2002 (with a new printing in 2004), was preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

Translation of Aristotle's Posterior Analytics I into Portuguese, with a few notes, experimental glossary and introduction. The translation, which was made at 2003/4, was preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

I focus on three mereological principles: the Extensionality of Parthood (EP), the Uniqueness of Composition (UC), and the Extensionality of Composition (EC). These principles are not equivalent. Nonetheless, they are closely related (and often equated) as they all reflect the basic nominalistic dictum, No difference without a difference maker. And each one of them—individually or collectively—has been challenged on philosophical grounds. In the first part I argue that such challenges do not quite threaten EP insofar as they are either self-defeating (...) or unsupported. In the second part I argue that they hardly undermine the tenability of EC and UC as well. (shrink)

Ever since Aristotle it has been accepted that there exists a combination of inductive and deductive reasoning and a sort of unified inductive-deductive methodology. If one analyzes the procedures and logic of scientific explanation and the methods of generating and justifying scientific knowledge, one recognizes the prototype of philosophy of science found in Aristotle’s inductive and deductive procedure that is described in his Posterior Analytics, Physics and Metaphysics, where heviewed scientific inquiry as a progression from observations to general principles and (...) back to observation. He maintained that the scientist should induce explanatory principles from the phenomena to be explained, and then deduce statements about the phenomena from premisses which include these principles. (shrink)

Many of our concepts are introduced to us via, and seem only to be constrained by, roughand-ready explanations and some sample paradigm positive and negative applications. This happens even in informal logic and mathematics. Yet in some cases, the concepts in question – although only informally and vaguely characterized – in fact have, or appear to have, entirely determinate extensions. Here’s one familiar example. When we start learning computability theory, we are introduced to the idea of an algorithmically computable function (...) (from numbers to numbers) – i.e. one whose value for any given input can be determined by a step-by-step calculating procedure, where each step is fully determined by some antecedently given finite set of calculating rules. We are told that we are to abstract from practical considerations of how many steps will be needed and how much ink will be spilt in the process, so long as everything remains finite. We are also told that each step is to be ‘small’ and the rules governing it must be ‘simple’, available to a cognitively limited calculating agent: for we want an algorithmic procedure, step-by-minimal-step, to be idiot-proof. For a classic elucidation of this kind, see e.g. Rogers (1967, pp. 1–5). Church’s Thesis, in one form, then claims this informally explicated concept in fact has a perfectly precise extension, the set of recursive functions. Church’s Thesis can be supported in a quasi-empirical way, by the failure of our searches for counterexamples. It can be supported too in a more principled way, by the observation that different appealing ways of sharpening up the informal chararacterization of algorithmic computability end up specifying the same set of recursive functions. But such considerations fall short of a demonstration of the Thesis. So is there a different argumentative strategy we could use, one that could lead to a proof? Sometimes it is claimed that there just can’t be, because you can never really prove results involving an informal concept like algorithmic computability.. (shrink)

Although the relationship of part to whole is one of the most fundamental there is, this is the first full-length study of this key concept. Showing that mereology, or the formal theory of part and whole, is essential to ontology, Simons surveys and critiques previous theories--especially the standard extensional view--and proposes a new account that encompasses both temporal and modal considerations. Simons's revised theory not only allows him to offer fresh solutions to long-standing problems, but also has far-reaching consequences for (...) our understanding of a host of classical philosophical concepts. (shrink)

In this paper I want to suggest that, while the argued philosophical distinction between logic, epistemolgoy and ontology is one of the many achievements of Aristotle, his predecessor Parmenides was in fact already operating with a theory of knowledge and an elementary propositional logic that are of abiding philosophical interest. As part of the thesis I shall be obliged to reject a number of interpretations of particular passages in his poem, including one or two currently fashionable ones. Since so much (...) turns on points of translation, I note for purposes of comparison what seem to be significant alternatives to my own in any particular instance. The line numbers are those of the DK text. (shrink)

Reading through the Corpus Aristotelicum we come across a group of expressions meant to indicate predicative relations, which lead us to think that Aristotle connected predication to a part-whole relation. He frequently calls the ‘εἴδη’, “species”, ‘μέρη’, “parts”, of their genera. More generally, the universal is said to contain that of which it is true. In a parallel way, what is contained by something is also what is under something else. Again, it is quite common for him to consider the (...) species as partaking of their genera. Although the relation of partaking is normally used to qualify the way in which species are related to their genera, sometimes also the relation between particulars and species or even genera is expressed in terms of partaking. (shrink)

Ever since ?ukasiewicz, it has been opinio communis that Aristotle's modal syllogistic is incomprehensible due to its many faults and inconsistencies, and that there is no hope of finding a single consistent formal model for it. The aim of this paper is to disprove these claims by giving such a model. My main points shall be, first, that Aristotle's syllogistic is a pure term logic that does not recognize an extra syntactic category of individual symbols besides syllogistic terms and, second, (...) that Aristotelian modalities are to be understood as certain relations between terms as described in the theory of the predicables developed in the Topics. Semantics for modal syllogistic is to be based on Aristotelian genus-species trees. The reason that attempts at consistently reconstructing modal syllogistic have failed up to now lies not in the modal syllogistic itself, but in the inappropriate application of modern modal logic and extensional set theory to the modal syllogistic. After formalizing the underlying predicable-based semantics (Section 1) and having defined the syllogistic propositions by means of its term logical relations (Section 2), this paper will set out to demonstrate in detail that this reconstruction yields all claims on validity, invalidity and inconclusiveness that Aristotle maintains in the modal syllogistic (Section 3 and 4). (shrink)

In a difficult but fascinating passage in Metaphysics Z.17, Aristotle puts forward a proposal, by means of a regress argument, according to which a whole or matter/form-compound is one or unified, in contrast to a heap, due to the presence of form or essence. This proposal gives rise to two central questions: (i) the question of whether form itself is to be viewed, literally and strictly speaking, as part of the matter/form-compound; and (ii) the question of whether form is to (...) be regarded as itself having parts. It is argued that both questions may be answered affirmatively, without giving rise to a regress worry. (shrink)

Since Freges terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this questionBegriffes syntaxhighercorresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcorans theory via predicate logic.

It was with this bitter intervention from Thrasymachus, occurring halfway through the first of its ten Books, that that work begins to come urgently alive. For the remainder of Book I the Socrates of the Dialogue asks questions and raises objections, while Thrasymachus keeps urging that in fact the just become through their very justice the victims of exploitation–the suckers!

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

Corcoran, John. 1974. Aristotelian Syllogisms: Valid arguments or true generalized conditionals?, Mind 83, 278–81. MR0532928 (58 #27178) This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed indirect proof. Lukasiewicz (...) evidence is presented fully; it is irrefutable. But, instead of considering the possibility that Aristotle’s discourses were not intended to express indirect proofs of universalized conditions presupposing axiomatic premises, Lukasiewicz came to the amazing conclusion that Aristotle did not understand indirect proof. This paper builds on the admirable Lukasiewicz scholarship to establish a conclusion diametrically opposed to the one Lukasiewicz asserted. This paper points out that if Aristotle had not been establishing an underlying logic but he was instead axiomatizing a theory of terms, Aristotelians could not claim for Aristotle the title Founder of Logic. People who take Euclid, Peano, and Zermelo to have first axiomatized geometry, arithmetic, and set theory, respectively, do not think that this qualifies them for the titles Founder of Geometry, Founder of Arithmetic, and Founder of Set Theory, respectively. Such people do think that this would qualify the three for the titles Founder of Axiomatic Geometry, Founder of Axiomatic Arithmetic, and Founder of Axiomatic Set Theory, respectively: titles that carry no honors in logic. Being the Founder of Axiomatic Term Theory would likewise carry no honors in the field of logic. CORRECTION: The paper inadvertently implied that Euclid was the first to axiomatize geometry. In order to understand Aristotle’s Analytics as a treatise on demonstration it helps to realize that axiomatized geometry was studied in Plato’s Academy when Aristotle was a student. Euclid was the author of the only ancient axiomatized geometry now available. (shrink)

Analyzes the poem "On Nature" by Parmenides, arguing that is actually a philosophical argument disguised as Homer-like mythological journey. Original.

Cet ouvrage n'est ni un commentaire ni une explication d'obedience historiciste ou deterministe. Par questionnement, lecture et interpretation, l'auteur a voulu produire une semantique philosophique. La doctrine des idees est ainsi reexaminee a la convergence des problemes du langage, de la science et de la cite (logos, episteme, polis). Elle ne peut plus des lors etre interpretee sous l'hypothese de l' idealisme. Elle se manifeste comme une serie de questions de sens ou s'indique une philosophie de la raison. Partout ou (...) le logos nous porte, c'est la qu'il faut aller, tel en serait le mot d'ordre, mais avec la precision qu'a l'articulation du mythique et du theorique, du tragique et du philosohique, et plus profondement de la deraison et du logos, le rationalisme platonicien n'est fait que de raison. (shrink)

Explores the origin and evolution of the Greek concept of nature up until the time of Plato.

A study of Pyrrhonean scepticism, consisting of a new translation of Sextus Empiricus' Outlines of Pyrrhonism, accompanied by an analytic introduction and an in-depth, section-by-section commentary - the first of its kind available.

Reprint of the original, first published in 1869.

This paper discusses whether there is room for knowledge of causal relations between events in Aristotle's theory of science as developed in the Posterior Analytics. My focus is on Aristotle's analysis of the fourth sense of kath' hauto or per se predication.

An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

Much of the last fifty years of scholarship on Aristotle’s syllogistic suggests a conceptual framework under which the syllogistic is a logic, a system of inferential reasoning, only if it is not a theory or formal ontology, a system concerned with general features of the world. In this paper, I will argue that this a misleading interpretative framework. The syllogistic is something sui generis: by our lights, it is neither clearly a logic, nor clearly a theory, but rather exhibits certain (...) characteristic marks of logics and certain characteristic marks of theories. In what follows, I will present a debate between a theoretical and a logical interpretation of the syllogistic. The debate centers on the interpretation of syllogisms as either implications or inferences. But the significance of this question has been taken to concern the nature and subject-matter of the syllogistic, and how it ought to be represented by modern techniques. For one might think that, if syllogisms are implications, propositions with conditional form, then the syllogistic, in so far as it is a systematic taxonomy of syllogisms, is a theory or a body of knowledge concerned with general features of the world. Furthermore, if the syllogistic is a theory, then it ought to be represented by an axiomatic system, a system deriving propositional theorems from axioms. On the other hand, if syllogisms are inferences, then the syllogistic is a logic, a system of inferential reasoning. And furthermore, it ought to be represented as a natural deduction system, a system deriving valid arguments by means of intuitively valid inferences. I will argue that one can disentangle these questions—are syllogisms inferences or implications, is the syllogistic a logic or a theory, is the syllogistic a body of worldly knowledge or a system of inferential reasoning, and ought we to represent the syllogistic as a natural deduction system or an axiomatic system—and that we must if we are to have a historically accurate understanding of Aristotle. (shrink)

I argue, firstly, that the accounts of 'accident' in Aristotle's Met. V 30 and in Top. I 5 cannot be used to elucidate each other: the Metaphysics passage tries to disentangle the uses of a Greek word, the Topics passage introduces technical terms for Aristotle's semantics. I then argue that the positive definition in Top. I 5 is to be understood in the following way: X is an accident of Y iff X belongs to Y and if there is a (...) Z such that X can belong to Z and also not belong to Z. Thus, being white is an accident of snow. I finally argue that certain shortcomings in the Topics account lead Aristotle to redefine accident in the Posterior Analytics. (shrink)

De acordo com Aristóteles, conhecemos algo cientificamente quando apreendemos a causa pela qual essa coisa é e apreendemos, também, certa relação necessária entre aquilo que pretendemos conhecer e o que descobrimos ser a causa adequada que explica por que tal fato é o caso. Além disso, o filósofo identifica o conhecimento científico com a posse de um silogismo científico ou demonstração. Neste trabalho, analisamos a relação entre a teoria demonstrativa que Aristóteles desenvolve, principalmente, no livro I dos Segundos Analíticos e (...) sua teoria silogística dos Primeiros Analíticos I e tentamos responder por que o conhecimento científico deve ser via silogismo. Também procuramos explicitar como as noções de causa e de necessidade, pelas quais Aristóteles define o conhecimento científico, são contempladas pela exigência de que as proposições de uma demonstração sejam per se. Finalmente, discutiremos como essas noções de per se, necessidade e causa se encaixam na estrutura silogística, uma vez que conhecer algo cientificamente é possuir um silogismo científico. (shrink)

This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".