Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this. In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system QS4M+BF+FIN. It (...) corresponds to the class of transitive, reflexive and final frames. With borderlineness defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague. Like Williamson's, the theory proposed here has no clear borderline cases in Sorites sequences. I argue that objections that there must be clear borderline cases ensue from the confusion of two notions of borderlineness—one associated with genuine higher-order vagueness, the other employed to sort objects into categories—and that the higher-order vagueness paradoxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections. (shrink)
This paper is an expanded written version of my reply to Rosanna Keefe’s paper ‘Modelling higher-order vagueness: columns, borderlines and boundaries’ (Keefe 2015), which in turn is a reply to my paper ‘Columnar higher-order vagueness, or Vagueness is higher-order vagueness’ (Bobzien 2015). Both papers were presented at the Joint Session of the the Aristotelian Society and the Mind Association in July, 2015. At the Joint Session meeting, there was insufficient time to present all of my points in response to Keefe’s (...) paper. In addition, the audio of the session, which is available online, becomes inaudible at the beginning of my reply to Keefe’s comments due to a technical defect. The following is a full version of my remarks. (shrink)
ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.
ABSTRACT: This paper discusses ancient versions of paradoxes today classified as paradoxes of presupposition and how their ancient solutions compare with contemporary ones. Sections 1-4 air ancient evidence for the Fallacy of Complex Question and suggested solutions, introduce the Horn Paradox, consider its authorship and contemporary solutions. Section 5 reconstructs the Stoic solution, suggesting the Stoics produced a Russellian-type solution based on a hidden scope ambiguity of negation. The difference to Russell's explanation of definite descriptions is that in the Horn (...) Paradox the Stoics uncovered a hidden conjunction rather than a hidden existential sentence. Sections 6 and 7 investigate hidden ambiguities in 'to have' and 'to lose' (including inalienable and alienable possession) and ambiguities of quantification based on substitution of indefinite plural expressions for indefinite or anaphoric pronouns, and Stoic awareness of these. Section 8 considers metaphorical readings and allusions that add further spice to the paradox. (shrink)
ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which (...) establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)
ABSTRACT: This paper is distinctly odd. It demonstrates what happens when an analytical philosopher and historian of philosophy tries their hand at the topic of reception. For a novice to this genre, it seemed advisable to start small. Rather than researching the reception of an author, book, chapter, section or paragraph, the focus of the paper is on one sentence: Aristotle’s Nicomachean Ethics 3.5, 1113b7-8. This sentence has markedly shaped scholarly and general opinion alike with regard to Aristotle’s theory of (...) free will. In addition, it has taken on a curious life of its own. Part one of the paper examines the text itself. Part two explores its reception from antiquity to the present day, including present-day popular culture, later ancient, Byzantine, Arabic, Latin Medieval, Renaissance, Victorian and contemporary scholarship. There are some surprises on the way. (The paper also serves as an introduction to the reception of the Nicomachean Ethics from its beginnings to the present.). (shrink)
ABSTRACT: This paper serves two purposes: (i) it can be used by students as an introduction to chapters 1-5 of book iii of the NE; (ii) it suggests an answer to the unresolved question what overall objective this section of the NE has. The paper focuses primarily on Aristotle’s theory of what makes us responsible for our actions and character. After some preliminary observations about praise, blame and responsibility (Section 2), it sets out in detail how all the key notions (...) of NE iii 1-5 are interrelated (Sections 3-9). The setting-out of these interconnections makes it then possible to provide a comprehensive interpretation of the purpose of the passage. Its primary purpose is to explain how agents are responsible for their actions not just insofar as they are actions of this kind or that, but also insofar as they are noble or base: agents are responsible for their actions qua noble or base, because, typically via choice, their character dispositions are a causal factor of those actions (Section 10). The paper illustrates the different ways in which agents can be causes of their actions by means of Aristotle’s four basic types of agents (Section 11). A secondary purpose of NE iii 1-5 is to explain how agents can be held responsible for consequences of their actions (Section 12), in particular for their character dispositions insofar as these are noble or base, i.e. virtues or vices (Section 13). These two goals are not the only ones Aristotle pursues in the passage. But they are the ones Aristotle himself indicates in its first sentence and summarizes in its last paragraph; and the ones that give the passage a systematic unity. The paper also briefly consider the issues of freedom-to-do-otherwise, free choice and free-will in the contexts in which they occur (i.e. in the final paragraphs of Sections 6, 7, 12, 13). (shrink)
ABSTRACT: ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor (...) did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)
The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity are in play (...) (Williamson-style "luminosity" or self-revealing clarity and concealeable clarity) and what their respective functions are in accounts of higher-order vagueness. On this basis, we argue first that, contrary to common opinion, higher-order vagueness and S4 are perfectly compatible. This is in response to claims like that by Williamson that, if vagueness is defined with the help of a clarity operator that obeys axiom 4, higher-order vagueness disappears. Second, we argue that, contrary to common opinion, (i) bivalence-preservers (e.g. epistemicists) can without contradiction condone axiom 4 (by adopting what elsewhere we call columnar higher-order vagueness), and (ii) bivalence-discarders (e.g. open-texture theorists, supervaluationists) can without contradiction reject axiom 4. Third, we rebut a number of arguments that have been produced by opponents of axiom 4, in particular those by Williamson. (The paper is pitched towards graduate students with basic knowledge of modal logic.). (shrink)
ABSTRACT: A detailed presentation of Stoic theory of arguments, including truth-value changes of arguments, Stoic syllogistic, Stoic indemonstrable arguments, Stoic inference rules (themata), including cut rules and antilogism, argumental deduction, elements of relevance logic in Stoic syllogistic, the question of completeness of Stoic logic, Stoic arguments valid in the specific sense, e.g. "Dio says it is day. But Dio speaks truly. Therefore it is day." A more formal and more detailed account of the Stoic theory of deduction can be found (...) in S. Bobzien, Stoic Syllogistic, OSAP 1996. (shrink)
ABSTRACT: This is a short companion piece to my ‘Found in Translation – Aristotle’s Nicomachean Ethics III.5 1113b7-8 and its Reception’ in which I examine in close textual analysis the philosophical question whether these two lines from the Nicomachean Ethics provide any evidence that Aristotle discussed free choice – as is not infrequently assumed. The result is that they do not, and that the claim that they do tends to be based on a mistranslation of the Greek. (There is some (...) inevitable overlap with Part 1 of the 'Found in Translation' paper.). (shrink)
ABSTRACT: This paper discusses the Stoic treatment of fallacies that are based on lexical ambiguities. It provides a detailed analysis of the relevant passages, lays bare textual and interpretative difficulties, explores what the Stoic view on the matter implies for their theory of language, and compares their view with Aristotle’s. In the paper I aim to show that, for the Stoics, fallacies of ambiguity are complexes of propositions and sentences and thus straddle the realms of meaning (which is the domain (...) of logic) and of linguistic expressions (which is the domain of linguistics), but also involve a pragmatic element; that the Stoics believe that the premises of the fallacies, when uttered, have only one meaning and are true, and thus should be conceded; that hence there is no need for a mental process of disambiguation in the listeners; that Aristotle, by contrast, appears to assume that the premises always have all their meanings, and accordingly recommends that the listeners explicitly disambiguate them, which presupposes a process of mental disambiguation. I proffer two readings of the Stoic advice that we ‘be silent’ when confronted with a fallacy of ambiguity in dialectical discourse, and explicate how each leads to an overall consistent interpretation of the textual evidence. Finally, I demonstrate that the method advocated by the Stoics works in all cases of fallacies of lexical ambiguity. (shrink)
ABSTRACT: I argue that there is no evidence that Epicurus dealt with the kind of free-will problem he is traditionally associated with; i.e. that he discussed free choice or moral responsibility grounded on free choice, or that the "swerve" was involved in decision processes. Rather, for Epicurus, actions are fully determined by the agent's mental disposition at the outset of the action. Moral responsibility presupposes not free choice but that the person is unforced and causally responsible for the action. This (...) requires the agent's ability to influence causally, on the basis of their beliefs, the development of their behavioral dispositions. The "swerve" was intended to explain the non-necessity of agency without undermining Epicurus' atomistic explanation of the order in the universe, viz. by making the mental dispositions of adults non-necessary. (shrink)
Much of chapters 2 to 6 is in agreement with publications from the last twenty years (including those of the reviewer); so for example Frede’s points that neither Aristotle nor the Stoics had a notion of free-will; that in Epictetus (for the first time) the notions of freedom and will were combined; that an indeterminist notion of free-will occurs first in Alexander. The achievement of these chapters lies in the way Frede carefully joins them together and uses them as a (...) basis for some substantive criticism and rewriting of the history of free-will regarding late antique Pagan and Christian authors, in particular Plotinus, Origen and Augustine. (shrink)
ABSTRACT: In this paper I show that, contrary to the prevalent view, in his De Interpretatione chapter 8, Aristotle is concerned with a kind of ambiguity, i.e. with homonymy; more precisely, with homonymy of linguistic expressions as it may occur in dialectical argument. The paper has two parts. In the first part, I argue that in the Sophistici Elenchi 175b39-176a5 Aristotle indubitably deals with homonymy in dialectical argument; that De Interpretatione 8 is a parallel to Sophistici Elenchi 175b39-176a5; that De (...) Interpretatione 8 is concerned with dialectical argument; that, hence, De Interpretatione 8, too, deals with homonymy in dialectical argument. In the second part I discuss objections that have been put forward against the view that De Interpretatione 8 is about homonymy and demonstrate that they do not succeed. (shrink)
ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of propositional logic; 4. (...) Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)
ABSTRACT: In contemporary discussions of freedom in Stoic philosophy we often encounter the following assumptions: (i) the Stoics discussed the problem of free will and determinis; (ii) since in Stoic philosophy freedom of the will is in the end just an illusion, the Stoics took the freedom of the sage as a substitute for it and as the only true freedom; (iii) in the c. 500 years of live Stoic philosophical debate, the Stoics were largely concerned with the same philosophical (...) problems of freedom. In this paper I argue that (i) can be upheld only in a very restricted way; (ii) is altogether untenable; and regarding (iii), that, although there may have occurred little change in the Stoic philosophical position on freedom over the centuries, we can detect more than one transformation of the philosophical problems that were at the forefront of the discussion. Moreover, that all the conceptions and problems of freedom were linked to Stoic ethics, and that the differences between them become transparent when one considers their various roles in this context. (shrink)
ABSTRACT: A systematic reconstruction of Chrysippus’ theory of causes, grounded on the Stoic tenets that causes are bodies, that they are relative, and that all causation can ultimately be traced back to the one ‘active principle’ which pervades all things. I argue that Chrysippus neither developed a finished taxonomy of causes, nor intended to do so, and that he did not have a set of technical terms for mutually exclusive classes of causes. Rather, the various adjectives which he used for (...) causes had the function of describing or explaining particular features of certain causes in particular philosophical contexts. I challenge the sometimes assumed close connection of Chrysippus’ notion of causation with explanation. I show that the standard view that the distinction between proximate and auxiliary causes and perfect and principal causes corresponds to the distinction between internal and external determining factors is not born out by the evidence, and argue that causes of the two types were not thought to co-operate, but rather conceived of as alternatives. (shrink)
ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is why Hipparchus’ (...) logic differed from Stoic logic, and consequently, whether Hipparchus actually refuted Chrysippus. This paper closes these explanatory gaps. (1) I reconstruct Hipparchus’ notions of conjunction and negation, and show how they differ from Stoic logic. (2) Based on evidence from Stoic logic, I reconstruct Chrysippus’ calculations, thereby (a) showing that Chrysippus’ claim of over a million conjunctions was correct; and (b) shedding new light on Stoic logic and – possibly – on 3rd century BCE combinatorics. (3) Using evidence about the developments in logic from the 3rd to the 2nd centuries, including the amalgamation of Peripatetic and Stoic theories, I explain why Hipparchus, in his calculations, used the logical notions he did, and why he may have thought they were Stoic. OPEN ACCESS LINK. (shrink)
ABSTRACT: A general interpretation and close textual analysis of Kant’s theory of the categories of freedom (or categories of practical reason) in his Critique of Practical Reason. My main concerns in the paper are the following: (1) I show that Kant’s categories of freedom have primarily three functions: as conditions of the possibility for actions (i) to be free, (ii) to be comprehensible as free and (iii) to be morally evaluated. (2) I show that for Kant actions, although qua theoretical (...) objects they are always already constituted by means of the theoretical categories, qua practical objects (objects of reason in its practical use, i.e. objects qua possibly good or bad) they are constituted by means of the categories of freedom; and that it is only in this way that actions, qua phenomena, can be a consequence of freedom, and can be understood and evaluated as such. (3) Since Kant's presentation of his theory of the Categories of Freedom is extremely brief, Kant's parallel theory of the theoretical categories in his Critique of Pure Reason is used as a guide for the interpretation of the practical categories and their systematic relevance. (Translation by Alex Worsnip, reviewed and approved by the author.). (shrink)
ABSTRACT: A very brief summary presentation of western ancient logic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).
The paper presents a new theory of higher-order vagueness. This theory is an improvement on current theories of vagueness in that it (i) describes the kind of borderline cases relevant to the Sorites paradox, (ii) retains the ‘robustness’ of vague predicates, (iii) introduces a notion of higher-order vagueness that is compositional, but (iv) avoids the paradoxes of higher-order vagueness. The theory’s central building-blocks: Borderlinehood is defined as radical unclarity. Unclarity is defined by means of competent, rational, informed speakers (‘CRISPs’) whose (...) competence, etc., is indexed to the scope of the unclarity operator. The unclarity is radical since it eliminates clear cases of unclarity and, that is, clear borderline cases. This radical unclarity leads to a (bivalence-compatible, non-intuitionist) absolute agnosticism about the semantic status of all borderline cases. The corresponding modal system would be a non-normal variation on S4M. (shrink)
Bobzien presents the definitive study of one of the most interesting intellectual legacies of the ancient Greeks: the Stoic theory of causal determinism. She explains what it was, how the Stoics justified it, and how it relates to their views on possibility, action, freedom, moral responsibility, moral character, fatalism, logical determinism and many other topics. She demonstrates the considerable philosophical richness and power that these ideas retain today.
ABSTRACT: Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ‘So-called second-order vagueness in ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss Shapiro’s arguments, arguing that (...) none is compelling. Lastly, we introduce the account of vagueness Shapiro would have obtained had he retained compositionality and show that it entails true higher-order vagueness. (shrink)
ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from Aristotle’s Topics and (...) Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)
ABSTRACT: This paper traces the evidence in Galen's Introduction to Logic (Institutio Logica) for a hypothetical syllogistic which predates Stoic propositional logic. It emerges that Galen is one of our main witnesses for such a theory, whose authors are most likely Theophrastus and Eudemus. A reconstruction of this theory is offered which - among other things - allows to solve some apparent textual difficulties in the Institutio Logica.
ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and modal theorems, and to make (...) clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy. (shrink)
ABSTRACT: For the most part, this paper is not a philosophical paper in any strict sense. Rather, it focuses on the numerous exegetical puzzles in Sextus Empiricus’ two main passages on time (M X.l69-247 and PH III.l36-50), which, once sorted, help to explain how Sextus works and what the views are which he examines. Thus the paper provides an improved base from which to put more specifically philosophical questions to the text. The paper has two main sections, which can, by (...) and large, be read independently. Each is about a topic which, to my knowledge, has so far not been treated in detail. The first section is concemed with the argument structures of the two main passages on time in Sextus, pointing out various irregularities in the overall argument in both passages, as well as parallels and differences, and asks the question what kinds of scepticism and sceptical methods we find in the various parts of each passage. The second section focuses on the doxographical accounts of time in the two passages: what they are, how they compare with surviving parallels, to what philosophers we can attribute those accounts for which Sextus himself provides either no, or more than one, possible ascriptions, and how Sextus treats the doxographical material. This discussion is inspired by the contributions Michael Frede offered on this topic the day before his untimely death. (shrink)
ABSTRACT: 1. This paper argues that Epicurus had a notion of moral responsibility based on the agent’s causal responsibility, as opposed to the agent’s ability to act or choose otherwise; that Epicurus considered it a necessary condition for praising or blaming an agent for an action, that it was the agent and not something else that brought the action about. Thus, the central question of moral responsibility was whether the agent was the, or a, cause of the action, or whether (...) the agent was forced to act by something else. Actions could be attributed to agents because it is in their actions that the agents, qua moral beings, manifest themselves. 2. As a result, the question of moral development becomes all important. The paper collects and discusses the evidence for Epicurus views on moral development, i.e. (i) on how humans become moral beings and (ii) on how humans can become morally better. It becomes clear that Epicurus envisaged a complex web of hereditary and environmental factors to shape the moral aspect of a human being. 3. In line with Epicurus’ theory of moral responsibility and moral development, Epicurus ethics does not have the function of developing or justifying a moral system that allows for the effective allocation of praise and blame. Rather, for him the function of ethics – and in fact of the whole of philosophy – is to give everyone a chance to morally improve. (shrink)
ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness. In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and how he made allowances (...) for higher-order vagueness, but if he did, this was not grounded on an epistemicist position. (shrink)
ABSTRACT: A detailed presentation of Stoic logic, part one, including their theories of propositions (or assertibles, Greek: axiomata), demonstratives, temporal truth, simple propositions, non-simple propositions(conjunction, disjunction, conditional), quantified propositions, logical truths, modal logic, and general theory of arguments (including definition, validity, soundness, classification of invalid arguments).
ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with a focus on issues that may be of interest to contemporary logicians and covering important topics in Post-Aristotelian logic that are frequently neglected (such as Peripatetic hypothetical syllogistic, the Stoic axiomatic system of propositional logic and various later ancient developments).
ABSTRACT: In this paper I argue that the ‘discovery’ of the problem of causal determinism and freedom of decision in Greek philosophy is the result of a combination and mix-up of Aristotelian and Stoic thought in later antiquity; more precisely, a (mis-)interpretation of Aristotle’s philosophy of deliberate choice and action in the light of Stoic theory of determinism and moral responsibility. The (con-)fusion originates with the beginnings of Aristotle scholarship, at the latest in the early 2nd century AD. It undergoes (...) several developments, absorbing Epictetan, Middle-Platonist, and Peripatetic ideas; and it leads eventually to a concept of freedom of decision and an exposition of the ‘free-will problem’ in Alexander of Aphrodisias’ On Fate and in the Mantissa ascribed to him. (shrink)
The ‘Dialectical school’ denotes a group of early Hellenistic philosophers that were loosely connected by philosophizing in the — Socratic — tradition of Eubulides of Megara and by their interest in logical paradoxes, propositional logic and dialectical expertise. . Its two best known members, Diodorus Cronus and Philo the Logician, made groundbreaking contributions to the development of theories of conditionals and modal logic. Philo introduced a version of material implication; Diodorus devised a forerunner of strict implication. Each developed a system (...) of modal notions that satisfies the basic logical requirements laid down by modern standard modal theories. In antiquity, Diodorus Cronus was famous for his so called Master Argument, which aims to prove that only the actual is possible. (shrink)
ABSTRACT: A brief critique of Bruno Haas’ interpretation of Kant’s categories of practical reason and a reply to his criticism of my paper 'Die Kategorien der Freiheit bei Kant' ('Kant's Categories of Freedom').
ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and Diodorus Cronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.
ABSTRACT: One-page entry on freedom in the philosophical (as opposed to political) sense in antiquity, noting (among other things) that a notion of freedom of choice that requires that the person not be causally predetermined in his/her actions is developed only in the 1st-3rd cents. CE in Alexander of Aphrodisias, building on elements of Aristotelian ethics and logic, Stoic psychology and perhaps Christian and Middle Platonic influences. Both German version (1998) and English translation (2011).
NOTE: The English translation is listed separately. ABSTRACT: A general interpretation and close textual analysis of Kant’s theory of the categories of freedom (or categories of practical reason) in his Critique of Practical Reason. My main concerns in the paper are the following: (1) I show that Kant’s categories of freedom have primarily three functions: as conditions of the possibility for actions (i) to be free, (ii) to be comprehensible as free and (iii) to be morally evaluated. (2) I show (...) that for Kant actions, although qua theoretical objects they are always already constituted by means of the theoretical categories, qua practical objects (objects of reason in its practical use, i.e. objects qua possibly good or bad) they are constituted by means of the categories of freedom; and that it is only in this way that actions, qua phenomena, can be a consequence of freedom, and can be understood and evaluated as such. (3) Since Kant's presentation of his theory of the Categories of Freedom is extremely brief, Kant's parallel theory of the theoretical categories in his Critique of Pure Reason is used as a guide for the interpretation of the practical categories and their systematic relevance. (shrink)
This paper shows that the following common assumption is false: that in modal-logical representations of higher-order vagueness, for there to be borderline cases to borderline cases ad infinitum, the number of possible distinct modalities in a modal system must be infinite. (Open access journal).
ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 Forerunners (...) of Modus Ponens and Modus Tollens 3.4 Wholly Hypothetical Syllogisms 4. Diodorus Cronus and Philo the Logician 5. The Stoics 5.1 Logical Achievements Besides Propositional Logic 5.2 Syntax and Semantics of Complex Propositions 5.3 Arguments 5.4 Stoic Syllogistic 5.5 Logical Paradoxes 6. Epicurus and the Epicureans 7. Later Antiquity. (shrink)
ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the ‘mixed hypothetical syllogisms’. The other type is the one to which the present paper is devoted. These arguments went by the name of ‘wholly hypothetical syllogisms’. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in different authors. For (...) instance, we find ‘If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C’. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is ‘is’, where it occurs, predicative, existential, or veridical? That is, should ‘A esti’ be translated as ‘it is an A’, ‘A exists’, ‘As exist’ or ‘It is true/the case that A’? If A, B, C are term letters, and ‘is’ is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments - even if the ancients thought they were all talking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded. (shrink)
A selection of Aristotle's most important philosophical works in English translation with an introduction and comments by Renford Bambrough with emphasis on metaphysical questions and a new afterword by Susanne Bobzien that focuses on how to study Aristotle and on Aristotle on determinism and freedom.
ABSTRACT: In this paper I argue (i) that the hypothetical arguments about which the Stoic Chrysippus wrote numerous books (DL 7.196) are not to be confused with the so-called hypothetical syllogisms" but are the same hypothetical arguments as those mentioned five times in Epictetus (e.g. Diss. 1.25.11-12); and (ii) that these hypothetical arguments are formed by replacing in a non-hypothetical argument one (or more) of the premisses by a Stoic "hypothesis" or supposition. Such "hypotheses" or suppositions differ from propositions in (...) that they have a specific logical form and no truth-value. The reason for the introduction of a distinct class of hypothetical arguments can be found in the context of dialectical argumentation. The paper concludes with the discussion of some evidence for the use of Stoic hypothetical arguments in ancient texts. (shrink)
ABSTRACT: Part 1 discusses the Stoic notion of propositions (assertibles, axiomata): their definition; their truth-criteria; the relation between sentence and proposition; propositions that perish; propositions that change their truth-value; the temporal dependency of propositions; the temporal dependency of the Stoic notion of truth; pseudo-dates in propositions. Part 2 discusses Stoic modal logic: the Stoic definitions of their modal notions (possibility, impossibility, necessity, non-necessity); the logical relations between the modalities; modalities as properties of propositions; contingent propositions; the relation between the Stoic (...) modal notions and those of Diodorus Cronus and Philo of Megara; the role of ‘external hindrances’ for the modalities; the temporal dependency of the modalities; propositions that change their modalities; the principle that something possible can follow from something impossible; the interpretations of the Stoic modal system by B. Mates, M. Kneale, M. Frede, J. Vuillemin and M. Mignucci are evaluated. -/- For a much shorter English version of Part 1 of the book see my ‘Stoic Logic’, in K. Algra et al. (eds), The Cambridge History of Hellenistic Philosophy, Cambridge 1999, 92-157. For a shorter, updated, English version of Part 2 of the book see my 'Chrysippus' Modal Logic and its Relation to Philo and Diodorus', in K. Doering / Th. Ebert (eds) Dialektiker und Stoiker (Stuttgart 1993) 63-84. (shrink)
ABSTRACT: English translation of the 2nd/3rd century Peripatetic Philosopher's Alexander of Aphrodisias commentary on Aristotle's non-modal syllogistic, i.e. on one of the most influential logical texts of all times. -/- Volume includes introduction on Alexander of Aphrodisias and the early commentators, translation with notes and comments, appendices with a new translation of Aristotle's text, a summary of Aristotle's non-modal syllogistic and textual notes.
In this paper I present the text, a translation, and a commentary of a long anonymous scholium to Aristotle’s Analytics which is a Greek parallel to Boethius’ De Hypotheticis Syllogismis, but has so far not been recognized as such. The scholium discusses hypothetical syllogisms of the types modus ponens and modus tollens and hypothetical syllogisms constructed from three conditionals (‘wholly hypothetical syllogisms’). It is Peripatetic, and not Stoic, in its theoretical approach as well as its terminology. There are several elements (...) of early Peripatetic hypothetical syllogistic preserved in it, and there is a large number of close parallels to Boethius’ De Hypotheticis Syllogismis which we find in no other source. It is very likely that there was a Greek source from which both the scholium and large parts of Boethius’ De Hypotheticis Syllogismis are ultimately derived. (shrink)