• The Combinatorics of Stoic Conjunction; or, Hipparchus Refuted, Chrysippus Vindicated
    In James Allen, Eyjólfur Kjalar Emilsson, Benjamin Morison & Wolfgang-Rainer Mann (eds.), Oxford Studies in Ancient Philosophy, Volume 40: Essays in Memory of Michael Frede, Oxford University Press. pp. 40--157. 2011.
  • Determinism and Freedom in Stoic Philosophy (review by Ricardo Salles) (review)
    Philosophical Quarterly 50 (200): 386-389. 2000.
  • Analyticity, Balance and Non-admissibility of Cut in Stoic Logic
    with Roy Dyckhoff
    Studia Logica 1-23. 2018.
    This paper shows that, for the Hertz–Gentzen Systems of 1933, extended by a classical rule T1 and using certain axioms, all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence that a particular derivable…Read more
  • Analyticity, Balance and Non-admissibility of Cut in Stoic Logic
    with Roy Dyckhoff
    Studia Logica 1-23. forthcoming.
    This paper shows that, for the Hertz–Gentzen Systems of 1933, extended by a classical rule T1 and using certain axioms, all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence that a particular derivable…Read more
  • Gestalt Shifts in the Liar Or Why KT4M Is the Logic of Semantic Modalities
    In Bradley Armour-Garb (ed.), Reflections on the Liar, Oxford University. pp. 71-113. 2017.
    ABSTRACT: This chapter offers a revenge-free solution to the liar paradox (at the centre of which is the notion of Gestalt shift) and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why -- and how -- truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our use of that notion. The chapter argues that, …Read more
  • Chrysippus and the epistemic theory of vagueness
    Proceedings of the Aristotelian Society 102 (1): 217-238. 2002.
    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…Read more
  • Did Epicurus discover the Free-Will Problem?
    Oxford Studies in Ancient Philosophy 19 287-337. 2000.
    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…Read more
  • 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.
  • The Philosophy of Aristotle (edited book)
    with Aristotle and Renford Bambrough
    Signet Classics. 2011.
    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.
  • Stoic Conceptions of Freedom and their Relation to Ethics
    Bulletin of the Institute of Classical Studies 41 (S68): 71-89. 1997.
    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…Read more
  • Logic, History of: Ancient Logic
    In Donald M. Borchert (ed.), Encyclopedia of Philosophy, Thomson Gale. 2006.
    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).
  • Ancient Logic (substantive revision Dec 29, 2015)
    Stanford Encyclopedia of Philosophy. 2015.
    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.
  • Found in Translation: Aristotle’s Nicomachean Ethics 3.5, 1113b7-8 and its Reception
    Oxford Studies in Ancient Philosophy 45 103-148. 2013.
    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 A…Read more
  • Freedom
    In Hubert Cancik, Christine F. Salazar & et al (eds.), Brill's New Pauly, Brill. 2011.
    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 (20…Read more
  • 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 overl…Read more
  • Moral responsibility and moral development in Epicurus’ philosophy
    In B. Reis & S. Haffmans (eds.), The Virtuous Life in Greek Ethics, Cambridge University Press. 2006.
    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 forc…Read more
  • 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 2n…Read more
  • Logic: The Stoics (Part Two)
    In Keimpe Algra, Jonathan Barnes & et al (eds.), The Cambridge History of Hellenistic Philosophy, Cambridge University Press. 1999.
    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 …Read more
  • Why the order of the figures of the hypothetical syllogisms was changed
    Classical Quarterly 50 (01): 247-251. 2000.
    ABSTRACT: At the turn of the second century AD there existed two different views on the ordering of the figures of the (wholly) hypothetical syllogisms. One goes back to Theophrastus, whereas the other (adopted e.g. by Alexander of Aphrodisias and Alcinous) seems to have been the result of a later change. This reversal of the order of figures has so far not received a satisfactory explanation. In this paper I show how it came about.
  • 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 obje…Read more
  • I—Columnar Higher-Order Vagueness, or Vagueness is Higher-Order Vagueness
    Aristotelian Society Supplementary Volume 89 (1): 61-87. 2015.
    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 Kr…Read more
  • Chrysippus' Modal Logic and Its Relation to Philo and Diodorus
    In K. Doering & Th Ebert (eds.), Dialektiker und Stoiker, Franz Steiner. pp. 63--84. 1993.
    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 m…Read more
  • 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 …Read more
  • Aristotle's De Interpretatione 8 is About Ambiguity
    In D. Scott (ed.), Maieusis: Essays in Ancient Philosophy, Oxford University Press. pp. 301. 2007.
    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 175…Read more
  • Afterword to The Philosophy of Aristotle (edited book)
    Signet. 2011.
    ABSTRACT: This is a little piece directed at the newcomer to Aristotle, making some general remarks about reading Aristotle at the beginning and end, with sandwiched in between, a brief and much simplified discussion of some common misunderstandings of Aristotle's philosophy, concerning spontaneity, causal indeterminism, freedom-to-do-otherwise, free choice, agent causation, logical determinism, teleological determinism, artistic creativity and freedom (eleutheria).
  • Stoic Logic
    In Brad Inwood (ed.), The Cambridge Companion to Stoic Philosophy, Cambridge University Press. 2003.
    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 o…Read more
  • ABSTRACT: Discussion (in German) of Robert Muller's "Les Megariques, Fragments et temoignages". Traduit et commentes. Paris, Vrin 1985, with focus on his commentary on ancient paradoxes.
  • 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 i…Read more