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973Wholly Hypothetical SyllogismsPhronesis 45 (2): 87-137. 2000.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, varie…Read more
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481Logic: The MegaricsIn Keimpe Algra, Jonathan Barnes, Jaap Mansfeld & Malcolm Schofield (eds.), The Cambridge History of Hellenistic Philosophy, Cambridge University Press. 1999.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.
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283Higher-order Vagueness, Radical Unclarity, and Absolute AgnosticismPhilosophers' Imprint 10 1-30. 2010.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 b…Read more
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865In defense of true higher-order vagueness: a discussion of Stewart Shapiro on higher-order vaguenessSynthese 180 (3): 317-335. 2011.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 ac…Read more
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3702Did 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
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1490The Stoics on fallacies of equivocationIn D. Frede & B. Inwood (eds.), Language and Learning, Proceedings of the 9th Symposium Hellenisticum, Cambridge University Press. 2006.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…Read more
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377This 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…Read more
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103Ancient 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.
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857LogicIn Simon Hornblower & A. Spawforth (eds.), The Oxford Classical Dictionary, 3rd edition, Oxford University Press. 1996.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).
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450FreedomIn 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
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99Die stoische Modallogik (Stoic Modal Logic)Koenigshausen and Neumann. 1986.The first monograph on Stoic modal logic. 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, imposs…Read more
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1431Moral responsibility and moral development in Epicurus’ philosophyIn Burkhard Reis & Stella 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
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65ABSTRACT: Paper currently being revised
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2054The Development of Modus Ponens in Antiquity: From Aristotle to the 2nd Century ADPhronesis 47 (4): 359-394. 2002.ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘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, Aristotl…Read more
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45Why the order of the figures of the hypothetical syllogisms was changedClassical 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.
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673Logic: The Stoics (part one)In Keimpe Algra, Jonathan Barnes, Jaap Mansfeld & Malcolm Schofield (eds.), The Cambridge History of Hellenistic Philosophy, Cambridge University Press. 1999.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)
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1000I—Columnar Higher-Order Vagueness, or Vagueness is Higher-Order VaguenessAristotelian 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
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1126If It's Clear, Then It's Clear That It's Clear, or is It? Higher-Order Vagueness and the S4 AxiomIn Ben Morison & Katerina Ierodiakonou (eds.), Episteme, etc.: Essays in honour of Jonathan Barnes, Oxford University Press. 2011.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-reveali…Read more
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504Die Kategorien Der Freiheit Bei Kant (Kant's Categories of Freedom)Kant 1 193-220. 1988.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
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1185Chrysippus and the epistemic theory of vaguenessProceedings 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
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