Susanne Bobzien | University of Oxford (original) (raw)

Papers in contemporary philosophy by Susanne Bobzien

Erkenntnis, 2024

This paper offers a generic revenge-proof solution to the Sorites paradox that is compatible with... more This paper offers a generic revenge-proof solution to the Sorites paradox that is compatible with several philosophical approaches to vagueness, including epistemicism, supervaluationism, psychological contextualism and intuitionism. The solution is traditional in that it rejects the Sorites conditional and proposes a modally expressed weakened conditional instead. The modalities are defined by the first-order logic QS4M+FIN. (This logic is a modal companion to the intermediate logic QH+KF, which places the solution between intuitionistic and classical logic.) Borderlineness is introduced modally as usual. The solution is innovative in that its modal system brings out the semi-determinability of vagueness. Whether something is borderline and whether a predicate is vague or precise is only semi-determinable: higher-order vagueness is columnar. Finally, the solution is based entirely on two assumptions. (1) It rejects the Sorites conditional. (2) It maintains that if one specifies borderlineness in terms of the-suitably interpreted-modal logic QS4M+FIN, then one can explain why the Sorites appears paradoxical. From (1)+(2) it results that one can tell neither where exactly in a Sorites series the borderline zone starts and ends nor what its extension is. Accordingly, the solution is also called agnostic.
(Note: this paper was written before Bobzien & Rumfitt 2020)
(Corrigendum: fn 12 at the end of the first line add: 'Adding' )

Journal of Philosophical Logic, 2019

ABSTRACT: Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptanc... more ABSTRACT: Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus (IPC) and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness.

Aristotelian Society Supplementary , Jan 2015

ABSTRACT: Most descriptions of higher-order vagueness in terms of traditional modal logic generat... more ABSTRACT: 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.

http://onlinelibrary.wiley.com/doi/10.1111/phib.12006/abstract, 2013

ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result... more 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.

B. Morison & K. Ierodiakonou (eds), Episteme, etc. , 2012

ABSTRACT: The purpose of this paper is to challenge some widespread assumptions about the role o... more ABSTRACT: 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 axiom 4 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.)

"ABSTRACT: The paper presents a new theory of higher-order vagueness. This theory is an improveme... more "ABSTRACT: 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.
To view paper, click on "View on hdl.handle.net" below."

Reflections on the Liar, 2017

ABSTRACT: This chapter offers a revenge-free solution to the liar paradox (at the centre of which... more 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, by using a truth operator rather than truth predicate, it is possible to provide a coherent, model-theoretic representation of truth with various desirable features. After investigating what features of liar sentences are responsible for their paradoxicality, the chapter identifies the logic as the normal modal logic KT4M (= S4M). Drawing on the structure of KT4M (=S4M), the author proposes that, pace deflationism, truth has content, that the content of truth is bivalence, and that the notions of both truth and bivalence are semideterminable.

This paper is an expanded written version of my reply to Rosanna Keefe’s paper ‘Modelling higher-... more 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.

This paper refutes a common objection to columnar higher-order vagueness: that, at least in its e... more This paper refutes a common objection to columnar higher-order vagueness: that, at least in its epistemic interpretation, it is incoherent. The paper shows how the objection has its roots in an incomplete grasp of the modal system S4.

ABSTRACT: Reviews and discussions of Stewart Shapiro’s recent book Vagueness in Context have most... more ABSTRACT: Reviews and discussions of Stewart Shapiro’s recent book Vagueness in Context have mostly focused on Shapiro’s ‘open-texture’ theory and his contextualism, with relative neglect of his theory of higher-order vagueness. The present paper aims to fill this gap. Shapiro argues that “there is no higher-order vagueness, strictly so-called” and that “so-called ‘higher-order vagueness’ is actually ordinary first-order vagueness in different predicates”. More specifically, Shapiro’s Thesis is:

(ST) So-called second-order vagueness in a predicate ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of the word “F”’.

Instead of true higher-order vagueness, Shapiro maintains, all we have is surrogate higher-order vagueness. He bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’, and supports it with several arguments. We briefly present the phenomenon (as Shapiro describes it) and Shapiro’s accounts of vagueness; then show that none of Shapiro’s arguments for (ST) is compelling; finally, we introduce the account of vagueness that Shapiro would have obtained had he consistently abided by the rules of compositionality, and show that this account both entails true higher-order vagueness and does not turn on the vagueness of ‘competent speaker’.

ABSTRACT: Hierarchical higher-order vagueness leads to incoherence when used as a means to avoid ... more ABSTRACT: Hierarchical higher-order vagueness leads to incoherence when used as a means to avoid a sharp boundary in the Sorites paradox (Sainsbury 1990, Wright 1992, Shapiro 2006). The challenge is to provide (i) a compositional notion of higher-order vagueness that (ii) allows infinite higher orders, (iii) retains the desired relevance to the Sorites, (iv) allows for a model-theoretic representation that reflects such relevance, but (v) does not run into paradox. The recently introduced alternative of columnar higher-order vagueness meets this challenge. The present paper explains what columnar higher-order vagueness is; gives a formalization of its core properties in terms of an axiomatic modal system; produces a modal semantics for its simplest (bivalent & classical) form and identifies its characteristic axiom; and supplies a philosophical interpretation of the semantics that utilizes both viewpoint sensitivity and extensional context sensitivity. The paper adds an illustration of how the semantics can be used as an infrastructure for epistemicist (and non-epistemicist) bivalent theories of vagueness and touches upon possible modifications for three-valued logics. It concludes with listing the considerable advantages columnar higher-order vagueness has over other theories of higher-order vagueness.

Books by Susanne Bobzien

https://www.whsmith.co.uk/products/determinism-freedom-and-moral-responsibility-essays-in-ancient-philosophy/susanne-bobzien/hardback/9780198866732.html, 2021

Determinism, Freedom, and Moral Responsibility brings together nine substantial essays on determi... more Determinism, Freedom, and Moral Responsibility brings together nine substantial essays on determinism, freedom, and moral responsibility in antiquity by Susanne Bobzien. The essays present the main ancient theories on these subjects, ranging historically from Aristotle followed by the Epicureans, the early Stoics, several later Stoics, and up to Alexander of Aphrodisias in the third century ce. The author discusses questions about rational and autonomous human agency and their compatibility with a large range of important philosophical issues, including their compatibility with divine predetermination and other theological questions; with atomism and continuum theory and with the physical sciences more generally; with the determination of character and its development from childhood through nature and nurture; with epistemic features such as ignorance of circumstances; with theories of necessity, possibility and contingency; with external or internal preceding causes and impediments; and with folk theories of fatalism. Room is also given to the questions of how human autonomous agency is related to moral development, to virtue and wisdom, and to blame and praise. Historically unified, philosophically profound, and methodologically rigorous, Bobzien's essays show that in Classical and Hellenistic philosophy these topics were all debated without reference to freedom to do otherwise or to a free will, and that the latter two notions were fully developed only later. The volume will be of interest both to philosophers and to historians of philosophy, with more than half of the essays accessible to advanced undergraduates.

ABSTRACT: This book is a comprehensive study of the Stoic theory of causal and teleological deter... more ABSTRACT: This book is a comprehensive study of the Stoic theory of causal and teleological determinism. It identifies the main problems the Stoics addressed, reconstructs the theory, and explores how they squared their determinism with their conceptions of possibility, action, freedom, and moral responsibility, and how they defended it against objections and criticism by other philosophers. It shows how the Stoics distinguished their causal determinism from ancient theories of logical determinism, fatalism, and necessitarianism, and shows that they developed a compatibilist theory with a rationalist component. Along the way many other related aspects of Stoic thought are discussed, including their views on the predictability of the future, the role of empirical sciences, character development, and moral freedom. The main Stoic theory of causal determinism goes back to the Stoic Chrysippus. There are some interesting developments of the theory in the later Stoa.

"ABSTRACT: Part 1 discusses the Stoic notion of propositions (assertibles, axiomata): their defin... more "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 shorter, updated, 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.

google book link:
http://books.google.com/books/about/Die_stoische_Modallogik.html?id=jlowAAAAYAAJ"

English translation of the 2nd/3rd century Peripatetic Philosopher's Alexander of Aphrodisias com... more 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.The 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.

Papers on Stoic & Hellenistic logic & language by Susanne Bobzien

ABSTRACT: We argue that the extant evidence for Stoic logic provides all the elements required fo... more ABSTRACT: We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. We consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality.

Philosophers' Imprint, 2020

ABSTRACT: We argue that the extant evidence for Stoic logic provides all the elements required fo... more ABSTRACT: We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one-and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. We consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle's with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality.

Open Access: http://hdl.handle.net/2027/spo.3521354.0020.031

Phronesis, 2020

ABSTRACT: Since Mates' seminal Stoic Logic there has been uncertainty and debate about how to tre... more ABSTRACT: Since Mates' seminal Stoic Logic there has been uncertainty and debate about how to treat the term anapodeiktos when used of Stoic syllogisms. This paper argues that the customary translation of anapodeiktos by 'indemonstrable' is accurate, and it explains why this is so. At the heart of the explanation is an argument that, contrary to what is commonly assumed, indemonstrability is rooted in the generic account of the Stoic epistemic notion of demonstration (apodeixis). Some minor insights into Stoic logic ensue.

History and Philosophy of Logic , 2019

ABSTRACT: This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from... more ABSTRACT: This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen's negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall's connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness.

Erkenntnis, 2024

Journal of Philosophical Logic, 2019

Aristotelian Society Supplementary , Jan 2015

http://onlinelibrary.wiley.com/doi/10.1111/phib.12006/abstract, 2013

B. Morison & K. Ierodiakonou (eds), Episteme, etc. , 2012

Reflections on the Liar, 2017

(ST) So-called second-order vagueness in a predicate ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of the word “F”’.

https://www.whsmith.co.uk/products/determinism-freedom-and-moral-responsibility-essays-in-ancient-philosophy/susanne-bobzien/hardback/9780198866732.html, 2021

google book link:
http://books.google.com/books/about/Die_stoische_Modallogik.html?id=jlowAAAAYAAJ"

Philosophers' Imprint, 2020

ABSTRACT: We argue that the extant evidence for Stoic logic provides all the elements required fo... more ABSTRACT: We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one-and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. We consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle's with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality.

Open Access: http://hdl.handle.net/2027/spo.3521354.0020.031

Phronesis, 2020

History and Philosophy of Logic , 2019

Studia Logica, 2019

ABSTRACT: This paper shows that, for the Hertz–Gentzen Systems of 1933 (without Thinning), extend... more ABSTRACT: This paper shows that, for the Hertz–Gentzen Systems of 1933 (without Thinning), extended by a classical rule T1 (from the Stoics) and using certain axioms (also from the Stoics), 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 (in contrast to one of Gentzen’s 1933 results) that a particular derivable sequent has no derivation that is “normal” in the sense that the first premiss of each cut is cut-free. We also infer that Cut is not admissible in the Stoic system, based on the standard Stoic axioms, the T1 rule and the instances of Cut with just two antecedent formulae in the first premiss. (OPEN ACCESS)

Oxford Studies in Ancient Philosophy, 2011

ABSTRACT: The 3rd BCE Stoic logician “Chrysippus says that the number of conjunctions constructib... more 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 310,95[4].” 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.

ABSTRACT: This paper discusses ancient versions of paradoxes today classified as paradoxes of pre... more 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 ("Have you stopped cheating on your spouse?") 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” 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.

ABSTRACT: This paper discusses the Stoic treatment of fallacies that are based on lexical ambigui... more 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.

Proceedings of the Aristotelian Society ( …, 2002

ABSTRACT : In his book 'vagueness', Tim Williamson presented a bold interpretation of the Stoic C... more ABSTRACT : In his book 'vagueness', Tim Williamson presented a bold interpretation of the Stoic Chrysippus’ position on the Sorites, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position which (ii) made allowances for higher-order vagueness. In this paper I argue (i) that the ancient evidence does not support the thesis that Chrysippus took an epistemicist position, but  is equally, if not better, supports that Chrysippus had a non-epistemic theory 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. I also (iii) show that Williamson's own arguments in support of his thesis that Chrysippus was an epistemicist are unsuccessful.

Oxford Studies in Ancient Philosophy, Jan 1, 1996

"ABSTRACT: For the Stoics, a syllogism is a formally valid argument, and the primary function of ... more "ABSTRACT: For the Stoics, a syllogism is a formally valid argument, and the primary function of their syllogistic is to establish the formal validity of arguments. Stoic syllogistic can be understood as a system of formal logic that relies on two types of argumental rules ((see note 1)): first, five rules (the accounts of the indemonstrables) which were used to 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 (D.L. 7.79), since its validity is evident in itself (Sextus, M. 2. 223) ((see note 2)); second, one unary and three presumably binary argumental rules, called themata, which allow one to establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (D.L. 7. 78). The function of these rules is not to generate non indemonstrable syllogisms from indemonstrable ones, but rather 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. The Stoic system may hence be called an 'argumental reductive system of deduction'.

In this paper, I present a reconstruction of this system of logic. The rules or accounts used for establishing that an argument is indemonstrable have all survived, and the indemonstrables are among the best-known elements of Stoic logic. However, their exact role and logical status in Stoic syllogistic are usually neglected. I expound how they are integrated in the system of deduction. The state of evidence for the themata is dismal. I suggest a reconstruction of the themata, based on a fresh look at some of the sources, and then offer a reconstruction of the general method of reduction of arguments and some general remarks on Stoic syllogistic as a whole and on the question of its completeness (much of which will not depend on the particular formulation of the themata I propose, but on more general considerations for a reconstruction).

Stoic logic is a propositional logic, and Stoic negation and conjunction are truth-functional. This has, naturally, led to comparisons with the 'classical' propositional calculus (as e.g. presented in Principia Mathematica), including repeated examinations of Stoic syllogistic on completeness in the modern sense. The Stoic theory of deduction invariably comes out as deficient, inferior, or simply outlandish in such comparisons, which has evoked adjusting additions and modifications -- tacit or explicit -- in previous reconstructions of the system. I suggest that this is the wrong approach; that the classical propositional calculus is the wrong paradigm; that Stoic logic has to be considered first of all in its own light; and that, if one looks for comparisons with contemporary logic, one can find some rather more interesting parallels when turning one's attention to non-truth-functional propositional logics, in particular to relevance logic.

--------------------------------------
(note 1) By an argumental rule I mean a rule that produces arguments from (zero or more) arguments, as opposed to a rule that produces propositions from (zero or more) propositions.
(note 2) The accounts of the indemonstrables, when interpreted as rules, are nullary argumental rules."

Döring/Ebert (eds), Dialektiker und Stoiker , Jan 1, 1993

ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Ph... more 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.

Phronesis 42.3, pp. 299-312., Jan 1, 1997

ABSTRACT: In this paper I argue (i) that the hypothetical arguments about which the Stoic Chrysip... more 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.

Summary presentation of the logic of Philo the Dialectician (aka Philo of Megara) and Diodorus Cr... more Summary presentation of the logic 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: A detailed presentation of Stoic theory of arguments, including truth-value changes of ... more 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."

For a more advanced treatment of Stoic syllogistic please see my paper of that name, in Oxford Studies in Ancient Philosophy, 1996."

ABSTRACT: A detailed presentation of Stoic logic, including their theories of assertibles (or pro... more ABSTRACT: A detailed presentation of Stoic logic, including their theories of assertibles (or propositions, Greek: axiomata), simple assertibles, non-simple assertibles (conjunction, disjunction, conditional), quantified assertibles, logical truths, modalities, and general theory of arguments (definition, validity, soundness, classification of invalid arguments)

Stanford Encyclopedia of Philosophy, Jan 1, 2004

ABSTRACT: The ‘Dialectical school’ denotes a group of early Hellenistic philosophers that were lo... more ABSTRACT: The ‘Dialectical school’ denotes a group of early Hellenistic philosophers that were loosely connected by philosophizing in the — Socratic — tradition of Eubulides of Miletus 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. This entry deals with all the above topics and provides a sketch of a solution to the Master Argument.

Discussion (in German) of Robert Muller's "Les Megariques, Fragments et temoignages". Traduit et ... more Discussion (in German) of Robert Muller's "Les Megariques, Fragments et temoignages". Traduit et commentes. Paris, Vrin 1985.

Maieusis: Essays in Ancient Philosophy in Honour …

ABSTRACT: In this paper I show that, contrary to the prevalent view, in his De Interpretatione ch... more 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.

Phronesis, Jan 1, 2002

"ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i... more "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, 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."

ABSTRACT: This paper traces the evidence in Galen's Introduction to Logic (Institutio Logica) for... more 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.

Rhizai. A Journal for Ancient Philosophy and Science, 2004

ABSTRACT: Galen’s Institutio Logica is the only introduction to logic in Greek that has survived ... more ABSTRACT: Galen’s Institutio Logica is the only introduction to logic in Greek that has survived from antiquity. In it we find a theory that bears some resemblance to propositional logic. The theory is commonly understood as being essentially Stoic. However, this understanding of the text leaves us with a large number of inconsistencies and oddities. In this paper I offer an comprehensive alternative interpretation of the theory. I suggest that it is Peripatetic at base, and has drawn on Stoic elements, but adapted them to an overall decidedly non-Stoic conception of logic and language, a conception indebted to Aristotelian logic in many respects. This interpretation makes it possible to reduce the seeming inconsistencies dramatically. The Peripatetic theory on which Galen draws was possibly developed in the first century BCE. Importantly, it differs from Stoic logic in that it shuns the latter’s syntactic approach, and considers certain linguistic assumptions and language conventions as part of the logical theory itself. My reconstruction of the theory results in a logic of propositions which differs wildly both from Stoic logic and from the ‘classical’ propositional logic of the 20th century. Interestingly, though, the theory in Galen shows that the ancients grappled with a number of logico-linguistic problems that over the last two decades have again become a matter of debate among contemporary logicians and linguists.

M.Lee (ed) Strategies of Argument: Essays in Ancient Ethics, Epistemology, and Logic, 2014

ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for ... more 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.

Phronesis: A Journal for Ancient Philosophy, 2000

ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One ty... more 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.

The Classical Quarterly, 2000

ABSTRACT: At the turn of the second century AD there existed two different views on the ordering ... more 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.

Mnemosyne, 2002

ABSTRACT: In this paper I present the text, a translation, and a commentary of a long anonymous s... more ABSTRACT: 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 on which both the scholium and large parts of Boethius’ De Hypotheticis Syllogismis are dependent.

A reply to Terence Irwin's paper 'Stoic Inhumanity', Delivered at a Corpus Christi Classical Semi... more A reply to Terence Irwin's paper 'Stoic Inhumanity', Delivered at a Corpus Christi Classical Seminar at Oxford in 1995. After a summary of Irwin's paper (Sections I and II) it is suggested that a full understanding of Stoic ethics requires one to take into account their understanding of Nature as Reason and as Fate, and of the world as the best possible one. As a result, and contrary to Irwin's view, it appears that for the Stoics it is more accurate to liken human life to a choreographed dance rather than to archery (Section III).

PDC Homepage Home » Products » Purchase. LOGIN; PRODUCTS: All Products; Online Resources; Journal... more PDC Homepage Home » Products » Purchase. LOGIN; PRODUCTS: All Products; Online Resources; Journals & Series; Digital Media; Books & Reference Works. MEMBERSHIPS: Societies & Associations; Conference Registrations. E-COLLECTION: About; Alphabetically; By Category; By Type; Price Lists; Terms and Conditions. SERVICES: Conference Exhibits; Conference Registrations; Electronic Publishing; Journal Advertising; Mailing Lists; Marketing ...

What is up to us? Studies on Causality and Responsibility in Ancient Philosophy, 2014

ABSTRACT: This is a short companion piece to my ‘Found in Translation – Aristotle’s Nicomachean E... 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 overlap with Part 1 of the 'Found in Translation' paper.)

Much of chapters 2 to 6 is in agreement with publications from the last twenty years (including t... more 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.

One-page entry on freedom in the philosophical (as opposed to political) sense in antiquity, noti... more 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.

ABSTRACT: This is a little piece directed at the newcomer to Aristotle, making some general remar... more 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).

The Inadvertent Conception and Late Birth of the Free-Will Problem, 1998

ABSTRACT: In this paper I argue that the ‘discovery’ of the problem of causal determinism and fre... 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 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.

K. Ierodiakonou (ed.), Topics in Stoic Philosophy

ABSTRACT: A systematic reconstruction of Chrysippus’ theory of causes, grounded on the Stoic tene... more 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.

Oxford Studies in Ancient Philosophy, 2000

ABSTRACT: I argue that there is no evidence that Epicurus dealt with the kind of free-will proble... more 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.

Revue de métaphysique et de morale, Jan 1, 2005

ABSTRACT: Although from the 2nd century BC to the 3rd AD the problems of determinism were discuss... more ABSTRACT: Although from the 2nd century BC to the 3rd AD the problems of determinism were discussed almost exclusively under the heading of fate, early Stoic determinism, as introduced by Zeno and elaborated by Chrysippus, was developed largely in Stoic writings on physics, independently of any specific "theory of fate ". Stoic determinism was firmly grounded in Stoic cosmology, and the Stoic notions of causes, as corporeal and responsible for both sustenance and change, and of effects as incorporeal and as predicates, are indispensable for a full understanding of the theory. Stoic determinism was originally not presented as causal determinism, but with a strong teleological element, in the context of a theory of natural motions, which makes use of a distinction between a global and an inner-worldly perspective on events. However, Chrysippus also employed his conception of causality in order to explicate his determinism, and can be shown to have maintained a universal causal determinism in the modern sense of the erm. The teleological and mechanical elements of early Stoic determinism were brought together in Chrysippus' conception of fate, which places elements of rationality in every cause.

ABSTRACT: 1. This paper argues that Epicurus had a notion of moral responsibility based on the ag... more 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.

R. Sorabji (ed.), Aristotle and After, 1997

ABSTRACT: In contemporary discussions of freedom in Stoic philosophy we often encounter the follo... more 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. (This is an early article that anticipates the main ideas of my book 'Determinism and Freedom in Stoic Philosophy' and which is accessible to a non-specialist audience. Where there are differences to the book, the views presented in the book supersede those presented in this article.)

Oxford Studies in Ancient Philosophy 45.2, 103-148, Nov 28, 2013

ABSTRACT: This paper is distinctly odd. It demonstrates what happens when an analytical philosoph... more 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.)

The Cambridge Companion to the Nicomachean Ethics, Jun 30, 2014

ABSTRACT: This paper serves two purposes: (i) it can be used by students as an introduction to ch... more 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).

What is up to us? Studies on Causality and Responsibility in Ancient Philosophy, 2014

This little paper is a companion piece to my ‘Found in Translation – Aristotle’s Nicomachean Ethi... more This little paper is a 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 famous two lines on what is up to us from the Nicomachean Ethics provide any evidence that Aristotle discussed free choice or free will – 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. Thus the sentence that is sometimes adduced as the main piece of evidence for the claim that Aristotle was an indeterminist with respect to choosing (prohairesis) and acting (praxeis, prattein) is no evidence for this claim at all. (There is some inevitable overlap with Part 1 of the 'Found in Translation' paper.)

Originally published in German in "Kant. Analysen–Probleme–Kritik", Vol. 1, Wuerzburg: Königshausen & Neumann (1988) 193-220. Translation by Alex Worsnip, reviewed and approved by the author.

ABSTRACT: A general interpretation and close textual analysis of Kant’s theory of the categories ... more 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.

Kant. Analysen–Probleme–Kritik, Vol.1, 1988, 193-220.

This is a very brief reply to Bruno Haas' criticism of my paper 'Die Kategorien der Freiheit bei ... more This is a very brief reply to Bruno Haas' criticism of my paper 'Die Kategorien der Freiheit bei Kant', now translated into English as 'Kant's Categories of Freedom' (both also available on Academia.edu).

Sextus Empiricus and ancient physics. Keimpe Algra & Katerina Ierodiakonou (eds.), Jul 2015

ABSTRACT: For the most part, this paper is not a philosophical paper in any strict sense. Rather,... more 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.

Brad Inwood (ed.), The Cambridge Companion to Stoic Philosophy, pp. 85-123, 2003

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-... more 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.

Stanford Encyclopedia of Philosophy, Dec 29, 2015

http://plato.stanford.edu/entries/logic-ancient/ ABSTRACT: A comprehensive introduction to anc... more http://plato.stanford.edu/entries/logic-ancient/

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

Very brief summary presentation of western ancient logic for the non-specialized reader. For a mo... more Very brief summary presentation of western ancient logic for the non-specialized reader. For a more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on Academia).

Frege, Hirzel, and Stoic logic, 2024

This paper is a discussion of Gabriel, Hülser and Schlotter's 2009 article on a possible causal r... more This paper is a discussion of Gabriel, Hülser and Schlotter's 2009 article on a possible causal relation between Stoic logic and Frege. It provides detailed argument for why Rudolf Hirzel cannot be taken as the qualified middleman in philosophical discussion with whom Frege learned what he 'borrowed' without acknowledgement from Stoic logic. Additionally, this paper offers some findings about some aspects of Frege's and Hirzel's lives and work habits, which may help us understand a little better Frege's connection to Hirzel and to Stoic logic as well as Frege's failure to acknowledge the Stoics. This paper is a purely historical offshoot of my essay 'Frege plagiarized the Stoics'. Zero direct insights into either Frege's or Stoic philosophy are offered.

Themes in Plato, Aristotle, and Hellenistic Philosophy, Keeling Lectures 2011-2018., 2021

ABSTRACT: In this essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on... more ABSTRACT: In this essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on a large scale in his work on the philosophy of logic and language as written mainly between 1890 and his death in 1925 (much of which published posthumously) and possibly earlier. I use ‘plagiarize' (or 'plagiarise’) merely as a descriptive term. The essay is not concerned with finger pointing or casting moral judgement. The point is rather to demonstrate carefully by means of detailed evidence that there are numerous (over a hundred) and extensive parallels in both formulation and content between the Stoics and Frege, so plentiful that one would be hard pressed to brush them off as a coincidence. These parallels include several that appear to occur in no other modern works that were published before Frege’s own and were accessible to him. Additionally, a cluster of corroborating historical data is adduced to support the suggestion, showing how easy it would have to been for Frege to plagiarize the Stoics. This (first) part of the essay is easy to read and vaguely entertaining, or so I hope.
(The whole volume in which the paper is published is open access. Google the title and choose the link from ics-dot-sas-dot-ac-dot-uk for download.)

Frege as Clickbait, 2023

Bobzien’s reply to a defamatory blogpost on her essay ‘Frege plagiarized the Stoics’ in which she... more Bobzien’s reply to a defamatory blogpost on her essay ‘Frege plagiarized the Stoics’ in which she is accused among other things of plagiarism (!), and deliberate deception, and which contains a large number of falsehoods. (This reply is a minor contribution to the discussion of 'Frege plagiarized the Stoics', simply setting the record straight. It contains no important philosophical content whatsoever.)

Themes in Plato, Aristotle, and Hellenistic Philosophy, Keeling Lectures 2011-2018., 2021

ABSTRACT: In this essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on... more ABSTRACT: In this essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on a large scale in his work on the philosophy of logic and language as written mainly between 1890 and his death in 1925 (much of which published posthumously) and possibly earlier. I use ‘plagiarize' (or 'plagiarise’) merely as a descriptive term. The essay is not concerned with finger pointing or casting moral judgement. The point is rather to demonstrate carefully by means of detailed evidence that there are numerous (over a hundred) and extensive parallels in both formulation and content between the Stoics and Frege, so plentiful that one would be hard pressed to brush them off as a coincidence. These parallels include several that appear to occur in no other modern works that were published before Frege’s own and were accessible to him. Additionally, a cluster of corroborating historical data is adduced to support the suggestion, showing how easy it would have to been for Frege to plagiarize the Stoics. This (first) part of the essay is easy to read and vaguely entertaining, or so I hope.
The published version of this paper is open access. See https://ics.sas.ac.uk/publications/themes-plato-aristotle-and-hellenistic-philosophy?fbclid=IwAR0FmeF913u6_OeYi4zIJ-fi5a3ZRRuLNn-FMk-vGzsgo2JPwfT9vHsoIzs

In this 2 1/2 page piece(ling) I introduce the terms 'to maleappropriate', 'maleappropriation', '... more In this 2 1/2 page piece(ling) I introduce the terms 'to maleappropriate', 'maleappropriation', 'maleappropriator', etc., for a familiar phenomenon and pattern of behaviour, following a couple of autobiographical remarks and followed by some brief suggestions about how to handle the phenomenon. That's all. (Nothing of philosophical depth here.)