Susanne Bobzien

ABSTRACT: 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.

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.

In this extended 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 both in formulation and --more importantly-- in content between the Stoics and Frege, parallels so plentiful that one would be hard pressed to brush them off as 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. (Corrigendum: At school, Frege likely had seven, not ten, years of intensive Latin and four years of intensive ancient Greek courses.)

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.

This paper discusses ancient versions of paradoxes today classified as paradoxes of presupposition and how their ancient solutions compare with contemporary ones. Sections 1–4 air ancient evidence for the Fallacy of Complex Question and suggested solutions, introduce the Horn Paradox, consider its authorship and contemporary solutions. Section 5 reconstructs the Stoic solution, suggesting the Stoics produced a Russellian-type solution based on a hidden scope ambiguity of negation. The difference to Russell’s explanation of definite descriptions is that in the Horn Paradox the Stoics uncovered a hidden conjunction rather than 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.

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. Some minor insights into Stoic logic ensue.

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 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.

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.

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 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

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.

Central passages: Alexander of Aphrodisias On Fate 181–3, 189, 192, 205, Nemesius On Human Nature 105.6–106.13; Although in the first three centuries AD there were several Stoic theories of fate in circulation, only one systematic exposition of a later Stoic compatibilist theory has survived. This is found in Alexander of Aphrodisias’ On Fate, with parallels in Nemesius. These are the only sources that provide a Stoic account of that which depends on us and its relation to Stoic fate theory. This chapter is devoted to this theory and its reception by opponents in later antiquity. It is shown that this theory goes back to a particular second century AD Stoic view, which, although ‘orthodox’, differs noticeably from Chrysippus’. The reason for the modifications can be found in the confrontation with the newly developed Middle Platonist and Peripatetic theories of fate and freedom, and the shift of emphasis to the predetermination of ‘mental events’ as opposed to actions only, which forced the discussion of Stoic type determinism and that which depends on us to a new level. It is in the context of the confrontation of these theories with the Stoic ones that problems similar to modern problems of free will and determinism arise, and both the Stoics and their opponents introduce new arguments designed to cope with the new state of the debate.

Central passages: Plutarch, Aud. Poet. 33d, Epictetus, Enchiridion 53.1, Seneca Letters 107.10; Hippolytus, Refutation of all Heresies 1.21.2 Eleutheria was an indispensable philosophical concept in early Stoic ethics, and became central in the moral philosophy of the Roman Stoa. The Stoic notion of eleutheria has been a source of modern misinterpretation and mis‐assessment of the early Stoic theory of fate and of Chrysippus’ compatibilism. In particular, it has been illegitimately confounded with Chrysippus’ notion of that which depends on us. There is no evidence that the Stoic concept of eleutheria and the question of that which depends on us were connected in any way before the Roman Stoa. This chapter contains first an analysis of Epictetus’ concept of that which depends on us and how it relates to the early Stoic concept; then an outline of the Stoic notion of eleutheria, its role in early Stoic philosophy and in Epictetus, and its connection with the concept of that which depends on us, and the specific philosophical contexts in which the two concepts belong. Finally, the chapter provides a discussion of a couple of passages, including the famous dog and cart simile, which are shown to be often wrongly associated with Chrysippus’ compatibilism, to belong rather in the wider context of Epictetan ethics, and to have had their origin in Cleanthes’ philosophy.

Central passages: Gellius Attic Nights 7.2; Cicero On Fate 8 11, 39–45; Plutarch On Stoic Self‐Contradictions 1055f –1056d. There are only three sources that attest undoubtedly that Chrysippus, in some way, dealt with the problem of causal determinism and moral responsibility. They report the so‐called cylinder analogy and a Chrysippan distinction of causes, and present the core of Chrysippus’ compatibilism. The discussion of these passages in this chapter shows that they fit in smoothly with Chrysippus’ other arguments, adding to the ‘preserved’ concepts of contingency and intentional action finally that of moral responsibility—all fully in accord with his theory of fate and causal determinism. The chapter describes the specific problem of moral responsibility and determinism that Chrysippus and his opponents encountered, and shows how it differs from problems that are today subsumed under labels such as ‘the free‐will problem’. In particular, it emerges that the conception of moral responsibility of Chrysippus and his contemporaries is grounded not on any concept of freedom to do otherwise, but on a kind of ‘agent autonomy’. This conception of moral responsibility leads to different problems for its justification within a deterministic system than a theory of freedom to do otherwise. Based on their theories of causation, of mind, of decision making, and of character determination, the Stoics provide a sophisticated solution to these difficulties, showing among other things how it is possible that the rational and moral aspects of human agents can manifest themselves in human actions. Chrysippus’ claim that human actions are, though fated, not necessary, becomes comprehensible if one takes on his distinction between the modal concept of something's being necessary, on the one hand, and the physical power ‘Necessity’, on the other. In Chrysippus’ arguments for the compatibility of fate and moral responsibility, we encounter no word for freedom. The freedom that is identified as relevant to the arguments is freedom from external hindrances and from force. This freedom was referred to generally by negative phrases such as ‘not externally hindered’ or ‘not necessitated’, but not by a single term or noun phrase; and it was regarded as a necessary condition for something's depending on us and happening because of us. By ‘that which depends on us’ and ‘that which happens because of us’ Chrysippus seems to have understood simply the things of which we, qua rational beings, are the possible or actual cause. Such causal origination is brought about by the faculty of assent. The freedom from force and external hindrances is guaranteed by the utilization of this very mechanism through which we become the cause of our actions. For it is part of the nature of this human mental capacity of assent that it is neither forced nor fully externally determined.

The Idle Argument is the classical argument for fatalism and the futility of action: ‘If it is fated that you will recover, you will, regardless of whether you consult a doctor. If it is fated that you won’t recover, you won’t, regardless... Either it is fated that you will recover or that you won’t. Therefore it is pointless to consult a doctor.’ In the first part of this chapter, the sources that preserve this argument are analysed in detail, and the various ways of understanding the argument, and the ambiguities in its expressions, are exposed. The main distinction turns out to be that between a reading of the argument as manifesting logical determinism, and a reading of it as manifesting causal determinism. Depending on which version one considers, in which way one understands the ambiguous phrases, and whether one takes them throughout in the same way, the argument may turn out as valid or invalid, its premisses as true or false, and it may or may not justify idleness. The second part of the chapter is dedicated to Chrysippus’ reply: He takes the Idle Argument to concern causal determinism, and to be a fallacy, and his refutation of it is designed to make clear the difference between common and garden fatalism and Stoic causal determinism, which is consistent and does not lead to idleness, since human action and inaction are just as fated as everything else. It is shown that Chrysippus’ refutation does not require the existence of an empirically accessible, universal relation of necessitation, nor a causal theory with universal laws of nature.

Central passages: Cicero On Fate 11–17; Alexander of Aphrodisias On Fate 208.15–21. Critics of the Stoics tried to show up an inconsistency between Chrysippus’ acceptance of divination, on the one hand, and his conception of contingency, on the other. The argument claims that, since theorems of divination connect, in a conditional, a proposition about the past with one about the future, and since the necessity of the former is transferred to the latter, future occurrences—as far as covered by divination—are all necessary. In the first part of this chapter, the argument is analysed in detail, and several logical difficulties contained in it are unravelled. The second part is concerned with Chrysippus’ counter‐argument. By determining that divinatory theorems are correctly expressed as negated conjunctions rather than conditionals, Chrysippus successfully blocks his opponents’ argument: what is genuinely predicted by diviners is not necessitated through the prediction, because the relation between sign and predicted future event does not ‘transmit’ necessity. Universal regularity between sign and predicted event does not suffice to make a future event necessary. There is no ‘causal chain’ connecting them. Theorems of other sciences, for example, medical theorems that express an empirical connection between things/events, make true Chrysippean conditionals. However, human freedom as conceived by the Stoics is not thereby threatened.

Central passages: Boethius On Interpretation II 234–5; Diogenes Laertius 7.75; Plutarch, On Stoic Self‐contradictions 1055d–f; Alexander of Aphrodisias On Fate 176.14–23. In the Stoic debate over fate and determinism, the modalities played a role in a number of different contexts. Chrysippus rejected Diodorus Cronus’ modal theory because of its built‐in necessitarian consequences. He developed his own set of modal notions, which, in themselves, do not lead to necessitarianism and which secure a necessary condition for free action—namely, the existence of occurrences that are both possible and non‐necessary. Chrysippus’ modalities are not epistemic. Some critics of the Stoics developed arguments to show that there is a conflict between Chrysippus’ modal notions and the Stoic theory of fate. Later Stoics replied to such objections by giving an epistemic interpretation of Chrysippus’ modal concepts. Critics of the Stoics objected that fate, qua Necessity, renders all events necessary. However, this objection is not justified within Chrysippus’ philosophy.

Central passages: Cicero On Fate 20–21, 26–28, 37, On Divination I 125–6. The first argument: Chrysippus assumes as true a weak, non‐modal form of logical determinism. From this assumption he argues for the truth of his theory of causal determinism, by showing that the latter is a necessary condition of the former. This argument differs considerably from the argument for the truth of future propositions to their necessity, which Epicurus is said to have attacked. Cicero confuses the two. The second argument: Chrysippus, as most Stoics, believed in divination as a science. He construes an argument from the existence of this science to his type of causal determinism by showing that causal determinism is a necessary condition for the existence of the science of divination.

Central passages: Plutarch On Stoic Self‐Contradictions 1045b–c; 104950, 1056; Stobaeus Ecl. I 79.1–12. The physical and ontological foundations of the Stoic theory of determinism are investigated: the active principle, causation, motion, and qualitative states and how they relate to the Stoic concept of propositions. Stoic teleological determinism grows out of the basic assumptions of Stoic cosmology and is thus firmly anchored in early Stoic physics. Stoic physics stands out in antiquity not so much because it is a deterministic system, but because it contains a worked‐out theory of universal, mechanical, causal determinism. In the Stoic theory of universal fate, the teleological and mechanical aspects of Stoic determinism are combined.

Methodological information and historical background: The book focuses on problems of determinism and freedom as they were conceived in antiquity, this being a necessary condition for a full understanding of the Stoic theory. The Stoic theory of determinism and freedom is central to their philosophy as a whole. The history of works on fate, determinism, and freedom from Plato to the end of antiquity is sketched. The difficulty of the fragmentary state of our sources and the lack of first‐hand sources, the inadequacy of von Arnim's collection of Stoic fragments on fate, and the limits of the present book are discussed.

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.

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.

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.