ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 Forerunners (...) of Modus Ponens and Modus Tollens 3.4 Wholly Hypothetical Syllogisms 4. Diodorus Cronus and Philo the Logician 5. The Stoics 5.1 Logical Achievements Besides Propositional Logic 5.2 Syntax and Semantics of Complex Propositions 5.3 Arguments 5.4 Stoic Syllogistic 5.5 Logical Paradoxes 6. Epicurus and the Epicureans 7. Later Antiquity. (shrink)

This paper examines an ancient debate over the rationality of perception. What leads the Stoics to affirm, and the Epicureans to deny, that to form a sense-impression is an activity of reason? The answer, we argue, lies in a disagreement over what is required for epistemic success. For the Stoics, epistemic success consists in believing the right propositions, and only rational states, in virtue of their predicational structure, put us in touch with propositions. Since they identify some sense-impressions as criteria (...) of truth and thus as the basis for epistemic success, the Stoics maintain that sense-impressions must be rational. The Epicureans agree with the Stoics that sense-impressions function as criteria of truth, and also agree broadly on what it means for a state to be rational, but deny that sense-impressions are rational because (1) they think that epistemic success must be supported by a state that is necessarily error-free and (2) accept that rational states can be false. In reconstructing this debate, we refine the standard interpretation of the fundamental difference between Epicurean and Stoic epistemology and also develop parallels with epistemological debates today. One upshot is a more nuanced appreciation of the merits of Epicurean epistemology vis-à-vis the Stoics. (shrink)

The Stoics’ theory of kataleptic impressions looks different once we attend to their analysis of the Sorites paradox. In defending this view, I reject the long-standing assumption that the Stoics develop their theory by focusing on sensory impressions. The Stoic approach to vagueness shows, for example, that non-sensory impressions can be seemingly indistinguishable by belonging to a series. It also draws attention to an understudied dimension of Stoic theory: in aiming to assent only to kataleptic impressions, one aims to avoid (...) not only assent to false impressions but also assent to those that are neither true nor false. (shrink)

Rorty goes on to connect the sorites paradox to analytic philosophy’s long standing concern with the correspondence theory of truth. How do our words hook up with reality? Do our categories map pre-existing contours? The nominalist answers that “facts” are just projections of our forms of speech. Rorty characterizes epistemicism as a hyper-realist backlash. In addition to thinking that our scientific terminology cuts nature at the joint, the epistemicist asserts that even the vague vocabulary of common sense has sharp thresholds.

De acuerdo con los principales enfoques al respecto la lógica de los estoicos es principalmente un sistema deductivo, lo que, en términos actuales, ha sido visto como un sistema de lógica proposicional. La obra de Crísipo acerca de los cinco argumentos indemostrables constituye la principal base de dicho sistema. En este artículo se examina la naturaleza de dichos cinco indemostrables así como el llamando teorema de Antipatro y los esquemas básicos de inferencia, o zemas. Por otra parte y en particular, (...) sostengo que dichos argumentos indemostrables tienen otro importante rol para la filosofía y la historia de la lógica, cual es el de constituirse en una justificación de la deducción, un problema central en el presente. Se analiza, primero, la justificación por los indemostrables y por el principio de condicionalización y, segundo, la justificación cognitiva de la lógica implícita en un sistema estoico. (shrink)

The Stoic philosopher Chrysippus wrote extensively on the liar paradox, but unfortunately the extant testimony on his response to the paradox is meager and mainly hostile. Modern scholars, beginning with Alexander Rüstow in the first decade of the twentieth century, have attempted to reconstruct Chrysippus? solution. Rüstow argued that Chrysippus advanced a cassationist solution, that is, one in which sentences such as ?I am speaking falsely? do not express propositions. Two more recent scholars, Walter Cavini and Mario Mignucci, have rejected (...) Rüstow's thesis that Chrysippus used a cassationist approach. Each has proposed his own thesis about Chrysippus? solution. I argue that Rüstow's view is fundamentally correct, and that the cassationist thesis gains greater plausibility when viewed in light of a passage in Sextus Empiricus? Adversus mathematicos that the previous commentators have ignored, and when understood within the broader context of Stoic logical theory and philosophy of language. I close with a brief remark on the significance of Chrysippus? work for the modern debate on the semantic paradoxes. (shrink)

There is a long history of philosophers granting a privileged epistemic status to cognition of directly present objects. In this paper, I examine three important historic accounts which provide different models of this cognitive state and its connection with its objects: that of the Stoics, who are corporealists and think that ordinary perception may have an epistemically privileged status, but who seem to struggle to accommodate non-perceptual cognizance; that of Augustine, who thinks that incorporeal objects are directly present to us (...) in ‘intellectual perception’, and that, by way of contrast, ordinary sense-perception does not have a privileged epistemic status; and that of William of Ockham, who allows for unmediated action at a distance and is fairly generous about what counts as being directly present. (shrink)

ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.

At Varro LL VI.56 and SE M 8.275-276, we find reports of the Stoic view that children and articulate non-rational animals such as parrots cannot genuinely speak. Absent from these testimonia is the peculiar case of the superficiality of the actor’s speech, which appears in one edition of the unstable text of PHerc 307.9 containing fragments of Chrysippus’ Logical Investigations. Commentators who include this edition of the text in their discussions of the Stoic theory of speech do not offer a (...) univocal account of the superficiality of the parrot’s, the child’s, and the actor’s speech. In this paper, I offer a reconstruction of the Stoic account of genuine and superficial speech and show that not only is there an account of superficial speech that univocally explains the superficiality of the speech of parrots, children, and actors, but that this account challenges traditional assumptions about the entities at the heart of the Stoic theory of language—lekta. It will turn out that genuine speech is the expression of a lekton by way of performing a speech act, and that this account of superficial speech can be used to explain other linguistic phenomena that are of interest to the Stoics, such as sentences in insoluble sophisms and sentences containing demonstratives that do not refer to anything in the subject term. Importantly, my reconstruction shows, against the near consensus view of lekta, that lekta do not primarily explain what makes an utterance meaningful. Rather, they primarily explain what makes an utterance an instance of genuine speech. (shrink)

Stoicism was one of the new philosophical movements of the Hellenistic period. The name derives from the porch (stoa poikilê) in the Agora at Athens decorated with mural paintings, where the members of the school congregated, and their lectures were held. Unlike ‘epicurean,’ the sense of the English adjective ‘stoical’ is not utterly misleading with regard to its philosophical origins. The Stoics did, in fact, hold that emotions like fear or envy (or impassioned sexual attachments, or passionate love of anything (...) whatsoever) either were, or arose from, false judgements and that the sage—a person who had attained moral and intellectual perfection—would not undergo them. The later Stoics of Roman Imperial times, Seneca and Epictetus, emphasise the doctrines (already central to the early Stoics' teachings) that the sage is utterly immune to misfortune and that virtue is sufficient for happiness. Our phrase ‘stoic calm’ perhaps encapsulates the general drift of these claims. It does not, however, hint at the even more radical ethical views which the Stoics defended, e.g. that only the sage is free while all others are slaves, or that all those who are morally vicious are equally so. Though it seems clear that some Stoics took a kind of perverse joy in advocating views which seem so at odds with common sense, they did not do so simply to shock. Stoic ethics achieves a certain plausibility within the context of their physical theory and psychology, and within the framework of Greek ethical theory as that was handed down to them from Plato and Aristotle. It seems that they were well aware of the mutually interdependent nature of their philosophical views, likening philosophy itself to a living animal in which logic is bones and sinews; ethics and physics, the flesh and the soul respectively (another version reverses this assignment, making ethics the.. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...) other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

The Stoic understanding of virtue is often taken to be a non-starter. Many of the Stoic claims about virtue – that a virtue requires moral perfection and that all who are not fully virtuous are vicious – are thought to be completely out of step with our commonsense notion of virtue, making the Stoic account more of an historical oddity than a seriously defended view. Despite many voices to the contrary, I will argue that there is a way of making (...) sense of these Stoic claims. Recent work in linguistics has shown that there is a distinction between relative and absolute gradable adjectives, with the absolute variety only applying to perfect exemplars. I will argue that taking virtue terms to be absolute gradable adjectives – and thus that they apply only to those who are fully virtuous – is one way to make sense of the Stoic view. I will also show how interpreting virtue theoretic adjectives as absolute gradable adjectives makes it possible to defend Stoicism against its most common objections, demonstrating how the Stoic account of virtue might once again be a player in the contemporary landscape of virtue theorizing. (shrink)