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)

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)

It has been noted before in the history of logic that some of Frege's logical and semantic views were anticipated in Stoicism. In particular, there seems to be a parallel between Frege's Gedanke (thought) and Stoic lekton; and the distinction between complete and incomplete lekta has an equivalent in Frege's logic. However, nobody has so far claimed that Frege was actually influenced by Stoic logic; and there has until now been no indication of such a causal connection. In this essay, (...) we attempt, for the first time, to provide detailed evidence for the existence of this connection. In the course of our argumentation, further analogies between the positions of Frege and the Stoics will be revealed. The classical philologist Rudolf Hirzel will be brought into play as the one who links Frege with Stoicism. The renowned expert on Stoic philosophy was Frege's tenant and lived in the same house as the logician for many years. In der Geschichte der Logik ist häufig bemerkt worden, dass einige der logischen und semantischen Auffassungen Freges in der Stoa antizipiert worden sind. Genannt wurden insbesondere die Parallelen zwischen dem Fregeschen Gedanken und dem stoischen Lekton sowie die Unterscheidung zwischen vollständigen und unvollständigen Lekta, die bei Frege ihre Entsprechung hat. Ein Wirkungszusammenhang ist allerdings nicht behauptet worden. Dazu gab es bislang auch keinen Anlass. Der vorliegende Beitrag versucht erstmalig, einen detaillierten Indizienbeweis für das Bestehen eines solchen Zusammenhangs vorzulegen. Dabei werden weitere charakteristische Übereinstimmungen zwischen Frege und der Stoa aufgewiesen. Als Mittelsmann wird der Altphilologe Rudolf Hirzel vorgestellt. Er wohnte lange Jahre als Mieter zusammen mit Frege im selben Haus und war ein anerkannter Experte der stoischen Philosophie. (shrink)

Cet article vise à comprendre la théorie stoïcienne de la deixis afin d’expliquer l’importance accordée par les stoïciens aux pronoms démonstratifs et aux énoncés qu’ils composent, c’est-à-dire les propositions dites définitives. Nous montrons que ces propositions sont privilégiées pour des raisons à la fois ontologiques et épistémologiques en raison des propriétés sémantiques de leur sujet. Elles sont privilégiées d’un point de vue ontologique parce que la deixis grâce à laquelle leur sujet fait référence au réel crée une relation privilégiée à (...) la matière, la catégorie ontologique stoïcienne fondamentale. De plus, ces sujets requièrent que leur référent existe et soit présent et saisissable. Ces énoncés sont d’autre part privilégiés d’un point de vue épistémologique parce qu’ils sont fondamentaux dans l’acquisition de la connaissance. Nous suggérons enfin que tous les énoncés apparemment définis ne le sont pas en effet, et considérons quand et sous quelles conditions une référence déictique est réussie. (shrink)

In this paper we give a detailed comparison of the key elements of Frege’s formal language of thought and apparently similar views in Stoic formal logic. That is, we compare their views on the following topics: connectives, negation, simple sentences, propositional content, predicates and their incompleteness, and quantifications. We show that in most of these cases the similarities between Frege’s views and the Stoic views are only superficial. Frege’s views are far more systematic, better developed and can in no case (...) directly or fully be traced back to Stoic ideas. Furthermore, we show that Prantl, pace Bobzien 2021, is in most of these cases not a reliable source with respect to Stoic logic and that it is very unlikely that Frege’s views on logic were influenced by Prantl’s interpretation of Stoic formal logic. (shrink)

Analogies between hearing and seeing already existed in ancient Greek theories of perception. The present paper follows the evolution of such analogies until the rise of 17th century optics, with due regard to the diversity of their origins and nature but with particular emphasis on their bearing on the physical concepts of light and sound. Whereas the old Greek analogies were only side effects of the unifying concepts of perception, the analogies of the 17th century played an important role in (...) constructing optical theories by imitation of acoustic theories, or vice versa. This transition depended on several factors including the changing relations between optics, music, mathematics, and physics, the diversity of early modern concepts of sound, and the rise of a new physics based on experimentation and mechanical explanation. (shrink)

This volume explores the relation between legal reasoning and logic from both a historical and a systematic perspective. The topics addressed include, among others, conditional legal acts, disjunctions in legal acts, presumptions and conjectures, conflicts of values, Jørgensen´s Dilemma, the Rhetor´s Dilemma, the theory of legal fictions and the categorization of contracts. The unifying problematic of these contributions concerns the conditional structures and, more particularly, the relationship between legal theory and legal reasoning in the context of conditions.

Chrysippus claims that some propositions perish. including some true conditionals whose consequent is impossible and antecedent is possible, to which he appeals against Diodorus?s Master Argument. On the standard interpretation. perished propositions lack truth values. and these conditionals are true at the same time as their antecedents arc possible and consequents impossible. But perished propositions are false, and Chrysippus?s conditionals are true when their antecedent and consequent arc possible, and false when their antecedent is possible and consequent impossible. The claim (...) of the Master Argument that Chrysippus rejects, then, is stronger ihan usually supposed. (shrink)

The article deals with the question of correct reconstruction of and solutions to the ancient paradoxes. Analyzing one contemporary example of a reconstruction of the so-called Crocodile Paradox, taken from Sorensen’s A Brief History of Paradox, the author shows how the original pattern of paradox could have been incorrectly transformed in its meaning by overlooking its adequate historical background. Sorensen’s quoting of Aphthonius, as the author of a certain solution to the paradox, seems to be a systematic failure since the (...) time of Politiano’s erroneous attributing it to Aphthonius. In the conclusion, the author claims that neglecting the historical background of the ancient paradoxes into account, we are neither able to evaluate their modern interpretations as adequate nor their solutions as successful. (shrink)

This paper aims to examine a very specific passage of Sextus Empiricus’s work: the final section of the second book of the Outlines of Pyrrhonism (=ph ii, 229–259). Here Sextus concentrates his attention on a very limited yet crucial topic, namely the question of the validity or invalidity and ‘pragmatic dissolution’ of an allegedly strong tool such as sophisms and their dialectical structure. Indeed, Pyrrhonists do not wander about aimlessly nor lack effective tools through which to dismantle the logical industry (...) of sophisms; their reference point is completely different, since they agree about some evident facts and live their life in accordance with κοινὸς βίος. (shrink)

The present PhD dissertation aims to examine the relation between modality and change in Aristotle’s metaphysics. -/- On the one hand, Aristotle supports his modal realism (i.e., worldly objects have modal properties - potentialities and essences - that ground the ascriptions of possibility and necessity) by arguing that the rejection of modal realism makes change inexplicable, or, worse, banishes it from the realm of reality. On the other hand, the Stagirite analyses processes by means of modal notions (‘change is the (...) actuality of what is virtual insofar as it is virtual’). In other words: to grasp what change is, one has to resort to the modal idiom of potentialities, while the fact that there is change is indicative of the fact that nature is full of modal properties. -/- Aristotle’s modal and kinetic realism finds a negative in the figure of the Megaric Diodorus Kronus. The polemical situation of Greek philosophy has indeed the dialectical advantage of not opposing the Aristotelian position to a sui generis straw man. Both in its reduction of modal judgements to temporal quantifications and in its dissolution of the reality of the state-of-being-in-motion in favour of a cinematographic view of processes, the philosophical figure of reductionist antirealism embodied by Diodorus constitutes an alternative that takes the opposite view of Aristotle’s realism. -/- The present study is structured as a discussion between these two positions. In the face of Diodorus’ antirealist challenges, Aristotle articulates modal and kinetic considerations: the answers he gives to Diodorus’ puzzles thus provide valuable insight into his metaphysics. Moreover, the examination of Aristotle’s and Diodorus’ metaphysics, because of their insight and originality, will not fail to interest the philosopher concerned with the metaphysical foundations of modern physics, insofar as the entanglement between modalities and processes is nowadays at the core of mechanics (phase spaces, path integrals, etc.). (shrink)

The essay deals with an important epistemological debate in the Lucullus: Can there be remembrance of false beliefs, as Cicero argues against his interlocutor, who defends Antiochus’ position? It is shown that Antiochus, like Aristoteles, considers ‘remember’ to be a double achievement verb: Remembrance occurs only if a correct past perception is faithfully transmitted to the present. Cicero, on the other hand, insists that faithful transmission can also occur with false beliefs. The distinction seems to be analogous to that between (...) valid and sound inference in contemporary Stoic logic. Finally, I discuss differences between ancient and modern forms of skepticism, address the issue of why misremembering plays no role in the Lucullus, and find an answer in Cicero’s doctrine of the orator. (shrink)

Adversus Mathematicos x is the second book dedicated by Sextus to the discussion of the physical doctrines put forward by dogmatic philosophers. An extensive section deals with Diodorus Cronus' arguments concerning movement.

Cicero's De fato: On Hellenistic Conditionals and Free Will. The Serbo-Croatian translation of Cicero's De fato, with comments and detailed analysis of some arguments and problems of the text. -/- (s/h): Tekst Ciceronovog spisa "de fato", prevod, komentari i u dodacima, detaljnija analiza pojedinih argumenata i problema sadržanih u tekstu.

El tratado Acerca de la indestructibilidad del mundo es uno de los textos filosóficos clave de Filón de Alejandría. El modo en el que el alejandrino “hace filosofía” es idiosincrático en la medida en que una parte esencial de su método se basa en su opinión de que el Antiguo Testamento coincide con lo que argumentan los filósofos griegos. En este artículo argumento que, a pesar de eso, la relevancia de Filón como fuente para el estudio de la filosofía antigua (...) difícilmente puede ser exagerada. El alcance de este ensayo es modesto: en primer lugar, explico la estructura del tratado; luego me centro en las secciones más “filosóficas”, de manera de aclarar cómo Filón incorpora algunos aspectos del platonismo a su proyecto de interpretar el Pentateuco a la luz de la filosofía griega, y cómo, aun cuando toma distancia de y critica a los estoicos, al mismo tiempo incorpora algunos detalles terminológicos y conceptuales de la Estoa, ya que los mismos son funcionales a su propio proyecto. (shrink)

Philosophie grecque est un ouvrage d'histoire de la philosophie du VIe siècle av. J.-C. au XVe siècle byzantin et qui vient s'ajouter aux nombreuses histoires de la philosophie ancienne que nous a données l'historiographie française du XXe siècle. Le rythme de ces publications, même limitées à la tradition française, demeure impressionnant. En effet, une recherche rapide nous indiquerait facilement un rythme de publication d'environ une histoire de la philosophie ancienne tous les trois ans au cours de ce siècleUne recherche plus (...) poussée augmenterait sans doute cette moyenne. Un esprit malin et tant soit peu insolent pourrait soutenir que Philosophie grecque est un ouvrage de trop sur les rayons déjà amplement garnis de nos bibliothèques et poserait la question fondamentale de la pertinence d'une nouvelle histoire de la philosophie ancienne en cette fin de siècle. (shrink)

Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention to the (...) complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

En el contexto de su crítica a la fenomenomenología husserliana Michel Henry apela a la caracterización de los errores de la perspectiva hetero-afectiva remitiéndose a sus orígenes en la tradición sintetizados en los parámetros de la “gnosis griega” y su compromiso con la racionalidad entendida como comprensión de “objetos puestos a distancia”. La revisión de los alcances de esta categoría revela, sin embargo, que existen tratamientos en el pensamiento griego que apelan a la auto-afección y la inmanencia para dar cuenta (...) de elementos que exceden la dimensión ek-stática. En este trabajo se revisa el planteo henryano para mostrar sus puntos de contacto con el estoicismo, especialmente a partir de la teoría de Hierocles a propósito de la oikeîosis. Este recorrido permitirá sugerir que entre ambos planteos existe una compatibilidad estructural que hace posible apelar a claves de interpretación similares para dar cuenta de la convivencia de mecanismos de explicación que apelan a lo auto-afectivo y lo hétero-afectivo en un conjunto coherente. (shrink)