Ancient Greek and Roman Philosophy: Topics

I argue that in the Phaedo, Plato maintains that the soul is located in space and is capable of locomotion and of interacting with the body through contact. Numerous interpreters have dismissed these claims as merely metaphorical, since they assume that as an incorporeal substance, the soul cannot possess spatial attributes. But careful examination of how Plato conceives of the body throughout his corpus reveals that he does not distinguish it from the soul in terms of spatiality. Furthermore, assigning spatial (...) attributes to the soul plays an important role in Plato’s account of the relation of body and soul. (shrink)

The aim of the book is to encourage discussion among experts on De ira, a text of philosophical nature, by reading it page by page, from a philosophical, philological, and literary perspective (a multidisciplinary choice which is the conditio sine qua non of all judicious research on Seneca). Moreover, the way in which each of these close readings is conducted adds an additional value: they each deal with a section of the text, presenting all the data necessary for its understanding. (...) All together, they cover the whole work. Each of them is also an attempt at a global interpretation of the treatise, examined through the particular framing of the textual passage around which the “Lectures plurielles” are conceived. Around this “polyphonic” analysis of the text, we have built a structure that aims to offer the reader a complete reference work on all the issues of the De ira. Sources, manuscript tradition, images, political and philosophical concepts, posterity – in short, all the aspects that a traditional commentary of the text would not have allowed us to distinguish so clearly – find their place here. This book is therefore aimed at specialists as well as students or anyone interested in the thought of emotions in antiquity. (shrink)

لا شك أن حقيقة موتنا هي أهم حقيقة عنا، على حد تعبير الفيلسوف الأمريكي «تود جيفورد ماي»؛ قد يكون الموت مأساويًا وتعسفيًا ولا معنى له للوهلة الأولى، لكنه في الوقت ذاته يفتح أمامنا الحياة الكاملة التي لم تكن لتوجد بدونه! فكيف يمكن أن نعيش في مواجهة النفي التام؟ كيف يجب أن نفكر في الموت؟ وهل يجب على الأطباء، الذين يُتهمون أحيانًا بأنهم دجالون يبيعون وهم الخلود، أن ينتبهوا أكثر لفلسفة الموت؟.

In this paper, we intend to explore the possible influences of legislative prose in the Anaximander’s cosmological prose construction, who would have been, according to Themistius, “the first Greek who dared to expose a written discourse about nature” (ἐθάρρησε πρῶτος ὧν ἴσμεν Ἑλλήνων λόγον ἐξενεγκεῖν περὶ φύσεως συγγεγραμμένον, Or. 26 p. 383 = DK12A7). Our aim is to clarify which notions of nature and justice are assumed in its emergent cosmology, considering that, at least from the lexical point of view, (...) it seems strongly suggestive to be undefined the barriers between the legal and cosmic order, between the Human and the Natural. Indeed, this is what the peripatetic tradition seems to suggest by judging Anaximander’s language extremely poetic (ποιητικωτέροις οὕτως ὀνόμασιν αὐτὰ λέγων), since he would use legal terms (διδόναι αὐτὰ δίκην καὶ τίσιν ἀλλήλοις τῆς ἀδικίας) to explain the natural processes of generation and corruption (ἡ γένεσίς ἐστι τοῖς οὖσι, καὶ τὴν φθορὰν εἰς ταῦτα γίνεσθαι, Simpl. in Phys. 24. 13–25 = DK12B1). ——— Objetivamos neste artigo explorar as possíveis influências da prosa legislativa na constituição da prosa cosmológica de Anaximandro de Mileto, que teria sido, segundo Temístio, “o primeiro grego que ousou expor um discurso escrito sobre a natureza” (ἐθάρρησε πρῶτος ὧν ἴσμεν Ἑλλήνων λόγον ἐξενεγκεῖν περὶ φύσεως συγγεγραμμένον, Or. 26 p.383 = DK12A7). Visamos aclarar que noções de natureza e de justiça estão sendo pressupostas nessa cosmologia então emergente, considerando que, ao menos do ponto de vista lexical, parece fortemente sugestivo serem indefinidas as barreiras entre a ordem jurídica e a cósmica, entre o âmbito humano e o natural. Com efeito, é o que parece já sugerir a tradição peripatética ao julgar o linguajar de Anaximandro extremamente poético (ποιητικωτέροις οὕτως ὀνόμασιν αὐτὰ λέγων) por o milésio empregar termos considerados do âmbito jurídico (διδόναι αὐτὰ δίκην καὶ τίσιν ἀλλήλοις τῆς ἀδικίας) para explicar os processos ditos naturais de geração e corrupção (ἡ γένεσίς ἐστι τοῖς οὖσι, καὶ τὴν φθορὰν εἰς ταῦτα γίνεσθαι, Simpl. in Phys. 24.13–25 = DK12B1). (shrink)

At the beginning of Republic 2 (358e–359b), Plato has Glaucon ascribe a social contract theory to Thrasymachus and ‘countless others’. This paper takes Glaucon’s description to refer both within the text to Thrasymachus’ views, and outside the text to a series of works, most of which have been lost, On Justice or On Law. It examines what is likely to be the earliest surviving work that presents a philosophical defence of law and justice against those who would prefer their opposites, (...) On Excellence by an anonymous author usually referred to as ‘Anonymus Iamblichi’; the views on these topics among the Socratics, including Crito, Simon the Cobbler, Aristippus of Cyrene, and Antisthenes; and Socrates’ debate with Hippias ‘On Justice’ in Xenophon’s Memorabilia (4.4.5–25). Its main contention is that the ‘countless others’ referred to by Glaucon points chiefly, but not solely, to the members of the circle of Socrates, who themselves espoused a range of views on justice and law, and their relations. (shrink)

Both Heraclitus and Democritus, as the philosophers of historia peri phuseôs, consider nature and human character, habit, law and soul as interrelated emphasizing the links between phusis, kinesis, ethos, logos, kresis, nomos and daimon. On the one hand, Heraclitus’s principle of change (panta rhei) and his emphasis on the element of fire and cosmic motion ultimately dominate his ethics reinforcing his ideas of change, moderation, balance and justice, on the other, Democritus’s atomist description of phusis and motion underlies his principle (...) of moderation and his ideas of health and measured life. In this series, particularly referring to the main principles of motion, moderation and justice, I attempt to describe a coherent pre-Socratic ethical perspective based on the Heraclitean and Democritean fragments. I explore the connections between their physics and ethics also borrowing from Nietzsche’s lectures and writings on the Pre-Socratics. I redefine such Heraclitean and Democritean concepts as harmony, order, perfection, health, self-control, contentment, cheerfulness, concord, sound judgment, wisdom, measure and balance and discuss them under the principles of motion (phusis), moderation (sophrosyne) and justice. In doing so, I also expose the relevance of the Heraclitean notion of logos (interpreting it as the underlying categorical principle of transition between phusis and ethos) in bringing together these ideas and principles. Finally, based on this pre-Socratic Weltanschauung, I assess the possibility of a coherent picture of humanity, its nature and conduct as extending from or fitting into or extending-from-when-fitting-into the cosmos of moving forces and atoms. (shrink)

This paper focuses on the Hasidic view, namely, that human flaws do not function as a barrier between a fallen humanity and a perfect deity, since the whole of creation stems from a divine act of self-contraction. Thus, we need not be discouraged by our own shortcomings, nor by those of our loved ones. Rather, seeing our flaws in the face of another should remind us that imperfection is an aspect of the God who created us. Such a positive approach (...) to human fallibility arouses forgiveness, mutual acceptance, and a hope for repair, and, therefore, has much to recommend itself. In the first part of the paper, I argue that the notion of a perfect God derives from the Greeks rather than the Hebrew Bible. A review of classical philosophies and the idea of God’s imperfection is followed by a consideration of several Jewish attempts to resolve the dichotomy between Divine perfection and an imperfect creation. I focus on Lurianic Kabbalah, Hans Jonas, and on the Hasidic concept of "Ayin " or “nothingness” as the very source of redemption. This Hasidic idea, which was further expanded upon by the Baal Shem Tov’s students, appears in a tale recounted by his great-grandson R. Nachman of Bratslav called “The Hanging Lamp.” I focus on the tale, which illustrates the idea that knowledge of human imperfection is itself a means of perfection and redemption. (shrink)

In this paper, through the example of Antonii Radyvylovskyi’s work, I examine the impact of Seneca’s texts on the philosophical component of Ukrainian church sermons from the Baroque period. The objective of this study is to investigate Radyvylovskyi’s use of Seneca’s texts in his own writing. The result should help better understand the ideological influence of ancient philosophy on the formation of the national philosophical tradition of the Baroque epoch. The contents of ideological borrowings from Seneca’s texts and the mechanisms (...) of their use are traced. A list of Seneca’s texts from which Radyvylovskyi quotes is provided. It is also shown that Radyvylovskyi uses Seneca’s authority in his moral teachings and philosophical thinking about the characteristics of human nature. We conclude by commenting on Radyvylovskyi’s creative use of Seneca’s ideas and the significant philosophical component of his written legacy. (shrink)

In this collection of essays, the author develops a new philosophy of life, which has in fact a long tradition. It goes back to some ancient Western thinkers, such as the Milesians, Heraclitus, Empedocles and Plato, for whom philosophy presupposes an affective engagement with the world and not merely its theoretical description or explanation. This classical tradition has been challenged by ideas of modernity, particularly by the idea that modern scientific knowledge is the highest form of human knowledge. However, as (...) the author argues, this idea is questionable. In his view, scientific knowledge represents merely a partial knowledge. Science looks at the world indifferently as if it were an object, an “It”, but in fact the world is not that. Love, an affective engagement, and not indifference, is the way to full knowledge. Furthermore, it is lov e that fosters life and brings all things into unity. Love and life are thus closely connected. Life is the central concept around which humanity can unite, forming a unity in diversity. The author claims that global solidarity among human beings can be achieved if there is the growing common understanding of what is right for life. (shrink)

This paper seeks to elucidate the distinctive nature of the rational impression on its own terms, asking precisely what it means for the Stoics to define logikē phantasia as an impression whose content is expressible in language. I argue first that impression, generically, is direct and reflexive awareness of the world, the way animals get information about their surroundings. Then, that the rational impression, specifically, is inherently conceptual, inferential, and linguistic, i.e. thick with propositional content, the way humans receive incoming (...) information from the world. When we suspend certain contemporary assumptions about propositional content, the textual evidence can be taken at face value to reveal why, for the Stoics, rational impressions are called thoughts (noēseis) and how the Stoics’ novel semantic entities called lekta (roughly, the meanings of our words) depend on rational impressions for their subsistence. (shrink)

NOTA PRELIMINAR: o texto a seguir representa a versão ampliada (e corrigida conforme as indicações dos pareceristas) do artigo homônimo, publicado na revista Archai em 2014. Por algum problema técnico, acabou sendo publicada, na época, a primeira versão, sem as melhorias sugeridas pelos avaliadores. Eis, então, a versão ‘definitiva’ do artigo “Zenão e a impossibilidade da analogia”: -/- A reductio ad absurdum foi elevada por Zenão de Eléia a único método que permitiria vislumbrar a verdadeira realidade, invisível tanto aos sentidos (...) quanto à maneira de pensar comum. Mostrando uma certa continuidade com os filósofos anteriores, não só na busca de um procedimento para que a especulação pudesse avançar, como também na mesma rota de afastamento daquilo que é mais próximo, conhecido e particular (visível) em direção àquilo que é menos conhecido, distante e universal (invisível), para dizê-lo em termos aristotélicos, Zenão utilizou-se de argumentos aporéticos como único caminho possível para poder entrever o ‘reino do Ser’. Esse, com efeito, é invisível não somente aos nossos sentidos, como também ao nosso raciocínio ordinário. Eis que somente a ‘via do não-ser’, a única que poderia ser trilhada após Parménides, como diz Wolff, nos permite ter uma ideia, por quanto vaga, daquilo que é ‘verdadeiramente invisível’. Tão invisível ao ponto de ser inalcançável até mesmo pelo pensamento. (shrink)

I argue, firstly, that the accounts of 'accident' in Aristotle's Met. V 30 and in Top. I 5 cannot be used to elucidate each other: the Metaphysics passage tries to disentangle the uses of a Greek word, the Topics passage introduces technical terms for Aristotle's semantics. I then argue that the positive definition in Top. I 5 is to be understood in the following way: X is an accident of Y iff X belongs to Y and if there is a (...) Z such that X can belong to Z and also not belong to Z. Thus, being white is an accident of snow. I finally argue that certain shortcomings in the Topics account lead Aristotle to redefine accident in the Posterior Analytics. (shrink)

This makes three main interpretative points about the progression from perception to universals described in 'Posterior Analytics' II.19: (1) The noun "'aisthesis'" as used in the chapter may refer not to the act of perceiving but to perceptual contents retained in memory. (2) An 'empeiria' (experience) should be understood as a capacity to generate expectations about new members of an unconceptualized kind based on memories of other members of the kind. (3) The famous rout analogy is a metaphor for the (...) perfection of such a capacity into a concept that can underwrite demonstrative knowledge (rather than mere expectation). (shrink)

-/- In Plato's work the "Sophist", Socrates, who typically occupies a central position in Plato's dialogues, is assigned a supporting role. This has led some scholars to argue for a shift in Plato's oeuvre, where he distances himself from Socrates and introduces a new main protagonist. However, this new protagonist remains unnamed and is only identified by his social position as Xenos, indicating that he is an outsider and a stranger whose identity is ambiguous. In this article, I argue that (...) Plato's decision to leave the character unnamed serves to raise a first problem: the question of whether this stranger is a friend or an adversary of philosophy. At the beginning of the dialogue, Socrates employs a series of references to Homer to bring into play a second problem: the problem of disguise. The third problem, “What is a sophist?”, is attributed to the Xenos. This is the only problem that is explicitly developed and is, therefore, the most prominent in the dialogue. If we relate these three problems to each other, it becomes clear that they represent contradictory intuitions without providing us with a strict criterion for deciding which of these intuitions is correct. By presenting these problems in their entanglement without providing a way out, Plato invites his readers to think without making explicit what the outcome of this thinking should be. -/- [In Dutch: In de "Sofist" speelt Sokrates, vaak het meest prominente personage in Plato’s dialogen, alleen maar een bijrol. Dit heeft veel interpreten ertoe verleid om een breuk in het oeuvre van Plato te postuleren, waarbij Plato afstand zou nemen van Sokrates ten behoeve van een nieuw personage. Ik zal echter laten zien dat Plato er bewust voor kiest om dit nieuwe personage naamloos te laten en hem alleen aan te duiden via zijn sociale positie als xenos (vreemdeling). Hiermee roept Plato, zo zal ik betogen, impliciet een eerste probleem op: is deze naamlo- ze Xenos een vriend of een vijand van de filosofie? Aan het begin van de dialoog wordt er door Sokrates een tweede probleem in spel gebracht: het probleem van de vermomming. Het derde probleem — ‘wat is een sofist?’ — wordt toegeschreven aan de Xenos. Dit is het enige probleem dat expliciet wordt uitgewerkt en is dan ook het meest prominent aanwezig in de dialoog. Als we deze drie problemen op elkaar betrekken dan wordt duidelijk dat ze tegenstrijdige intuïties vertolken, zonder dat we een strikt criterium krijgen aangereikt om te beslissen welke van deze intuïties de juiste is. Door deze problemen in een nog niet ontwarde kluwen te presenteren, nodigt Plato zijn lezers uit tot denken, zonder expliciet te maken wat de uitkomst van dit denken zou moeten zijn.]. (shrink)

This essay argues that the Ancient Greek's tales of cannibalism were not really about cannibalism at all, but about more typically Greek issues (such as the transfer of political power, the guest-host relationship, the initiation of youths into adulthood, and so on). Cannibalism is rather the image used to designate the negative extremes of human behavior as conceived by the Hellenic world: social breakdown, barbarism, reversion to animality, and ultimately, the inability to live under the institution of the polis.

This chapter presents several of the dominant ideas and intellectual debates about human beauty from archaic Greece to early Christianity. At issue are ideals of character, ethical ideals of who one should be and how one should live. What constitutes beauty and why beauty matters change alongside conceptions of body and soul, virtue and happiness, and the relationship between human beings and the divine.

Review of the first comprehensive companion to the growing scholarship on ancient Greek and Roman aesthetics.

O elenchus é o método pelo qual Sócrates evidencia as incoerências entre a tese de seu interlocutor e seu sistema de crenças. Na visão de Gregory Vlastos, o método utilizado por Sócrates no Teeteto não é elêntico porque ele não visa a refutação direta da tese inicial de Teeteto. Argumentando contra a visão de Vlastos defendo que Sócrates constrói ao final da primeira parte do diálogo objeções fundamentadas em premissas aceitas por Teeteto que culminam no objetivo clássico do elenchus. Além (...) disso, argumento que mesmo que Sócrates não tivesse de fato refutado a tese original de Teeteto, ainda poderíamos defender que o método é elêntico, pois Teeteto consente com as premissas que igualam sua tese a tese de Protágoras. (shrink)

This paper explores an idea of Stoic descent that is largely neglected nowadays, the idea that an argument is valid when the conditional formed by the conjunction of its premises as antecedent and its conclusion as consequent is true. As it will be argued, once some basic features of our naıve understanding of validity are properly spelled out, and a suitable account of conditionals is adopted, the equivalence between valid arguments and true conditionals makes perfect sense. The account of validity (...) outlined here, which displays one coherent way to articulate the Stoic intuition, accords with standard formal treatments of deductive validity and encompasses an independently grounded characterization of inductive validity. (shrink)

This paper revisits Aristotle’s discussion of akrasia in NE VII. 1–10. I try to offer a scientific reading of the book, according to which NE VII. 1–10 closely instantiates the main guidelines of Aristotle’s Posterior Analytics. I propose that NE VII. 1–2, which aims to establish the fact that akrasia exists, corresponds to the ὅτι-stage of an Aristotelian scientific inquiry, and NE VII. 3–10, which aims to explain both the cause and the object of akrasia, corresponds to the διότι-stage of (...) the inquiry. (shrink)

En este artículo presentamos una posible vía para interpretar las nociones de posibilidad y necesidad desarrolladas en el seno de la lógica megárico-estoica como operadores modales aléticos. Se introducirá la semántica megárico-estoica como trasfondo metafísico de las definiciones de necesidad y posibilidad y se ofrecerán argumentos para abandonar las interpretaciones predominantes que incluyen variables temporales ad hoc. Tras proponer la lectura de las definiciones diodóricas desde una semántica modal relacional se señalará una serie de temas que merecen ser revisitados desde (...) esta óptica. (shrink)

The article deals with some current pioneering formal reconstructions and interpretations of the problem well known in antiquity as The Master Argument. This problem is concerning with enrichment of formal logical systems with modal and temporal notions. The opening topic is devoted to reconstruction of Arthur Prior. while the other here included approach to the problem arc mostly reactions. revisions or additions to this one.

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. (shrink)

This article aims to show that it is impossible to put Cicero’s testimonies regarding The Fabius Argument in a consistent inferential order. Either we must suppose that additional premises are tacitly assumed in the text or we must com-pare it with other sources, which leads to inconsistencies in the proof’s reconstruction. Cicero’s reconstruction of the progression of the argument has formal shortcomings, and the paper draws attention to some of these deficiencies. He interpreted sources in a revised and intentionally simplified (...) way, with the aim of undermining the views of his opponents, casting them as inconsistent and similar to views held by Diodorus. Rather than being a consistently interpreted argument faithfully transcribed from the Stoic sources, Cicero’s Fabius Argument is ultimately anti-Stoic. (shrink)

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.

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” (...) in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry. (shrink)

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. (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)

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)

Rather than considering ordinary language as deficient and incapable of grasping the structure of reality, the Stoics set out a theory, based on their notion of a lekton, by which ordinary language is a reflection of the structure of lekta which themselves are constitutive of reality.

Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...) Q is one whose existentialization, ∃ x Q, is logically true; otherwise, Q is existential-import-free or simply import-free.How abundant or widespread is existential import? How abundant or widespread are existential-import predicates in themselves or in comparison to import-free predicates? We show that existential-import predicates are quite abundant, and no less so than import-free predicates. Existential.. (shrink)

John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the conclusion follows from the premises: (...) there must be something deductions can show. Corcoran calls a proposition that follows from given premises a hidden consequence of those premises if it is not obvious that the proposition follows from those premises. By a Euclidean geometry we mean an extended discourse beginning with basic premises—axioms, postulates, definitions—1) treating a universe of geometrical figures and 2) resembling Euclid’s Elements. There were Euclidean geometries before Euclid (fl. 300 BCE), even before Aristotle (384–322 BCE). Bochenski, Lukasiewicz, Patzig and others never new this or if they did they found it inconvenient to mention. Euclid shows no awareness of Aristotle. It is obvious today—as it should have been obvious in Euclid’s time, if anyone knew both—that Aristotle’s logic was insufficient for Euclid’s geometry: few if any geometrical theorems can be deduced from Euclid’s premises by means of Aristotle’s deductions. Aristotle’s writings don’t say whether his logic is sufficient for Euclidean geometry. But, there is not even one fully-presented example. However, Aristotle’s writings do make clear that he endorsed the goal of a sufficient system. Nevertheless, incredible as this is today, many logicians after Aristotle claimed that Aristotelian logics are sufficient for Euclidean geometries. This paper reviews and analyses such claims by Mill, Boole, De Morgan, Russell, Poincaré, and others. It also examines early contrary statements by Hintikka, Mueller, Smith, and others. Special attention is given to the argumentations pro or con and especially to their logical, epistemic, and ontological presuppositions. What methodology is necessary or sufficient to show that a given logic is adequate or inadequate to serve as the underlying logi of a given science. (shrink)

As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 (...) proof of the completeness of Aristotle’s syllogistic. (shrink)

ABSTRACT: Discussion (in German) of Robert Muller's "Les Megariques, Fragments et temoignages". Traduit et commentes. Paris, Vrin 1985, with focus on his commentary on ancient paradoxes.

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. (shrink)

Aristoteles Περὶ ἑρμηvείας Erklärungen Griechisch-deutsch ins Deutsche übersetzt von Gottfried Scherer -/- In seiner Schrift Erklärungen handelt Aristoteles von Namen, die alles, vieles oder Einzelnes bezeichnen, von Prädikatswörtern, die bestimmende oder zufällige Eigenschaften angeben, und von Worten und deren Kombinationsmöglichkeiten. Dabei untersucht er konkret die Struktur von Aussagesätzen, die er von anderen Redensarten abgrenzt, und stellt fest, dass sie etwas als existent und zutreffend, als wahr oder falsch bezeichnen. Er gibt an, wann mehrwertige Aussagen entstehen und beschreibt, was für Gattungsnamen (...) und was für Eigennamen gilt. Er definiert lakonisch, was ein Mensch im Unterschied zu anderen Lebewesen ist, und unterscheidet verschiedene Möglichkeiten, Namen und Prädikatswörter zu negieren. Ausführlich diskutiert er die Frage, ob logisch richtige Kombinationen von Bejahungen und Verneinungen Tatsachen präjudizieren oder ob Tatsachen unabhängig von Logik entstehen - Tatsachen und deren Feststellung werden ausdrücklich nicht erörtert, weil sich darüber nicht streiten lasse. Er gibt Hinweise darauf, wie notwendige, hypothetische und wirksame Bestimmungen zu verwenden seien und beschreibt Möglichkeiten, solche Aussagen schlüssig zu benutzen. Seine formalen Überlegungen demonstriert er an Beispielen, in denen er sich auch auf das Zeitgeschehen bezieht. -/- Mit dieser Übersetzung, die sich weitgehend an der Bekkerschen Ausgabe der Aristotelischen Schriften orientiert, soll ein lesbarer Text vorgelegt werden, der systematisch versucht, die griechischen Wortbedeutungen lebendig werden zu lassen. Auf eine Interpretation des Textes im Sinne traditioneller oder moderner Logiken oder auf eine an den Massengeschmack der 20er und folgender Jahre angepasste oder an andere Zeitgeister angelehnte Verdeutschung wurde bewusst verzichtet. Die Übersetzung möchte dem Leser Lust machen, selber zu denken - und sich intensiver mit Aristoteles zu beschäftigen. -/- . (shrink)

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 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' (including inalienable and alienable possession) 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. (shrink)

ABSTRACT: A very brief summary presentation of western ancient logic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).

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.

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. (shrink)

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." A more formal and more detailed account of the Stoic theory of deduction can be found (...) in S. Bobzien, Stoic Syllogistic, OSAP 1996. (shrink)

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

ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and Diodorus Cronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.

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. (shrink)

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. (shrink)