Pyrrhonism and the Dialectical Methods: The Aims and Argument of PH II

The aim of this paper is to show how PH II constitutes an original, ambitious, and unified skeptical inquiry into logic. My thesis is that Sextus’s argument in Book II is meant to accomplish both its stated goal (to investigate the topics typically grouped together by dogmatists under the heading of “logic”) and an unstated goal. The unstated goal is, in my view, interesting in itself and sheds new light on Sextus’s methodology. The goal is: to suspend judgement on the effectiveness of dogmatic methodologies

Greek and Roman Logic

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

Platonic Division and the Origins of Aristotelian Logic

Aristotle's syllogistic theory, as developed in his Prior Analytics, is often regarded as the birth of logic in Western philosophy. Over the past century, scholars have tried to identify important precursors to this theory. I argue that Platonic division, a method which aims to give accounts of essences of natural kinds by progressively narrowing down from a genus, influenced Aristotle's logical theory in a number of crucial respects. To see exactly how, I analyze the method of division as it was originally conceived by Plato and received by Aristotle. I argue that, while Plato allowed that some divisions fail to rigorously investigate the essence, he began a program continued by Aristotle (and others in antiquity and the middle ages) of seeking norms for division that would apply in any domain whatsoever. This idea of a rigorous, general method was taken up and developed by Aristotle in his syllogistic. Aristotle also used Plato's conception of predication as parthood in his semantics for syllogistic propositions. As part of my argument, I prove that a semantics based on Platonic divisional structures is sound and complete for the deduction system used in the literature to model Aristotle's syllogistic

Platonic Division and the Origins of Aristotelian Logic

Aristotle's syllogistic theory, as developed in his Prior Analytics, is often regarded as the birth of logic in Western philosophy. Over the past century, scholars have tried to identify important precursors to this theory. I argue that Platonic division, a method which aims to give accounts of essences of natural kinds by progressively narrowing down from a genus, influenced Aristotle's logical theory in a number of crucial respects. To see exactly how, I analyze the method of division as it was originally conceived by Plato and received by Aristotle. I argue that, while Plato allowed that some divisions fail to rigorously investigate the essence, he began a program continued by Aristotle (and others in antiquity and the middle ages) of seeking norms for division that would apply in any domain whatsoever. This idea of a rigorous, general method was taken up and developed by Aristotle in his syllogistic. Aristotle also used Plato's conception of predication as parthood in his semantics for syllogistic propositions. As part of my argument, I prove that a semantics based on Platonic divisional structures is sound and complete for the deduction system used in the literature to model Aristotle's syllogistic

Plato on Poetic and Musical Representation

Plato’s most infamous discussions of poetry in the Republic, in which he both develops original distinctions in narratology and advocates some form of censorship, raises numerous philosophical and philological questions. Foremost among them, perhaps, is the puzzle of why he returns to poetry in Book X after having dealt with it thoroughly in Books II–III, particularly because his accounts of the “mimetic” aspect of poetry are, on their face, quite different. How are we to understand this double treatment? Here I will focus on a single aspect of this question, the compatibility of the notion of μίμησις and its cognates in the two books. As Nickolas Pappas has said, “Whether Books 3 and 10 offer compatible accounts of mimêsis, and how one might make them compatible, remains the most controversial question about Plato’s aesthetics”.2 I will show that there is a single notion of μίμησις operative throughout, namely that of representation by resemblance. I will take an unusual tack. I will not begin with the most problematic part of Book III for this interpretation about poetic, linguistic μίμησις, but with the later sections on musical μίμησις. Once we have an account of this, I claim, it is easier to see how narrative μίμησις is also a kind of representation by resemblance

Everything is Conceivable: A Note on an Unused Axiom in Spinoza’s Ethics

Spinoza's Ethics self-consciously follows the example of Euclid and other geometers in its use of axioms and definitions as the basis for derivations of hundreds of propositions of philosophical si..

The Puzzle of the Sophist

The many definitions of sophistry at the beginning of Plato’s Sophist have puzzled scholars just as much as they puzzled the dialogue’s main speakers: the Visitor from Elea and Theaetetus. The aim of this paper is to give an account of that puzzlement. This puzzlement, it is argued, stems not from a logical or epistemological problem, but from the metaphysical problem that, given the multiplicity of accounts, the interlocutors do not know what the sophist essentially is. It transpires that, in order to properly account for this puzzle, one must jettison the traditional view of Plato’s method of division, on which divisions must be exclusive and mark out relations of essential predication. It is then shown on independent grounds that, although Platonic division in the Sophist must express predication relations and be transitive, it need not be dichotomous, exclusive, or express relations of essential predication. Once the requirements of exclusivity and essential predication are dropped, it is possible to make sense of the reasons that the Visitor from Elea and Theaetetus are puzzled. Moreover, with this in hand, it is possible to see Plato making an important methodological point in the dialogue: division on its own without any norms does not necessarily lead to the discovery of essences