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

Local processing in neurites of VGluT3- expressing amacrine cells differentially organizes visual information

Neurons receive synaptic inputs on extensive neurite arbors. How information is organized across arbors and how local processing in neurites contributes to circuit function is mostly unknown. Here, we used two-photon Ca2+ imaging to study visual processing in VGluT3-expressing amacrine cells (VG3-ACs) in the mouse retina. Contrast preferences (ON vs. OFF) varied across VG3-AC arbors depending on the laminar position of neurites, with ON responses preferring larger stimuli than OFF responses. Although arbors of neighboring cells overlap extensively, imaging population activity revealed continuous topographic maps of visual space in the VG3-AC plexus. All VG3-AC neurites responded strongly to object motion, but remained silent during global image motion. Thus, VG3-AC arbors limit vertical and lateral integration of contrast and location information, respectively. We propose that this local processing enables the dense VG3-AC plexus to contribute precise object motion signals to diverse targets without distorting target-specific contrast preferences and spatial receptive fields.</jats:p

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

Division and Animal Sacrifice in Plato’s Statesman

In the Statesman (287c3-5), Plato proposes that the philosophical divider should divide analogously to how the butcher divides a sacrificial animal. According to the common interpretation, the example of animal sacrifice illustrates that we should “cut off limbs” (kata mele), that is, divide non-dichotomously into functional parts of a living whole. We argue that this interpretation is historically inaccurate and philosophically problematic: it relies on an inaccurate understanding of sacrificial butchery and leads to textual puzzles. Against the common interpretation, we argue that the example of animal sacrifice illustrates that correct division minimizes (it cuts into the smallest number possible) by first dividing dichotomously and then dividing non-dichotomously into “parts,” not “limbs.” We will show that both the philosophical divider and sacrificial butcher proceed exactly in this way. By taking Plato’s comparison to the historical practice of animal sacrifice seriously, our interpretation provides better solutions to several textual puzzles than the common interpretation.In the Statesman (287c3-5), Plato proposes that the philosophical divider should divide analogously to how the butcher divides a sacrificial animal. According to the common interpretation, the example of animal sacrifice illustrates that we should “cut off limbs” (kata mele), that is, divide non-dichotomously into functional parts of a living whole. We argue that this interpretation is historically inaccurate and philosophically problematic: it relies on an inaccurate understanding of sacrificial butchery and leads to textual puzzles. Against the common interpretation, we argue that the example of animal sacrifice illustrates that correct division minimizes (it cuts into the smallest number possible) by first dividing dichotomously and then dividing non-dichotomously into “parts,” not “limbs.” We will show that both the philosophical divider and sacrificial butcher proceed exactly in this way. By taking Plato’s comparison to the historical practice of animal sacrifice seriously, our interpretation provides better solutions to several textual puzzles than the common interpretation.In the Statesman (287c3-5), Plato proposes that the philosophical divider should divide analogously to how the butcher divides a sacrificial animal. According to the common interpretation, the example of animal sacrifice illustrates that we should “cut off limbs” (kata mele), that is, divide non-dichotomously into functional parts of a living whole. We argue that this interpretation is historically inaccurate and philosophically problematic: it relies on an inaccurate understanding of sacrificial butchery and leads to textual puzzles. Against the common interpretation, we argue that the example of animal sacrifice illustrates that correct division minimizes (it cuts into the smallest number possible) by first dividing dichotomously and then dividing non-dichotomously into “parts,” not “limbs.” We will show that both the philosophical divider and sacrificial butcher proceed exactly in this way. By taking Plato’s comparison to the historical practice of animal sacrifice seriously, our interpretation provides better solutions to several textual puzzles than the common interpretation.In the Statesman (287c3-5), Plato proposes that the philosophical divider should divide analogously to how the butcher divides a sacrificial animal. According to the common interpretation, the example of animal sacrifice illustrates that we should “cut off limbs” (kata mele), that is, divide non-dichotomously into functional parts of a living whole. We argue that this interpretation is historically inaccurate and philosophically problematic: it relies on an inaccurate understanding of sacrificial butchery and leads to textual puzzles. Against the common interpretation, we argue that the example of animal sacrifice illustrates that correct division minimizes (it cuts into the smallest number possible) by first dividing dichotomously and then dividing non-dichotomously into “parts,” not “limbs.” We will show that both the philosophical divider and sacrificial butcher proceed exactly in this way. By taking Plato’s comparison to the historical practice of animal sacrifice seriously, our interpretation provides better solutions to several textual puzzles than the common interpretation.In the Statesman (287c3-5), Plato proposes that the philosophical divider should divide analogously to how the butcher divides a sacrificial animal. According to the common interpretation, the example of animal sacrifice illustrates that we should “cut off limbs” (kata mele), that is, divide non-dichotomously into functional parts of a living whole. We argue that this interpretation is historically inaccurate and philosophically problematic: it relies on an inaccurate understanding of sacrificial butchery and leads to textual puzzles. Against the common interpretation, we argue that the example of animal sacrifice illustrates that correct division minimizes (it cuts into the smallest number possible) by first dividing dichotomously and then dividing non-dichotomously into “parts,” not “limbs.” We will show that both the philosophical divider and sacrificial butcher proceed exactly in this way. By taking Plato’s comparison to the historical practice of animal sacrifice seriously, our interpretation provides better solutions to several textual puzzles than the common interpretation.In the Statesman (287c3-5), Plato proposes that the philosophical divider should divide analogously to how the butcher divides a sacrificial animal. According to the common interpretation, the example of animal sacrifice illustrates that we should “cut off limbs” (kata mele), that is, divide non-dichotomously into functional parts of a living whole. We argue that this interpretation is historically inaccurate and philosophically problematic: it relies on an inaccurate understanding of sacrificial butchery and leads to textual puzzles. Against the common interpretation, we argue that the example of animal sacrifice illustrates that correct division minimizes (it cuts into the smallest number possible) by first dividing dichotomously and then dividing non-dichotomously into “parts,” not “limbs.” We will show that both the philosophical divider and sacrificial butcher proceed exactly in this way. By taking Plato’s comparison to the historical practice of animal sacrifice seriously, our interpretation provides better solutions to several textual puzzles than the common interpretation.In the Statesman (287c3-5), Plato proposes that the philosophical divider should divide analogously to how the butcher divides a sacrificial animal. According to the common interpretation, the example of animal sacrifice illustrates that we should “cut off limbs” (kata mele), that is, divide non-dichotomously into functional parts of a living whole. We argue that this interpretation is historically inaccurate and philosophically problematic: it relies on an inaccurate understanding of sacrificial butchery and leads to textual puzzles. Against the common interpretation, we argue that the example of animal sacrifice illustrates that correct division minimizes (it cuts into the smallest number possible) by first dividing dichotomously and then dividing non-dichotomously into “parts,” not “limbs.” We will show that both the philosophical divider and sacrificial butcher proceed exactly in this way. By taking Plato’s comparison to the historical practice of animal sacrifice seriously, our interpretation provides better solutions to several textual puzzles than the common interpretation

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

Division, Syllogistic, and Science in Prior Analytics I.31

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship between division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science

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