Plato: Collection and Division

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 the textual puzzles than the common interpretation. (shrink)

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). 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 be- tween 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. (shrink)

In Plato’s Republic, Socrates argues that in the ideal city women and men in the guardian class should receive the same education (451e–52a, 456d–57a) and do the same work (453b–56b); indeed, Socrates emphasizes that the highest office in the ideal city, of philosopher-rulers, will include philosopher-queens and not just philosopher-kings (540c). Socrates’ conclusions might be thought to recognize equality as a value, but in this chapter, we argue that the basis for assigning men and women the same work is a (...) judgment of sameness in nature: with respect to civic contribution, women’s nature is the same as men’s, although on the whole inferior. Fundamentally, the judgment that women and men ought to do the same work irrespective of sex is a method of collecting and dividing kinds according to nature, so that the “ought” is scientific rather than moral. (shrink)

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. (shrink)

Plato’s invention of the metaphor of carving the world by the joints gives him a privileged place in the history of natural kind theory in philosophy and science; he is often understood to present a paradigmatic but antiquated view of natural kinds as possessing eternal, immutable, necessary essences. Yet, I highlight that, as a point of distinction from contemporary views about natural kinds, Plato subscribes to an intelligent-design, teleological framework, in which the natural world is the product of craft and, (...) as a result, is structured such that it is good for it to be that way. In Plato’s Philebus, the character Socrates introduces a method of inquiry whose articulation of natural kinds enables it to confer expert knowledge, such as literacy. My paper contributes to an understanding of Plato’s view of natural kinds by interpreting this method in light of Plato’s teleological conception of nature. I argue that a human inquirer who uses the method identifies kinds with relational essences within a system causally related to the production of some unique craft-object, such as writing. As a result, I recast Plato’s place in the history of philosophy, including Plato’s view of the relation between the kinds according to the natural and social sciences. Whereas some are inclined to separate natural from social kinds, Plato holds the unique view that all naturalness is a social feature of kinds reflecting the role of intelligent agency. (shrink)

The main aim of the French logician and philosopher Petrus Ramus was to provide a method of teaching the liberal arts enabling the completion of the undergraduate program of studies in 7 years. This method was based on a new logic, in which the complex structure of Aristotle’s Organon and of the Summulae logicales of Peter of Spain is reduced to two main doctrines: the invention of arguments, by which it is possible to find the notions for reasoning and disputing (...) in any discipline, and the disposition of arguments in judgment, i.e., in propositions and syllogisms. Since this logic applies both to demonstrative and to probable reasoning, Ramus and Rudolph Agricola, who first introduced it, labeled it as dialectic. Ramus completed this twofold dialectic with a method, according to which disciplines have to be taught by providing general definitions, to be explained by subsequent dichotomous divisions. According to Ramus, this method ensures a well-ordered hierarchy and division of disciplines, and an efficient means to teach them in a shorter time than in the pedagogical programs of Juan Luis Vivès, Johann Sturm, and Philipp Melanchthon. This method had its main diffusion in the pre-university institutions such as the German gymnasia and gymnasia illustria (e.g., of Herborn), while in Reformed and Catholic universities the acceptance of Ramism was hindered by the predominance of the Aristotelian curriculum. (shrink)

In this paper, I articulate three kinds of division that Plato and Aristotle acknowledge to be proper, valid methods of division, namely, diairesis, parallel division, and chiasmus. I attempt to explain the relationship among the three kinds of division, namely, how they transform from one to another. Starting with Plato’s division of constitution in the Statesman, I illuminate that from ostensible diairesis emerges a parallel division, and the parallel division causes a cross-division to occur. Thus, the sixfold division of constitution (...) is not a diairesis but rather is a 3 x 2 cross-division. Inheriting the three kinds of division from Plato, Aristotle advances the form by providing a theoretical explanation to the transformation of the three kinds of division. In Topics Z6, Aristotle prescribes two conditions under which a parallel division can originate from or construct ostensible diairesis and how the parallel division further causes a cross-division to occur. (shrink)

Conceptualism—the view that universals are mental entities without an external, independent, or substantial reality—has enjoyed popularity at various points throughout the history of philosophy. While Plato’s Theory of Forms is not a conceptualist theory of universals, we find at Parmenides 132b–c the startling conceptualist suggestion from a young Socrates that each Form might be a noēma, or a mental entity. This suggestion and Parmenides’ cryptic objections to it have been overshadowed by their placement directly after the notoriously difficult Third Man (...) Argument, and before the Likeness Regress. However, in the background of 132b–c, we find illuminating assumptions behind Parmenides’ arguments against the Theory of Forms in the first half of the dialogue. We also find in this text a set of implied criteria for Platonic concepthood. While in the Platonic corpus, Forms are explanantia for many of the phenomena explained by concepts in contemporary philosophy, concepts do seem to have an important epistemic role in Plato’s philosophy. An account of Platonic concepthood therefore opens the door for new ways of understanding the Platonic corpus as a whole. My focus in this paper is to uncover these assumptions and criteria through a close reading of Socrates’ conceptualist suggestion and Parmenides’ truncated objections to it at Parmenides 132b–c. (shrink)

Despite Aristotle’s claim in Topics I that all dialectical argument is either syllogism or epagōgē, modern scholars have largely neglected to assess the role of epagōgē in Platonic dialectic. Though epagōgē has no technical use in Plato, I argue that the method of collection (which, along with division (diairēsis), is central to many of the dialogues’ accounts of dialectic) functions as the Platonic predecessor to Aristotelian epagōgē. An analysis of passages from the Sophist and Statesman suggests that collection is a (...) purificatory practice. I argue that collection is not only Plato’s account of generalization from a sensible many to an intelligible many, as suggested by the Phaedrus, but also functions as a method of diacritical selection that allows inquiry to move from the intelligible many produced by division to the intelligible unity of a definition. This reading contributes a deeper understanding of the mutual relationship of division and collection within Platonic dialectic as well as a way of unifying the accounts of dialectic in the Sophist and Statesman with the otherwise idiosyncratic account of dialectic in the Republic. Finally, this analysis of Platonic epagōgē sheds light on the connection between inquiry and argument present in Aristotle’s use of epagōgē. (shrink)

At 252e1 to 253c9 in Plato’s Sophist, the Eleatic Visitor explains why philosophy is a science. Like the art of grammar, philosophical knowledge corresponds to a generic structure of discrete kinds and is acquired by systematic analysis of how these kinds intermingle. In the literature, the Visitor’s science is either understood as an expression of a mature and authentic platonic metaphysics, or as a sophisticated illusion staged to illustrate the seductive lure of sophistic deception. By showing how the Visitor’s account (...) of the science of philosophy is just as comprehensive, phantasmatic and self-concealing as the art of sophistry identified at the dialogue’s outset, this paper argues in favor of the latter view. (shrink)

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. (shrink)

In both the Phaedrus and Statesman dialogues, the dialectician's method of division is likened to the butchery of sacrificial animals. Interpreting the significance of this metaphor by analyzing ancient Greek sacrificial practice, this essay argues that, despite the ubiquity of the method of division in these later dialogues, Plato is there stressing the logical priority of the method of collection, division's dialectical twin. Although Plato prioritizes the method of collection, the author further argues that, through a kind of 'domestication' of (...) natural kinds, collection renders natural kinds knowable only by constructing them as implicitly divisible. As a result, the method of collection reflects not the wholeness of being but a constructed unity, the internal multiplicity of which makes possible each subsequent division. (shrink)

Au début du Sophiste, Socrate demande au visiteur éléate ce qu’ont pensé des genres philosophe, sophiste et politique, « ceux » qui sont de ce lieu-là ». L’article a pour but d’éclairer cette dernière expression et en particulier son mot clef « topos ». Il est montré que les significations de ce terme, dans son contexte, sont multiples et que cette diversité, loin d’apporter la confusion, permet au contraire et précisément d’ouvrir les diverses perspectives du dialogue. At the beginning of (...) the Sophist, Socrates asks the Eleatic Visitor how the three kinds Philosopher, Sophist and Statesman, have been understood by “those who are in this place”. The purpose of this paper is to enlighten this periphrasis and specially its key-word “topos”. We have showed that, in its context, this word has four main meanings, and that this diversity, far from causing confusion, opens up the dialogue to various perspectives. (shrink)

This paper focuses on two methodological questions that arise from Plato’s account of collection and division. First, what place does the method of collection and division occupy in Plato’s account of philosophical inquiry? Second, do collection and division in fact constitute a formal “method” (as most scholars assume) or are they simply informal techniques that the philosopher has in her toolkit for accomplishing different philosophical tasks? I argue that Plato sees collection and division as useful tools for achieving two distinct (...) goals – generating real definitions and discovering the basic natural kinds of a given domain of knowledge – both of which occupy a preliminary stage in his account of philosophical inquiry. As to the second question, I claim that the evidence for seeing collection and division as a formal method is weak. Although Plato calls the procedure a technê and a methodos, he makes no real attempt to formalize it in any way. For Plato, collection and division do not constitute an algorithmic process that can be learned from a rule book. Instead the ability to collect and divide properly are skills that good dialecticians must acquire through the kind of hands-on training illustrated by the Sophist and Statesman. Whereas Aristotle insists on formal rules for making proper divisions, Plato seems to emphasize the need to recognize where the natural joints of the world are. In this sense, Plato’s Sophist and Statesman and Aristotle’s Topics and Analytics present two very different pictures of collection and division. (shrink)

In Platons Dialog Sophistes wird nach der Definition des Sophisten gefragt; das führt zum Begriff des Nichtseienden und schließlich unter dem Stichwort 'Dialektik' auf die Frage nach dem Seienden. Daß Platon dabei von der sophistischen Methode ausgeht, das Seiende als bloße Spitze einer Begriffspyramide zu deuten, haben seine Interpreten seit jeher als irgendwie widersprüchlich empfunden. Dieser Kommentar ist für Leser gedacht, die bereit sind, den Sophistes genau zu studieren, aber dabei einen Begleiter haben möchten, der ihnen in möglichst direkter und (...) knapper Form hilft, den oft schwierigen einzelnen Schritten zu folgen und zugleich die Übersicht über das nicht weniger schwierige Ganze zu behalten. Er will nicht in die kaum noch überschaubare wissenschaftliche Diskussion einführen, sondern nur das dort zunehmend ins Hintertreffen geratende unmittelbare Verständnis des Wortlauts sicherstellen. Er ist "kritisch", weil er zum unbefangenen Lesen anhalten möchte. Damit wendet er sich nicht gegen die idealistische Interpretation von Platons Dialogen, der Platon seinen Ruhm als Philosoph verdankt, sondern will zeigen, daß es falsch wäre, den Platon, der im Sophistes Grundlegendes u. a. über Begriffsbildung und Sprache zu sagen hat, darüber zu vernachlässigen. (shrink)

The Sophist and Statesman are late Platonic dialogues, whose relative dates are established by their stylistic similarity to the Laws, a work that was apparently still “on the wax” at the time of Plato's death (Diogenes Laertius III.37). These dialogues are important in exhibiting Plato'sviews on method and metaphysics after he criticized his own most famous contribution to the history of philosophy, the theory of separate, immaterial forms, in the Parmenides. The Statesman also offers a transitional statement of Plato's political (...) philosophy between the Republic and the Laws. The Sophist and Statesman show the author's increasing interest in mundane and practical knowledge. In this respect they seem more down-to-earth and Aristotelian in tone than dialogues dated to Plato's middle period like the Phaedo and the Republic. This essay will focus on method and metaphysics. (shrink)

At the beginning of his Metaphysics, Aristotle attributed several strange-sounding theses to Plato. Generations of Plato scholars have assumed that these could not be found in the dialogues. In heated arguments, they have debated the significance of these claims, some arguing that they constituted an 'unwritten teaching' and others maintaining that Aristotle was mistaken in attributing them to Plato. In a prior book-length study on Plato's late ontology, Kenneth M. Sayre demonstrated that, despite differences in terminology, these claims correspond to (...) themes developed by Plato in the Parmenides and the Philebus. In this book, he shows how this correspondence can be extended to key, but previously obscure, passages in the Statesman. He also examines the interpretative consequences for other sections of that dialogue, particularly those concerned with the practice of dialectical inquiry. (shrink)

In this paper I reexamine Plato's method of collection and division, and specifically of collection. If collection and division are simply methods for mapping out genus-species trees, then it is hard to understand why Plato is so excited about them. But a close study of Plato's examples shows that these methods are something broader, and shows why Plato would regard collection as an important tool for coming to know "elements" in any domain of inquiry. In the first section I focus (...) on a notoriously problematic example of collection from the "Philebus," Theuth's discovery of the letters of the alphabet; I show how Plato interprets this discovery as a process of collection, and draw conclusions about what Plato takes collection to be. In the process, I try to bring out Plato's analysis of what is involved in learning to read and write a language, which he takes as paradigmatic for other knowledge. In the second section, stepping back from the "Philebus" passage and applying its lessons, I describe the function of collection and division, for the late Plato, in coming to know "elements," including the Forms, or the most basic Forms. Reflection on Plato's use of collection suggests a (relatively non-mystical) account of what it is to know non-complex intelligible entities, and of how we can come to know them. I also use Plato's descriptions of collection and division to suggest a Platonic context for the notion of the separation of the Forms, to which the late Plato remains firmly committed. (shrink)

A close exegesis of the principles of the so-called "god-given method" of dialectic in the Philebus (16bff., 23cff.) and an account of the division of the fifteen kinds of art that "care" for the well-formed city in the Statesman (287bff., 303cff.). I show how this division conforms to and, so, illustrates the "god-given method.".

Some biologists and philosophers of biology have seen in Plato an especially objectionable version of essentialism or topology. Although kinds of animals are mentioned in almost all of Plato's dialogues, in none of them is there an explicity stated doctrine of animal kinds. An examination of the dialogues has, moreover, failed to reveal some implicit but consistent and unambiguous view of kinds that Plato might have held.

This is part one of an examination of Plato's Method of Collection and Division, a method which Plato describes in the later dialogues as the method of dialectic. Included are chapters on the Phaedrus, Sophist and Statesman as well as a separate survey of the passages in those dialogues in which the method is mentioned. Questions concerning the requirements for making a collection or a division and the connection between collections and division are addressed. Also included is discussion of the (...) connection between collections and divisions and true forms. ;An interpretation of the Phaedrus is offered that sees the method of collection and division as playing a major role in the dialogue. It is shown that the structure and unity of the Phaedrus are intricately connected with the points Plato is making about the method. ;The actual collections and divisions that are made in the Sophist and Statesman are examined with an eye towards formulating a view of the sophisticated version of the method that Plato is offering. It is suggested that this sophisticated view is possible only after the discussion of not-being in the Sophist, and even then there are some conflicts in the requirements of the theory. A glance ahead at one dialogue which is not covered in this study, the Philebus, indicates how Plato might resolve some of the conflicts in his requirements for the theory. The suggestion is that there is much more to be learned about the theory from the Philebus and other late dialogues. ;It is clear from this study that a complete understanding of the Method of Collection and Division is necessary for a complete understanding of Plato's metaphysics in general. This study points towards the questions that the second part of this examination must answer. (shrink)

Critical discussion of J.M.E. Moravcsik's paper on Plato's method of division.

Applying the analytical methods of modern logic to problems of interpretation in Plato, the author traces the development of Plato's analytic method from the crude form expressed in the Phaedo to the considerably more sophisticated and powerful techniques practiced in the later methodological dialogues.

There are many passages in Plato which look as if they alluded to well-worn practices, discussions, or lessons in the Academy. As is natural with allusions, they are often marked by a puzzling brevity or oddity of expression. One need not assume that they are always conscious allusions; for every writer has moments of obscurity which are due not so much to his conclusions as to his reaching them along lines that have long been familiar to Mm. To appreciate his (...) whole meaning the reader has then to infer as best he can the writer's train of thought. I wish to suggest that the language in which Dialectic is described in the later Dialogues presupposes a particular and probably familiar method of illustrating it. This was a geometrical illustration of the rules of Division by means of a divided line. By failing to notice it readers have not been led into any important misunderstanding of the Academy's rules. But I hope it will appear that the recognition of it makes Plato's manner of describing Division intelligible to an extent that is otherwise difficult. It is only a tentative suggestion, and would perhaps not have been worth making but for the possibility that some points of interest might at the same time emerge for those who were unconvinced by it. (shrink)