Plato: Hypothesis

This paper re-constructs Plato's ‘philosophy of geometry’ by arguing that he uses a geometrical method of hypothesis in his account of the cosmos’ generation in the Timaeus. Commentators on Plato's philosophy of mathematics often start from Aristotle's report in the Metaphysics that Plato admitted the existence of mathematical objects in-between ( metaxu) Forms and sensible particulars ( Meta. 1.6, 987b14–18). I argue, however, that Plato's interest in mathematics was centred on its methodological usefulness for philosophical inquiry, rather than on questions (...) of mathematical ontology. My key passage of interest is Timaeus’ account of the generation of the primary bodies in the cosmos, i.e. fire, air, water and earth ( Tim. 48b–c, 53b–56c). Timaeus explains the primary bodies’ origin by hypothesising two right-angled triangles as their starting-point ( arkhê) and describing their individual geometrical constitution. This hypothetical operation recalls the hypothetical method which Socrates introduces in the Meno (86e–87b), as well as the use of hypotheses by mathematicians which is described in the Republic (510b–c). Throughout the passage, Timaeus is focussed on explicating the bodies in terms of their formal structure, without however considering the ontological status of the triangles in relation to the physical world. (shrink)

The Parmenides has been unduly overlooked in discussions of hypothesis in Plato. It contains a unique method for testing first principles, a method I call ‘exploring both sides’. The dialogue recommends exploring the consequences of both a hypothesis and its contradictory and thematizes this structure throughout. I challenge the view of Plato’s so-called ‘method of hypothesis’ as an isolated stage in Plato’s development; instead, the evidence of the Parmenides suggests a family of distinct hypothetical methods, each with its own peculiar (...) aim. Exploring both sides is unique both in its structure and in its aim of testing candidate principles. (shrink)

Through detailed analysis of Plato’s Meno, I identify and set general argumentative rules (useful both to scientists and philosophers) concerning how to use definitions. I show how the character Socrates establishes strong requirements for knowledge in general, i.e., that the knowledge of the definition of a thing must be prior to the knowledge of properties or instances of that thing. Socrate’s requirements and the way he characterizes a definition (as coextensive to the definiendum, not circular, true and explanatorily relevant) lead (...) Meno to aporia and to enunciate the famous Meno’s Paradox concerning the impossibility of inquiry for knowledge. That only occurs because Meno is unable to identify Socrate’s dialectical move: strong requirements for knowing a definition, the priority of the knowledge of the definition and the taking of all knowledge to be like the knowledge by acquaintance. After the paradox, Socrate’s proceeds the discussion using hypotheses to map the truth conditions of some theses Meno is inquiring about. I explain what are Meno’s paradox, the socratic definition and the Method of Hypotheses, in a way só as to find in this classical text in the history of philosophy general principles of argumentation that are still usefull today. (shrink)

At a crucial juncture in Plato’s Sophist, when the interlocutors have reached their deepest confusion about being and not-being, the Eleatic Visitor proclaims that there is yet hope. Insofar as they clarify one, he maintains, they will equally clarify the other. But what justifies the Visitor’s seemingly oracular prediction? A new interpretation explains how the Visitor’s hope is in fact warranted by the peculiar aporia they find themselves in. The passage describes a broader pattern of ‘exploring both sides’ that lends (...) insight into Plato’s aporetic method. (shrink)

Η παρούσα διατριβή πραγματεύεται τη σχέση που συνδέει την μυθική σύνθεση και την διαλεκτική μέθοδο στο πλατωνικό έργο. Οι περισσότεροι μελετητές, βασιζόμενοι στις ποιητικές κριτικές του Πλάτωνος στην Πολιτεία, υποστηρίζουν ότι ο φιλόσοφος εξορίζει την ποίηση και την τέχνη εν γένει, από την ιδανική πολιτεία του, και, κατά συνέπεια, δεν θα έπρεπε ο ίδιος να συνθέτει και να χρησιμοποιεί μύθους. Ενάντια σε αυτή τη θεώρηση, επιχειρώ να δείξω, αφενός, ότι ο Πλάτων διακρίνει δύο είδη ποιήσεως· το ένα το υιοθετεί, το (...) άλλο το εξορίζει. Στην πρώτη περίπτωση, η ποίηση είναι ωφέλιμη, διότι καθιστά αρμονικές και ενάρετες τις ψυχές των πολιτών, τρέφοντας στον κατάλληλο βαθμό το ενδιάμεσο ψυχικό τμήμα, δηλαδή το θυμοειδές, και συναρμόζοντας το με το ανώτερο, ήτοι το λογιστικό. Στη δεύτερη, είναι επιβλαβής, επειδή ενσπείρει σε αυτές τη δυσαρμονία και τη διαφθορά, ενδυναμώνοντας υπερβολικά την υποδεέστερη ψυχική δύναμη, που είναι το επιθυμητικό. Βάσει της ανωτέρω διάκρισης, υποστηρίζω ότι τα πλατωνικά μυθολογήματα συνιστούν πρότυπα της απλής και ωφέλιμης μυθολογίας και ότι η χρήση τους αποσκοπεί στην εγχάραξη της αρετής στις ψυχές των αναγνωστών/ακροατών τους. Εισηγούμαι, επιπλέον, ότι ο μύθος, ως πλατωνική σύνθεση, εμφανίζεται μετά την εισαγωγή της θεωρίας της ανάμνησης και της υποθετικής μεθόδου στον Μένωνα, γεγονός που καταδεικνύει ότι η λειτουργία του πλατωνικού μύθου είναι, θεμελιωδώς, συνυφασμένη με την πλατωνική μέθοδο. (shrink)

Plato’s Parmenides and Lysis have a surprising amount in common from a methodological standpoint. Both systematically employ a method that I call ‘exploring both sides’, a philosophical method for encouraging further inquiry and comprehensively understanding the truth. Both have also been held in suspicion by interpreters for containing what looks uncomfortably similar to sophistic methodology. I argue that the methodological connections across these and other dialogues relieve those suspicions and push back against a standard developmentalist story about Plato’s method. This (...) allows for a better understanding of why exploring both sides is explicitly recommended in the Parmenides and its role within Plato’s broader methodological repertoire. (shrink)

This volume, a lightly-edited version of Professor Samuel Scolnicov’s 1974 Ph.D. thesis, is a fitting tribute to his impressive career. It will perhaps be most useful for those interested in better understanding Scolnicov’s work and his views on Plato as a whole, not least for the comprehensive list of his publications that requires a full twelve pages of print. Scholars with an interest in Plato’s method of hypothesis will also find some useful remarks on key passages in the Meno, Phaedo, (...) and Republic as well as on Greek mathematical analysis.Illuminating other aspects of Scolnicov’s work is clearly part of the intention behind enabling broader access to this study. As Harold Tarrant notes in his introduction... (shrink)

The aim of this paper is two-fold: firstly, to argue for the claim that the two problems of geometry presented in the Meno seems to be connected to each other, and secondly, to offer, in connection with the first claim, a conjecture concerning the nature of the second problem of geometry brought up in the dialogue at 86e. This paper offers, in particular, a historical reconstruction of how we should understand this problem of construction in geometry.

Journal Name: Apeiron Issue: Ahead of print.

I argue that recollection, in Plato's Meno , should not be taken as a method, and, if it is taken as a myth, it should not be taken as a mere myth. Neither should it be taken as a truth, a priori or metaphorical. In contrast to such views, I argue that recollection ought to be taken as an hypothesis for learning. Thus, the only methods demonstrated in the Meno are the elenchus and the hypothetical, or mathematical, method. What Plato's (...) Meno demonstrates, then, is that we cannot be philosophers if we fail to make use of the mathematician's hypothetical method. (shrink)

This essay discusses Socrates' use of hypothetical choices as an early version of what was to become in the twentieth century the discipline of decision theory as expressed by one of its prominent proponents, F. P. Ramsey. Socrates' use of hypothetical choices and thought experiments in the dialogues is a way of reassuring himself of an interlocutor's philosophical potential. For example, to assess just how far Alcibiades is willing to go to attain his goal of being a great Athenian leader, (...) we employ Ramsey's concept of Mathematical Expectation. Mathematical Expectation operates on the assumption that it is not enough to measure probability; we must also measure our belief to apportion our belief to the probability. In other words, it illustrates how strongly or to what degree a person holds a particular belief. If a person's belief in X lacks enough doubts to cancel the belief out, the probability of his acting on this belief is higher than if his belief in X was plagued by a greater number of doubts. (shrink)

The review argues that Plato makes a valid distinction between inferior hypothetical and superior unhypothetical methods. Given the distinction, the book confuses the hypothetical for unhypothetical dialectic.

This paper aims to achieve a better understanding of what Socrates means by "συμφωνε[unrepresentable symbol]ν" in the sections of the "Phaedo" in which he uses the word, and how its use contributes both to the articulation of the hypothetical method and the proof of the soul's immortality. Section I sets out the well-known problems for the most obvious readings of the relation, while Sections II and III argue against two remedies for these problems, the first an interpretation of what the (...) συμφωνε[unrepresentable symbol]ν relation consists in, the second an interpretation of what sorts of thing the relation is meant to relate. My positive account in Section IV argues that we should take the musical connotations of the term seriously, and that Plato was thinking of a robust analogy between the way pitches form unities when related by certain intervals, and the way theoretical claims form unities when related by explanatory co-dependence. Section V surveys the work of IV from the point of view of the initial difficulties and suggests further consequences for the hypothetical method, including the logical relation between the συμφωνν[unrepresentable symbol]ν and διαφωνε[unrepresentable symbol]ν relations, and the need for care in ordering the results of a hypothesis. (shrink)

This paper aims to achieve a better understanding of what Socrates means by "συμφωνε[unrepresentable symbol]ν" in the sections of the "Phaedo" in which he uses the word, and how its use contributes both to the articulation of the hypothetical method and the proof of the soul's immortality. Section I sets out the well-known problems for the most obvious readings of the relation, while Sections II and III argue against two remedies for these problems, the first an interpretation of what the (...) συμφωνε[unrepresentable symbol]ν relation consists in, the second an interpretation of what sorts of thing the relation is meant to relate. My positive account in Section IV argues that we should take the musical connotations of the term seriously, and that Plato was thinking of a robust analogy between the way pitches form unities when related by certain intervals, and the way theoretical claims form unities when related by explanatory co-dependence. Section V surveys the work of IV from the point of view of the initial difficulties and suggests further consequences for the hypothetical method, including the logical relation between the συμφωνν[unrepresentable symbol]ν and διαφωνε[unrepresentable symbol]ν relations, and the need for care in ordering the results of a hypothesis. (shrink)

Socrates’ autobiography in Phaedo signifies an attempt to incorporate earlier philosophical thinking in a progressive evolution culminating in the Platonic theory of Forms. In the “second sailing”, the “hypothesis of Forms” is not a hypothetical assumption, an arbitrary claim or conjecture, but something to be “sup-posed” prior to any further knowledge or statement. The careful reading and reconstruction of the famous simile of the “sun in eclipse” leads to crucial consequences concerning the attempt to “take refuge in the logoi”. The (...) Forms “sup-posed” in the logoi do not indicate a new “transcendent” object, but aim at the same target as that of the senses: at the truth of beings of our world. The “second sailing” follows a different route, but has the same direction as the “first sailing” of the physiologoi. (shrink)

In Socrates' account of his earlier investigations into the nature of causation in the "Phaedo", he describes a method that uses hypotheses. He posited as true those propositions that appeared to harmonize ("sumphonein") with his hypothesis and as false those propositions that failed to harmonize with his hypothesis. Earlier commentators on this passage have maintained that it is impossible to give a univocal reading of the occurrences of "sumphonein"' such that the method that Socrates describes is at all reasonable. It (...) is argued in this paper that such a reading is possible. (shrink)

In Socrates' account of his earlier investigations into the nature of causation in the "Phaedo", he describes a method that uses hypotheses. He posited as true those propositions that appeared to harmonize ("sumphonein") with his hypothesis and as false those propositions that failed to harmonize with his hypothesis. Earlier commentators on this passage have maintained that it is impossible to give a univocal reading of the occurrences of "sumphonein"' such that the method that Socrates describes is at all reasonable. It (...) is argued in this paper that such a reading is possible. (shrink)

There is growing recognition in Phaedo scholarship of a parallel between the deuteros plous passage and the introduction to Simmias' speech: both speak of attempting to discover or to learn the truth about things, and then, if that proves impossible, to resort to divine or human logoi, the former being the "safer" of the two. It is contended that that model governs Socrates reply to Cebes: he first tried to discover the truth about causes by himself; then he tried to (...) learn it from Anaxagoras; and then, having failed in both endeavors, he resorted to logoi, both "divine" in the hypothesis of the forms and "human" in the hypothesis of intermediates, the former being the "safest" recourse. Finally, a defense is provided for the thesis that in calling the deuteros plous "deuteros," Socrates is being ironical. (shrink)

This paper examines socrates' method for determining whether virtue is taught, And discusses some of the opposing interpretations that have been offered (e.G., By robinson and hackforth). Some major conclusions are: that hypotheses that have been deduced from other hypotheses can still be called hypotheses; that it is false that there can be only one hypothesis per argument; and that the several hypotheses in a given argument need not all be hypothesized with the same degree of confidence.

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.

A distressing number of philosophers and classicists think that the deuteros plous or “second best” mentioned at Phaedo 99c9-dl is the hypothetical method. Many of them will even tell you that Plato says the hypothetical method is the deuteros plous, and that they are not merely interpreting his meaning. They usually back off, however, when challenged on this point, for there jus isn’t any such statement by Plato. Nor, I think, does Plato give us any justification at all for taking (...) the deuteros plous as the hypothetical method. I will argue in this paper that he is referring rather to the explanation of things in terms of their formal causes, and that this sort of explanation is “second best” when compared to a teleological explanation in terms of final causes. The hypothetical method of the dialectician is simply the logical device or apparatus by means of which the theory of ideas and the attendant notion of formal causation are introduced into the discussion; it is not a “second best” method and is not inferior to anything else. (shrink)