The purpose of this paper is to reassess some mathematical examples in Plato’s dialogues which at a first glance may appear to be nothing more than trivial puzzles. In order to provide the necessary background for this analysis, I shall begin by sketching a brief overview of Plato’s mathematical passages and discuss the criteria for aptly selecting them. Second, I shall explain what I mean by ‘mathematical examples,’ and reflect on their function in light of the discussion on παραδείγματα outlined (...) in the Sophist and the Statesman. Against this framework, I shall move to a close examination of specific examples drawn from the Theaetetus (154c–55d), the Republic (523c–24d), and the Phaedo (96d–97b, 100e–101d). By placing these examples in the broader context of pre-Euclidean mathematics, I shall show that their mathematical content is often less elementary than might appear at first sight. Moreover, by placing emphasis on the specific philosophical concerns that motivated their introduction, I shall argue that the examples are not merely nonsensical jokes. Even if their illustrative purpose is not always immediately clear, and even if they can sound playful and bizarre, they in fact fulfil an important function: by virtue of their power to generate wonder or confusion, they serve as exercises and act as a trigger with respect to the difficult philosophical issues they are intended to clarify. (shrink)

The present PhD dissertation aims to examine the relation between modality and change in Aristotle’s metaphysics. -/- On the one hand, Aristotle supports his modal realism (i.e., worldly objects have modal properties - potentialities and essences - that ground the ascriptions of possibility and necessity) by arguing that the rejection of modal realism makes change inexplicable, or, worse, banishes it from the realm of reality. On the other hand, the Stagirite analyses processes by means of modal notions (‘change is the (...) actuality of what is virtual insofar as it is virtual’). In other words: to grasp what change is, one has to resort to the modal idiom of potentialities, while the fact that there is change is indicative of the fact that nature is full of modal properties. -/- Aristotle’s modal and kinetic realism finds a negative in the figure of the Megaric Diodorus Kronus. The polemical situation of Greek philosophy has indeed the dialectical advantage of not opposing the Aristotelian position to a sui generis straw man. Both in its reduction of modal judgements to temporal quantifications and in its dissolution of the reality of the state-of-being-in-motion in favour of a cinematographic view of processes, the philosophical figure of reductionist antirealism embodied by Diodorus constitutes an alternative that takes the opposite view of Aristotle’s realism. -/- The present study is structured as a discussion between these two positions. In the face of Diodorus’ antirealist challenges, Aristotle articulates modal and kinetic considerations: the answers he gives to Diodorus’ puzzles thus provide valuable insight into his metaphysics. Moreover, the examination of Aristotle’s and Diodorus’ metaphysics, because of their insight and originality, will not fail to interest the philosopher concerned with the metaphysical foundations of modern physics, insofar as the entanglement between modalities and processes is nowadays at the core of mechanics (phase spaces, path integrals, etc.). (shrink)

One Stoic response to the skeptical indistinguishability argument is that it fails to account for expertise: the Stoics allow that while two similar objects create indistinguishable appearances in the amateur, this is not true of the expert, whose appearances succeed in discriminating the pair. This paper re-examines the motivations for this Stoic response, and argues that it reveals the Stoic claim that, in generating a kataleptic appearance, the perceiver’s mind is active, insofar as it applies concepts matching the perceptual stimulus. (...) I argue that this claim is reflected in the Stoic definition of the kataleptic appearance, and that it respects their more general account of mental representation. I further suggest that, in attributing some activity to the mind in creating each kataleptic appearance, and in claiming that the expert’s mind allows her to form more kataleptic appearances than the amateur, the Stoics draw inspiration from the wax tablet model in Plato’s Theaetetus (190e–196d), where Socrates distinguishes the wise from the ignorant on the basis of how well they match sensory input with its appropriate mental ‘seal’ (σφραγίς). (shrink)

With the use of a particular metaphor, which appears at the end of the Cratylus and is taken up with perfect symmetry at the beginning of the Theaetetus, Plato certainly wanted to indicate the succession of Cratylus–Theaetetus as an order for reading the two dialogues, which Trasillus faithfully reproduced in structuring the second tetralogy of Platonic dialogues. The claim of the theory of ideas, with which the Cratylus ends, must therefore be considered the background in which to place not only (...) the analysis of the name carried out in the Cratylus, but also the discussion and criticism of the epistemological theories examined and refuted in the Theaetetus. The transition from the discussion of the name to that of the logos is another important theoretical element that connects the two dialogues. Another one is the theory of knowledge, already precisely elaborated in the Cratylus, and taken up and deepened in the Theaetetus. Finally, the theme of false and error is a third theoretical element common to the two dialogues, which, starting from Euthydemus, finds its solution in the Sophist. (shrink)

Nāgārjuna, the famous founder of the Madhyamika School, proposed the positive catuṣkoṭi in his seminal work, Mūlamadhyamakakārikā: ‘All is real, or all is unreal, all is both real and unreal, all is neither unreal nor real; this is the graded teaching of the Buddha’. He also proposed the negative catuṣkoṭi: ‘“It is empty” is not to be said, nor “It is non-empty,” nor that it is both, nor that it is neither; [“empty”] is said only for the sake of instruction’ (...) and the no-thesis view: ‘No dharma whatsoever was ever taught by the Buddha to anyone’. In this essay, I adopt Gricean pragmatics to explain the positive and negative catuṣkoṭi and the no-thesis view proposed by Nāgārjuna in a way that does not violate classical logic. For Nāgārjuna, all statements are false as long as the hearer understands them within a reified conceptual scheme, according to which substance is a basic categorical concept; substances have svabhāva, and names and sentences have svabhāva. (shrink)

The digression of Plato’s Theaetetus (172c2–177c2) is as celebrated as it is controversial. A particularly knotty question has been what status we should ascribe to the ideal of philosophy it presents, an ideal centered on the conception that true virtue consists in assimilating oneself as much as possible to god. For the ideal may seem difficult to reconcile with a Socratic conception of philosophy, and several scholars have accordingly suggested that it should be read as ironic and directed only at (...) the dramatic character Theodorus. When interpreted with due attention to its dramatic context, however, the digression reveals that the ideal of godlikeness, while being directed at Theodorus, is essentially Socratic. The function of the passage is to introduce a contemplative aspect of the life of philosophy into the dialogue that contrasts radically with the political-practical orientation characteristic of Protagoras, an aspect Socrates is able to isolate as such precisely because he is conversing with the mathematician Theodorus. (shrink)

In Metaphysics Γ 4-6 Aristotle argues that Protagoras is committed not just to denying the PNC, but also to asserting its contrary. In this paper, I offer an analysis of this commitment. I try to show that Aristotle is working with a specific idea in mind: a Protagoreanism ontologically linked to the flux doctrine, as Plato suggested in Theaetetus 152-160.

We examine the discussion about the definition of knowledge as true judgment accompanied by logos in Theaetetus 201c-210c, in order to ascertain which of the recent alternative interpretations is more consistent with the text. To accomplish this, we intend to analyze the text and explore in detail the secondary literature about it.

Russell’s theory of memory as acquaintance with the past seems to square uneasily with his definition of acquaintance as the converse of the relation of presentation of an object to a subject. We show how the two views can be made to cohere under a suitable construal of ‘presentation’, which has the additional appeal of bringing Russell’s theory of memory closer to contemporary views on direct reference and object-dependent thinking than is usually acknowledged. The drawback is that memory as acquaintance (...) with the past falls short of fulfilling Russell’s requirement that knowledge by acquaintance be discriminating knowledge – a shortcoming shared by contemporary externalist accounts of knowledge from memory. (shrink)

The paper offers an interpretation of a disputed portion of Plato’s Theaetetus that is often called the Secret Doctrine. It is presented as a process ontology that takes two types of processes, swift and slow motions, as fundamental building blocks for ordinary material objects. Slow motions are powers which, when realized, generate swift motions, which, in turn, are subjectively bundled to compose sensible objects and perceivers. Although the reading of the Secret Doctrine offered here—a new version of the “Causal Theory (...) interpretation”—is not without problems, these problems are acknowledged in Plato’s text, confirming that this interpretation is correct. (shrink)

Plato articulates a deep perplexity about inquiry in ?Meno's Paradox??the claim that one can inquire neither into what one knows, nor into what one does not know. Although some commentators have wrestled with the paradox itself, many suppose that the paradox of inquiry is special to Plato, arising from peculiarities of the Socratic elenchus or of Platonic epistemology. But there is nothing peculiarly Platonic in this puzzle. For it arises, too, in classical Indian philosophical discussions, where it is formulated with (...) great clarity, and analysed in a way that casts it in a new light. We present three treatments of the puzzle in Indian philosophy, as a way of refining and sharpening our understanding of the paradox, before turning to the most radical of the Indian philosophers to tackle it. The Indian philosophers who are optimistic that the paradox can be resolved appeal to the existence of prior beliefs, and to the resources embedded in language to explain how we can investigate, and so move from ignorance to knowledge. Highlighting this structural feature of inquiry, however, allows the pessimist philosopher to demonstrate that the paradox stands. The incoherence of inquiry is rooted in the very idea of aiming our desires at the unknown. Asking questions and giving answers rests on referential intentions targeting objects in a region of epistemic darkness, and so our ?inquiry sceptic? also finds structurally similar forms of incoherence in the pragmatics of interrogative discourse. (shrink)

In this paper I discuss the dialogues between 'Protagoras', Theodorus and Socrates in "Theaetetus" 161-171 and emphasise the importance for this passage of a dilemma which refutation is shown to pose for relativism at 161e-162a. I argue that the two speeches delivered on Protagoras' behalf contain material that is deeply Socratic and suggest that this feature of the speeches should be interpreted as part of Plato's philosophical case against relativism, reflecting the relativist's own inability to defend his theory from attempts (...) to refute it. I then discuss Theodorus' role in the refutation of Protagoras and argue that his voice is needed to get relativism disproved in the self-refutation argument of 171a-c. I conclude with a brief discussion of the image of Protagoras at 171d. (shrink)

Any comprehensive interpretation of the "Theaetetus" has to provide answers to, among others, two very general questions concerning that dialogue: "What is Plato's relation to the problems faced in the "Theaetetus"?" and "What is the significance of the absence of the Forms from the discussion of the "Theaetetus", given their undoubted relevance to the topic of the dialogue, i.e. knowledge?" Predominantly, the answer given to the first question in the literature has been that the problems are those that Plato is (...) trying to tackle and the one to the second question, when it has been addressed at all, that the Forms are left out of the discussion because Plato no longer thought them relevant, either for having abandoned or seriously revised them, by the time of writing the "Theaetetus". In this study of the Wax Block and the Aviary models of judgment that occur in the second part of the "Theaetetus" as part of its discussion of the problem of false judgment, I argue that the problems faced there actually arise because of the neglect of Forms. The discussion of the second part is, I contend, carried out on a materialist ontology, an ontology assumed because it suits the definition of knowledge as true judgment which inaugurates that part of the dialogue, an ontology in no way subscribed to by Plato. The Wax Block is, I explain, a materialist model and fails in the case of judgments about numbers for treating them on a par with material subjects, ignoring their intelligible status. In particular, it fails to distinguish judging 5 and 7 to be 11 from judging 12 to be 11 because of its neglect of Forms; Plato would distinguish those judgments by distinguishing 5 and 7 from 12 with help from his part-whole analysis, to which the Forms are essential. (shrink)

This paper examines a passage in the Theaetetus where Plato distinguishes knowledge from true belief by appealing to the example of a jury hearing a case. While the jurors may have true belief, Socrates puts forward two reasons why they cannot achieve knowledge. The reasons for this nescience have typically been taken to be in tension with each other . This paper proposes a solution to the putative difficulty by arguing that what links the two cases of nescience is that (...) in neither case do the jurors act from an epistemic virtue and that doing so is a necessary condition of knowledge. Appreciating that it is a necessary condition of knowledge that it be the result of an epistemic agent's agency in a distinctive way provides a satisfying solution to the difficulty Burnyeat detected and also does justice to an otherwise neglected aspect of Plato's epistemology: his talk of cognitive capacities and virtues and his focus on what it is that is active and passive in epistemic processes. (shrink)

In this paper, I examine several key issues relating to the definition of knowledge as perception in the first part of Plato's Theaetetus. I begin by explaining the workings of the ‘secret doctrine’ of perception, which is introduced in order to support the idea that perception is incorrigible, and then turn to examine the two refutations of the definition of knowledge as perception which appear at the end of the first part of the Theaetetus. I shall present and explain distinct (...) lines of interpretation pertaining to these passages and explore the consequences they attempt to draw regarding Plato's views on the perceptual world, the nature of perception and how these bear on his conception of knowledge. (shrink)

In this second installment on the Theaetetus, I discuss Theaetetus' second and third definitions of knowledge, namely, ‘true judgment’ and then ‘true judgment with the addition of an account’. I offer a brief description of Socrates' intricate examination of these suggestions, concentrating especially on the discussion of false judgment and that of the so-called ‘Dream Theory’. I then proceed to map different lines of interpretation for these passages that have been offered by scholars writing in the last 40 years.

Two readings of the much-discussed περιτροπή argument of "Theaetetus" 170c-171c have dominated the literature. One I call "the relativity reading". On this reading, the argument fails by ignoratio elenchi because it "carelessly" omits "the qualifications 'true for so-and-so' which [Protagoras'] theory insists on" (Bostock 1988: 90). The other reading I call "the many-worlds interpretation". On this view, Plato's argument succeeds in showing that "Protagoras' position becomes utterly self-contradictory" because "he claims that everyone lives in his own relativistic world, yet at (...) the same time he is forced by that very claim to admit that no one does" (Burnyeat 1976b: 48). I discuss and criticise both readings, and present a third, according to which the point of the argument is, very roughly, that Protagoras is committed to equating truth and truth-for, and so, further, to their intersubstitutability. This further commitment proves fatal to his argument. (shrink)

The Stoic theory of knowledge was founded by Zeno on a perceptual and crudely materialistic base, but subsequently developed into an elaborate theory involving λεκτ which has proved difficult to reconstruct. The evolution of the school, influenced not only by internal differences but also by interaction with the Platonic Academy, certainly contributed to this development. Hence any adequate reconstruction of the Stoic theory of knowledge must take account of the differences among the positions of the different representatives of the school (...) with respect to the criticism put foward by the Academics. I propose here to clarify Zeno's position, showing how Arcesilaus' criticism helped to expose certain lacunae and thus to bring about changes in doctrine on the part both of Zeno himself and of his immediate successors. (shrink)

At Theaetetus 163d-164b Socrates objects to the thesis that knowledge is perception by pointing out that a man who has seen something can still remember it, and so has knowledge of it; but this is impossible, if knowledge is perception, since he is no longer perceiving it.To this Protagoras is made to reply with two sentences at 166b 1–4: .Cornford translates ‘ For instance, do you think you will find anyone to admit that one's present memory of a past impression (...) is an impression of the same character as one had during the original experience, which is now over? It is nothing of the sort’.Cornford understands this as the suggestion that the memory and the original perception are of different things: ‘ All that the objection in fact established was that “ perception” must be stretched to include awareness of memory images’. So too Lee: ‘Protagoras’ “way out”… appears to be to say that what we now know is not properly X but rather our memory trace of X - some present πά θ ο ς quite distinct from X and very different from that ’. McDowel. (shrink)

On the face of it, Plato's treatment of aisthesis is decidedly ambiguous. Sometimes he treats aisthesis as a faculty which, though distinct from all rational capacities, is nonetheless capable of forming judgments such as ‘This stick is bent’ or ‘The same thing is hard and soft’. In the Theaetetus, however, he appears to separate aisthesis from judgment, isolating the former from all prepositional, identificatory and recognitional capacities. The dilemma is easily expressed: Is perception a judgmental or cognitive capacity, or is (...) it a non-judgmental, non-cognitive capacity? If the former, how does perception differ from belief? If the latter, is perception a faculty of the rational or irrational soul? Not surprisingly, the topic has received much scrutiny over the years. And equally unsurprisingly, the debate has turned as much on what it means for a capacity to be judgmental, cognitive, non-judgmental or non-cognitive, as on whether Plato says that it is of either kind. (shrink)

In this paper I explore a famous part of Plato’s Theaetetus where Socrates develops various models of the mind (picturing it first as a wax tablet and then as an aviary full of specimen birds). These are to solve some puzzles about how it is possible to make a mistake. On my interpretation, defended here, the discussion of mistakes is no digression, but is part of the refutation of Theaetetus’s thesis that knowledge is “true doxa”. It reveals that false doxa (...) is possible only if there is a certain stock of abstract knowledge, conceptual knowledge, that is not awareness of the particular individual that is being described. The individual must be identified under some description, or seen as something of a certain kind. Error can only occur if the description applied misdescribes the situation, but then if it is to be applied falsely it must first have been known from somewhere else. So knowledge cannot be reduced to the application of descriptions to particulars, but is to be found in the prior possession of abstract descriptions that can be deployed in identifying particular individuals on the ground. (shrink)

Scholars who have taken interest in Theaetetus' educational theme argue that Plato contrasts an inferior, even dangerous, sophistic education to a superior, philosophical, Socratic education. I explore the contrasting exhortations, methods, ideals and epistemological foundations of Socratic and Protagorean education and suggest that Socrates' treatment of Protagoras as educator is far less dismissive than others claim. Indeed, Plato, in Theaetetus, offers a qualified defence of both Socrates and Protagoras. Socrates and Protagoras each dwell in the middle ground between the extremes (...) presented in the dialogue's digression, which contrasts the life of the philosopher and the life of the courtroom orator. Both Socrates and Protagoras demonstrate a serious engagement with both politics and philosophy. Theodorus presents an educational option in which theory is divorced from politics while an ignoble sophistic education is presented as political but divorced from theory. Protagorean education, in Theaetetus, emerges as superior to a base sophistic education, though it remains inferior to Socratic education. (shrink)

The standard interpretation of "Theaetetus" 152-160 has Plato attribute to Protagoras a relativistic theory of truth and existence. It is argued here that in fact the individuals of Protagorean worlds are inter-Personal. (thus the Protagorean theory has public objects, but private truth). Also, a new interpretation is offered of Plato's use of heraclitean flux to model relativism. The philosophical and semantic consequences of the interpretation are explored.

The Cratylus begins with a paradox; it ends with a paradox; and it has a paradox in between. But this disturbing characteristic of the dialogue has been overshadowed, not to say ignored, in the literature. For commentators have seen it as their task to discover exactly what theory of language Plato himself, despite his declared perplexity, intends to adopt as he rejects the alternatives of Hermogenes and Cratylus. A common view, then, has been to suppose that the πορίαι of the (...) dialogue are mere camouflage for the hidden dogma, whatever that may be. A favoured candidate, of course, has been the theory of transcendent forms, in some preliminary version. As a consequence, the dialogue has often been seen as a precursor to the great metaphysical works of Plato's middle period such as the Phaedo or the Republic. Not so, I shall argue. My case is that this dialogue centres upon a series of paradoxes which are both powerful and unsettling. Their final effect is to attack the theory of forms, not to defend it. They are, I suggest, genuine proposals of philosophical difficulty, rather than mere artifice to disguise an idealist truth. As such, they belong, and may clearly be seen to belong, with works of the critical period which subject the theory of forms to scrutiny. Thus the πορίαι of the Cratylus have their counterparts in the Parmenides, the Theaetetus and the Sophist. I propose, then, that the dialogue was written during the late, critical period of Plato's philosophical activity. (shrink)

Several contemporary virtue scholars trace the origin of the concept of intellectual virtues back to Aristotle. In contrast, my aim in this paper is to highlight the strong indications showing that Plato had already conceived of and had begun developing the concept of intellectual virtues in his discussion of the ideal city-state in the Republic. I argue that the Platonic conception of rational desires satisfies the motivational component of intellectual virtues while his dialectical method satisfies the success component. In addition, (...) I show that Plato considers episteme as the primary intellectual virtue. Episteme, which is quite similar to Pritchard’s The nature and value of knowledge: three investigations, Oxford University Press, Oxford, 2010) conception of understanding, is a cognitive achievement that cannot be attained by luck or testimony. The realization that Plato was the first to conceive of and develop the concept of intellectual excellences is not merely of historic significance. I illustrate, through the example of Zagzebski’s virtue theory, how the Platonic conception of intellectual virtues could prove promising in contemporary debates on virtue epistemology theories. (shrink)

The account of knowledge in Plato’s Theaetetus, as true belief meta logou, seems to lead to a regress, which may be avoided by defining one kind of knowledge as true belief that rests on a different kind of knowledge. I explore a specific version of this move: to define knowledge as true belief that results from a successful and proper exercise of a rational capacity (a dunamis meta logou).

One of Plato’s central tenets is that we can know forms. In Parmenides 133b4–134b5, Plato presents an argument whose sceptical conclusion is that we can’t know forms. Although he indicates that the argument doesn’t succeed, he also says it’s difficult to explain how it fails. Commentators have suggested a variety of flaws. I argue that the argument can be defended against some, though not all, of the alleged flaws. But I also argue that Plato hints at a crucial distinction that (...) hasn’t been brought to bear in this context, and that indeed he is sometimes thought not to draw: that between the content and object of knowledge. Once we are clear about this distinction, we can see that the sceptical argument doesn’t imply that we can’t know forms. (shrink)

The version of the paradox of false judgement examined at Tht. 188c10–189b9 relies on the assumption that to judge falsehoods is to judge the things which are not. The presentation of the argument displays several syntactic ambiguities: at several points it allows the reader to adopt different syntactic connections between the components of sentences. For instance, when Socrates says that in a false judgement the cognizer is “he who judges the things which are not about anything whatsoever” (188d3–4), how should (...) the clause “about anything whatsoever” be construed? In common with “he who judges” and “the things which are not” (in which case the cognizer would be “he who judges about anything whatsoever the things which are not about it”), or exclusively with “he who judges” (in which case the cognizer would be “he who judges about anything whatsoever the things which are not”)? The most plausible answer is that both construals are envisaged. Accordingly, the argument has two branches corresponding to these two alternative construals. In particular, it attempts to show that in both cases the cognizer will address what does not exist – an impossibility. The idea that a false judgement is concerned with what is not about its reference has a clear echo in the Sophist. The way in which the problem is handled in the Theaetetus provides a hint that can help to find a solution for the hotly debated issue of the interpretation of the Sophist’s account of false statement. (shrink)

Two readings of the much-discussed περιτροπή argument of "Theaetetus" 170c-171c have dominated the literature. One I call "the relativity reading". On this reading, the argument fails by ignoratio elenchi because it "carelessly" omits "the qualifications 'true for so-and-so' which [Protagoras'] theory insists on" (Bostock 1988: 90). The other reading I call "the many-worlds interpretation". On this view, Plato's argument succeeds in showing that "Protagoras' position becomes utterly self-contradictory" because "he claims that everyone lives in his own relativistic world, yet at (...) the same time he is forced by that very claim to admit that no one does" (Burnyeat 1976b: 48). I discuss and criticise both readings, and present a third, according to which the point of the argument is, very roughly, that Protagoras is committed to equating truth and truth-for, and so, further, to their intersubstitutability. This further commitment proves fatal to his argument. (shrink)

Protagoras believes that all beliefs are true. Since Protagoras' belief that all beliefs are true is itself a belief, it follows from Protagoras' belief that all beliefs are true that Protagoras' belief is true. But what about the belief that Protagoras' belief is false? Doesn't it follow, by parallel reasoning and not at all trivially, that if all beliefs are true and there is a belief that Protagoras' belief is false, then Protagoras' belief is false?

This article aims at reconstructing the logic and assessing the force of Socrates' argument against Protagoras' 'Measure Doctrine' at Theaetetus 171a–c. I examine and criticise some influential interpretations of the passage, according to which, e.g., Socrates is guilty of ignoratio elenchi by dropping the essential Protagorean qualifiers or successfully proves that md is self-refuting provided the missing qualifiers are restored by the attentive reader. Having clarified the meaning of MD, I analyse in detail the broader section 170a–171d and argue, against (...) an extensive scholarly consensus, that it contains two slightly different formulations of the same argument, and not two distinct arguments, that Socrates does not highlight his own strategy at 171a–c as especially clever, and that his argument successfully shows that md turns out to be untenable for Protagoras himself when submitted to scrutiny in dialectical contexts, without aiming at proving its absolute falsehood. Finally, I clarify the philosophical import of the final image of Protagoras' momentary return from the underworld. (shrink)

En este trabajo intento mostrar que la función de la doctrina heraclítea en el Teeteto es argumentar a favor de la equivalencia entre la tesis de Protágoras y la definición de Teeteto “la percepción es conocimiento”, y que de esta manera la doctrina apoya la relatividad del conocimiento. Esta lectura va en contra de quienes sostienen que Platón introduce la doctrina porque la cree correcta acerca de lo sensible, y va un paso más allá de la interpretación que afirma que (...) Platón introduce la doctrina como una tesis ontológica para apoyar la tesis de Protágoras. (shrink)

This paper considers the use that Plato makes of the Principle of Non-Contradiction in his engagements with eristic refutations. By examining Plato’s use of the principle in his most detailed engagements with eristic—in the Sophist, the discussion of “agonistic” argumentation in the Theaetetus, and especially the Euthydemus—I aim to show that the pressure exerted on Plato by eristic refutations played a crucial role in his development of the PNC, and that the principle provided him with a much more sophisticated means (...) of demarcating philosophical argumentation from eristic than he is generally thought to have. In particular, I argue that Plato’s qualified formulation of the PNC restricts the class of genuine contradictions in such a way that reveals the contradictions that eristics produce through their refutations to be merely apparent and that Plato consistently appeals to his qualified conception of genuine contradiction in his encounters with eristics in order to demonstrate that their refutations are merely apparent. The paper concludes by suggesting that the conception of genuine contradiction afforded by the PNC did not just provide Plato with a way of demarcating genuine from eristic refutations, but also with an answer to substantive philosophical challenges that eristics raised through their refutations. (shrink)

Theaetetus, asked what knowledge is, replies that geometry and the other mathematical disciplines are knowledge, and so are crafts like cobbling. Socrates points out that it does not help him to be told how many kinds of knowledge there are when his problem is to know what knowledge itself is, what it means to call geometry or a craft knowledge in the first place—he insists on the generality of his question in the way he often does when his interlocutor, asked (...) for a definition, cites instead cases of the concept to be defined. (shrink)

Section 1 contrasts the approaches to Plato of F.M.Cornford and Gilbert Ryle, two of the early twentieth century’s leading Plato interpreters. Then I trace and evaluate attempts to discern in Plato’s Theaetetus a recognition of the role of the proposition. Section 2 focuses on the hunting of the proposition in Socrates’ Dream in the Theaetetus. Ryle, inspired by Logical Atomism, argued that Plato there anticipated an insight about the difference between names and propositions that Russell credited to Wittgenstein. I rehearse (...) difficulties for understanding the logos of the Dream as a proposition, preferring a reading of logos there as something like definition: a reading Wittgenstein also adumbrated. Section 3 examines attempts by writers such as Burnyeat and Kahn to find Plato allocating a starring role to the proposition in the argument at Theaetetus 185–6: perception, since it cannot grasp being, cannot grasp truth and hence cannot be knowledge. On their reading a grasp of being is understood as a grasp of something propositional. Problems for the propositional reading include Socrates’ talk of grasping ‘the truth of something’ (alētheia tinos), and the way the dialogue develops after 186. (shrink)

This paper argues for a possible-worlds interpretation of the arguments marshalled by Socrates against Protagoras in Plato’s Theaetetus. Specifically, it reads Protagoras’ position as implying a limited form of modal realism, and evaluates both the self-refutation sequence at 170a–71d and the Future Argument at 177c–9c on the basis of this reading. It emerges that Socrates’ project is only partly successful: while the three main arguments of the self-refutation sequence force Protagoras into ever more awkward and metaphysically top-heavy positions, and the (...) Future Argument is psychologically compelling, these arguments do not force a collapse of the relativist position. Protagoras can still defend himself, though the cost is high. (shrink)

Stanford Encyclopedia of Philosophy article.