In Plato’s Statesman, the Eleatic Stranger leads Socrates the Younger and their audience through an analysis of the statesman in the service of the interlocutors’ becoming “more capable in dialectic regarding all things”. In this way, the dialectical exercise in the text is both intrinsically and instrumentally valuable, as it yields a philosophically rigorous account of statesmanship and exhibits a method of dialectical inquiry. After the series of bifurcatory divisions in the Sophist and early Statesman, the Stranger changes to a (...) non-bifurcatory method of dividing to account for the statesman, but does not explain the reason for this change. I argue that the change is prepared by the elements discussed in the digression from 277a2 to 287b2. Here the Stranger makes use of four concepts that are crucial for understanding this change: the notion of paradigm, the paradigms of care and the weaver, and the notion of due measure. I claim that the notion of paradigm clarifies the nature of dialectical inquiry, care and weaving act as paradigms appropriate to dialectical practice, and an account of due measure offers insight into the constitutive ratios that govern the structuring of kinds pursued through dialectical inquiry. I suggest that the non-bifurcatory method is intended to articulate knowledge in the strictest sense, or knowledge of the forms, presenting a method of inquiry into being and its structure that will foster the turning of the soul from things to forms that Socrates describes in the Republic. (shrink)

At Sophist 253d-e the Eleatic Visitor offers a notoriously obscure description of the fields of one-and-many that the dialectician “adequately discerns.” Against the readings of Stenzel, Cornford, Sayre, and Gomez-Lobo, I propose an interpretation of that passage that takes into account the trilogy of Theaetetus-Sophist-Statesman as its context. The key steps are to respond to the irony of Socrates’ refutations at the end of the Theaetetus by reinterpreting the last two senses of logos as directed to forms and to recognize (...) their correlation with the two different modes of diairesis practiced by the Eleatic Visitor. These steps position us to recognize in the Visitor’s remarks at Sophist 253d-e a schematic description of the two kinds of eidetic field that the two modes of diairesis trace. (shrink)

This paper argues that the hypothesis proposed in the Meno is the proposition ‘virtue is good’ alone, and that its epistemic nature is essentially insecure. It has been an object of huge scholarly debate which other hypothesis Socrates posited with regard to the relationship between virtue and knowledge. This debate is, however, misleading in the sense of making us believe that the hypothesis that virtue is good is regarded as a truism in the light of the process of positing a (...) higher hypothesis described in the Phaedo and the Republic. I argue that the hypothesis in question is presented as a result of the earlier discussion of Meno's third definition of virtue, which implies the consequence that morally correct actions are beneficial whether or not accompanied by conventional goods such as wealth and honour. The underlying role of presenting it as a hypothesis is therefore to postpone demonstrating the truth of a controversial thesis which needs a substantial justification. In conclusion, I s... (shrink)

I argue that, in the Prior Analytics, higher and above the well-known ‘reduction through impossibility’ of figures, Aristotle is resorting to a general procedure of demonstrating through impossibility in various contexts. This is shown from the analysis of the role of adunaton in conversions of premises and other demonstrations where modal or truth-value consistency is indirectly shown to be valid through impossibility. Following the meaning of impossible as ‘non-existent’, the system is also completed by rejecting any invalid combinations of terms (...) in deductions or conversions. The notion of impossibility reaches the core of Aristotle's system in the Prior Analytics. On the one hand, the use of adunaton shows that he is following one of the two requisites for demonstrative science formulated in the Posterior Analytics, i.e. to demonstrate that it is impossible for things to be otherwise than stated. On the other hand, that demonstrations through impossibility are rooted in the notion of contradiction supp.. (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 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)

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.

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)

Dramatic changes or revolutions in a field of science are often made by outsiders or 'trespassers,' who are not limited by the established, 'expert' approaches. Each essay in this diverse collection shows the fruits of intellectual trespassing and poaching among fields such as economics, Kantian ethics, Platonic philosophy, category theory, double-entry accounting, arbitrage, algebraic logic, series-parallel duality, and financial arithmetic.

Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...) along with a new concept to abstractly model the functions of a brain. (shrink)

The argument in Plato's Philebus presents three successive formulations of the hedonist principle. Commentators often take Socrates' argument in the dialogue to be dealing solely with the third formulation, which states that pleasure, rather than intelligence, is closer in nature to the good. I argue that, nonetheless, in the dialogue Socrates remained concerned to provide a direct refutation of the first formulation, that is, of the straightforward claim that pleasure is the good for all living beings. ;Chapter One ascribes to (...) the Philebus a conception of intrinsic good, which is then shown to underlie the dialogue's notion of true pleasures. Chapter Two examines in detail the problem of the "one and many" concerning pleasure, and argues that this is the problem of forms in relation to other forms, rather than that of forms in relation to particulars. This interpretation is the one that is consistent both with Protarchus' understanding of hedonism in the dialogue, and with the dialogue's methodological passages, i.e., the passages on the "god-given method" and on the four ontological kinds. In Chapter Three, it is shown how division into forms is required by Socrates' conception of the nature of pleasure. Some of the forms of pleasure are ways in which falsity is admitted into the nature of pleasure. Three accounts of false anticipatory pleasures---those of Kenny and Gosling, Mooradian, and Penner---are examined in some detail. (shrink)

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.