The focus on this contribution is on the ‘late-learners’ digression. In Sph. 251a8-c6, the Eleatic Stranger briefly discusses the view of some ‘young and old late-learners’ who hold that, from a logico-metaphysical point of view, unlike ‘a man is a man’ or ‘a good is good’, the statement ‘a man is good’ is neither a well-formed nor a grammatical sentence. Usually, modern commentators devote little energy to interpreting this passage since they are content to note that it suffices to discriminate (...) identity and predication to avoid the sophism. The aim of this paper is to show that the position of the ‘late-learners’ is in fact more subtle than it seems, since it is widely open to many readings, and that the chosen reading of the digression has a direct impact on the general interpretation of the rest of the dialogue (communication of kinds, semantic distinction between names and verbs, etc.). To this end, the view of the ‘late-learners’ will be compared with a similar position discussed in a quite different philosophical ecosystem: the White-Horse Paradox forged by Gōngsūn Lóng, a dialectician of the ‘School of Names’. This paradox states that the sentence ‘a white horse is not a horse’ is true. Many readings of the White-Horse Paradox have been offered: some of these readings are the same as those suggested for the ‘late-learners’ view, but others are absent from the scholarly literature, although they provide interesting insights into the interpretation of Sph. 251a8-c6. (shrink)

(1) An introduction to the principles of conceptual modelling, combinatorial heuristics and epistemological history; (2) the examination of a number of perennial epistemological-methodological schemata: conceptual spaces and blending theory; ars inveniendi and ars demonstrandi; the two modes of analysis and synthesis and their relationship to ars inveniendi; taxonomies and typologies as two fundamental epistemic structures; extended cognition, cognitio symbolica and model-based reasoning; (3) Plato’s notions of conceptual spaces, conceptual blending and hypothetical-analogical models (paradeigmata); (4) Ramon Llull’s concept analysis and combinatoric (...) spaces; (5) Gottfried Leibniz’s development of compositional analysis and synthesis as a general modelling method and a paradigm for ars inveniendi; (6) Fritz Zwicky’s revival of the morphological method of analysis and construction, and its subsequent computerised applications. (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.

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)

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.

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)

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)

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.

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)

Here I interpret a central passage in Plato's Sophist by focusing on understudied elements that provide insight into the fit of the dialogue's parts and the Sophist-Statesman diptych as a whole. I argue that the Eleatic Stranger's account of what the dialectician "adequately views" at Sophist 253d1-e3 involves both division and the communion of ontological kinds, not just one or the other as has been typically argued. I also consider other key passages and the turn throughout the dialogue from imagistic (...) opining toward noetic understanding. (shrink)

Há muita discussão sobre como interpretar o papel do argumento ‘Saber ou não Saber’ em Teeteto 188a-c. Alguns intérpretes supõem que esse papel é dialético e Platão não está comprometido com sua verdade. Outros pensam que o argumento revela a confusão de Platão sobre o tema da opinião falsa à época do Teeteto. Em minha análise, há uma terceira via que faz mais justiça ao que Platão está desenvolvendo em 188a-c. Penso que em 188a-c temos uma versão do princípio platônico (...) da infalibilidade. (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)

The strange and challenging stretch of dialectic with which Plato’s Sophist begins and ends has confused and frustrated readers for generations, and despite receiving a fair amount of attention, there is no consensus regarding even basic issues concerning this method. Here I offer a new account of bifurcatory division as neither joke nor naïve method, but instead a valuable, propaedeutic method that Plato offers to us readers as a means of embarking upon the kind of mental gymnastics that will stretch (...) us properly in preparation for further, more challenging dialectical work. Considering several interpretive issues, I argue that bifurcatory division is a process of collective inquiry into the common through which an account, both definitional and taxonomical, is discovered. Depending on the level of understanding exhibited by the inquirers, this account may or may not allow for noetic understanding of the object in the deepest sense. (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)

In Plato’sStatesman, 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” (285d7). 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 theSophistand earlyStatesman, 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 ofparadigm, the paradigms ofcareandthe weaver, and the notion ofdue 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 theRepublic. (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)