La exposición y crítica de las doctrinas antiguas tiene un lugar importante en los escritos de Aristóteles. Sin embargo, ciertas dudas se han vuelto corrientes acerca de la confiabilidad de sus descripciones. Más aún, se ha sostenido que Aristóteles deforma la comprensión histórica a través de la introducción de conceptos y términos propios. En este libro se aborda el problema a través de un análisis de las críticas que Aristóteles dirige a la teoría platónica de las Ideas, que permite explicar (...) la constitución y desarrollo de importantes conceptos aristotélicos a partir de la confrontación dialéctica con las doctrinas de su maestro. En efecto, las dificultades genuinas que Aristóteles descubre en el platonismo constituyen el motor para gestar nuevos conceptos, que no son ajenos, sino que surgen como implicaciones del examen crítico. Así, la imposición de términos propios no debe interpretarse como distorsión, sino como el modo que Aristóteles adopta para exhibir su particular solución a los problemas que los filósofos anteriores dejaron sin solución. (shrink)

What does Plato mean in saying that, for all forms, “F-ness is F”? In such claims, I argue, ‘F’ is being used metonymically to refer to the property of being productive of F-ness rather than to the property of being F, in a way consistent with univocity and the rejection of a genuine Self-Predication Assumption. I explain and defend this productive metonymy reading and show how it can resolve the troubling argument at Phaedo 74b7-c6.

In Plato’s Timaeus, two different theories – the Receptacle theory and the geometrical particle theory – are presented to explain change in the natural world. In this paper, I argue that there is tension between the two theories. After examining several possible solutions for this tension, I conclude that Plato does not present it as something ready to be solved within the dialogue but, rather, as something to be understood in a way that maintains both theories. Finally, I also argue (...) that the contrast between the two theories in the Timaeus derives from a similar contrast in the Phaedo. (shrink)

In this paper, I explore the origins of the ‘problem of universals’. I argue that the problem has come to be badly formulated and that consideration of it has been impeded by falsely supposing that Platonic Forms were ever intended as an alternative to Aristotelian universals. In fact, the role that Forms are supposed by Plato to fulfill is independent of the function of a universal. I briefly consider the gradual mutation of the problem in the Academy, in Alexander of (...) Aphrodisias, and among some of the major Neoplatonic commentators on Aristotle, including Porphyry and Boethius. (shrink)

Book Review of Leibniz, God, and Necessity by Michael Griffin.

Resumo O argumento do Terceiro Homem presente no “Parmênides” constitui uma formidável objeção à teoria das Ideias, à qual Platão não apresentou resposta explícita. A despeito disso, cremos ser possível haurir da filosofia platônica uma solução para a referida objeção, solução esta que estaria verossimilmente à disposição do filósofo. Sendo assim, compreende-se que Platão não tenha sido forçado a renunciar à teoria das Ideias, ao menos no que se refere às dificuldades que o Terceiro Homem lhe opõe.The Third Man Argument (...) presented in the “Parmenides” is a formidable objection to the Theory of Forms, one which Plato did not provide an explicit answer to. In spite of that we believe it is possible to draw from Plato’s philosophy a solution to the referred objection, and one which likely would be available to the philosopher. Thus, it becomes clear that Plato was not forced to renounce his Theory of Forms, at least with regard to the difficulties that the Third Man Argument raises to it. (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.

Plato is commonly considered a metaphysical dualist conceiving of a world of Forms separate from the world of particulars in which we live. This paper explores the motivation for postulating that second world as opposed to making do with the one we have. The main objective is to demonstrate that and how everything, Forms and all, can instead fit into the same world. The approach is exploratory, as there can be no proof in the standard sense. The debate between explaining (...) Plato’s ontology with a single world and requiring a two-world model to make sense of the same thing is typically about scouring the Platonic corpus for evidence and turning to Aristotle for help where we need it. The aim here is to dig deeper than what either of them, or anyone else, has said or implied about the number or worlds, searching instead for any insight that might be gained from the way Forms are supposed to exist versus what we ourselves might understand by existence. Although the paper is, at its most basic level, about the existence of the Forms, the intention is not to prove that they exist, nor to evaluate the proofs and objections already on record, but to consider how they might exist and what follows if they do. Dialogue toward consensus on why we think the Forms exist, and why we think they do not, could perhaps provide a smoother “second sailing” in waters where we have been unable to agree whether they do and where they would if they did. (shrink)

This chapter discusses the first part of Aristotle's Posterior Analytics A-33, 88b30-89a10. I claim that Aristotle is not concerned with an epistemological distinction between knowledge and belief in general. He is rather making a contrast between scientific knowledge (which is equivalent to explanation by the primarily appropriate cause) and some explanatory beliefs that falls short of capturing the primarily appropriate cause.

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)

This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. The paper also shows how the always-self-predicative universals of category theory provide the "opposite bookend" to the never-self-predicative universals of iterative set theory and thus that the paradoxes arose from having (...) one theory (e.g., Frege's Paradise) where universals could be either self-predicative or non-self-predicative (instead of being always one or always the other). (shrink)

Despite Diotima’s irresistible virtues and attractiveness across the millennia, she spells trouble for philosophy. It is not her fault that she has been misunderstood, nor is it Plato’s. Rather, I suspect, each era has made of Diotima what it desired her to be. Her malleability is related to the assumption that Plato invented her, that she is a mere literary fiction, licensing the imagination to do what it will. In the first part of my paper, I argue against three contemporary (...) ‘majority views’ about Diotima that I regard as false. The first is that we can be certain she is fictional;1 a second is that Diotima is our best evidence for Plato’s feminism; the third, that she is Plato’s mouthpiece for the higher mysteries in the Symposium. After I have set aside what I regard as false, I proceed in the second half of my paper to develop Diotima’s positive contribution to philosophical psychology, her naturalistic account of the psyche as mortal, unified, and developmental. Whether the view Plato assigns to her is one that he held I do not pretend to know; but it is a powerful, defensible, and coherent view that inspired positive aspects of Freudian psychology in the twentieth century. Freud’s insight, in fact, makes clear how erōs can be developed in relation to the bad as well as the good. (shrink)

A commentary on the Symposium as a challenge and a gift to Athens. I begin with a reflection on three dates: 416 bce, the date of Agathon’s victory party, c. 400, the approximate date of Apollodorus’ retelling of the party, and c. 375, the approximate date of the ‘publication’ of the dialogue, and I argue that Plato reminds his contemporary Athens both of its great poetic and legal and scientific traditions and of the historical fact that the way late fourth (...) century Athens appropriated them in some way led to the city’s demise at the turn of the century; thus the dialogue is Plato’s challenge to his contemporary Athens to recognize and overcome its flawed relation to its cultural resources. Heard in this way, the key moments are Aristophanes’ implied critique of Pausanias and Eryximachus and Socrates’ implied critique of Aristophanes and Agathon. Proceeding by a close reading, I argue that Plato exposes, for those moved to rise to his challenge, the failure of his great predecessors to conceive the divine in a way that, worthy of the height and otherness divinity requires, can provide substantive orientation for the burgeoning new reason that animates the city’s culture. (shrink)

The article tries to prove that the famous formula "epekeina tês ousias" has to be understood in the sense of being beyond being and not only in the sense of being beyond essence. We make hereby three points: first, since pure textual exegesis of 509b8–10 seems to lead to endless controversy, a formal proof for the metaontological interpretation could be helpful to settle the issue; we try to give such a proof. Second, we offer a corollary of the formal proof, (...) showing that not only self-predication of the form of the Good, but of any form is not possible, that is: no form of F has the form of F. Third, we apply Spinoza’s distinction between an ens imaginarium and a chimaera to Plato’s Idea of the Good. (shrink)

A discussão nos livros dos Tópicos giram em torno dos debates dialéticos e seus elementos. Aristóteles discorre sobre os gêneros, as propriedades e os chamados acidentes e suas relações predicativas em categorias. Interessa-nos, sobretudo, compreender o papel desempenhado pela Definição e qual sua relação com os demais instrumentos para a dialética.