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)

The paper attempts to reconstruct Vlastos’ method of research into the history of philosophy using his Degrees of Reality as a case study. To do so, I rely on the extensive materials available in the Vlastos Archive. Through the palimpsest of superimposed revisions in his documents as well as the letters exchanged with his colleagues, I will go through the gestation of a whole new perspective in dealing with Plato’s conception of the reality of abstract objects. Furthermore, the focus on (...) the process rather than on the results will provide an inside view on Vlastos’ ground-breaking use of analytical tools in developing research in the field of history of philosophy. (shrink)

The argument at Phaedo 74 B 4‐C 6 that the equal itself is ‘something different from’ sets of physical equals depends on Leibniz's Law: there is a property that perceptible equals have that the equal itself does not have. What I call the ‘epistemic interpretation’ holds that the property is an epistemic one: having appeared unequal. The ‘ontological interpretation’ holds that the property is not epistemic, but simply the property of being unequal. The most natural reading of the text favours (...) the epistemic interpretation; scholarly support for the ontological interpretation is based on the widely held view that on the epistemic interpretation the argument is manifestly invalid. But this view implicitly relies on an impoverished sense of ‘appearing’ as equivalent to ‘being thought’. Drawing on an analogy with colour perception, I elaborate an experiential sense of ‘appearing’ which makes Plato's argument on the epistemic interpretation philosophically defensible. (shrink)

In diesem Aufsatz wird eine axiomatisierte logische Rekonstmktion der Platonischen Prädikationstheorie vorgeschlagen, aufbauend auf der Ähnlichkeitsrelation. Die Theorie ist konsistent und trivial. Selbst-Prädikation bereitet darin keine Schwierigkeiten und das Dritte-Mann-Argument wird als harmlos aufgezeigt. Es werden Kriterien dafür, daß etwas ein Standardgegenstand (eine Form oder Idee) ist, aufgestellt und ausgeführt, daß diese die Platonische Ideentheorie implizieren. Die Grenzen von Piatons Prädikationstheorie werden klar gemacht; sie ist von der adjektivischen (linguistischen) Prädikation abgeleitet und kann ontologisch nur diesen Typ der Prädikation abdecken, (...) nicht aber substantivische Prädikation. Schließlich wird gezeigt, daß die Existenz Gottes in der Platonischen Prädikationstheorie bewiesen werden kann. (shrink)

Name der Zeitschrift: Deutsche Zeitschrift für Philosophie Jahrgang: 65 Heft: 6 Seiten: 1031-1056.

I discuss Aristotle’s opening argument against Platonic Forms in _Metaphysics_ A.9, ‘the Razor’, which criticizes the introduction of Forms on the basis of an analogy with a hypothetical case of counting things. I argue for a new interpretation of this argument, and show that it involves two interesting objections against the introduction of Forms as formal causes: one concerns the completeness and the other the adequacy of such an explanatory project.

Few arguments from the past have stirred up as much interest as Aristotle’s “Third man” and not so many texts have received as much attention as its account in chapter 22 of the Sophistici elenchi. And yet, several issues about both remain highly controversial, starting from the very nature of the argument at stake and the exact signification of some of its features. The essay provides a close commentary of the text, dealing with its main difficulties and suggesting an overall (...) interpretation of Aristotle’s discussion of the “Third Man” argument. (shrink)

Que la philosophie ancienne ait bénéficié de certains raffinements méthodologiques dus à la philosophie analytique n’est guère mis en question, même par ceux qui ne s’en réclament pas. À la grande époque de la philosophie analytique, certains de ses meilleurs représentants étaient encore fort versés en histoire de la philosophie et appliquaient leurs compétences analytiques à ce qu’ils considéraient comme des problèmes centraux chez les auteurs anciens. Cet article suggère à travers deux exemples que, s’agissant de Platon, cette attention n’a (...) pas eu seulement des effets revigorants, mais également déformants. Dans le premier cas, la méthode diérétique si chérie de Platon a été marginalisée par d’éminents philosophes analytiques qui l’ont considérée comme triviale et inintéressante. Dans le second cas, le problème de l’« auto‑prédication » des Idées, qui est celui de savoir si les Idées sont des entités qui possèdent les propriétés qu’elles représentent, a été considéré d’une importance décisive pour la théorie platonicienne des Idées. À cause de ses conséquences supposément désastreuses, mentionnées une unique fois dans le Parménide, on a pensé que Platon avait renoncé à cette théorie sous sa forme classique. Au cours des dernières années, l’importance de la méthode diérétique a été réévaluée et celle du problème de l’auto-prédication réduite à de plus justes proportions. Cela ne diminue pas la valeur des contributions des philosophes analytiques à l’étude de Platon, mais signifie seulement qu’elles doivent n’être acceptées qu’avec précaution. (shrink)

The opening chapters of Anselm's Monologion contain a ‘proof’ of a perfect being, which has received far less attention than the more famous Proslogion proof, and the ontological arguments derived from it. I wish to rectify this by developing an argument in defence of a crucial premise of the Monologion proof. This premise states that ‘the Good’, i.e. that in virtue of which numerically distinct things may all be good, must itself be a supremely good thing. I motivate the argument (...) before considering objections to both premises, as well as putative ‘parodies’ of my argument. Part of the motivation of my argument will involve the claim that the Good, if it is good at all, must be a paradigm good thing. I conclude that theists have a second kind of ontological argument at their disposal. (shrink)

Truth of x (independently of any description of x) that it is f. A property f which holds of x but is not per se of x is said to hold per accidens of x. The essence of an individual is the sum of its per se properties. We can formulate the following: doctrine a: concrete individuals do not have essences though abstract entities do. Doctrine b: concrete individuals have essences but they do not individuate, whereas abstract entities have essences (...) which do individuate. Assumption i: we shall say that a thing exists insofar as it has an essence. Assumption ii: we shall say that we know a thing when we know what its per se properties are. We argue that plato held doctrine a and aristotle doctrine b (with assumptions i and ii). (edited). (shrink)

In a 1985 article entitled “The Art of Glaukos,” Diskin Clay suggested that the enigmatic passage at the beginning of the geological myth in Phaedoreferred toRepublic10, where the soul is likened to the sea-creature Glaucus whose true nature, like the soul’s, is obscured by the distortions imposed by underwater life. Starting with a defense of Clay’s ingenious suggestion, my purpose is to compare Phaedoto Glaucus, with its true nature obscured by traditional assumptions about the order in which Plato composed his (...) dialogues, and thus how they should be read. At least part of the reason that Clay’s thesis has not been embraced is because it clashes with the dogma that Phaedocannot refer back to Republic; I want to challenge that dogma. Borrowing from Catherine Zuckert the notion that, since Phaedocomes at the end of Socrates’ story, it can usefully be read as the culmination of the Platonic dialogues, I will show how a “late” Phaedo—i.e., a reading of the dialogue that is open to the possibility that it refers to more than one dialogue generally considered to be later than it with respect to composition—recovers its true nature, presently encrusted with the oysters and seaweed of an outdated developmentalism that has obscured this culminating masterpiece of Plato’s dramatic and philosophical art. (shrink)

Infinite regress arguments are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These consequences of our customary way of (...) using this tool indicate that there is a need for a theory to re-orient our practice. My general approach to contribute to such a theory, consists of collecting and evaluating as many infinite regress arguments as possible, comparing and contrasting many of the formal and non-formal properties, looking for recurring patterns, and identifying the properties that appeared essential to those patterns. Two very general questions guided this work: How are infinite regresses generated in infinite regress arguments? How do infinite regresses logically function as premises in an argument? In answering these questions I clarify the notion of an infinite regress; identify different logical forms of infinite regresses; describe different kinds of infinite regress arguments; distinguish the rhetoric from the logic in infinite regress arguments; and suggest ways of improving our discussion and our practice of constructing and evaluating these arguments. (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.

Me propongo explicar que los términos sustanciales usados individuadoramente constituyen la expresión lingüística que fija la referencia a un objeto en el Organon de Aristóteles, y mostrar que esa expresión opera allí como principium individuationis. El artículo desarrolla dos tesis principales: Es legítimo adjudicar a Aristóteles una teoría descriptiva de la referencia, en la cual las propiedades esenciales incluidas en la definición constituyen condiciones suficientes para referir, dado un contexto donde los términos sustanciales se usan para individuar. Los individuos sustanciales (...) se ubican justificadamente en la base ontológica de las Categorías en virtud de que son los objetos de la referencia, y también de que se desempeñan como sujetos últimos de la predicación. My main goal is to explain that the substantial terms fix the reference to an object, and to show that this expression is the principium individuationis, within the Aristotelian Organon. The paper works out two main theses: Aristotle may be ascribed a descriptive theory of reference in which the essential properties included in the definition constitute sufficient conditions for referring to an object, provided that in the context the substantial terms are used to individualize. Substantial individuals are justifiably included at the bottom of the ontology in the Categories by virtue of their being the objects of reference, and also by virtue of their role as ultimate subjects of predication. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory of categories, (...) dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also 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. (shrink)

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)

In the following pages, the reader will find a detailed study of what Aristotle considered the most difficult aporia formulated in Metaphysics III (Beta), which is answered in chapter 2 of Book X (Iota): the Eleventh Aporia. In such aporia, Aristotle rivals: (i) the conception assumed by the ancient Physiologoi, which takes the One to be an underlying nature whose being is not exhausted by being One, and (ii) the Platonic-Pythagorean view, which prefers to conceive the One in itself, according (...) to its own determinations and apart from any connection with some reality outside it. (shrink)

The Eleventh Aporia results from the breakup of the entire Greek philosophy previous to Aristotle in two manners of conceiving and proposing the first principles (archai), specially the One (to hen): (i) the manner by which Physiologoi conceived the One as a principle, namely, assuming an underlying nature, different from the One in itself, not adequately characterized by the simple fact of being one and which is denoted by the concept of One, and (ii) the manner inaugurated by the Pythagoreans (...) and later endorsed by Plato, marked by the abandonment of the appeal to an underlying nature and by conceiving the One in itself (auto to hen) as a principle, depriving it of any connection with some reality not strictly characterized by being one. Aristotle faces this aporia in Metaphysics Iota 2 and, according to the interpretation I propose: (a) refuses the Pythagorean-Platonic manner of conceiving and proposing principles, (b) endorses the course of action of the Physiologoi, and, in doing so, (c) steps back and retakes the “project” of the Physiologoi at the point where it was interrupted, namely, during the search for a principle of motion. From this scenario, I will try to show that the final outcome of the Eleventh Aporia can be the introduction of the Prime Mover as the properly Aristotelian (and cosmological) candidate to the title of One between the principles. (shrink)