This chapter contains sections titled: Going Beyond Nature in Order to Explain it Technē, epistēmē and alēthēs doxa Mathematics, pure and applied Observation and Experimental Verification Bibliography.

Este trabajo pretende ser una referencia útil para los estudiosos de la filosofía de Platón. Aporta un enfoque original a la investigación de los procesos lógicos que condicionan que unas formas participen de otras. Con la introducción del concepto de participación relacional, abre una posible vía de solución a las distintas versiones del argumento del «tercer hombre». Puede resultar de interés asimismo el método de generación de los números a partir de lo par y lo impar, propuesto en la interpretación (...) de Parménides 143e-144a. El escrito tiene continuidad en un segundo artículo acerca del ser y la verdad en Platón. (shrink)

It is widely known that Aristotle rules out the existence of actual infinities but allows for potential infinities. However, precisely why Aristotle should deny the existence of actual infinities remains somewhat obscure and has received relatively little attention in the secondary literature. In this paper I investigate the motivations of Aristotle’s finitism and offer a careful examination of some of the arguments considered by Aristotle both in favour of and against the existence of actual infinities. I argue that Aristotle has (...) good reason to resist the traditional arguments offered in favour of the existence of the infinite and that, while there is a lacuna in his own ‘logical’ arguments against actual infinities, his arguments against the existence of infinite magnitude and number are valid and more well grounded than commonly supposed. (shrink)

This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach (...) to mathematics and a top-down naturalisation. Articulating my particular understanding of what realism and naturalism should commit us to, I propose a creative fusion of Badiou’s attention to metamathematical results with a structural-informational metaphysics, proposing a ‘matherialism’ uniting the more daring speculative insights of the former with the naturalist and empiricist commitments motivating the latter. (shrink)

It is a notion commonly acknowledged that in his work Timaeus the Athenian philosopher Plato (_c_. 429–347 BC) laid down an early chemical theory of the creation, structure and phenomena of the universe. There is much truth in this acknowledgement because Plato’s “chemistry” gives a description of the material world in mathematical terms, an approach that marks an outstanding advancement over cosmologic doctrines put forward by his predecessors, and which was very influential on western culture for many centuries. In the (...) present article, I discuss inter-transformations among Plato’s four types (fire, air, water, and earth) as well as the interpretation they received in the literature. I find that scientists and scholars generally emphasized (and often misunderstood) mathematical aspects of these “reactions” over the philosophical ones. I argue that Plato’s “chemistry” in fact bears on crucial topics of his philosophical system, such as Forms, Becoming, causation and teleology. I propose that consideration of these doctrines help to understand not only the sense of his “chemical” reactions, but also the reason why their stoichiometry is by surface balance and is restricted only to types that come to be and pass away but not to those that provoke the inter-transformations. (shrink)

In general, scholars have viewed the mathematical detail of Plato’s Divided Line discussion in Republic VI-VII as irrelevant to the substance of his epistemology.Against this stance this essay argues that this detail serves a serious and instructive purpose and makes manifest some central features of Plato’s account of human knowledge.

This paper presents a new interpretation of the objects of dianoia in Plato’s divided line, contending that they are mental images of the Forms hypothesized by the dianoetic reasoner. The paper is divided into two parts. A survey of the contemporary debate over the identity of the objects of dianoia yields three criteria a successful interpretation should meet. Then, it is argued that the mental images interpretation, in addition to proving consistent with key passages in the middle books of the (...) Republic, better meets those criteria than do any of the three main positions. (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)