El pasaje de la _Física _ (218b21-219a) ha llevado a postular un concepto de tiempo deter minado por las condiciones perceptivas de la psyche. Se muestra cómo las condiciones de percepción son un punto de partida en la investigación: lo que es primero y más cercano a los sentidos y más conocido para los seres humanos. El punto de llegada es la conexión necesaria entre la existencia del tiempo y la del cambio. La percep ción del cambio de los durmientes (...) de Cerdeña permite determinar los elementos que componen la experiencia del tiempo y proceder a determinar aquellos que compo nen la existencia de este. (shrink)

This paper offers a novel interpretation of the nature and role of logical argumentation in Aristotle’s natural philosophy. In contrast to the standard domain interpretation, which makes logikôs argumentation the contrary of phusikôs, relying on principles drawn from outside the domain of natural science, I propose that the essential or defining feature of logikôs argumentation is the use of principles that are general relative to the question under investigation. My interpretation is developed and illustrated with a close textual analysis of (...) Aristotle’s explanation of mule sterility in Generation of Animals II 8. (shrink)

We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are (1) the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and (2) the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. Armed (...) with this account, we are ineluctably driven to introduce a highly constructive notion of (outer) measure based exclusively on the total magnitude of potentially infinite collections of line segments. The Paradox of Measure then consists in the proof that every finite or potentially infinite collection of points lacks magnitude with respect to this notion of measure. We observe that the Paradox of Measure, thus understood, troubled analysts into the 1880’s, despite their knowledge that the linear continuum is uncountable. The Paradox was ultimately resolved by Borel in his thesis of 1893, as a corollary to his celebrated result that every countable open cover of a closed line segment has a finite sub-cover, a result he later called the “First Fundamental Theorem of Measure Theory.” This achievement of Borel has not been sufficiently appreciated. We conclude with a metamathematical analysis of the resolution of the paradox made possible by recent results in reverse mathematics. (shrink)

There are two distinct but interrelated questions concerning Aristotle’s account of infinity that have been the subject of recurring debate. The first of these, what I call here the interpretative question, asks for a charitable and internally coherent interpretation of the limited pieces of text where Aristotle outlines his view of the ‘potential’ (and not ‘actual’) infinite. The second, what I call here the philosophical question, asks whether there is a way to make Aristotle’s notion of the potential infinite coherent (...) and rigorous with modern tools that can stand as a rival to the widely-accepted view of the infinite as characterized in a mathematical theory of sets. In this paper, I argue that the theoretical roles that Aristotle intends his account of the potential infinite to fulfill lead to a deep and irresoluble tension that can help explain the persistence of debates on both of these questions. I do so by turning to the places where Aristotle attempts to argue for or against the existence of particular infinite processes to show that he slides between different underlying notions of when changes are possible. Making these underlying notions clear can help us better understand the role of Aristotle’s account in the history of philosophy, the possible pitfalls for a contemporary theory of the potential infinite, and what each of these debates might learn from each other. (shrink)

Through a detailed analysis of the various modes of argumentation employed by Aristotle throughout his natural scientific works, I aim to contribute to the growing scholarship on the relation between Aristotle’s theory of science and his actual scientific practice. I challenge the standard reading of Aristotle as a methodological empiricist and show that he permits a variety of non-empirical arguments to support controversial theses in properly scientific contexts. Specifically, I examine his use of logical (logikôs) argumentation in the discussion of (...) mule sterility in Generation of Animals II 8, rational (kata ton logon) argumentation in his discussion of cardiocentrism throughout the biological works, and the method of division in Posterior Analytics II 13. (shrink)