Forthcoming in Long Platonism: The Routes of Plato’s Reception to the Italian Renaissance, eds. Eva Anagnostou-Laoutides, George Steiris, George Arabatzis. I argue that Plato’s Divided Line, expounded in Republic 509D6-511E4, is a likely ancestor of the Islamic Degrees of Being schema (marāṭib al-wujūd). This is also an argument for the relevance of Islamic Platonism to Plato studies. I will show that Line and Schema have at least the following in common: a. Both present four modes of cognition rather than a (...) simple dichotomy between knowledge and belief. b. Both define modes of cognition according to their objects, resulting in four pairs of cognition/object. c. Both are hierarchical in terms of the pairs’ approximation to reality; cognitions and their objects are ranked by their closeness to truth. d. In both, the goal is to provide a program by which one comes to know what is real. Of course, each of them is more than what they share. The Schema develops and expands the role of imagination in cognition, drawing out ambiguities in Plato’s treatment of images to accommodate an ontologically distinct realm interrelating the visible and the intelligible. (shrink)

There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...) continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous. (shrink)

Aristotle’s solution to Zeno’s arrow paradox differs markedly from the so called at-at solution championed by Russell, which has become the orthodox view in contemporary philosophy. The latter supposes that motion consists in simply being at different places at different times. It can boast parsimony because it eliminates velocity from the ontology. Aristotle, by contrast, solves the paradox by denying that the flight of the arrow is composed of instants; rather, on my reading, he holds that the flight is a (...) unity which is ontologically prior to the temporal parts that may be abstracted from it. I label this position temporal holism; and an entity that is ontological prior to its temporal parts lasting. Lasting, I argue, is the key to Aristotle’s solution to the arrow paradox, but it has received insufficient attention in the relevant literature. I therefore set out here to investigate lasting and highlight its major role in Aristotle’s metaphysics more broadly, and in his solution to other problems of change. I show, too, how lasting within a contemporary context underwrites a parsimonious and intuitive solution to the arrow paradox that retains instantaneous velocity, and hence solves a problem for those who think velocity is required within the ontology to underwrite certain causal roles. (shrink)

Although Aristotle does not explicitly address persistence, his account of persisting may be derived from a careful consideration of his account of change. On my interpretation, he supposes that motions are mereological unities of their potential temporal parts – I dub such mereological unities ‘lasting’. Aristotle’s persisting things, too, are lasting, I argue. Lasting things are unlike enduring things in that they have temporal parts; and unlike perduring things in that their temporal parts are not actual, but rather are potential. (...) Lasting, that is Aristotle’s persisting, is thus a distinctive alternative to enduring and perduring. I assess this alternative showing it to be attractive. (shrink)

Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this rea­ son, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the (...) concept of abstraction. In our work, I will try to explain the mathematical abstraction that Aristotle has developed to understand mathematical philosophy. (shrink)

This study is the first part of an attempt to settle a vigorous debate among historians of medieval philosophy by harnessing the resources of analytic philosophy. The debate is about whether Avicenna's epistemology is rationalist or empirical. To settle the debate, I first articulate in this article the three core theses of rationalism and one core thesis of empiricism. Then, I probe Avicenna's epistemology in his major works according to the first core thesis of rationalism (the intuition thesis). In the (...) end, I find Avicenna committed to this thesis in at least one substantive way, namely, in his claim to intuit the intelligible forms or essences. This suffices to count Avicenna as rationalist. In a subsequent article, I shall probe Avicenna's epistemology according to the other two core theses of rationalism, presenting further evidence that he was a rationalist, not an empiricist. (shrink)

The word “as” enables one to make contexts and aspects of things explicit while attributing properties or descriptions to them. For example “John is rational as a mathematician”; “John is irrational as a driver.” This paper examines the idea according to which all propositions containing “as” should be targeted as potential inferences about the subject; as for the examples given—about John. If the inference is valid—the conception in question holds—one can get rid of “as.” I argue against that view by (...) bringing up several contexts in which “as” is not supposed to express an inference. On this basis I come up with a different (non-inferential) typology which does justice, I believe, to ordinary as well as philosophical uses of the little word at stake. (shrink)

The purpose of this work is to address the relation existing between ancient Greek practical geometry and ancient Greek pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically (...) explicit in definitions, like that of segments in Euclid’s Elements. Then, we will address how in pure geometry we, so to speak, “refer back” to practical geometry. This occurs in two ways. One, in the propositions of pure geometry. The other, when applying pure geometry. In this case, geometrical objects can represent practical figures like, e.g., a practical segment. (shrink)

A trope is an abstract particular. Trope theorists maintain that tropes exist and argue that they can solve important philosophical problems, such as explaining the nature of properties. While many contemporary interpreters of Aristotle read him as a trope theorist, few commentators distinguish different versions of trope theory. Which, of any, of these versions did Aristotle hold? Classical trope theorists say that individuals just are bundles of tropes. This essay offers a reading of Categories 2-5 and Metaphysics VII-VIII that aligns (...) Aristotle's view with nonclassical trope theory, according to which objects are more than just bundles of tropes. (shrink)

This book is concerned with Aristotle’s definition of the human capacity for rational thinking (nous) offered in De anima. For Aristotle, nous is the principle, and ultimate explanans, of all the phenomena of human thinking. The book presents an in-depth interpretation of De anima III 4–8 as a single and coherent philosophical argument. More specifically, the book argues for the following views: (i) Rationalism. Humans come to know the world via two fundamentally different cognitive powers: nous and perception. They are (...) fundamentally different cognitive powers because the nature of their corresponding object is fundamentally different; -/- (ii) Essentialism. The human power for thinking is defined as a capacity for directly grasping the essences of everything there is, including itself. It is this very capacity that Aristotle shows to be the principle of all other kinds of human thinking; -/- (iii) Separatism. Human nous is unmixed with the body, has no dedicated bodily organ, and is separable from the body. As a result, it cannot be assimilated to any of the other parts of the soul. While nous belongs to our essence as human beings, it is not part of the natural world; -/- (iv) Embeddedness in the cognitive soul. Human nous is embedded in a cognitive soul. Among other things, this means that the distinctive activity of human nous—thinking—can only take place in the context of a larger set of activities which are common to the body and the soul. (shrink)

Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this reason, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the concept (...) of abstraction. In our work, I will try to explain the mathematical abstraction that Aristotle has developed to understand mathematical philosophy. (shrink)

Bilimsel soyutlama temsil edilecek belirli bir hedefin sahip olduğu bazı özelliklerin ihmal edilmesi işlemidir. Her temsil tanım gereği soyutlama içermektedir. Nitekim temsili yapılacak ya da modellenecek hedef sistemde ihmal edilmesi uygun görülen birçok faktör bulunmaktadır. Soyutlamanın bilimsel araştırma için vazgeçilmez bir unsur olduğu fikri tartışma götürmeyecek düzeyde bir hakikat olarak görülmektedir. Ne var ki temsile ilişkin bu işlemin doğası hususunda böylesi tartışmasız bir hakikate sahip değiliz. Bu makalede, ilk olarak, soyutlamaya ait felsefi literatürde yer alan kimi standart görüşleri ele alıyorum. (...) Daha sonra standart görüşlere göre soyutlamanın çok daha rafine versiyonu detaylı olarak analiz edip bu görüşün, bilimde görsel temsillerden biri olan kartografik haritalar için yeterli bir kuramsal zemin sağlamadığını ileri sürüyorum. (shrink)