Much of Aristotle's thought developed in reaction to Plato's views, and this is certainly true of his philosophy of mathematics. To judge from his dialogue, the Meno, the first thing that struck Plato as an interesting and important feature of mathematics was its epistemology: in this subject we can apparently just “draw knowledge out of ourselves.” Aristotle certainly thinks that Plato was wrong to “separate” the objects of mathematics from the familiar objects that we experience in this world. His main (...) arguments on this point are in Chapter 2 of Book XIII of the Metaphysics. There are three distinct lines of argument: The first concerns the objects of geometry ; the second deals with the Platonist principles which are applied to arithmetic and geometry; the third is about substance as living things, especially animals, and perhaps man in particular. In addition to the above, this article also examines Aristotle's treatment of infinity. (shrink)

Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of fictionalism also faces a (...) difficult challenge: there is evidence that Aristotle would deny the fictionalist position that mathematics is false. I argue that, in Aristotle's view, the fiction of mathematics is not to treat what does not exist as if existing but to treat mathematical objects with an ontological status they lack. This form of fictionalism is consistent with holding that mathematics is true. (shrink)

Did classical kalām debates about how thing and existent relate to each other pave the way for Avicenna's distinction between essence and existence? There are some indications that the concept of thingness may have played a bridging role between the mutakallimūn's discussions and those of Avicenna. Nevertheless, Avicenna's appeals to thingness occur most densely in passages devoted to analyzing the relationship between efficient and final causes, an entirely Aristotelian topic. A philological question arises: should these passages be emended to read (...) causality in place of thingness? I argue that the balance of evidence compels us to retain thingness. For Avicenna, thingness is the respect in which the final cause is prior to the efficient cause ; existence, by contrast, is the respect in which the efficient cause is prior to the final cause. In fact, over the course of Avicenna's career a progression from the kalām problematic of šay' v. maw[gcaron]ūd to his own problematic of māhiyya v. wu[gcaron]ūd can be detected in his discussions of efficient and final causation. (shrink)

It has long been a truism of the history of philosophy that intentionality is an invention of the medieval period, and within this standard narrative, the central place of Arabic philosophy has always been acknowledged. Yet there are many misconceptions surrounding the theories of intentionality advanced by the two main Arabic thinkers whose works were available to the West, Avicenna and Averroes. In the first part of this paper I offer an overview of the general accounts of intentionality and intentional (...) being found in the linguistic, psychological, and metaphysical writings of Avicenna and Averroes, and I trace the terminology of “intentions” to a neglected passage from Avicenna’s logic. In the second part of the paper I examine the way that Avicenna and Averroes apply their general theories of intentionality to the realm of sense perception. I offer an explanation of why Avicenna might have chosen to denominate the objects of the internal sense faculty of estimation as “intentions”, and I explore the implications of Averroes’s decision to attribute intentionality to the external senses and the media of perception. (shrink)

One of the chief innovations in medieval adaptations of Aristotelian psychology was the expansion of Aristotle's notion of imagination orphantasiato include a variety of distinct perceptual powers known collectively as the internal senses. Amongst medieval philosophers in the Arabic world, Avicenna offers one of the most complex and sophisticated accounts of the internal senses. Within his list of internal senses, Avicenna includes a faculty known as “estimation”, to which various functions are assigned in a wide variety of contexts. Although many (...) philosophers in the Arabic world as well as in the Latin West accepted Avicenna's positing of an estimative faculty, Avicenna's best-known critics, al-Ghazâlî and Averroes, found Avicenna's arguments in support of a distinct estimative faculty problematic. For different reasons, both Averroes and Ghazâlî raised the basic question of whether one needed to posit a distinct faculty of estimation to supplement the perceptual abilities of the other internal senses, and whether the notion of an estimative power as defined by Avicenna was internally coherent. Such criticisms suggest that the Avicennian conception of estimation is not entirely unambiguous, and that a correct understanding of Avicenna's motivations for delineating an estimative power requires a careful study of the diverse activities assigned to it throughout Avicenna's philosophical writings. (shrink)

Elements of Mind (EM) has two themes, one major and one minor. The major theme is intentionality, the mind’s direction upon its objects; the other is the mind–body problem. I treat these themes separately: chapters 1, and 3–5 are concerned with intentionality, while chapter 2 is about the mind–body problem. In this summary I will first describe my view of the mind–body problem, and then describe the book’s main theme. Like many philosophers, I see the mind–body problem as containing two (...) sub–problems: the problem of mental causation and the problem of consciousness. I see these problems forming the two horns of a dilemma. Just as the problem of mental causation pushes us towards physicalism, so the problem of consciousness pushes us away from it. Each problem reveals the inadequacy of the solution to the other. Essentially the problem of mental causation is the conflict between (i) the apparent fact that mental states and events have effects in the physical world and (ii) a general principle about the causal nature of the physical world, which is sometimes called the ‘causal closure’ or the ‘causal completeness’ of the physical world. This principle says that all physical effects have physical causes which are enough to bring them about. The problem then is simple: how can a mental cause have a physical effect if that effect also has a physical cause which is enough to bring it about? Barring massive overdetermination of our actions by independent causes, it seems that the best answer is to identify the mental and the physical causes. And this is traditionally how physicalists have argued for their identity theory of mind and body. However, many physicalists reject the identity theory, and therefore they have to solve the mental causation problem in some other way. At present, there is no consensus among physicalists on which of the currently proposed solutions is correct. In chapter 2 of EM I propose an alternative, which I call ‘emergentism’. Inspired by the rejection of the identity theory, Emergentism is the idea that mental properties are genu.. (shrink)

Whether aristotle wrote a work on mathematics as he did on physics is not known, and sources differ. this book attempts to present the main features of aristotle's philosophy of mathematics. methodologically, the presentation is based on aristotle's "posterior analytics", which discusses the nature of scientific knowledge and procedure. concerning aristotle's views on mathematics in particular, they are presented with the support of numerous references to his extant works. his criticism of his predecessors is added at the end.

Few philosophers that have been studied as much as Ibn Sīnā have been as much misunderstood. His extraordinary ability to reflect upon and write in a variety of styles about seemingly every topic in every domain has steered his thought from philosophy and theology to mysticism and esoterism. Instead of helping us to learn and understand better Ibn Sīnā than he has previously been understood, the recent surge of Avicennan studies only adds more confusion to the already complex social context (...) which he was living in. (shrink)

: The concepts of intention and intentionality were particularly significant notions within the Christian, Jewish, and Islamic medieval philosophical traditions, and they regained philosophical importance in the twentieth century. The theories of intention and intentionality of the medieval Islamic philosopher and physician Ibn Sina and the phenomenological philosopher and mathematician Edmund Husserl are examined, compared, and contrasted here, showing that Ibn Sina's conception of intention is naturalistic and, in its naturalism, is influenced by the medical professional culture to which Ibn (...) Sina belonged. As well, Husserl's anti-naturalistic conception of intentionality is influenced by his background as a mathematician and by his desire to ground mathematics and the empirical sciences in a truly scientific philosophy. In conclusion, an argument is presented for the superiority of the Husserlian transcendentalist account of intentionality over the Avicennian naturalistic account, on the grounds that the latter falls prey to psychologism and reductionism, the two specters that according to Husserl must haunt all naturalistic accounts of consciousness. (shrink)

Avicenna's discussion of space is found in his comments on Aristotle's account of place. Aristotle identified four candidates for place: a body's matter, form, the occupied space, or the limits of the containing body, and opted for the last. Neoplatonic commentators argued contra Aristotle that a thing's place is the space it occupied. Space for these Neoplatonists is something possessing dimensions and distinct from any body that occupies it, even if never devoid of body. Avicenna argues that this Neoplatonic notion (...) of space is untenable on the basis of three arguments. In general he maintains that bodies' impenetrability is explained by reference to dimensionality. Consequently, if it is dimensionality that explains impenetrability, and yet as the Neoplatonists hold space inherently possesses dimensions, material bodies could never interpenetrate space and so occupy it and thus bodies could never have a place. The conclusion is patently false. In additions Avicenna argues that the method used to arrive at the possibility of space is illicit, and so Neoplatonist cannot show that space is even possible. Thus, concludes Avicenna, Aristotle's initial account must be correct. The paper outlines the historical context of this debate and then treats Avicenna's arguments against space in detail. (shrink)

Although he does not have an explicit theory of supposition as is found in the works of Latin medieval philosophers, Avicenna has two doctrines giving something equivalent: the threefold distinction of quiddity, corresponding to a division of simple, personal and material supposition, and his analyses of truth conditions for categorical propositions, where sentential context determines in part the reference of their terms. While he does address which individuals are being referred to by the universal terms used there, Avicenna concentrates more (...) on the varied temporal durations of the predications being made. In Western terms, he has incorporated ampliation and restriction into the theory of supposition itself. (shrink)