InMetaphysicsΘ.6, 1048b14-17, Aristotle treats the problem of what it is for the infinite to exist potentially, i.e. to be potentially actual. According to my interpretation, Aristotle argues that to exist potentially is for the infinite to have a potentiality which cannot be actualized in reality but only in thought, because it is a potentiality the process of whose actualization cannot be brought to an end.

This article reconstructs Henri Bergson’s argument at the beginning of the second chapter of his Essai sur les données immédiates de la conscience for his view that every idea of number involves sp...

What is time? Just like everything else in the world, our understanding of time has changed continually over time. This article tracks this question through the history of Western philosophy and looks at major answers from the likes of Aristotle, Kant, and McTaggart.

At Physics IV,8, 216a26-7, Aristotle cracks a joke. It is one of the relatively few deliberate jokes in the corpus, and its occurrence here is not without significance. Aristotle in these chapters is arguing against those who believe in the existence of the void, or vacuum, or empty space; he says, ‘even if we consider it on its own merits the so-called vacuum will be found to be really vacuous.'To be sure, this is not a very funny joke; what is (...) interesting about it, though, is that it underlines the general attitude of dismissive flippancy that seems to run through Aristotle's consideration of the void. He seems to refuse to take the hypothesis of the void at all seriously. He never argues directly that the void does not or cannot exist, but contents himself with criticizing the arguments that other thinkers had advanced in its favour. (shrink)

Like many realists about causation and causal powers, Aristotle uses the language of necessity when discussing causation, and he appears to think that by invoking necessity, he is clarifying the manner in which causes bring about or determine their effects. In so doing, he would appear to run afoul of Humean criticisms of the notion of a necessary connection between cause and effect. The claim that causes necessitate their effects may be understood—or attacked—in several ways, however, and so whether the (...) view or its criticism is tenable depends on how we understand the necessitation claim. In fact, Aristotelian efficient causation may be said to involve two distinct necessary connections: one is a relation between causes considered as potential, while the other relates them considered as active. That is, the claims that (1) what has the power to heat necessarily heats what has the power to be heated, and that (2) a particular flame which is actually under a pot necessarily heats it, both of which appear to be true for Aristotle, involve distinct notions of necessity. The latter kind of necessity is based on the facts, as Aristotle sees them, about change, whereas the former is based in the nature of properties. Though different, both kinds of necessity are instances of what contemporary philosophers would call metaphysical necessity, and together they also amount to a theory of causal determination. (shrink)

The current debate over Aristotle's commitment to prime matter is centered on diachronic considerations found in his theory of substantial change. I argue that an appeal to this theory is not required in order to establish his commitment to the existence of prime matter. By drawing on Physics II.1's conception of what it is for an element to have a nature - that is, to have an inner source of movement and rest - I introduce a synchronic justification for the (...) existence of prime matter. By trading on the relationship between the thing that has a source of change and the source it has , I show that something that has a source in itself cannot be identical with its source, and that a type of matter that has no nature of its own (a kind of prime matter) is required to block this identification at the level of the elements. (shrink)

On Zeno Beach there are infinitely many grains of sand, each half the size of the last. Supposing Aristotle denied the possibility of Zeno Beach, did he have a good argument for the denial? Three arguments, each of ancient origin, are examined: the beach would be infinitely large; the beach would be impossible to walk across; the beach would contain a part equal to the whole, whereas parts must be lesser. It is attempted to show that none of these arguments (...) was Aristotle’s. Indeed, perhaps Aristotle’s finitism applied to magnitude only, not plurality. (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)

Perhaps the real paradox of Zeno's Arrow is that, although entirely stationary, it has, against all odds, successfully traversed over two millennia of human thought to trouble successive generations of philosophers. The prospects were not good: few original Zenonian fragments survive, and our access to the paradoxes has been for the most part through unsympathetic commentaries. Moreover, like its sister paradoxes of motion, the Arrow has repeatedly been dismissed as specious and easily dissolved. Even those commentators who have taken it (...) seriously have propounded solutions with which they profess themselves to be perfectly satisfied. So my question is: will Zeno's Arrow survive into the millennium just begun? (shrink)

Frege argues that number is so unlike the things we accept as properties of external objects that it cannot be such a property. In particular, (1) number is arbitrary in a way that qualities are not, and (2) number is not predicated of its subjects in the way that qualities are. Most Aristotle scholars suppose either that Frege has refuted Aristotle's number theory or that Aristotle avoids Frege's objections by not making numbers properties of external objects. This has led some (...) to conclude that Aristotle's accounts of arithmetical and geometrical objects differ substantially. I close this supposed gap by showing that Aristotle's arithmetical objects, like geometrical objects, are just certain sensible things qua certain properties they in fact possess. Specifically, numbers are pluralities qua quantitative or relational properties like ten units or ten. I show that this view is resistant to the Fregean concerns about arbitrariness and numerical predication. (shrink)

Recently, many philosophers have been interested in using locative relations to clarify and pursue debates in the metaphysics of material objects. Most begin with the relation of exact location. But what if we begin instead with the relation known as weak location – the relation an object x bears to any region not completely bereft of x? I explore some of the consequences of pursuing this route for issues including coincidence, extended simples, and endurance, with an eye to evaluating the (...) prospects for taking weak location as our fundamental locative relation. (shrink)

When I raise my arm, what makes it the case that my arm's going up is an instance of my raising my arm? In this paper, I discuss Aristotle's answer to this question. His view, I argue, is that my arm's going up counts as my raising my arm just in case it is an exercise of a certain kind of causal power of mine. I show that this view differs in an interesting way both from the Davidsonian ‘standard causal (...) account’ of action and from accounts put forward by recent critics of Davidson, such as Hornsby, Alvarez and Hyman. (shrink)

When I raise my arm, what makes it the case that my arm's going up is an instance of my raising my arm? In this paper, I discuss Aristotle's answer to this question. His view, I argue, is that my arm's going up counts as my raising my arm just in case it is an exercise of a certain kind of causal power of mine. I show that this view differs in an interesting way both from the Davidsonian ‘standard causal (...) account’ of action and from accounts put forward by recent critics of Davidson, such as Hornsby, Alvarez and Hyman. (shrink)

Recent interpreters portray Aristotle as a Protagorean antirealist, who thinks that colors and other perceptibles do not actually exist apart from being perceived. Against this, I defend a more traditional interpretation: colors exist independently of perception, to which they are explanatorily prior, as causal powers that produce perceptions of themselves. They are not to be identified with mere dispositions to affect perceivers, or with grounds distinct from these qualities, picked out by their subjective effect on perceivers (so-called “secondary qualities”). Rather, (...) they are intrinsic qualities of objects, which are in reality just as they appear to be. At the same time, Aristotle rejects any “simple theory of color” according to which the essence and nature of colors is fully revealed in experience. Although the character of perceptibles as they are experienced is “better known to us,” their essence and nature only comes to be known through a correct theory. (shrink)

In Physics 4.11, Aristotle says that changes are continuous because magnitude is continuous. I suggest that this is not Aristotle’s considered view, and that in Generation and Corruption 2.10 Aristotle argues that this leads to the unacceptable consequence that alterations can occur discontinuously. Physics 6.4 was written to amend this theory, and to argue that changes are continuous because changing bodies are so. I also discuss the question of Aristotle’s consistency on the possibility of discontinuous alterations, such as freezing.

El estudio del tiempo en Physica IV.10-14 presenta grandes dificultades, una de ellas es el vínculo entre tiempo y alma realizada en 223a21-28. Este pasaje fue discutido por varios especialistas modernos durante el siglo XX. Si bien no hay consenso unánime, la “interpretación realista” estuvo muy extendida durante el siglo pasado. En este trabajo me propongo discutir un pasaje de la premisa 223a25-26 en el argumento de Aristóteles respecto de este vínculo. En primer lugar, rechazo la “interpretación realista” según la (...) cual el tiempo como número puede existir independientemente del alma. Luego, muestro que la numerabilidad del tiempo impide su independencia respecto del alma, a diferencia de lo que ocurre con ‘lo sensible’. (shrink)

Aristotle’s most fundamental distinction between changes and other activities is not that ofMetaphysicsΘ.6, between end-exclusive and end-inclusive activities, but one implicit inPhysics3.1’s definition of change, between the activity of something incomplete and the activity of something complete. Notably, only the latter distinction can account for Aristotle’s view, inPhysics3.3, that ‘agency’—effecting change in something, e.g. teaching—does not qualify strictly as a change. This distinction informsDe Anima2.5 and imparts unity to Aristotle’s extended treatment of change inPhysics3.1-3.

The twelfth century philosopher-theologian Fakhr al-Dīn al-Rāzī is well known for his critique of Avicennan metaphysics. In this paper, I examine his critique of Avicenna's physics, and in particular his rejection of the Avicennan and Aristotelian theory of place as the inner boundary of a containing body. Instead, Fakhr al-Dīn defends a definition of place as self-subsisting extension, an idea explicitly rejected by Aristotle and Avicenna after him. Especially in his late work, theMaṭālib, Fakhr al-Dīn explores a number of important (...) philosophical issues with reference to this theory of place, including the principle that two indiscernible things must be identical and the idea that motion and rest are always relative.RésuméLe philosophe-théologien du XIIesiècle Fakhr al-Dīn al-Rāzī est bien connu pour sa critique de la métaphysique avicennienne. Nous examinons, dans cet article, sa critique de la physique d'Avicenne, et en particulier son rejet de la théorie avicennienne et aristotélicienne du lieu – lieu comme limite interne du corps englobant. Alternativement, Fakhr al-Dīn défend une théorie du lieu comme extension auto-subsistante, doctrine explicitement révoquée par Aristote et Avicenne à sa suite. En particulier dans son œuvre tardive, lesMaṭālib, Fakhr al-Dīn explore plusieurs questions philosophiques importantes en rapport avec cette théorie du lieu, dont: le principe voulant que deux choses indiscernables soient identiques, et l'idée selon laquelle mouvement et repos sont toujours relatifs. (shrink)

Despite the language we saw in the previous chapter, which allowed for time apprehension by perception and marking, in Physics iv 14, Aristotle famously argues that time is dependent on nous.

The problem of time has been present throughout history of philosophy since its beginnings. However to consider what is time is not a matter of technical theorization, conversely, this results interesting in as much as a reflection on the nature of world, and even the human particularities, cannot evade time problem. Aristotle is a stage under obligation in history of philosophy. My main purpose is to understand why time is problematic and what difficulties we have to meet with (chapter one). (...) On the other hand, I'm interested in the way Aristotle give an account of these difficulties in virtue of the relation among movement or change, magnitude and time, as well as the latter character of number (chapters two and three). Finally, is necessary to present some subsequent problems related with the time theory at stake (chapter four). (shrink)