國立清華大學哲學研究所 專任助理教授 陳斐婷 西方思想經典：亞里斯多德《物理學》 國立清華大學哲學研究所 專任助理教授 陳斐婷

Aristotelian Teleology

Standard Objections to Teleology “Why not suppose that nature acts not for something or because it is better, but of necessity? Zeus’ rain does not fall in order to make the grain grow, but of necessity. For it is necessary that what has been drawn up is cooled, and that what has been cooled and become water comes down, and it is coincidental that this makes the grain grow.” (Physics 2.8, 198b17-21) “Why not suppose, then, that the same is true of the parts of natural organisms? On this view, it is of necessity that, for example, the front teeth grow sharp and well adapted for biting, and the back ones broad and useful for chewing food; this <useful> result was coincidental, not what they were for. The same will be true of all the other parts that seem to be for something.” (Physics 2.8, 198b23-28)

Aristotle’s Reply “This argument, then, and other like it, might puzzle someone. In fact, however, it is impossible for things to be like this. For these <teeth and other parts> and all natural things come to be as they do either always or usually, whereas no result of luck or chance comes to be either always or usually.” (Physics 2.8, 198b33-36) (1) Natural things exhibit great regularity. (2) But chance by definition involves an absence of regularity.

Aristotle’s Reply “If these seem either to be coincidental results or to be for something, and they cannot be coincidental or chance results, they are for something.” (Physics 2.8, 199a4-5) (3) Regularities are either coincidental results or for something. (4) But what happens regularly cannot be a matter of coincidence or chance. (following from 1, 2, 3)

Aristotle’s Argument (1) Natural things exhibit great regularity. (2) But chance by definition involves an absence of regularity. (3) Regularities are either coincidental results or for something. (4) But what happens regularly cannot be a matter of coincidence or chance. (following from (1), (2), (3)) (5) Therefore what happens regularly must be for something.

Further Challenges: Challenge of Agency If we notice that our neighbor always wears a suit and takes the car to work on Mondays and Wednesdays, but wears a sports jacket and cycles on every other day, we suppose there to be some reason for this. ARISTOTLE’S REPLY. Against this Aristotle argues that final explanation does not require deliberation. The absence of deliberation in nature does not prove an absence of final explanation, because (according to Aristotle) after all a craftsman need not deliberate about what the product is produced for.

Challenge of Mechanical Necessity But on other occasions we may speak of mechanical necessity, implying that what always happens in the same way—in accordance with natural laws—is precisely not designed or intended for a purpose. ARISTOTLE’S REPLY. Discovering what the organ or the activity is for is more than discovering mechanical regularity. It involves discovering the connection between this organ or activity and what other parts do, and how they all contribute to the whole life of the animal.

First Challenge to the Purpose of Life In an animal we select from the regularities that contribute to the preservation of the animal, and say that they are for something, serve a purpose. But many other regularities seem to be simply law-governed chemical or physical processes that may serve no purpose. ARISTOTLE’S REPLY. Two kinds of non-purposive regularities: (1) purposive regularities still require some non-purposive or pre-purposive regularities. (2) some non-purposive regularities may be seen as accidental concomitants or results of purposive regularities.

Challenge Two to the Purpose of Life Granted that we can explain the function of some part or activity by reference to the preservation of the whole animal, does it make sense to speak of the function of the animal as a whole? Does it and its life serve a purpose? ARISTOTLE’S REPLY Step One: By insisting that the individual dog is a member of the species dog Aristotle provides something beyond the individual that the individual life does help to preserve. The point of a dog’s life is to maintain the species, living a canine life and bringing on a new generation. But why are dogs programmed to maintain their species? Step Two: Aristotle sees every kind of thing in the universe as imitating in its own way the changeless activity of god: the stars do so by constant circular motion, animals by maintaining themselves and their species, elements (fire, air, water, earth). Everything that happens in the universe strive toward something unchanging and eternal.

Aristotle’s Challenge to Absolute Necessity “Is what is necessary, necessary on hypothesis, or can it also be unconditionally necessary? People suppose that there is necessity in what comes to be, as a man might think that a city wall had come to be necessarily, because heavy things are by nature such as to sink down, and light things such as to rise to the surface—which is why the stones and foundations go down, the earth goes above them because it is lighter…” Unconditional necessity E.g., From bricks and stones a house necessarily follows. Hypothetical necessity (with telos) E.g., From bricks and stones a house necessarily follows if a house is to be produced. “It is necessary for a thing to be made of iron, if it is to be a saw, and do its work. So it is on some hypothesis that the necessary is necessary… For the necessity is in the matter, the final explanation is in the form.”

Aristotle on magnitude

Introduction Aristotle characterizes physics or “the science of nature” as pertaining to magnitudes, motion, and time (Phys. 3.4, 202b30-1). Indeed, the Physics is largely concerned with an analysis of motion, particularly local motion, and the other concepts that Aristotle believes are requisite to that analysis. K. Algra has usefully distinguished three function that a concept of space may fulfill within a physical theory: (a) a kind of prime stuff or reservoir of physical possibilities, (b) a framework of (relative) locations, and (c) a container, the fixed stage where things play our their comedy, a space in which things are and through which they can move, to paraphrase Epicurus (Algra 1995: 15-16).

Magnitude Aristotle clearly rejects one version of function (a) and one version of function (c). A conception of space that is a kind of prime stuff or reservoir of possibilities (such as that of Plato’s receptacle in the Timaeus) is rejected by Aristotle in favor of his conception of matter. And he also certainly does not accept a conception of space (like the atomists’ void) as having its own substantial ontological status, which could serve as a container for bodies and their local motions. Note that function (a) and (c) both identify space with extension (Algra 1995: 18). Although Aristotle rejects the versions of (a) and (c) that are mentioned above, he does employ an important notion of extension, which has what might be termed spatial characteristics. This is his conception of μέγεθος (magnitude).

Discrete quantity and continuous quantity In Categories 6 Aristotle distinguishes discrete quantity (πόσον) from continuous quantity (συνεχές). He includes lines, surfaces, bodies, time, and place in the latter. In Metaphysics 5.13, Aristotle also distinguishes quantity that is continuous from that which is non-continuous. A magnitude, he says, is quantity that is measurable (as opposed to numerable or countable), and a magnitude is divisible into parts that are continuous (1020a7-11). Among magnitudes, “that which is continuous in one [dimension] is length, that in two breadth, and that in three depth…Limited (or finite) length is a line, limited breadth a surface, and limited depth body” (1020a11-14).

Continuity and contiguity In many Euclidean constructions a principle of continuity of geometrical magnitude is assumed: it guarantees the existence of points at the intersection of two lines, the existence of lines at the intersection of two surfaces or planes, etc. In Physics 5.3, having stipulated that “something is contiguous (ἐχόμενον) [to something] that is successive to and touches it” (227a6), Aristotle proceeds as follows: I say that something is continuous, which is a kind of being contiguous, whenever the limit of both things at which they touch becomes one and the same and, as the word implies, they are stuck together (συνέχεται). But this is not possible if the extremities are two. It is clear from this definition that continuity pertains to those things from which there naturally results a sort of unity in virtue of their contact. (Physics 5.3, 227a10-15)

Continuity and infinity In Physics 6.1 “it is impossible that what is continuous be composed of indivisibles, e.g., a line from points” (231a24-5). So there is always a line segment between any two points (231ab9). In Physics 3.7 “what is continuous is in each case divisible to infinity (207b16-17). In Physics 6.2 “I shall call continuous that which is in each case divisible to [parts] that are continuous” (232b24-25). “Each partition of a continuous magnitude into proper parts yields parts each of which is pairwise continuous magnitudes of the same dimension ad infinitum.” (Michael J. White 1992: 29) Physics 3.4-8 on infinity There is no actual infinity. There are neither infinitely large objects nor an infinite number of objects. However, there are potential infinities in the sense that, for example, an immortal god could theoretically sit down and count up to an infinitely large number but that this is impossible in practice.

Aristotle on place

Beginning of Physics 4 Aristotle begins Physics 4 with the claim that natural philosopher must acquire knowledge of place, for two reasons: (1) “Everyone assumes that the things that exist are somewhere. But what does not exist is nowhere.” (208a29-31) (2) “The most general and proper kind of motion is motion with respect to place, which we call locomotion.” (208a31-32) In Physics 4.1 Aristotle proceeds to distinguish, as the kinds and parts of place, the six directions of left, right, back , front, up and down at its center—and he identifies (at least some of) these places as the natural places of the four basic elements, each being a place where an element will go if not impeded and thus having a kind of power (208b8-22). There is then, a positional function for Aristotle’s conception of place. The emphasis is on the role of place in local motion.

Criteria for an adequate conception of place “It is necessary to recognize that place would not be investigated if there were not motion with respect to place (Phys. 4.4, 211a12-13). In the same chapter Aristotle lists the criteria for an adequate conception of place: We hypothesize (1) first that place contains that of which it is the place and that it is not [a part] of that thing. (2) Further, that a primary or first place is neither smaller nor larger [than the thing]. (3) And further, that it can be left behind [by the thing] and is separable [from it]. In addition to these requirements, (4) that every place admits of up and down and that each of the [elementary] bodies is carried to and remains in its proper place and that this is what makes [a place] either up or down. (Physics 4.4, 210b34-211a6)

Aristotle dismisses the form and the matter Aristotle lists four potential candidates for a conception of place that satisfy the above criteria: “The form [of the body having a place], the matter, some sort of extension between the extremities [of the body], or the extremities if there does not exist an extension in addition to the magnitude of the body that comes to be in the place in question.” (Phys. 4.4, 211b7-9) The first three candidates Aristotle quickly dismisses. Form and matter belong to a body in such a way that the body cannot leave behind one place and enter another, as is required for locomotion. Form, understood as shape, might seem to be place, since “the extremities of what surrounds and of what is surrounded are in the same [locus]? Both [shape and place] are boundaries, but not of the same thing: form/shape is the boundary of the thing, while place is the boundary of the surrounding body.” (Phys. 4.4, 211b11-14) Aristotle here hints at his final account of place.

Aristotle dismisses the extension Aristotle dismisses the third account of place as the extension coincident with the bulk of a body and confined by the extremities or shape of the body. What he seems to have in mind is a three dimensional extension that is distinct from but positionally coincident with the three-dimensional magnitude of the body itself; being distinct from the body, it can be left behind by the body when the body moves (changes place). If place is a three-dimensional entity that is separate from the three-dimensional body that it contains, would require its own separate place etc. ad infinitum.

The account of place Aristotle accepts a specification of the fourth candidate: “place is the primary unmoveable boundary of that which surrounds [a body having a place] (Phys. 4.4, 212a20-21). He adds, “a place seems to be a sort of surface and, as it were, a vessel and container” (Phys. 4.4, 212a28-29) THE STANDARD INTERPRETATION: the place of a body is the primary (two-dimensional) surface of the stationary surrounding bodyor “physical matrix or medium” containing the body; this surface of the surrounding maxtrix would by topologically coincident with but formally distinct from the (two-dimensional) shape or surface of the body itself. (Michael White, 2009, 270) This conception fits Aristotle’s criteria: (1) place so defined contains the body whose place it is; (2) it is neither larger nor smaller than that body, and (3) it is left behind when the body moves and is separable from the body.

Problems of the account of place The problematic aspects of this account of place are, however, well known: (1) Things that are not three-dimensional physical objects (e.g., points, lines, surfaces) would not seem to have their own proper places. (2) It is not clear that things contained in moving or moveable vessel and matrices (e.g., olive oil in a jar or a boat in a flowing river) could have proper places. (3) It is not clear that Aristotle’s account of place, as standardly interpreted, can satisfy the final criterion in Aristotle’s list.