More notes on Physics Beta (B)


Chapter 2. Comparison between what the Greeks called "physics" and some other related areas of investigation: "mathematics", "astronomy", "harmonics", "optics".

a. Here are some general characterizations of what the Greeks took these areas of investigation to include and to study. That is, these characterizations are not unique to Aristotle.

Recall that 'physics', 'phusike', refers to the study (and hopefully to the knowledge) of phusis. 'Phusis', usually translated as 'nature', means "that which grows and changes", or "everything that exhibits growth or change". Motion would be included under change.

'Mathematics', 'mathematike', included arithmetic, geometry, and to some extent number theory. That is, it studied numbers, ideal shapes (e.g. not observable things that appear circular, but perfect circles, the kind whose curves are made up of points that have no thickness), and their properties.

'Astronomy', 'astrologia', studied the apparent motions of the sun, moon, stars, and planets. There was no way to investigate systematically what the celestial bodies were made of, how far away they were, how they formed, and so on. What astronomy studied, then, were the paths that stars followed in the sky over an evening or through the year; the angles at which celestial bodies rose and set with respect to the horizon; the angles and curves formed between the paths of stars and planets; etc. - in other words, astronomy studied mathematical relationships pertainng to the apparent paths and periods of celestial objects. Astronomy used mathematical methods to study a certain set of angles, lines, and curves, namely those formed by the apparent motions of observable objects in the sky.

'Harmonics', ‘harmonike', studied musical relationships, generally relationships between pitches or tones. The Pythagoreans had discovered that the relationship between any two pitches is proportional to the ratio between the lengths of the strings (on a stringed instrument such as a lyre) or the lengths of the open parts of the bore (on a wind instrument such as a flute). Thus harmonic relationships could be expressed numerically, and harmonics studied relationships between those number combinations that were relevant to each musical mode or scale that was in use.

'Optics', ‘optike', studied things like what happened to beams of light when they passed through prisms or water, what happened to images reflected in metal or water, and so on. For example, if you submerge half of a straight object in a pool of water, the object will appear to be bent or angled, and its length will appear to change. Optics studied the angles and proportions that are observed in such phenomena.
It therefore appears that mathematics, physics, and astronomy all studied something about the movements of the celestial bodies in the sky. Mathematics studied the circular or elliptical paths traced by the stars, e.g., in their ideal forms; and mathematics developed theorems about these curves not in themselves but in so far as they are members of larger classes of curves. Also, even if mathematics studied an ellipse that was traced by the apparent movement of a star through the sky, it did not deal with time or change as such. Mathematics studied only the eternally stable ellipse, not the motion of the star tracing the elliptical path.Astronomy used mathematical methods, theorems, etc. to study the curves traced by stars - specifically these curves, not all related curves. Physics studied the motions as motions, not (or not only) as that which happens to generate certain curves. At 193b25-30, Aristotle notes that physics also seems to discuss what the Sun and Moon are, what their shapes are, and whether the Earth and the universe are spherical or not.

If mathematics looks at this question of sphericality, it does not look at it with respect to the fact that the shapes involved are shapes of visible and to some extent tangible bodies; mathematics is interested instead in properties of spheres as such, not in where those spheres may or may not be found. Physics, astronomy, optics, and harmonics, are interested not in lines, angles, curves, and numbers as such, but in lines, angles, curves, and numbers in so far as they are found in or expressive of things that move, or movements. The concerns of physics go beyond those of astronomy, harmonics, and optics in that physics studies further issues pertaining to mobile (or movable), changing (or mutable) things as such.


b. Physics, if it is to be like "other" arts*, will involve the study of both the "matter" (the stuff out of which things are composed or made up or constituted) and the "form" (the arrangement, order, form, or shape that things have). That is, it will not look only at the geometric forms of things and their movements, nor only at the ratios of size, weight, speed, etc. that might appear, nor only at the composition of the movable things involved; but at all of these.

Physics will also study that for the sake of which things move or change, for in a way this is "nature" too (194a30); and will study whatever is needed for this "final cause" to be in effect. "Nature" can be an "end" or that for the sake of which things happen or are the way they are in something like the following way. If something is in continuous motion, A. says, and if there is some end to that motion, this end is the "final cause" (194a30). "Nature" would seem to have to be taken to be continuously moving, not in the sense that everything in nature must necessarily be considered to be in motion at all times, but in the sense that at any given point some thing in nature must be taken to be moving, if there is to be "nature" (that which grows and changes) at all. Why? For one thing, if all motion were to stop, there would cease to be any "nature" (that which grows and changes) at all: nothing would be growing or changing. Secondly, if motion(s) in nature were to be discontinuous, it would seem that we could not trace or identify sources of motion (not necessarily a problem unless you want knowledge of causes and principles to be possible).


What then would the "end" or "aim" of motion and change be? From what we have seen, we could not coherently identify this as the finishing-point of "nature". But it could be something like the order that exists, or the direction that "nature" takes (which may not have an endpoint), or the way in which that which has a principle of motion and standstill develops and interacts. In that way, "nature" itself could be said to be that for the sake of which movement and change go on.

This conception invokes the notion of things taking particular forms and not other ones. The study of these forms, as was noted above, will be part of physics. But, A. warns, the physicist will only study form or "whatness" (what it is to be something) up to a point (see footnote * in this outline). The physicist will study what it is to be certain things, and will look at the role of form in the things that have principles of motion, etc.; but he/she will not investigate just what form itself is and how or in what sense it exists. (Don't worry--we get to look at this and many other equally fabulous questions in the Metaphysics!)

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* It may be asked whether physics really is an "art" (techne), or whether it is really known to be one. Certainly it is not a "productive" art, an art such as farming or carpentry, whose main concern is producing things; nor is it evidently an art like music, whose aims are pleasure,diversion, the fulfillment of social or religious goals, or some combination of these. The Greeks acknowledged other kinds of things as arts, though, including so-called "non-productive" arts such as mathematics and astronomy, arts that were thought not to aim, or not necessarily to aim, at producing things in the sense of bringing new objects into the world. What all the kinds of arts had in common, and what distinguished even the "productive" arts from methods of production that do not involve "art", was supposed to be that "having an art" involved some degree of knowledge of how the things treated by that art work, and that "having an art" involved knowing something about why certain things happen. "Art", that is, was supposed to involve knowing "causes" and "principles", at least to some extent. A person who had an art would not in general be expected to know first causes and principles (though there may have been some confusion about this; see Metaphysics A1-2), but he or she would be expected to know (i.e. to be able to give a convincing explanation that had some predictive success...) something about why things happen. For example, a farmer would not be expected to have demonstrable knowledge of why plants exist or of what the ultimate nature of the sun is (these would have to do with first causes and principles, ultimate reasons and sources for that which exists), but he or she would be expected to be able to give an account of the growth of particular plants that correlated quantity and quality of sunlight with some aspect of each kind of plant so as to explain (give an account that had predictive success regarding) what sort of light to give each in order to assure that it grew in the desired way.

One could reasonably ask whether a farmer who gave such an account but who could not explain why it was true really knows what makes plants grow, or whether he/she should be said to have "knowledge" in the strong sense (episteme). After all, if knowing the "why" of things is needed in order for one to have understanding and to have knowledge that was real (i.e. not something mistaken or unclear that one merely believes to be knowledge), as Aristotle reports that his contemporaries believed (Metaphysics A1-2, Physics A1), then it would seem that one would need to know "first causes and principles" in order to have (and to be assured of having) knowledge of anything. No one was actually found to have such knowledge, and it's not clear that anyone could be shown to be qualified to judge whether anyone had this knowledge (see Plato's Apology of Socrates, Theaetetus, Sophist, Gorgias, and Protagoras, as well as Aristotle's Metaphysics A, for some investigation of this). Then, exactly what was it that those who "had art" had, what was its relation to demonstrable knowledge, and how can we tell? This problem had been noticed by Aristotle's time, for example by Protagoras, Gorgias, Socrates, and Plato; and conceivably by Heracleitus, Parmenides, and Zeno.

If physics turns out to be an "art", if it involves such apparent or purported knowledge of causes and principles, it would seem to be susceptible to the same questions and problems as the "other" arts, as outlined here.


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