Aristotle's natural motion and modern inertial motion

Last week, in my history of science class, we finished the unit on ancient science and medicine. At the end of the unit, I asked my students the (ill-posed) question: so is any of this stuff we've been reading science or not? (We read Plato's Timaeus, Aristotle's Physics II and On the Heavens, Ptolemy's Almagest, and bits of Epicurus as well as Hippocratic writers.)

One sentiment that came to the fore was that the ancients were (on average) more willing to countenance teleological explanations in natural sciences than we are. I think this is definitely right on the whole. But I did want to ask a question about an example sometimes forwarded in defense of this claim. Aristotle says that part of what makes the element earth earth is its tendency to move towards the center of the universe (since Aristotle thought the planet Earth was at rest in the center of the universe). Air and fire move away from the center of the universe, and the celestial matter moves in a circle around the center. These 'natural motions' are taken to appeal to final causes in a way that modern science does not: water and earth have a 'goal' or 'end' (Greek telos), viz., the center of the universe. And (so the story goes) matter from the Early Modern period onwards, starting with Descartes at the latest, is not like that at all.

I, unfortunately, cannot make out a substantive difference here -- we can describe Aristotle and the moderns in the same terms: we can make Aristotle sound more modern, or make Newton et al. sound more teleological. In the modern dynamical picture, we have inertial motion: a body in motion will maintain that motion (speed and direction), unless acted upon by an outside force. If the telos of an Aristotelian hunk of earth is the center of the universe, the telos of a modern bit of matter is (something like) self-preservation. Its goal is resistance to change (of direction and speed).

Alternatively, we can characterize Aristotle as more modern: Aristotle is describing what happens to a bit of fire or water if it's just "left alone," i.e., what does a body do when it is free of any interference? Aristotle clearly disagrees with the moderns about what a body does when "left alone"... but Einstein disagreed with Newtonians over the same issue. In other words, we can think of the difference (on this topic) between Aristotle and the moderns as a disagreement over which trajectories are the ones bodies will follow when no external forces act upon them. Teleology doesn't appear here at all.

Of course, I could be overlooking something obvious in the Aristotelian text. Hopefully any real Aristotle scholars out there reading this will tell me if I have. If you want to check the text of On the Heavens for yourself, it’s online here.

The reasonable effectiveness of mathematics... for Ptolemy

The class I am teaching this term covers the emergence of Early Modern philosophy and science. The first five weeks are devoted to a whirlwind tour of Ancient Greek natural philosophy (plus a bit of Renaissance thought), and the last 10 weeks cover 17th century philosophy and the scientific revolution.

We spent half of the past week discussing Ptolemy, and I was struck by something that I had noticed before, but never really appreciated. It is very natural for Ptolemy to use fully 'mathematized' explanations for astronomical phenomena, but not for (most) other physical processes. Why? On Ptolemy's view, astronomical objects share more properties with mathematical objects than they do with terrestrial objects. He thought that astronomical objects are eternal and their properties are unchanging -- like the number 5, but unlike terrestial ones. We give a mathematical treatment of astronomical phenomena because they exhibit properties of mathematical objects.

The application of mathematical methods in Ptolemaic astronomy helps bring into focus the so-called problem of the unreasonable effectiveness of mathematics, which some days appears to me to be an unequivocal pseudo-problem. Ptolemy's application of mathematics to physical phenomena, I think, appears extremely well-justified compared to our own: astronomical phenomena can be mathematized because they share peculiar features with mathematical objects, features that the mundane, material objects in our immediate surroundings lack. During and after the scientific revolution, we preserved and expanded Ptolemy's mathematizing proclivities, but we apparently relinquished his justification for treating the natural world mathematically.

Update (10/02/05): Kenny over at Antimeta just put up an interesting post on the (un)reasonable effectiveness of mathematics too, and it is in (small) part a comment on my post.