What's Aristotle to do without inertia?

Let's start looking at the reductio ad absurdum (which I explained in my last post) with Aristotle, since he liberally uses it as a logical technique not always most carefully. Aristotle is a careful thinker, but with the shear quantity of arguments he made in his dense body of surviving works there's bound to be more than a few stinkers. Now that the Large Hadron Collider has been recently started up, in commemoration of the fact that the earth has not been swallowed into nonexistence, let's talk about some of Aristotle's physics. This is a particularly good topic as well, since it is one place where Aristotle makes some of his notoriously odd conclusions.

One problem that Aristotle deals with in his physics is the conservation of motion. Undoubtedly it happened - all types of projectiles were thrown in warfare in the Olympics and just in the everyday fun of throwing stones at your friends to harass them - but how did it retain its motion after it left the hand or bowstring or whatever? Without the concept of inertia this could be a puzzling problem. Aristotle, brings up this problem in his discussion of the void, which he rejects for a number of reason. In this discussion, in Book IV.8 (215a14-19, he thinks that there can be only two possibilities, that either 1) the thrown object causes some sort of cyclonic motion, whereby it displaces air in front of it, and it circles behind it and pushes it forward or 2) the the thrown object pushes forward a column of air in front of it at a greater speed, and the column of air drags the arrow behind it. The second one seems completely implausible since it still demands explanation of how the column of air continues in motion, which is good reason to reject it and accept (1). But ultimately, it's silly to imagine that these are the only two possibilities.

In fact, his explanation of how a thing keeps moving seems to contradict his argument that a void is impossible because objects would move within it at infinite speed (215b1-216a8). He basically says that the speed of an object is equal to force divided by the resistance of the medium (f/r). This first of all doesn't make sense, since if this cyclonic motion were pushing the object, the increased resistance in front would be more than made up by increased push from behind, meaning objects would move equally fast through all mediums (which contradicts experience). But Aristotle argues that a void is impossible because it would offer no resistance, making r=0, producing f/0, which equals infinity. This doesn't follow because one would only have to make a small adjustment in the formula (eg. f/(r+c) where c is a positive number) to avoid infinities and still agree with empirical observation (and yes, I know the Greeks didn't use algebra, but it's so much easier to use to explain to contemporary audiences. One could easily express it geometrically too).

In short, this is the best argument for the nature of motion that Aristotle could make.