Zeno's Paradoxes and the Republican Problem of Principle

Brian Palmer over at Slate wrote an article this week explaining how Zeno's Paradox of Achilles and the Tortoise works. It got me thinking of how people usually react to the story when they first hear it--I've taught this paradox to college students in Montreal almost every semester since 2006 as a brief introduction to the Eleatic school of philosophy. I'll let Palmer summarize the story:

My students (most of them are not philosophy majors) generally react with a quizzical, unreflective, "That's stupid!" And it is stupid; that's Zeno's point, which is what I try to teach them. The paradox presents a fundamental contradiction between the mathematical principle at play (the infinite divisibility of a line) and reality (we all know that Homer's "swift runner" will win). But that is not all--Zeno's paradoxes are not just brain teasers. Rather, Zeno is trying to demonstrate that, when there is a contradiction between principle and reality, there is something wrong. It is not necessarily the case that the principle is wrong (a geometric line is, indeed, infinitely divisible), but, at the very least, it must be recognized that the principle does not apply in this particular case (actual distances are contiguous, not continuous, like geometric lines). Now, Zeno's specific point was the irrationality of all motion and change, as Palmer notes; more broadly speaking he is suggesting that the principles of mathematics do not apply to motion, and since mathematics are the foundation of rationality, motion and change are irrational. This principle does not apply here.

The current crop of Republican presidential front-runners all present themselves as men of principle, whether the issue is gay marriage, gun control, entitlements, what-have-you. But it is becoming clear that they don't understand the point Zeno made more than two millennia ago. Take the idea of cutting government assistance to the poor spelled out in the Ryan budget. The principle is that government assistance disincentivizes looking for work. The principle makes sense in the abstract--if you receive money without working, why would you bother to work. However, studies show that that is simply not how assistance plays out in reality. The so-called welfare trap is virtually non-existent.

There is nothing wrong with being a "man of principle". Indeed, principles are necessary to guide human action in an unpredictable world (some theories suggest human consciousness evolved precisely because we cannot predict every possible outcome of our behavior in an environment we do not control). Nevertheless, it is important to understand how principles arise. Principles of the sort at play in politics, economics, psychology and the like (as opposed to a priori principles, which play a role in purely theoretical disciplines) are derived from experience (through induction and statistical reasoning). What this means is that you cannot be a "man of principle" while ignoring experience--the experience of people on food stamps, or unemployment insurance, for example. And I don't mean experience in the sense of anecdote (though it never hurts to walk a mile in the shoes of another to understand his or her world). An economist or politician who ignores case studies, statistics, evidence provided by sociologists and bean counters, is not a "man of principle"--indeed, he can have no principle.