ZENO'S ARROW: One of the best known of the paradoxes with which a whole contingent of early Greek logicians liked to amuse themselves; this one illustrated the impossibility of motion or change. The flight of an arrow, said Zeno, is an apparent example of motion. But at any given moment of its flight, the arrow is either where it is or where it is not. If it moves where it is, it must be standing still, and if it moves where it is not, then it can't be there; thus it can't move. This sort of thing drove Zeno's friends crazy, of course, concerned with reconciling the basic features of permanence and change. It also gave rise to a vast literature that set about trying to prove, disprove, or avoid Zeno's conclusions. In fact, you could probably still get a lively dinnertable conversation going on the suject today, given the right crowd and plenty to drink.
PLATO'S CAVE: The famous allegory with which Plato, using Socrates as his mouthpiece, tries to explain the nature of human knowledge. Picture, says Socrates, a bunch of people who've spent their whole lives chained up in an underground den, unable to turn around. Behind them a fire is blazing, but all they can see are their own shadows on the wall of the cave in front of them. Never having seen anything else, they naturally mistake these shadows for reality. In the same way, the rest of us mistake the world as we know it for the real world, whereas the objects, and even the qualilities, of this world are only shadows of the pure forms that exist in the realm of ideas. Now, what does this mean for you? It means, for example, that somewhere above us in that realm of forms and ideas, there is one, and only one, perfect automobile, of which the lemon you've been driving is merely a crude imitation (you probably suspected something of the sort already). By training your mind to contemplate the idea of the perfect driving machine rather than the expensive heap of scrape metal in your driveway, you can eventually struggle up out of the cave into the sunlight where you'll see the car with perfect clarity. True, you will be confined to driving the idea of the car on the idea of a highway, but Plato never claimed that being a philosopher was easy,and at least you can be pretty certain you'll never encounter much traffic in the realm of ideas.
BURIDAN'S ASS: A famous stumbling block to the concept of free will. An ass, placed equidistant from two identical bundles of hay, has no basis for choosing one over the other and ends up starving to death. Although it was first suggested by Aristotle in connection with astronomy, the image is traditionally attributed to the medieval French philosopher Jacques Buridan, who claimed that a man must choose that which his reason tells him is the greater good, but that he may delay making a decision until his reason has had sufficient time to gather all the information it needs. Actually, it's a starving dog that Buridan refers to; the ass was his critics' idea.
OCCAM'S RAZOR: "Entities ought not to be multiplied, except from necessity." The maxim for which William of Occam, the Franciscan scholar, is best remembered. Actually, Occam never really said this, but he did say, "It is vain to do with more what what can be done with fewer," which adds up to the same thing; moreover, he did uphold the principle of eliminating all unnecessary facts or hypothetical entities in analying a subject, and he did dissect every question as if with a razor.
PASCAL"S WAGER: The pragmatic approach to God, and Pascal's attempt to save the skeptical soul through common sense reasoning. Basically, his argument goes: OK, so you'll never know for sure whether or not God exists, it's all a cosmic game of heads or tails. But you have everything to gain and nothing to lose by betting on his existance. Remember, you're only staking one finite, so-so little life -- no, not even that, only the way you live that life -- against chance to win an infinity of an infinitely happy life. If you win (if God exists), you've won everything; if you lose (if God doesn't exist), you haven't really lost a thing. And don't say you'd rather not play, because you have no choice; you're already in the game.
