Here’s the problem:
If a puzzling chain of reasoning is to take our attention it must point to a problem about the world. Paradoxes, dilemmas, and antinomies are among those puzzling arguments about the world that most attract our attention. However, if any paradox, dilemma, or antinomy were to be true of the world, it would stop. We know, however, that the world doesn’t stop. Thus, paradoxes, dilemmas, and antinomies must not be true about the world. If they are true at all they are true about something else. But then, paradoxes, dilemmas, and antinomies are not interesting chains of reasoning that bring our attention to potential problems in the world. They could be discharged (as many students usually do) on the basis of irrelevance, ridicule, and even stupidity. Yet, most of the development in science (if not all through its history) is the result of tackling a puzzling chain of reasoning such as a paradox, a dilemma, or an antinomy. It follows then that puzzling chains of reasoning (such as paradoxes, dilemmas and antinomies) cannot be true about the world (for it would stop), but we still can help it and go on and solve them, or die trying.
Here’s a proposal:
Puzzling chains of reasoning such as paradoxes, dilemmas, and antinomies are second level arguments that are true about our own mental states. These puzzling arguments result from the revision of our beliefs about the world, they give us a map of our own representation of the world, they tell us where the map has gone astray, or where it has come to a halt without hints of where to go or how to move. As a matter of fact, this is attractive enough for us to realize that something is wrong with the map.
And, here’s the important claim:
All this map problems could be equally dismissed if they were not to play a central role. Our representation of the world is not something independent, external, or separate from the world. Knowledge, belief and all the other mental states are, also, the world. They are part of what goes on in the environment. So, in a very strong and direct sense puzzling chains of reasoning are in fact true about the world. And the world does stop. Not, perhaps, the trees, rivers and oceans. But the world that faces the paradox, dilemma, or antinomy; the mind just can’t keep going on.
By solving paradoxes we are, in fact, helping the world go round and round.