We spend our lives at learning things, yet always find exceptions and mistakes. Certainty seems always out of reach. This means that we have to take some risks to keep from being paralyzed by cowardice. But to keep from having accidents, we must accumulate two complementary types of knowledge:
We search for islands of consistency within which ordinary reasoning seems safe. We work also to find and mark the unsafe boundaries of those domains.
In civilized communities, appointed guardians post signs to warn about sharp turns, thin ice, and animals that bite. And so do our philosophers, when they report to us their paradoxical discoveries — those tales of the Liar who admits to lying and the Barber who shaves all the people who do not shave themselves. These valuable lessons teach us which thoughts we shouldn't think; they are the intellectual counterparts to Freud's emotion censors. It is interesting how frequently we find paradoxical nonsense to be funny, and when we come to the section on jokes, we'll see why this is so. When we look closely, we find that most jokes are concerned with taboos, injuries, and other ways of coming to harm — and logical absurdities can also lead to harm.
We tell our children not to cross the road unless they are sure no car is coming. But what do we mean by sure? No one can ever really prove that no car is coming, since there is no way to rule out the possibility that some mad scientist has found a way to make cars invisible. In ordinary life we have to deal with usual instead of true. All we can really ask a child to do is look both ways before you cross. In the real world, it makes no sense to ask for absolute certainty.
Unfortunately there are no simple, foolproof ways to get around the inconsistencies of common sense. Accordingly, we each must learn specific ways to keep from various mistakes. Why can't we do that logically? The answer is that perfect logic rarely works. One difficulty is finding foolproof rules for reasoning. But the more serious problem is that of finding foolproof bases for our arguments. It is virtually impossible to state any facts about the real world that actually are always true. We observed this when we discussed Birds can Fly. This statement applies to typical birds, but not to birds imprisoned in small cages, chained with leg irons, or under the influence of high-gravity fields. Similarly, when you're told, Rover is a dog, you'll assume that Rover has a tail, since your frame for a typical dog has a terminal for a tail. But should you learn that Rover lacks a tail, your mind won't self-destruct; instead, you'll change your Rover-frame — but still expect most other dogs to keep their tails.
Exceptions are a fact of life because few facts are always true. Logic fails because it tries to find exceptions to this rule.