Book Review : Highways and Byways of the Mind

Labyrinths of Reason: Paradox, Puzzles and the Frailty of Knowledge by William Poundstone (Doubleday: $18.95; 274 pages)

I wish I knew why I continue to be fascinated by philosophy, particularly in questions of knowledge, such as: How do we know what we know? When is something proved? Are there limits to what we can know? What are they?

Like many philosophical questions, these matters have been thought about for millennia, and, sadly, we are no closer to the answers today than the ancient Greeks were.

One intriguing question is why we think about these things at all. What quirk of mind brings us back to these same puzzling and insoluble dilemmas that are largely irrelevant to everyday life? Why all the razzmatazz?


After all, there are no philosophers on the freeway. No one thinks twice about whether the cars are really there or what the consequences of hitting one will be. Faith in our senses guides us through most things we do. Why not carry it into all realms and stop worrying about how we can be sure and related conundrums?

No harm if you do, but in the 20th Century, the questions themselves have been sharpened, and the ambiguity of the answers is also more clearly understood.

Things We’ll Never Know

“We don’t see everything, not even everything implicit in our experience,” William Poundstone concludes at one point in “Labyrinths of Reason,” his exceptionally good, crystal-clear survey of the limits of knowledge. “There are things going on out there that we will never appreciate.”


Starting with simple paradoxes and puzzles, Poundstone shows how the ambiguities and unanswerable questions of reason do not simply go away if you ignore them. Swept under the rug, they accumulate there until they are a noticeable bulge, affecting questions about the nature of meaning and mind itself.

Can you think of a common English word that begins and ends with the letters UND?

How do you go about looking for an answer? You could try the brute-force method, starting with undAund, undBund, through undZund, then on to undAAund, undABund, through undZZund. But you will be at it a very long time.

Many people hit on the right word without too much thought, certainly not by the brute-force approach. How do they do it? No one knows.

Thinking of Nothing

Where is mind, anyway? It’s in the brain presumably, but where? Poundstone asks whether the circuits of a pocket calculator have any awareness that they are doing arithmetic. Not that we can tell. But we certainly have awareness that we are doing arithmetic, or reading the newspaper or thinking about whatever it is that we are thinking about. Question: Could we be aware that we are thinking about nothing? Probably not. The awareness itself would be the thinking.

But how do we know, Poundstone asks, that we are really experiencing all that we think we are experiencing? How do we know that our brains are not simply stuck in laboratory vats filled with nutrients and attached to electrodes that scientists stimulate to create the sensations we experience? We don’t know, and we can’t know, though it seems unlikely.

This “brains in vats” riddle is the starting point for Poundstone’s book, which then proceeds through paradoxes of induction and deduction, ambiguity and certainty, to show that there are inherent, inviolable limits of knowledge. Along the way, Poundstone discusses many famous paradoxes, such as the paradox of the unexpected hanging, the prisoner’s dilemma and Newcomb’s paradox, with many variations and twists.


Classic Paradox

The unexpected hanging goes like this: a convicted man is sentenced to be hanged at dawn in the coming week, but the judge tells him that he will not know beforehand which day he will die. The prisoner is delighted. He reasons that the judge’s sentence cannot be carried out:

He cannot be executed on Saturday (the last day of the week), because once he made it past Friday morning, he’d know for sure that the execution would be Saturday, and that would violate the judge’s rule. He would know beforehand which day he was going to die. So Saturday is out.

Working backwards, that means he cannot be executed on Friday, either. Once he survived through Thursday morning, and knowing that he couldn’t be hanged on Saturday, he would know for sure that he was to be hanged on Friday. That, too, violates the judge’s order.

By the same reasoning, he can’t be hanged on Thursday, Wednesday or any other day.

So the prisoner sleeps soundly. Until Tuesday morning, when the executioner arrives and the prisoner is hanged. Despite the prisoner’s airtight reasoning, the sentence was carried out, and the judge’s order was obeyed. The prisoner didn’t know beforehand what day he was going to be hanged.

For Non-Philosophers

Poundstone deftly discusses these matters and many, many more in an extremely lucid way. He is not the first writer to tackle these subjects for non-specialized readers, but he does it very well. If you have had trouble reading Douglas Hofstadter or Raymond Smullyan but are interested in these things nonetheless, Poundstone may be your man. His book is easier--but no less deep--than others on similar topics.


“In few other fields is it possible for the interested non-expert to sample so much of the true flavor of the field and have fun doing it,” Poundstone writes. His book demonstrates the truth of the statement.

Oh, the common word that begins and ends with UND. Try underground.