We use ‘reason’ continually in everyday life. Our lives depend on it. (We infer from the information that some things are poisonous, that they are poisonous—and hence unhealthy—for us as well. etc., etc.)

Yet, remarkably, our very best uses of reason tell us that our very best uses of reason sometimes lies to us.

Reason involves “seeing” that if I have 3 apples and 2 oranges (and knowing that apples and oranges are fruits) I must have at least 5 fruits. And it involves inferring that this chair will likely hold me up next time I sit on it from the fact that it has held me 100 times before. The former ‘deductive’ sort of inferences are much better understood than the latter ‘inductive’ inferences—about which there is considerable philosophical debate. (“The Problem of Induction”) And how we are able to “see” such things is, I think, deeply mysterious. (See The Mystery of Knowing.) Philosophers have used the metaphor of light and seeing back to at least Plato, the early moderns used the term ‘intuition,’ and we still use the term ‘insight. But how exactly we are able to do this is, I think, utterly unknown.

But it plainly does work, generally. And our lives depend upon it.

But consider ‘The Liar Paradox:’

Consider the sentence (“The Liar Sentence”):  ‘This sentence is not true.’

Suppose it’s true. But then it is not true—because that is what it says. But nothing can be both true and not true at the same time. So, contrary to our initial supposition, the sentence cannot be true.

So the sentence must not be true. But then what it says is true, so the sentence must be true. But then it would be both true and not-true. But we’ve already agreed that that is impossible. So the sentence cannot be not-true.

So it cannot be true and it cannot be not-true. But surely it’s got to be one or the other!

So our best reasoning tells us that

  1. This sentence (The Liar Sentence) cannot be true.
  2. It cannot be not-true. But
  3. It must be one or the other.

And our best reasoning tells us that

  • These things [ 1) – 3) ] cannot all be true.

So our best reasoning tells us that

  • At least one of these things—which our best reasoning tells us—must not be true.

So our best reasoning tells us that sometimes our best reasoning tells us things which are not true.

This is all very perplexing, and, indeed, many of the world’s most brilliant minds have tried and failed to “solve” this paradox. Or at least no proposed solution has convinced most others who have studied the paradox that their solution is correct.

This paradox seems to even make an appearance in the Bible, believe it or not. The apostle Paul wrote (Titus 1:12), “One of Crete’s own prophets has said it: ‘Cretans are always liars, . . . .’ ” He is thought to been referring to Epimenides, a ‘Cretan.’)

Once you see how the paradox works you can see that literally infinitely many other paradoxes like it can be generated. E.g., also famously: It seems like there should be a set of all those sets which are not members of themselves. But if you assume that there is, you can quickly deduce that that set both is and is not a member of itself. (“Russell’s Paradox”) And it seems as though there should a universal set—the set of everything. But Cantor demonstrated that the “power set” of any set (the set of subsets of that set) is larger than the original set. So the power set of the universal set is larger than the universal set. But surely no set can be larger than the set that includes everything!

What is one to make of all this?

Surely not that our use of reason is generally unreliable, or that one ought abandon its use. Doing this would result in death, literally.

But I see no alternative to this conclusion, which, ironically, our best reasoning leads us to:

Sometimes our best reasoning does not tell us the truth.

-July 2017