This was written in 2009. (Revised 2022.) It explains the notion of a logical paradox in a way that comes naturally to me. The conclusion drawn at the end is probably the main thing for me (“We are blinder than we can imagine in matters of straightforward logical reasoning”) but it is not always emphasized by others!

We could easily run through a few more paradoxes but they tell the same broad tale and the essential points have been made.

Some people treat paradoxes as exercises in reasoning. A “seemingly flawless” argument is presented, but it leads to a “seemingly absurd” conclusion, so the challenge is to uncover the flaw in the reasoning, or else explain why the conclusion is not really absurd.

Many of these may be resolved with a little effort and the exercises are often rewarding and entertaining. For one last example, here’s a cheeky “proof” of the existence of a unicorn from the mischievous American logician Raymond Smullyan:

To prove that there exists a unicorn, it’s enough to prove the stronger proposition that there exists anIt’s not trivial to explain where this “proof” goes wrong, and anyone who spars with problems like these and learns the art of overcoming them will come quickly to appreciate the curious case of the absolutely flawless reasoning with the completely unacceptable conclusion!existingunicorn. (An “existing unicorn” is just a unicorn that exists.)For, obviously, if there exists anexistingunicorn, then there must exist a unicorn!So all we have to do is prove that anexistingunicorn exists. But that’s not very hard. How could an existing unicornnotexist? That would be a contradiction!

Indeed, there is such a thing as savouring a paradox before grappling with it and this experience is available to anyone who is open to it. Sadly, this fact is often lost upon those who regard paradoxes as nothing but affronts to their intelligence.

A really good paradox appears only once in a while, catching everyone by surprise, e.g., once every half century or so. We actually

I wish I could have shown a few more examples above of the patient pursuit and eventual snaring of such elusive prey; the exposing of the precise error in a subtly fallacious line of reasoning. This is an art form in itself and a few examples would have been good to see. (The lone example provided was in the section on logical fatalism, where we took down the Idle Argument.) But I have tried to provide some on the rest of this site and so have focused on the more general lesson available to us here, which I’m afraid is this:

Paradoxes reveal that we are often blinder than we can imagine in matters of straightforward logical reasoning ...

Achilles & the tortoise

The surprise exam

Newcomb’s problem

Newcomb’s problem (sassy version)

Seeing and being

Logic test!

Philosophers say the strangest things

Favourite puzzles

Books on consciousness

Philosophy videos

Phinteresting

Philosopher biographies

Philosopher birthdays

Draft

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