A Book, and a Crafty Law Student

An old Dover publication I only recently stumbled upon is one of the best I've seen at succinctly covering many of the most trenchant paradoxes and self-reference issues underlying mathematics:

Bryan Bunch's "Mathematical Fallacies and Paradoxes" (1982) covers a wide selection of, guess what, fallacies and paradoxes; some fairly light, others deeper and heavier. Below I've totally re-adapted one of the many self-reference paradoxes contained in the volume:

To demonstrate what a fine teacher he is, Larry the Lawyer contracts with each of his students such that they need only pay him for his individual instruction IF and ONLY IF they win their first law case. If they lose that first case they pay him no fee.
However, one of his students, Squiggy, upon completing the course, opts simply not to try any cases at all to avoid paying any fee. Perturbed, Larry feels compelled to sue Squiggy for payment (since avoiding trial cases in order to avoid payment was not intended as an option). Once the case comes to court Squiggy represents himself. IF he loses, then by the original contract he does NOT have to pay Larry! IF he wins the suit then the court will have ruled that he does NOT have to pay! Squiggy appears well on his way to being a superb lawyer....

The Bunch book definitely isn't for everyone (not even for all math buffs), but if you have an especial interest in the paradoxes and intrinsic issues that underlie uncertainty in mathematics, as well as in science and knowledge more generally, it's worth a look.