What I've been thinking about...
Three Flavors of Paradox
For my money, a paradox is a statement or a situation that doesn’t work out logically. It yields some sort of a contradiction, like concluding some fact must be both true and false.
Late philosopher Willard Van Orman Quine identified three types of paradoxes:
I’d claim only the third type, Antimony, is a real paradox as I’ve learned the word. The others are cool party tricks and brain teasers, but real paradoxes have Philosophical implications.
I feel that only the third type are more than curiosities, but there are some other types of statements that I think could be part of a classification system along with paradoxes.
Some sentences are not paradoxical, but do make use of paradox and self-reference to guarantee their truth or falsehood. For example:
This sentence is not provable.
If one assumes this sentence is false, then a contradiction results, however there is no contradiction if we assume the sentence true. Therefore it is true (and for those who don’t know, the idea of this sentence is what’s behind nothing less that Godel’s Incompleteness Theorem.)