A paradox is a statement or group of statements that leads to one of the following:
- a contradiction
- a situation which defies intuition
- a result that is merely "puzzling".
The following types of paradox have been identified:
A veridical paradox is a counter-intuitive result which can be demonstrated to be true.
A falsidical paradox is a result which, as well as being absurd on the surface, is the result of faulty reasoning and so is genuinely false.
Such apparent paradoxes can be classified as fallacies.
An antinomy is a self-contradictory statement which arises as the result of a valid argument from a set of premises which contains an inherent ambiguity or contradiction.
Such apparent paradoxes can also often be classified as fallacies.
A dialetheia is a statement which is paradoxical through the fact that it is both true and false at the same time.
As such, it is incompatible with Aristotle's Law of the Excluded Middle and Principle of Non-Contradiction, and therefore does not in general appear in the context of conventional mathematics.
- Results about paradoxes can be found here.
- 1944: Eugene P. Northrop: Riddles in Mathematics ... (previous) ... (next): Chapter One: What is a Paradox?
- 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $1$: Introduction: $\S 1.1$: The origins of mathematical logic