Definition:Paradox
Definition
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".
Logical Paradox
A logical paradox is a paradox which arises from the application of formal techniques of propositional or predicate logic.
Hence a logical paradox arises from an inherent contradiction in the set of axioms.
Semantic Paradox
A semantic paradox is a paradox arising from semantic interpretations of linguistic ambiguities and imprecision.
Types of Paradox
The following types of paradox have been identified:
Veridical Paradox
A veridical paradox is a counter-intuitive result which can be demonstrated to be true.
Falsidical Paradox
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.
Antinomy
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.
Dialetheia
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.
Also see
- Results about paradoxes can be found here.
Sources
- 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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): paradox
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): paradox
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): paradox