W. V. Quine (1962) distinguished between three classes of paradoxes.

·         A veridical paradox produces a result that appears absurd but is demonstrated to be true nevertheless. Thus, the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a person's fifth birthday is the day he turns twenty, if born on a leap day. Likewise, Arrow's impossibility theorem involves behaviour of voting systems that is surprising but true.

·         A falsidical paradox establishes a result that not only appears false but actually is false; there is a fallacy in the supposed demonstration. The various invalid proofs (e.g. that 1 = 2) are classic examples, generally relying on a hidden division by zero. Another example would be the inductive form of the Horse paradox.

·         A paradox which is in neither class may be an antinomy, which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the Grelling-Nelson paradox points out genuine problems in our understanding of the ideas of truth and description.

 

A fourth kind has sometimes been asserted since Quine's work.

A paradox which is both true and false at the same time in the same sense is called a dialetheia. In Western logics it is often assumed, following Aristotle that no dialetheia exist, but they are sometimes accepted in eastern traditions and in Paraconsistent logics.

 

See also list of paradoxes – www.quickturtle.eu.