Quine had three classes of paradox: > A veridical paradox produces a result that appears absurd but is demonstrated to be true nonetheless. Thus the paradox of

Quine had three classes of paradox: > A veridical paradox produces a result that appears absurd but is demonstrated to be true nonetheless. Thus the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a twenty-one-year-old would have had only five birthdays if he had been born on a leap day. Likewise, Arrow's impossibility theorem demonstrates difficulties in mapping voting results to the will of the people. The Monty Hall paradox demonstrates that a decision which has an intuitive 50–50 chance is in fact heavily biased towards making a decision which, given the intuitive conclusion, the player would be unlikely to make. In 20th-century science, Hilbert's paradox of the Grand Hotel and Schrödinger's cat are famously vivid examples of a theory being taken to a logical but paradoxical end. > A falsidical paradox establishes a result that not only appears false but actually is false, due to a fallacy in the demonstration. The various invalid mathematical proofs (e.g., that 1 = 2) are classic examples, generally relying on a hidden division by zero. Another example is the inductive form of the horse paradox, which falsely generalises from true specific statements. Zeno's paradoxes are 'falsidical', concluding, for example, that a flying arrow never reaches its target or that a speedy runner cannot catch up to a tortoise with a small head-start. > A paradox that 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, which may be alternatively interpreted as a special case of the third kind, has sometimes been described since Quine's work. > A paradox that is both true and false at the same time and 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 (e.g. in the Mohists,[12] the Gongsun Longzi,[13] and in Zen[14]) and in paraconsistent logics. It would be mere equivocation or a matter of degree, for example, to both affirm and deny that "John is here" when John is halfway through the door but it is self-contradictory simultaneously to affirm and deny the event. https://en.wikipedia.org/wiki/Paradox https://en.wikipedia.org/wiki/Paradox