Veridical paradox facts for kids

In 1962, W. V. Quine said there were three classes of paradoxes:

• A veridical paradox seems absurd but is shown to be true. Thus, the paradox of Frederic's birthday in The Pirates of Penzance notes 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 shows difficulties in mapping voting results to the will of the people. The Monty Hall paradox shows that a decision which seems to be a 50-50 chance is in fact heavily biased towards making a decision which 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. Most of them rely on a hidden division by zero. Another example is the inductive form of the horse paradox, which falsely generalizes from true specific statements. Zeno's paradoxes are falsidical, concluding for example that a flying arrow never reaches its target or that a hare 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 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, the Gongsun Longzi, and in Zen) 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 to simultaneously affirm and deny the event in some sense.