Paradox

• Paradox

  • Overview

    • A paradox is a statement or situation that seems self-contradictory or absurd yet is supported by reasoning that looks sound. From the Greek paradoxon, "contrary to expectation."

  • Kinds of paradox

    • Veridical — the conclusion sounds absurd but is true. The Monty Hall problem and the birthday paradox, in which 23 people are enough for even odds that two share a birthday, both hold up under calculation.
    • Falsidical — the conclusion is false because the argument hides a mistake. Zeno's paradoxes of motion fall apart once an infinite sum of shrinking steps is allowed to add up to a finite distance.
    • Antinomy — accepted reasoning leads to a true contradiction, which forces a change to the assumptions. The liar paradox ("this sentence is false") and Russell's paradox about the set of all sets that do not contain themselves are the classic cases; Russell's led to the axioms of modern set theory.

  • What paradoxes are good for

    • A paradox marks the spot where an intuition or a theory breaks. Working one out usually means giving up an assumption nobody had noticed they were making, which is why paradoxes have driven changes in logic, mathematics and physics.
    • Person/Erwin Schrödinger/Cat is a paradox built on purpose, to show where a theory of quantum measurement leads.

  • Examples in the garden

    • Jevon's Paradox — efficiency gains that make a resource cheaper can raise its total use.

  • Sources

    • Stanford Encyclopedia of Philosophy: Paradoxes and Contemporary Logic
    • Wikipedia: Paradox