Lessons in Paradoxes

A paradox is an apparently sound argument with an apparently false conclusion.

The existence of a paradox implies a lack of understanding, so we try
to dissolve the paradox by employing one of the following resolutions:

  1. Deny that the reasoning is valid
  2. Deny that the premises are true
  3. Realize that the conclusion is true

Paradoxes are caused by allowing an unfounded assumption to slip by.
We can learn some valuable lessons by looking at the nature of this assumption.

Don't confuse two different levels that appear similar

  • Pascal's Wager
  • Anselm's Ontological Argument
  • Self-referential statements may have no truth value

  • Lying Sisters
  • Curry's Paradox
  • In general, be careful with the math

  • Two Envelopes
  • Zeno's Paradox of Motion
  • Achilles and the Tortoise
  • Logic cannot operate on undefined terms

  • Sorites Arguments
  • Arbitrarily large does not imply infinite

  • Zeno's Paradox of Plurality
  • If the universe is deterministic, then thought is too

  • Newcomb's Paradox
  • English is not so great for logic

  • Modal Ambiguity
  • Other Notes

    • Most philosophical debates are caused by two people assuming different definitions for the same term. The issue arises often because each person may think that their definition is self-evident and so they forget to check for consistency with the other person's definition.