Paradox

'''Paradox''

• etymology:
  • from Greek paradoxon for "contrary opinion
    • para = prior
    • dox = opinion

• definition:
  • a conflicting or self-contradictory opinion or situation
  • creates an absurdity, a puzzle or something unlikely
  • = a problem that
    • has no solution
    • the solution is never-ending
    • or the solution yields an outcome that negates the original problem

Paradox: when you can't have it both ways...

Paradox uses

• paradoxes are logically "invalid" or "invalid arguments"
  • since they can't be solved
  • like an irrational number that goes on forever
• however, paradoxes are useful thought experiments

Famous paradoxes

God paradox

• can God make a rock so big He can't move it?

Plato's Beard paradox

• if something does not exist, is not that non-existence a form of existence?
  • see https://en.wikipedia.org/wiki/Plato%27s_beard

Russell's paradox

• "a list of all lists that do not contain themselves"

Ship of Theseus

• if a ship were, over time, repaired so much that every part was replaced, would it be the same ship it was originally?

Zeno's paradoxes

Dichotomy paradox

• if you keep walking half-way to somewhere, you will never get there

Achilles and the tortoise paradox

• "In a race, the quickest runner can never over­take the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
  • as recounted by Aristotle, Physics VI:9, 239b15

click EXPAND for explanation from Wikipedia entry: https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Paradoxes_of_motion

In the paradox of Achilles and the tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Suppose that each racer starts running at some constant speed, one faster than the other. After some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say 2 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere the tortoise has been, he still has some distance to go before he can even reach the tortoise. As Aristotle noted, this argument is similar to the Dichotomy.[13] It lacks, however, the apparent conclusion of motionlessness.

Paradox of the grain of millet

* if a single grain of millet (a seed) makes no sound upon falling, yet 1,000 grains that fall do make a sound, how can 1,000 nothings create a sound?

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Visual paradoxes

>> Escher to do

List of paradoxes in other articles

* >> to do : list/ links