Paradox

Paradox

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

• 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 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

Buridan's bridge paradox

• Plato: "If your next statement is true, I will allow you to cross the bridge. If your next statement is false, I will throw you in the water"
• Socrates: "You will throw me in the water."

Free Will paradox

• if God knows what will happen to us, how can contradict it?
  • and if we cannot contradict it, there is no free will

Irresistible force paradox

• when an unstoppable force hits an immovable object

Government Temporary Powers paradox

• nothing lasts longer than a "temporary" government power or program

Omnipotence paradox

• if God is omnipotent (all powerful), can He 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

Problem of Evil paradox

• if God is good, then how can evil exist?

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

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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?

Science & technology paradoxes

Information or black hole paradox

* from physicist Steven Hawking * a black hole does not absorb every particle, so over time it will disappear into nothing * how can that be? ** see Information paradox simplified (physicsworld.com)

Visual paradoxes

>> Escher to do

Riddles

* while not paradoxes (because they can be solved), riddles present interesting intellectual scenarios for students

The truth-teller & the liar riddle

* two monsters guard a fork in the road ** one path leads to perdition, the other to salvation ** one monster always lies and the other always tells the truth ** you are permitted to ask each monster one question ** what do you ask in order to learn which path is the one to salvation? click EXPAND for the solution

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* If you ask each one which path to salvation the other would say, they bill both tell you the path to perdition; so choose the other for salvation
** If Path A is salvation and Path B is perdition:
*** then Liar Monster will say the other will say that the path to Salvation is Path B (which leads to perdition)
*** while Truthful Monster will say that the Lying Monster will say the path to Salvation is Path B, as well
*** therefore, Path A is the path to salvation

Assorted or humorous paradoxes

Buttered cat paradox

* cats always land on their feet ** may be supported by the "cat righting reflex" which is the ability of cats to right-themselves mid-air, thus landing on their feet * buttered toast always lands with the butter-side down ** an experiment showed that buttered toast will land butter-side down 81% of the time (see Buttered cat paradox - Wikipedia

Intentionally blank page

* when a published or printed document states, "intentionally blank page" in order to indicate that the blank page in the document is there on purpose ** then the page is no longer blank

List of paradoxes in other articles here

* If life is unfair for everybody, wouldn't that make it fair? ** (w/ thanks to Henry) * * >> to do : list/ links * also from : https://en.wikipedia.org/wiki/List_of_paradoxes