Paradox: Difference between revisions

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click EXPAND for the solution
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 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<br>
** If Path A is salvation and Path B is perdition:
** If Path A is salvation and Path B is perdition:<br>
*** then Liar Monster will say the other will say that the path to Salvation is Path B (which leads to perdition)
*** then Liar Monster will say the other will say that the path to Salvation is Path B (which leads to perdition)<br>
*** while Truthful Monster will say that the Lying Monster will say the path to Salvation is Path B, as well  
*** while Truthful Monster will say that the Lying Monster will say the path to Salvation is Path B, as well <br>
*** therefore, Path A is the path to salvation
*** therefore, Path A is the path to salvation
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Revision as of 20:53, 10 April 2022

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[edit | edit source]

  • 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[edit | edit source]

Buridan's bridge paradox[edit | edit source]

  • 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[edit | edit source]

  • 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[edit | edit source]

  • when an unstoppable force hits an immovable object

Government Temporary Powers paradox[edit | edit source]

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

Omnipotence paradox[edit | edit source]

  • if God is omnipotent (all powerful), can He make a rock so big He can't move it?

Plato's Beard paradox[edit | edit source]

Problem of Evil paradox[edit | edit source]

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

Russell's paradox[edit | edit source]

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

Ship of Theseus[edit | edit source]

  • 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[edit | edit source]

Dichotomy paradox[edit | edit source]

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

Achilles and the tortoise paradox[edit | edit source]

  • "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[edit | edit source]

* 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[edit | edit source]

Information or black hole paradox[edit | edit source]

* 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[edit | edit source]

>> Escher to do

Riddles[edit | edit source]

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

The truth-teller & the liar riddle[edit | edit source]

* 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

* 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

List of paradoxes in other articles here[edit | edit source]

* 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