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'''Paradox''' | |||
[[File:Puck-paradox.jpg|thumb|Paradox: when you can't have it both ways...]] | |||
* etymology: | * etymology: | ||
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*** the solution is never-ending | *** the solution is never-ending | ||
*** or the solution yields an outcome that negates the original problem | *** or the solution yields an outcome that negates the original problem | ||
== Paradox uses == | == Paradox uses == | ||
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* however, paradoxes are useful thought experiments | * however, paradoxes are useful thought experiments | ||
== | == Classic paradoxes == | ||
=== God paradox === | |||
* can | === 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 === | === Plato's Beard paradox === | ||
* if something does not exist, is not that non-existence a form of existence? | * if something does not exist, is not that non-existence a form of existence? | ||
** see https://en.wikipedia.org/wiki/Plato%27s_beard | ** 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 === | === Russell's paradox === | ||
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* if a ship were, over time, repaired so much that every part was replaced, would it be the same ship it was originally? | * 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 == | |||
* Zeno of Elea was a Greek philosopher, c. 495-430 BC who lived in the Greek colonies on Italy | |||
** he preceded Socrates and Plato | |||
* he was taught by Parmenides, who is thought to have visited Athens and influenced Socrates when he Socrates was a young man | |||
** Parmenides distinguished between "Aletheia," for truth and "Doxa" or opinion, or the world of our senses | |||
** considered the founder of "ontology", or the study of existence and reality | |||
** Plato and Aristotle credited Zeno as inventor of the "dialectic," or process of "reasoned discourse" by which a truth is established (aka, "Socratic method") | |||
* Zeno developed his paradoxes to defend Parmenides' teachings | |||
* click EXPAND for the story told by the ancient Greek biographer, Diogenes Laërtius, about Zeno biting the tyrant's ear | |||
<div class="mw-collapsible mw-collapsed"> | |||
Diogenes Laertius wrote that Zeno opposed the rule of Nearchus the tyrant of Elea (Greek colony in Italy) and conspired to overthrow him. Nearchus discovered the plot and had Zeno tortured to reveal the names of his co-conspirators. Zeno refused to say, but told Nearchus that he had a secret to divulge and that he would whisper it in Nearchus' ear, whereupon, Zeno bit Nearchus' ear and didn't let go until he was killed, at which point the ear came off in Zeno's grip. See [https://en.wikipedia.org/wiki/Zeno_of_Elea| Zeno of Elea (wikipedia)]</div> | |||
* Plato discusses Zeno's paradoxes in "Parmenides," a dialogue between Socrates and Zeno's teacher, Permenides | |||
** the point being that a paradox demonstrates an absurdity, such as | |||
<pre>Or suppose one of us to have a portion of smallness; this is but a part of the small, and therefore the absolutely small is greater; if the absolutely small be greater, that to which the part of the small is added will be smaller and not greater than before.</pre> | |||
from [https://gutenberg.org/cache/epub/1687/pg1687-images.html\ Parmenides by Plato (Project Gutenberg)] | |||
=== 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. | * "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 | ** as recounted by Aristotle, Physics VI:9, 239b15 | ||
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</div> | </div> | ||
==== Paradox of the grain of millet | === Zeno's indivisibility of time === | ||
* many of his paradoxes rely on the idea that time and space are infinitely divisible and thus yield absurd conclusions | |||
* therefore, according to Zeno (and Parmenides) motion is an illusion | |||
** ironically, video or motion pictures are made up of still images that create the illusion of motion when shown in rapid succession | |||
=== Arrow paradox === | |||
* at any given instant, a flying arrow is in a certain place, so, since its entire flight is made up on such motionless instants, motion is impossible. | |||
** | |||
* a described by Aristotle in [https://archive.org/details/aristotle_physics ''Physics'' VI:9, 239b5] | |||
If everything when it occupies an equal space is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion. | |||
=== Dichotomy paradox === | |||
* if you keep walking half-way to somewhere, you will never get there | |||
* Aristotle described it in [https://archive.org/details/aristotle_physics ''Physics'' VI:9, 239b10] as: | |||
That which is in locomotion must arrive at the half-way stage before it arrives at the goal. | |||
=== Moving rows paradox === | |||
* given three rows of four individuals (rows A, B, & C) | |||
** if row A is not moving, and rows B and C are moving in oppositive directions past row A at equal speeds | |||
** since B and C both move past A at one speed, they move past each other at double the speed they move past the stationary row A | |||
** thereby half of a time is equal to its double | |||
* | |||
=== Paradox of place === | |||
* since everything has a place, and a place is a thing, then every place has a place, ''ad infinitum'' (onward forever) | |||
=== 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? | * 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? | ||
See | |||
* [https://iep.utm.edu/zenos-paradoxes/ Zeno’s Paradoxes | Internet Encyclopedia of Philosophy (utm.edu)] | |||
==== | == 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 [https://physicsworld.com/a/information-paradox-simplified/ Information paradox simplified (physicsworld.com)] | |||
== Visual paradoxes == | == Visual paradoxes == | ||
>> Escher to do | >> 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 | |||
<div class="mw-collapsible mw-collapsed"> | |||
* 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:<br> | |||
*** 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 <br> | |||
*** therefore, Path A is the path to salvation | |||
</div> | |||
== 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 | |||
<br>and<br> | |||
* '''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 [[wikipedia:Buttered_cat_paradox|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 | * >> to do : list/ links | ||
* also from : https://en.wikipedia.org/wiki/List_of_paradoxes | |||