Difference between revisions of "Paradox"
Karl Jones (Talk | contribs) |
Karl Jones (Talk | contribs) |
||
| (4 intermediate revisions by 2 users not shown) | |||
| Line 5: | Line 5: | ||
Some [[Logic|logical]] paradoxes are known to be ''invalid arguments'' (see [[Validity]]) but are still valuable in promoting [[critical thinking]]. | Some [[Logic|logical]] paradoxes are known to be ''invalid arguments'' (see [[Validity]]) but are still valuable in promoting [[critical thinking]]. | ||
| − | Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused [[Axiom|axioms | + | Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused [[Axiom|axioms]] of [[mathematics]] and logic to be re-examined. |
One example is [[Russell's paradox]], which questions whether a "list of all lists that do not contain themselves" would include itself. [[Bertrand Russell]] showed that attempts to found [[set theory]] on the identification of [[Set (mathematics)|sets]] with properties or predicates were flawed. | One example is [[Russell's paradox]], which questions whether a "list of all lists that do not contain themselves" would include itself. [[Bertrand Russell]] showed that attempts to found [[set theory]] on the identification of [[Set (mathematics)|sets]] with properties or predicates were flawed. | ||
| Line 30: | Line 30: | ||
* [[Impossible Programs]] | * [[Impossible Programs]] | ||
* [[Logic]] | * [[Logic]] | ||
| + | * [[Mathematics]] | ||
| + | * [[Philosophy]] | ||
| + | * [[Recursion]] | ||
* [[Russell's paradox]] | * [[Russell's paradox]] | ||
| − | * [[Set (mathematics) | + | * [[Self-reference]] |
| + | * [[Set (mathematics)]] | ||
* [[Set theory]] | * [[Set theory]] | ||
* [[Ship of Theseus]] | * [[Ship of Theseus]] | ||
| + | * [[Unexpected hanging paradox]] | ||
* [[Validity]] | * [[Validity]] | ||
| Line 39: | Line 44: | ||
* [https://en.wikipedia.org/wiki/Paradox Paradox] @ Wikipedia | * [https://en.wikipedia.org/wiki/Paradox Paradox] @ Wikipedia | ||
| + | |||
| + | [[Category:Logic]] | ||
| + | [[Category:Mathematics]] | ||
| + | [[Category:Paradox]] | ||
| + | [[Category:Philosophy]] | ||
Latest revision as of 10:51, 17 September 2016
A paradox is a statement that apparently contradicts itself and yet might be true (or wrong at the same time).
Contents
Description
Some logical paradoxes are known to be invalid arguments (see Validity) but are still valuable in promoting critical thinking.
Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined.
One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself. Bertrand Russell showed that attempts to found set theory on the identification of sets with properties or predicates were flawed.
Curry's paradox
Others, such as Curry's paradox, are not yet resolved.
Ship of Theseus
Examples outside logic include the Ship of Theseus from philosophy (questioning whether a ship repaired over time by replacing each of its wooden parts would remain the same ship).
Paradoxical images
Paradoxes can also take the form of images or other media. For example, M.C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly.
Common usage
In common usage, the word "paradox" often refers to statements that are ironic or unexpected, such as "the paradox that standing is more tiring than walking".
See also
- Critical thinking
- Impossible Programs
- Logic
- Mathematics
- Philosophy
- Recursion
- Russell's paradox
- Self-reference
- Set (mathematics)
- Set theory
- Ship of Theseus
- Unexpected hanging paradox
- Validity
External links
- Paradox @ Wikipedia
