Editing Paradox (section)

{{Short description|Logically self-contradictory statement}}
{{Other uses}}

A '''paradox''' is a [[logic]]ally self-contradictory statement or a statement that runs contrary to one's expectation.<ref>{{Cite web|url=http://mathworld.wolfram.com/Paradox.html|title=Paradox|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-12-05}}</ref><ref>"By “paradox” one usually means a statement claiming something that goes beyond (or even against) ‘common opinion’ (what is usually believed or held)." {{cite SEP
|title   = Paradoxes and Contemporary Logic
|url-id  = paradoxes-contemporary-logic
|date    = 2017-02-22
|edition = Fall 2017
|last    = Cantini
|first   = Andrea
|last2   = Bruni
|first2  = Riccardo
}}</ref> It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.<ref>{{cite web|title=paradox|url=http://www.oxforddictionaries.com/us/definition/american_english/paradox|archive-url=https://web.archive.org/web/20130205104405/http://oxforddictionaries.com/us/definition/american_english/paradox|url-status=dead|archive-date=February 5, 2013|website=Oxford Dictionary|publisher=Oxford University Press|access-date=21 June 2016}}</ref><ref>{{cite news|last1=Bolander|first1=Thomas|title=Self-Reference|url=http://plato.stanford.edu/entries/self-reference/|access-date=21 June 2016|publisher=The Metaphysics Research Lab, Stanford University|date=2013}}</ref> A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time.<ref>{{cite journal | last1 = Smith | first1 = W. K. | last2 = Lewis | first2 = M. W. | year = 2011 | title = Toward a theory of paradox: A dynamic equilibrium model of organizing | journal = Academy of Management Review | volume = 36 | issue = 2| pages = 381–403 | doi=10.5465/amr.2009.0223| jstor = 41318006 }}</ref><ref>{{cite journal | last1 = Zhang | first1 = Y. | last2 = Waldman | first2 = D. A. | last3 = Han | first3 = Y. | last4 = Li | first4 = X. | year = 2015 | title = Paradoxical leader behaviors in people management: Antecedents and consequences | url = https://www.researchgate.net/publication/275720775 | format = PDF | journal = Academy of Management Journal | volume = 58 | issue = 2| pages = 538–566 | doi=10.5465/amj.2012.0995}}</ref><ref>{{cite journal | last1 = Waldman | first1 = David A. | last2 = Bowen | first2 = David E. | year = 2016 | title = Learning to Be a Paradox-Savvy Leader | journal = Academy of Management Perspectives | volume = 30 | issue = 3| pages = 316–327 | doi = 10.5465/amp.2015.0070 | s2cid = 2034932 }}</ref> They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites".<ref>{{Cite journal |last1=Schad |first1=Jonathan |last2=Lewis |first2=Marianne W. |last3=Raisch |first3=Sebastian |last4=Smith |first4=Wendy K. |date=2016-01-01 |title=Paradox Research in Management Science: Looking Back to Move Forward |url=https://openaccess.city.ac.uk/id/eprint/15616/3/ANNALS-final.pdf |journal=Academy of Management Annals |volume=10 |issue=1 |pages=5–64 |doi=10.5465/19416520.2016.1162422 |issn=1941-6520}}</ref>

In [[logic]], many paradoxes exist that are known to be [[Validity (logic)|invalid]] arguments, yet are nevertheless valuable in promoting [[critical thinking]],<ref>{{cite journal |last=Eliason |first=James L. |url=http://connection.ebscohost.com/c/articles/9604072434/using-paradoxes-teach-critical-thinking-science |archive-url=https://web.archive.org/web/20131023061500/http://connection.ebscohost.com/c/articles/9604072434/using-paradoxes-teach-critical-thinking-science |url-status=dead |archive-date=2013-10-23 |title=Using Paradoxes to Teach Critical Thinking in Science |journal=Journal of College Science Teaching |volume=15 |issue=5 |pages=341–44 |date=March–April 1996 |url-access=subscription }}</ref> while other paradoxes have revealed errors in definitions that were 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 and showed that attempts to found [[set theory]] on the identification of sets with [[Property (philosophy)|properties]] or [[Predicate (mathematical logic)|predicates]] were flawed.<ref name=":1">{{Citation|last1=Irvine|first1=Andrew David|title=Russell's Paradox|date=2016|url=https://plato.stanford.edu/archives/win2016/entries/russell-paradox/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2016|publisher=Metaphysics Research Lab, Stanford University|access-date=2019-12-05|last2=Deutsch|first2=Harry}}</ref><ref>{{cite book | last1=Crossley | first1=J.N. | last2=Ash | first2=C.J. | last3=Brickhill | first3=C.J. | last4=Stillwell | first4=J.C. | last5=Williams | first5=N.H. | title=What is mathematical logic? | zbl=0251.02001 | location=London-Oxford-New York | publisher=[[Oxford University Press]] | year=1972 | isbn=0-19-888087-1 | pages=59–60}}</ref> Others, such as [[Curry's paradox]], cannot be easily resolved by making foundational changes in a logical system.<ref>{{Citation|last1=Shapiro|first1=Lionel|title=Curry's Paradox|date=2018|url=https://plato.stanford.edu/archives/sum2018/entries/curry-paradox/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Summer 2018|publisher=Metaphysics Research Lab, Stanford University|access-date=2019-12-05|last2=Beall|first2=Jc}}</ref>

Examples outside logic include the [[ship of Theseus]] from philosophy, a paradox that questions whether a ship repaired over time by replacing each and all of its wooden parts one at a time would remain the same ship.<ref>{{Cite web|url=https://faculty.washington.edu/smcohen/320/theseus.html|title=Identity, Persistence, and the Ship of Theseus|website=faculty.washington.edu|access-date=2019-12-05}}</ref> Paradoxes can also take the form of images or other media. For example, [[M. C. Escher]] featured [[Perspective (visual)|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.<ref>{{cite web |url=http://aminotes.tumblr.com/post/653017235/the-mathematical-art-of-m-c-escher-for-me-it |title=The Mathematical Art of M. C. Escher |website=Lapidarium notes |editor-first=Amira |editor-last=Skomorowska |access-date=2013-01-22}}</ref>

Informally, the term ''paradox'' is often used to describe a counterintuitive result.