Editing Curry's paradox (section)

{{Short description|Mathematical paradox named after Haskell Curry}}
{{for|Paul Curry's optical illusion and dissection puzzle|Missing square puzzle}}
'''Curry's paradox''' is a [[paradox]] in which an arbitrary claim ''F'' is proved from the mere existence of a sentence ''C'' that says of itself "If ''C'', then ''F''". The paradox requires only a few apparently-innocuous logical deduction rules. Since ''F'' is arbitrary, any logic having these rules allows one to prove everything. The paradox may be expressed in natural language and in various [[logic]]s, including certain forms of [[set theory]], [[lambda calculus]], and [[combinatory logic]].

The paradox is named after the logician [[Haskell Curry]], who wrote about it in 1942.<ref name=":0" /> It has also been called '''Löb's paradox''' after [[Martin Hugo Löb]],<ref>{{cite book |last1=Barwise |first1=Jon |author-link1=Jon Barwise |last2=Etchemendy |first2=John |author-link2=John Etchemendy |title=The Liar: An Essay on Truth and Circularity |year=1987 |publisher=Oxford University Press |location=New York |isbn=0195059441 |page=23 |url=http://www.oup.com/us/catalog/general/subject/Philosophy/LogicMathematics/?view=usa&ci=9780195059441 |access-date=24 January 2013}}</ref> due to its relationship to [[Löb's theorem]].