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Linguist [[Noam Chomsky]], among many others, has argued that the lack of an upper bound on the number of grammatical sentences in a language, and the lack of an upper bound on grammatical sentence length (beyond practical constraints such as the time available to utter one), can be explained as the consequence of recursion in natural language.<ref>{{cite book|last=Pinker|first=Steven|title=The Language Instinct|year=1994|publisher=William Morrow}}</ref><ref>{{cite journal | doi = 10.1016/j.cognition.2004.08.004 | title = The faculty of language: What's so special about it? | year = 2005 | last1 = Pinker | first1=Steven | last2 = Jackendoff | first2=Ray | journal = Cognition | volume = 95 | issue = 2 | pages = 201–236 | pmid=15694646| citeseerx = 10.1.1.116.7784 | s2cid = 1599505 }}</ref>
This can be understood in terms of a recursive definition of a syntactic category, such as a sentence. A sentence can have a structure in which what follows the verb is another sentence: ''Dorothy thinks witches are dangerous'', in which the sentence ''witches are dangerous'' occurs in the larger one. So a sentence can be defined recursively (very roughly) as something with a structure that includes a noun phrase, a verb, and optionally another sentence. This is really just a special case of the mathematical definition of recursion.{{Clarification needed|date=August 2025}}
This provides a way of understanding the creativity of language—the unbounded number of grammatical sentences—because it immediately predicts that sentences can be of arbitrary length: ''Dorothy thinks that Toto suspects that Tin Man said that...''. There are many structures apart from sentences that can be defined recursively, and therefore many ways in which a sentence can embed instances of one category inside another.<ref>{{Cite web|url=https://www.thoughtco.com/recursion-grammar-1691901|title=What Is Recursion in English Grammar?|last=Nordquist|first=Richard|website=ThoughtCo|language=en|access-date=2019-10-24}}</ref> Over the years, languages in general have proved amenable to this kind of analysis.
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{{See also|Mathematics and art|Infinity mirror}}
The [[Matryoshka doll]] is a physical artistic example of the recursive concept.<ref>{{cite web |last1=Tang |first1=Daisy |title=CS240 -- Lecture Notes: Recursion|date=March 2013|publisher=California State Polytechnic University, Pomona |url=http://www.cpp.edu/~ftang/courses/CS240/lectures/recursion.htm|archive-url=https://web.archive.org/web/20180317100946/https://www.cpp.edu/~ftang/courses/CS240/lectures/recursion.htm|archive-date=2018-03-17 |access-date=24 September 2015 |quote=More examples of recursion: Russian Matryoshka dolls. Each doll is made of solid wood or is hollow and contains another Matryoshka doll inside it. }}</ref>
Recursion has been used in paintings since [[Giotto]]'s ''[[Stefaneschi Triptych]]'', made in 1320. Its central panel contains the kneeling figure of Cardinal Stefaneschi, holding up the triptych itself as an offering.<ref>{{cite web |title=Giotto di Bondone and assistants: Stefaneschi triptych |url=http://mv.vatican.va/3_EN/pages/PIN/PIN_Sala02_03.html |publisher=The Vatican |access-date=16 September 2015}}</ref><ref>{{Cite book |title=Physical (A)Causality: Determinism, Randomness and Uncaused Events |url=https://books.google.com/books?id=gxBMDwAAQBAJ&pg=PA12 |first=Karl |last=Svozil |year=2018 |publisher=Springer |pages=12| isbn=9783319708157 }}</ref> This practice is more generally known as the [[Droste effect]], an example of the [[Mise en abyme]] technique.
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