Editing Intuition (section)

====Contemporary philosophy====
Intuitions are customarily appealed to{{clarify|reason=by whom? by philosophers? or do philosophers claim that this is what people generally do?|date=August 2023}} independently of any particular theory of how intuitions provide evidence for claims. There are divergent accounts of what sort of mental state intuitions are, ranging from mere spontaneous judgment to a special presentation of a necessary truth.<ref>{{cite book|first=M.|last=Lynch|chapter=Trusting Intuitions|editor-first1=P.|editor-last1=Greenough|editor-first2=M.|editor-last2=Lynch|title=Truth and Realism|pages=227–238}}</ref> Philosophers such as [[George Bealer]] have tried to defend appeals to intuition against [[Willard Van Orman Quine|Quinean]] doubts about [[conceptual analysis]].<ref>{{cite book|first=G.|last=Bealer|chapter=Intuition and The Autonomy of Philosophy|editor-first1=M.|editor-last1=Depaul|editor-first2=W.|editor-last2=Ramsey|title=Rethinking Intuition: The Psychology of Intuition and Its Role In Philosophical Inquiry|year=1998|pages=201–239}}</ref>

A different challenge to appeals to intuition comes from [[experimental philosophy|experimental philosophers]], who argue that appeals to intuition must be informed by the methods of social science.{{citation needed|date=August 2015}}

The [[metaphilosophy|metaphilosophical]] assumption that philosophy ought to depend on intuitions has been challenged by experimental philosophers (e.g., Stephen Stich).<ref>{{Cite journal|last1=Mallon|first1=Ron|last2=Machery|first2=Edouard|last3=Nichols|first3=Shaun|last4=Stich|first4=Stephen|date=September 2009|title=Against Arguments from Reference|journal=Philosophy and Phenomenological Research|volume=79|issue=2|pages=332–356|doi=10.1111/j.1933-1592.2009.00281.x|issn=0031-8205}}</ref> One of the main problems adduced by experimental philosophers is that intuitions differ, for instance, from one culture to another, and so it seems problematic to cite them as evidence for a philosophical claim.<ref>{{Citation|last1=Weinberg|first1=Jonathan M.|title=Normativity and Epistemic Intuitions|date=2012-08-13|work=Collected Papers, Volume 2|pages=159–190|publisher=Oxford University Press|doi=10.1093/acprof:oso/9780199733477.003.0008|isbn=978-0-19-973347-7|last2=Nichols|first2=Shaun|last3=Stich|first3=Stephen}}</ref> [[Timothy Williamson]] responded to such objections against philosophical methodology by arguing that intuition plays no special role in philosophy practice, and that skepticism about intuition cannot be meaningfully separated from a general [[skepticism]] about judgment. On this view, there are no qualitative differences between the methods of philosophy and [[common sense]], the sciences, or mathematics.<ref>{{cite book|last=Williamson|first=Timothy|year=2008|url=https://books.google.com/books?id=YN2KGBgKwOcC&q=intuition|title=The Philosophy of Philosophy|publisher=John Wiley & Sons |isbn=9780470695913 }}{{page needed|date=August 2023}}</ref> Others like Ernest Sosa seek to support intuition by arguing that the objections against intuition merely highlight {{clarify|text=a verbal disagreement|date=August 2023}}.<ref>{{Citation|last=Sosa|first=Ernest|title=A Defense of the Use of Intuitions in Philosophy|work=Stich|pages=101–112|year=2009|publisher=Wiley-Blackwell|doi=10.1002/9781444308709.ch6|isbn=978-1-4443-0870-9}}</ref>

=====Philosophy of mathematics and logic=====
[[Intuitionism]] is a position advanced by [[L. E. J. Brouwer]] in [[philosophy of mathematics]] derived from Kant's claim that all [[mathematics|mathematical knowledge]] is knowledge of the pure forms of the intuition—that is, intuition that is not empirical.

[[Intuitionistic logic]] was devised by [[Arend Heyting]] to accommodate this position (it has also been adopted by other forms of [[constructivism (mathematics)|constructivism]]). It is characterized by rejecting the [[law of excluded middle]]: as a consequence it does not in general accept rules such as [[double negation elimination]] and the use of {{lang|la|[[reductio ad absurdum]]}} to prove the existence of something.{{citation needed|date=August 2015}}