logical intuition

Plato and Aristotle considered intuition a means for perceiving ideas, significant enough that for Aristotle, intuition comprised the only means of knowing principles that are not subject to argument.{{cite journal | last=Piętka| first=Dariusz| title=The Concept of Intuition and Its Role in Plato and Aristotle| journal=Organon| year=2015|volume=47|pages=23-40| url=https://ihnpan.pl/wp-content/uploads/2016/03/2_pietka.pdf}}

Henri Poincaré distinguished logical intuition from other forms of intuition. In his book The Value of Science, he points out that:

{{quote|...[T]here are many kinds of intuition. I have said how much the intuition of pure number, whence comes rigorous mathematical induction, differs from sensible intuition to which the imagination, properly so called, is the principal contributor.{{cite web| last=Poincaré| first=Henri| title=Intuition and Logic in Mathematics, from the book The Value of Science| year=1905| url=http://www-history.mcs.st-andrews.ac.uk/Extras/Poincare_Intuition.html}}}}

The passage goes on to assign two roles to logical intuition: to permit one to choose which route to follow in search of scientific truth, and to allow one to comprehend logical developments.{{cite book| last=Poincaré| first=Henri| title=The Value of Science| year=1905| url=http://www-history.mcs.st-andrews.ac.uk/Extras/Poincare_Intuition.html}}

Bertrand Russell, though critical of intuitive mysticism,{{cite web| last=Popova| first=Maria| title=A Largeness of Contemplation: Bertrand Russell on Intuition, the Intellect, and the Nature of Time| year=2016| publisher=BrainPickings.org| url=https://www.brainpickings.org/2016/05/13/bertrand-russell-mysticism-logic-time/}} pointed out that the degree to which a truth is self-evident according to logical intuition can vary, from one situation to another, and stated that some self-evident truths are practically infallible:

{{quote|When a certain number of logical principles have been admitted, the rest can be deduced from them; but the propositions deduced are often just as self-evident as those that were assumed without proof. All arithmetic, moreover, can be deduced from the general principles of logic, yet the simple propositions of arithmetic, such as 'two and two are four', are just as self-evident as the principles of logic.{{cite book| last=Russell| first=Bertrand| title=Problems of Philosophy| year=1912| url=http://www.ditext.com/russell/rus11.html}} Chapter XI "On Intuitive Knowledge"}}

Kurt Gödel demonstrated based on his incompleteness theorems that intuition-based propositional calculus cannot be finitely valued.{{cite book| last=Kennedy| first=Juliette| title=Kurt Gödel| year=2015| publisher=Stanford Encyclopedia of Philosophy| url=https://plato.stanford.edu/entries/goedel/#GodRat}} Gödel also likened logical intuition to sense perception, and considered the mathematical constructs that humans perceive to have an independent existence of their own.{{cite web| last=Ravitch| first=Harold| title=On Gödel's Philosophy of Mathematics| year=1998| url=http://www.friesian.com/goedel/chap-2.htm}} Under this line of reasoning, the human mind's ability to sense such abstract constructs may not be finitely implementable.{{cite web| last=Solomon| first=Martin| title=On Kurt Gödel's Philosophy of Mathematics| year=1998| url=http://calculemus.org/lect/07logika/godel-solomon.html}}

Dissent regarding the value of intuition in a logical or mathematical context may often hinge on the breadth of the definition of intuition and the psychological underpinning of the word.{{cite web| author=XiXiDu| title=Intuition and Mathematics| year=2011| url=https://www.lesswrong.com/posts/5twHzuzCxgFWHZRsg/intuition-and-mathematics}}{{Cite journal|url=https://pdfs.semanticscholar.org/0f4d/e7143b287281e4e20a4d3fa203eacf1aa67e.pdf|title=Why is Intuition so Important to Mathematicians but Missing from Mathematics Education?|last=Burton|first=Leone|date=2014|website=Semantic Scholar|s2cid=56059874|url-status=live|archive-url=https://web.archive.org/web/20191021192440/https://pdfs.semanticscholar.org/0f4d/e7143b287281e4e20a4d3fa203eacf1aa67e.pdf|archive-date=2019-10-21|access-date=October 21, 2019}} Dissent regarding the implications of logical intuition in the fields of artificial intelligence and cognitive computing may similarly hinge on definitions. However, similarity between the potentially infinite nature of logical intuition posited by Gödel and the hard problem of consciousness posited by David Chalmers suggest that the realms of intuitive knowledge and experiential consciousness may both have aspects that are not reducible to classical physics concepts.{{cite web| last=Aas| first=Benjamin| title=Body-Gödel-Mind: The unsolvability of the hard problem of consciousness| year=2011| url=http://necsi.edu/events/iccs2011/papers/199.pdf| access-date=2018-05-08| archive-date=2022-02-25| archive-url=https://web.archive.org/web/20220225170022/https://necsi.edu/events/iccs2011/papers/199.pdf| url-status=dead}}

• Intuition
• Epistemology
• Philosophy of mind
• Philosophy of mathematics
• Cognition
• Numerical cognition
• Consciousness
• Hard problem of consciousness
• Panpsychism
• Transcendental idealism
• Intuitionism
• Intuitionistic logic
• Continuum hypothesis
• Logical truth

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Category:Logic