Home > Quasi-empiricism in mathematics
Quasi-empiricism in mathematics is the movement in the philosophy of mathematics to reject as pointless the foundations problem in mathematics, and re-focus philosophers on mathematical practice itself, in particular relations with physics and social sciences.A key argument is that mathematics and physics, as perceived by humans, have grown together, may simply reflect human cognitive bias, and that the rigorous application of empirical methods or mathematical practice in either field is insufficient to disprove credible alternate approaches.
Hilary Putnam argued convincingly in 1975 that real mathematics had accepted informal proofs and proof by authority, and made and corrected errors all through its history, and that Euclid's system of proving theorems about geometry was peculiar to the classical Greeks and did not evolve in other mathematical cultures in China, India, and Arabia. This and other evidence led many mathematicians to reject the label of Platonists, along with Plato's ontology—which, along with the methods and epistemology of AristotleAristotle ( Greek Αριστοτλης Aristotelēs) ( 384 BCE March 7, 322 BCE) was a Greek scientist and philosopher. Along with Plato, he is often considered to be one of the two most influential philo, had served as a foundation ontologyIn computer science jargon, a foundation ontology or upper ontology is a hierarchy of entities and associated rules (both theorems and regulations) that attempts to describe those general entities that do not belong to a specific problem domain. See ontol for the Western world since its beginnings. A truly international culture of mathematics would, Putnam and others argued, necessarily be at least 'quasi'-empirical (embracing 'the scientific method' for consensus if not experiment).
Eugene WignerEugene Paul Wigner ( Hungarian Wigner Pal Jeno) ( November 17, 1902 January 1, 1995) was a Hungarian- American physicist and mathematician. He was one of a generation of physicists of the 1920s who remade the world of physics. It was a collection of peopl had noted in 1960Events January-February January 1 Independence of Cameroon January 9 Aswan High Dam construction begins in Egypt January 11 Chad declares its independence. January 14 Ralph Chubb, the gay poet and printer, dies at Fair Oak Cottage in Hampshire. January 23 that this culture need not be restricted to mathematics, physics, or even humans. He stated further that "The miracle of the appropriateness of the language of mathematics for the
formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for
worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning."
This simultaneous "hope" and "bafflement" regarding the undeserved "gift" was a frank admission that quasi-empiricism could apply to physics as well, and that other branches of learning need not necessarily be so compatible with mathematics as understood in the context of physics or hard sciences.
See also: philosophy of mathematics, foundations of mathematicsMathematical logic The term foundations of mathematics is sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. The search for foundations of mathema
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Philosophy of mathematics
