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Preintuitionism - The introduction of natural numbers | | Preintuitionism - The introduction of natural numbers: Encyclopedia II - Preintuitionism - The introduction of natural numbers | | The Pre-Intuitionists, as defined by Brouwer, differed from the Formalist standpoint in several ways. In the introduction of natural numbers, or how the natural numbers are defined/denoted. For Poincaré the definition of a mathematical entity is the construction of the entity itself and not an expression of an underlying essence or existence.
Which is to say that no mathematical object exists without our construction of it, both in mind and language.
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See also:Preintuitionism, Preintuitionism - The introduction of natural numbers, Preintuitionism - The principle of complete induction, Preintuitionism - Arguments over the excluded middle, Preintuitionism - Other Pre-Intuitionists | | | Preintuitionism, Preintuitionism - Arguments over the excluded middle, Preintuitionism - Other Pre-Intuitionists, Preintuitionism - The introduction of natural numbers, Preintuitionism - The principle of complete induction | | |
| | | Preintuitionism: Encyclopedia II - Preintuitionism - The introduction of natural numbers
Preintuitionism - The introduction of natural numbers
The Pre-Intuitionists, as defined by Brouwer, differed from the Formalist standpoint in several ways. In the introduction of natural numbers, or how the natural numbers are defined/denoted. For Poincaré the definition of a mathematical entity is the construction of the entity itself and not an expression of an underlying essence or existence.
Which is to say that no mathematical object exists without our construction of it, both in mind and language.
Other related archivesBertrand Russell, Borel, Brouwer, Cambridge, Cantor, Couturat, Dedekind, Formalist, Giuseppe Peano's, Hermann Weyl, Hilbert, Intuition, Kronecker, L. E. J. Brouwer, Law of excluded middle, Lebesgue, Leopold Kronecker, Logicism, Peano's, Poincaré, Russell, Zermelo, analytic, axiom, axiomatic theory of natural numbers, complete induction, existence proofs, general logic, induction, infinite, knowledge, language, mathematical philosophy, natural numbers, non-constructive, rigorous, situations, synthetic, vicious circle
 Adapted from the Wikipedia article "The introduction of natural numbers", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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