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Pre-intuitionism
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==The introduction of natural numbers== {{multiple issues|section=y| {{unsourced|section|date=June 2024}} {{confusing|section|reason=it is unclear what is Poincaré's opinion, what is Brouwer's interpretation of Poincaré's thoughts and what is editor's interpretation.|date=June 2024}} {{Original research|section|reason=In particular, the second paragraphis seems a wrong interpretation of what precedes; this may also be interpreted as meaning that the definition of mathematical objects does not need to rely to some exernal reality, and that Peano's axioms form a definition of natural numbers.|date=June 2024}}}} The pre-intuitionists, as defined by [[L. E. J. Brouwer]], differed from the [[Formalism (philosophy of mathematics)|formalist]] standpoint in several ways,<ref name=CW/> particularly in regard to the introduction of natural numbers, or how the natural numbers are defined/denoted. For [[Henri Poincaré|Poincaré]], the definition of a mathematical entity is the construction of the entity itself and not an expression of an underlying essence or existence. This is to say that no mathematical object exists without human construction of it, both in mind and language.
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