The Introduction of Natural Numbers
The Pre-Intuitionists, as defined by Brouwer, differed from the Formalist standpoint in several ways, particularly in regard to 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.
This is to say that no mathematical object exists without human construction of it, both in mind and language.
Read more about this topic: Preintuitionism
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