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
Famous quotes containing the words introduction, natural and/or numbers:
“Such is oftenest the young man’s introduction to the forest, and the most original part of himself. He goes thither at first as a hunter and fisher, until at last, if he has the seeds of a better life in him, he distinguishes his proper objects, as a poet or naturalist it may be, and leaves the gun and fish-pole behind. The mass of men are still and always young in this respect.”
—Henry David Thoreau (1817–1862)
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“Green grow the rushes-O
What is your one-O?”
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