The book calls for (and attempts to begin) a cognitive idea analysis of mathematics which analyzes mathematical ideas in terms of the human experiences, metaphors, generalizations and other cognitive mechanisms which gave rise to them. Ultimately, it is held, mathematics is a result of the human cognitive apparatus and must therefore be understood in cognitive terms. This idea analysis is distinct from mathematics itself and cannot be performed by mathematicians not sufficiently trained in the cognitive sciences.
The position of platonism in the philosophy of mathematics is rejected: all we know and can ever know is human mathematics, the mathematics arising from our brains, and the question whether a "transcendent mathematics" objectively exists is thus unanswerable and close to meaningless.
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