Where Mathematics Comes From
Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being is a book by cognitive linguist George Lakoff and psychologist Rafael E. NÃÂúÃÂñez. The book seeks to establish a cognitive science of mathematics, or a theory of embodied mathematics.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. Some would contend, however, that such a view is untenable for the simple reason that any and all worlds containing cognitive entities capable of dreaming up mathematical concepts must operate according to the principles of sentential logic. If one accepts logicism in its only coherent form, one must reject the outright denial of Lakoff, even if one accepts the findings of his research.
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