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Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being
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am 16. Oktober 2009
Some readers have dismissed "Where Mathematics Come From" as being "postmodern", i.e. advocating arbitrariness of mathematical reasoning. These reviewers don't seem to have made it to the end. The authors are actually very clear about their viewpoint: They disapprove of the romance of mathematics (that basically claims, mathematical truths have an objective existence independent of human cognition, and by the same token logic accounts for the (only) correct way of reasoning). But at the same time they acknowledge the universal nature of mathematical reasoning and its effectiveness in dealing with real world phenomena. There is a simple reason for the correspondence between human-made math and reality and it is given in chapter 15: Humans share a common brain structure, they live in fairly similar surroundings dealing with the same basic issues of everday life. Mathematics as well as language is modeled according to real life needs and conditions. Therefore mathematical reasoning is not arbitrary, albeit culturally shaped (c.f. the idea of "essence" leading to the need for axiomatization or the notion that all human reason is some kind of calculation).
It is relatively easy to corroborate the author's thesis, that the development of mathematics can be accurately described in terms of application of metaphorical structures and conceptual blending mechanisms on mathematical concepts and thereby creating new concepts and so forth. Just take a contemporary mathematical advanced textbook on calculus or algebra and compare it to the writings of mathematicians before the invention of differential calculus (in Lakoffs/Nunez terms: the construction of infinitesimals and the mapping of numbers on the points on a line)or even Euler. The difference is striking: The idea that mathematical insights should rely on some essential axioms whence all mathematical truth can be derived must have seemed outlandish to mathematicians before the 19th century (although proved to be incorrect for quite some time now the notion of mathematics as being independent and self-sustaining seems to be quite widespread still).
Of course, by exploiting the possibilies of metaphorical cross-mapping within mathematics itself mathematics has liberated itself from reality to a great extent and turned into an art. Why else would mathematicians claim that beauty, simplicty and truth are closely interrelated?
The authors (and myself) obviously love mathematics and hold mathematicians in high esteem. And even more so by the fact that mathematics is "only" human.

A great reader for anyone who loves mathematics and wonders how it connects to common sense!
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