George Lakoff - Embodied Mind - Mathematics


According to Lakoff, even mathematics is subjective to the human species and its cultures: thus "any question of math's being inherent in physical reality is moot, since there is no way to know whether or not it is." By this, he is saying that there is nothing outside of the thought structures we derive from our embodied minds that we can use to "prove" that mathematics is somehow beyond biology. Lakoff and Rafael E. Núñez (2000) argue at length that mathematical and philosophical ideas are best understood in light of the embodied mind. The philosophy of mathematics ought therefore to look to the current scientific understanding of the human body as a foundation ontology, and abandon self-referential attempts to ground the operational components of mathematics in anything other than "meat".

Mathematical reviewers have generally been critical of Lakoff and Núñez, pointing to mathematical errors. (Lakoff claims that these errors have been corrected in subsequent printings.) Their book has yet to elicit much of a reaction from philosophers of mathematics, although the book can be read as making strong claims about how that philosophy should proceed. The small community specializing in the psychology of mathematical learning, to which Núñez belongs, is paying attention.

Lakoff has also claimed that we should remain agnostic about whether math is somehow wrapped up with the very nature of the universe. Early in 2001 Lakoff told the American Association for the Advancement of Science (AAAS): "Mathematics may or may not be out there in the world, but there's no way that we scientifically could possibly tell." This is because the structures of scientific knowledge are not "out there" but rather in our brains, based on the details of our anatomy. Therefore, we cannot "tell" that mathematics is "out there" without relying on conceptual metaphors rooted in our biology. This claim bothers those who believe that there really is a way we could "tell". The falsifiability of this claim is perhaps the central problem in the cognitive science of mathematics, a field that attempts to establish a foundation ontology based on the human cognitive and scientific process.

Read more about this topic:  George Lakoff, Embodied Mind

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