What is Mathematics? And why is it now time to address
this question scientifically? A view from Cognitive Science
What is mathematics and what are its foundations? The question
of the nature of mathematics has been addressed primarily
within the confines of the philosophy of mathematics (e.g.,
formal logical) and mathematics proper (e.g., metamathematics),
with little, or no input from other scientific disciplines.
Given current scientific developments --- especially concerning
new findings about how human abstraction and imagination work
--- this is arguably an unnecessarily narrow approach to the
investigation of such deep and important question. In this
presentation I'll discuss results in cognitive science ---
the interdisciplinary scientific investigation of the mind,
which gathering advances in neuroscience, psychology, linguistics,
and anthropology, among others, has empirically investigated
mathematics as a human conceptual system --- one that is abstract,
precise, objective, effective, and formalizable, but that
is human nonetheless. Discussing cognitive studies in infinitesimal
calculus and set theory, I'll argue that the time has come
to approach the study of the nature of Mathematics with empirical
observations and testable explanations, and not just with
old philosophical beliefs and dogmas. The portrait of mathematics
has a human face, and it is up to us to get to know it!
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