Roberto Poli
Title:
THE UNREASONABLE INEFFECTIVENESS OF MATHEMATICS IN COGNITIVE SCIENCES
Abstract:
My argument is that it is possible to gain better understanding of the
"unreasonable effectiveness" of mathematics in study of the physical
world only when we have understood the equally "unreasonable
ineffectiveness" of mathematics in the cognitive sciences (and, more
generally, in all the forms of knowledge that cannot be reduced to
knowledge about physical phenomena. Biology, psychology, economics,
ethics, and history are all cases in which it has hitherto proved
impossible to undertake an intrinsic matematicization even remotely
comparable to the analysis that has been so fruitful in physics.) I
will consider some conceptual issues that might prove important for
framing the problem of cognitive mathematics (= mathematics for the
cognitive sciences), namely the problem of n-dynamics, of identity, of
timing, and of the specious present. The above analyses will be
conducted from a partly unusual perspective regarding the problem of
the foundations of mathematics.