Lawvere's Prophecy
In 1992, category theorist William Lawvere made a prophecy:
It is my belief that in the next decade and in the next century the technical advances forged by category theorists will be of value to dialectical philosophy, lending precise form with disputable mathematical models to ancient philosophical distinctions such as general vs. particular, objective vs. subjective, being vs. becoming, space vs. quantity, equality vs. difference, quantitative vs. qualitative etc. In turn the explicit attention by mathematicians to such philosophical questions is necessary to achieve the goal of making mathematics (and hence other sciences) more widely learnable and useable. Of course this will require that philosophers learn mathematics and that mathematicians learn philosophy.
—Lawvere, Categories of space and quantity
Here is a program for how category theory will be of
service in politics and spirituality (for Lawvere, a
Marxist-Leninist, dialectical philosophy
was the
ground of both of these things). Namely, the same
people will have to learn both mathematics and
philosophy, and then by listening to the voices of
philosophical distinctions with great attention, they will
clarify them in precise mathematics.
This prophecy can be generalized: to apply category theory to a domain X, some people will have to learn both category theory and X.
See the
NIST report for thoughts on how CT for X
can happen
practically.