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.
I think getting technical precision on philosophical concepts like these will play a crucial role in the kind of math I’m envisioning.
I’m not sure exactly what you’re asking—I wonder how much my reply to Adam Shai addresses your concerns?
I will also mention this quote from the category theorist Lawvere, whose line of thinking I feel pretty aligned with:
I think getting technical precision on philosophical concepts like these will play a crucial role in the kind of math I’m envisioning.
Very helpful, thank you.