Michael kind of broke down today; so he asked me to write about our newest adventure…Category Theory.
Why? Well, he and I are very excited to say that we have been invited to a reading group for Category Theory!!! One of our colleagues at the collegium said that we satisfied the [moronic] intellectual requirement (basically we needed to know that one number was bigger than another, and about transitive relations!!!), and we are really ignorant of mathematics generally.
Given that Michael and I come from Artistic, seminary and literary backgrounds; the thought of taking a mathematics ‘class’ among philosophers and mathematicians was very arousing. That’s the thing I love about philosophy; we could at one point be talking about semantics and truth, or scientific method and knoweldge, biology and metaphysics, or art and morality. Philosophy is the unity of all human endeavour, and (if the former claim is correct) the philosopher is the most cultivated of all people, but not the most able. The idea of the renaissance man; who engages in poetry, rhetoric, syntax, figures, rudiments and grammar…that was the way we were taught to be. Anyway…
What the hell is category theory? I don’t really know! Apparently, it is a way of describing some aspect of a discourse in mathematics (say, arithmetic) through another discourse (namely the categoric one). So; question:
How is Category Theory similar or dissimilar to Number Theory and Set Theory insofar as they may be construed as a way of modelling one discourse subsuming the vocabulary of the subject discourse?
Some contraversial suggestions I have heard… (I remain not only agnostic, but IGNORANT about these):
Category theory could be placed as a foundation for mathematics
Category theory has implications towards constructing particular logics (such as ‘higher order’ systems) and has applications towards computation
Category theory is useful, or can be used towards theoretical physics modelling
You know, despite the weird things we post about, Michael and I are really just dumbasses. Despite that, Michael has this weird dream to try and emulate Kant’s life…particularly the idea of having intellectual circles where they discuss politics and metaphysics; and a servant named Lampe…
Get well soon, M