About axiomatic philosophy

A little background

Axiomatic philosophy is what I sometimes call the way I prefer to do philosophy. Not every post here is going to be done that way, but the intention is to at least keep the possibility of putting things axiomatically in mind.

The basic idea is fairly simple, and goes back to Hume's fork. There are principally two valid forms of philosophical argument:

• Empirical arguments, the standards of which are the same as those of the empirical sciences.
• Non-empirical arguments, the standards of which are the same as those of mathematics.

Sure, there are also borderline cases, but as long as you can either prove what you say mathematically, or present testable empirical evidence for it and then prove it based on that evidence, you're in the clear.

Experimental philosophy is one way to work along the first prong of the fork. Axiomatic philosophy is a way to work along the second. It is mainly inspired by the form mathematics started to take in the 20th century, and by some types of mathematical physics and economics. 

How to do axiomatic philosophy

If you want to argue for something in philosophy, prove it. Set up some axioms, make some definitions, and then create a mathematical proof that shows why what you want to argue for holds.

Sure, it will of course depend on what axioms you set up, as well as what kind of logic you are working in. You can argue for those as well by proving them from other axioms or logics, but you can of course never prove everything. That's just life. By at least proving something, you trace out connections and further our understanding, even if it is only marginally.

Why do philosophy axiomatically?

Because philosophy, like much of natural science, deals with what is fundamentally absurd. Like really fucked up. It is very, very different from the way we usually experience our world, so our commonsense intuitions tell us nothing at all about it. Or rather, they sometimes tell us things, but we have no reason to take those things seriously since they developed for other, unrelated purposes.

Axiomatic philosophy is one way to try to work with philosophical problems anyway - despite their fundamental unsolvability. By creating axiomatic theories, models, definitions and proofs around some concepts, we create meaning from the absurd. It is constructive rather than analytic, as we don't pretend that we are uncovering anything that was already there. All we are doing is to create systems. New ways of thinking more exactly about things that we can never know.

Reading more

The following is a talk I gave a while ago about axiomatic philosophy:

Philosophy as a Deductive-Axiomatic Science

If you are interested in my thoughts about conceptual analysis, there is a paper published (under my old name) in Metaphilosophy that discusses that:

The Square Circle

I'll try to get a non-paywalled version of it up somewhere if there is interest. Unfortunately, I can't seem to find my own version anywhere right now.