What kind of math is used in the following Causal Decision Theory book?

Question

I am coming from a philosophical background (studied informally) and I want to learn decision theory. The following book The Foundations of Causal Decision Theory by James Joyce is the gold standard for decision theory. I know only college algebra. I was wondering what kind of math is used in this book?

Answer 1

You may be in for a long haul

1. Review Calculus, this is mostly for the notation and also as a gateway into proofs and the correct ways to approach problems, intuition, etc.
2. Set theory, Sometimes addressed in other courses, but certainly worth your time
3. Statistics, mostly as a pre-requisite to studying probability
4. Probability, study this formally, you really need to understand the concepts and the notation.
5. Any proof heavy course: Analysis, number theory, abstract algebra, or topology.

If you instead want a shortcut, so that you understand what the book says without having to understand the math, you could probably get away with just an in depth course on Probability.

Sorry, I don't have any book reccomendations.

Answer 2

I think that @Mathaddict is perhaps too pessimistic. You can in fact get quite far in the material in Joyce with just algebra. The hardest part of the mathematics is understanding what the symbols mean in philosophical terms. That's what you have to do to "grasp the concepts". Your philosophy training will help a lot with that.

The central idea is the interplay between probability and utility or value. To understand that you start with the fair value of a bet. A web search will find many discussions of fair or expected value. (Your other question on this site suggests that you have already begun your struggle with this.)

I suggest that your best strategy is to start in on Joyce. When you encounter math/algebra that stumps you, try to look it up or ask (perhaps here).

Disclaimer: One of Joyce's starting points is a theory of decision developed by Dick Jeffrey. By fortunate coincidence I met Jeffrey years ago and we discovered that the "serious" mathematics in my brand new thesis was just what he needed for his theory. But you don't have to study that mathematics (or even the prerequisites for that mathematics) in order to work with the philosophy of decision theory. I don't think Jeffrey ever did, although he could have had he needed to.

Good luck.