Jessica Collins

Set theory; concepts such as Vitali sets, Von Neumann - Morgenstern utility, infinities, diagonalizations, etc.

There are a lot of specifics this course taught me that are largely contained within the scope of this class and the options for further study it opens up. Arguably however, the most important thing it demonstrated to me was that some of the greatest breakthroughs in any given field of study are not always the ones that upend theories or even directly tackle problems within those theories head on. One of Ramsey's greatest strengths seemed to me to be that of evasion. Instead of confronting problems directly, he could gently change direction of an argument or line of thought and avoid them all together. Throughout this course, I became more aware of this both in his writings and my life outside the classroom. Often, creative problem solving is finding a way to simply avoid the problem. I am quite grateful for having been able to learn how to pick up on this and work to apply it as an analytical/practical skill outside the classroom.

large and small infinities, a bunch of probability and set theory ideas that went way over my head, and alittle decision theory

Well I tried to learn a comprehensive understanding of Frank P. Ramsey's work and life. I was successful in the biographic aspect but not so much in the technical work.

A heavy amount of focus has been given to probability and a third or so has been given to decision theory. We studied the mathematical and philosophical foundations of probability theories, interpretations of probability, etc, as well as the foundational works in decision theory and some challenges to them.

This course is not for the faint of heart. With that being said: there is no feeling like laying on the battlefield broken but victorious.

Probability Axioms, Algebra formalisms, Infinite sets and cardinality, Axiom of Choice, Cantor's diagonalization, von Mises frequency theory, Consistency of the axioms of frequency theory, de Finetti's exchangeability and subjective formalism of objective chance, decision theory and preference relations

I would definitely recommend this class to anyone because Frank Ramsey is a hidden genius who I believe does not get as much widespread recognition as he deserves considering how incredibly advanced he was for his time, and that is not even mentioning the fact he did all this before the age of 26 1 Columbia University: Arts & Sciences Spring 2022 Course: PHILUN3912_004_2022_1-SEMINAR : PHILUN3912_004_2022_1 - SEMINAR Instructor: Jessica Collins

The course is difficult without background in formal math.

I gained a deeper understanding of probability and decision-making frameworks, along with their philosophical underpinnings. It sharpened my critical thinking and helped me analyze decisions more systematically.