Cool Logic

Vasily Romanovskiy (ILLC)

Ramsey's Representation Theorem for degrees of belief

November 26th at 17:00, in SP904 D1.111

In his pioneering ‘Truth and Probability’ (1931), Frank Ramsey sets out an influential account of the nature, measurement, and norms of partial belief. The centrepiece of this work is a representation theorem that allows Ramsey to construct a unique probability function representing an agent’s subjective degrees of confidence. In many ways, this marks the birth of decision theory as a field and the birth of the subjective interpretation of probability. In this expository talk we will examine the philosophical background underlying Ramsey’s goals in this work, we will re-construct the main formal moves Ramsey makes in proving his representation theorem and finally, we will criticise some of the philosophically contentious assumptions that permeate throughout ‘Truth and Probability’ (1931). Taking a broader perspective, representation theorems are the underbelly of much work in theoretical economics, the underbelly behind claims like ‘humans are rational’. This talk will give a first-hand look at (just) one such representation theorem, but the illustrative purposes this will serve will hopefully be felt by anyone who is a slave of some defunct economist. Which, if some are to believed, includes all of us.