Mathematical rules of reasonable expectation
Proposition A: The Condensed Matter group Christmas dinner is on Tuesday evening.
Proposition B: Turnout at this week's Theory Club is low.
If A implies B, Aristotle would tell us that the only logical deduction we can make is that a high attendance on Wednesday would imply that there had been no Christmas dinner the night before. On the other hand, if no-one shows up, that doesn’t necessarily mean that there had been a festive knees-up the night before, but it makes this proposition more plausible.
It turns out that one can assign a number to each proposition that serves as a measure of its plausibility, and that by putting very light constraints on how these plausibilities should relate to each other, obtain a set of algebraic rules that they must satisfy. These rules coincide with those of probability theory, but at no point do we need to make reference to ensemble an theory clubs and Christmas dinners. I shall attempt to explain why and what I would like this to mean.
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..