April 17, 2011

A scientist modelling a scientist modelling science

The is a follow up from Nathaniel’s post. One of the ways that the probabilities of probabilities can be used is in asking what experiments would be best for a scientist to do. We can do this because scientists would like to have a logically consistent system that describes the world but make measurements which are not completely certain – the interpretation of probability as uncertain logic is justified.

Lets make a probabilist model of scientific inquiry. To do this, the first component we need is a model of “what science knows”, or equally, “what the literature says”. For the purposes here, I will only consider what science knows about one statement: “The literature says X is true”. I’ll write this as $p(X|L)$ and its negation as $p(\bar{X}|L) = 1 - p(X|L)$. This is a really minimal example.