An Introduction to Pure Inductive Logic

Richard Whyman, University of Leeds. Part of the postgraduate logic seminar series.

Typically in mathematics we begin with some ideal abstract universe of which we know all of the relevant details before concerning ourselves with what statements are definitely true and what statements are definitely false in this universe.

However, the real world is not so kind to us and in many scenarios we find ourselves in a situation in which we are given only partial knowledge before being forced to take some course of action based on what we think ought to be true. For example, if we flip a possibly weighted coin n times and record the results, what can we inductively conclude about the probability of the n+1th coin flip as resulting in heads? Is it worth betting on that outcome? Or what about a scenario in which we begin zero-knowledge, should we consider some sentences as being more likely to be true than others? If so, how likely are they?

Pure inductive logic aims at giving answers to these questions.

Richard Whyman, University of Leeds