Monday, 7 June 2010

Rational inference in science

One of the side-effects of working in science is that you end up thinking a lot about how we reason and learn. What rules do we choose in order to do this? Do we have a range of options? This is pretty important, as it underpins everything we do as scientists (or thinkers of any kind, come to that).

The term 'Rational Inference' is a good way to describe how we do this. It covers both logical deduction (for when we have definite facts: if A and B are true, then C must also be true) and induction (for when there is uncertainty: D and E are true probably, which implies that F is also likely to be true). Rational inference is how we reason in science, whether using experimental results, observations of the universe or even (the most obvious example) mathematics, and how we learn more about laws that describe how the world works.

The fascination for me is that we have a mathematical theory that tells us how rational inference must work - probability theory. If you're comfortable with a Bayesian perspective on the subject (and are therefore happy to allow probabilities to represent states of knowledge), then probability theory contains logical deduction as a special case when all probabilities are either zero (false) or one (true). It also extends this to allow for different degrees of plausibility (0 < probability < 1), giving us the capability to represent any state of knowledge from false, through 'maybe', to true.

This also gives us an answer to the question "am I using the right set of rules to make my inferences?". The physicist Richard Cox provided a proof (using only very general starting assumptions) that any consistent mathematical rules for handling degrees of plausibility must be those of probability theory (or equivalent to them). Meaning the answer to our question is "yes!" - and we realise we are using the only set of mathematical rules for rational inference that make any sense.

So we find ourselves with a uniquely correct approach to reasoning in science (and anywhere else), along with a set of mathematical rules to use. There are philosophical considerations along the way (such as whether to adopt a Bayesian or Frequentist viewpoint) but if you're comfortable with the idea that your degrees of plausibility can include states of knowledge, you've got a unique set of mathematical rules that tell you how to make rational inferences about the world.

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