Statistical inference and Aristotle's Rhetoric.

Formal logic operates in a closed system where all the information relevant to any conclusion is present, whereas this is not the case when one reasons about events and states of the world. Pollard and Richardson drew attention to the fact that the reasoning behind statistical tests does not lead to logically justifiable conclusions. In this paper statistical inferences are defended not by logic but by the standards of everyday reasoning. Aristotle invented formal logic, but argued that people mostly get at the truth with the aid of enthymemes--incomplete syllogisms which include arguing from examples, analogies and signs. It is proposed that statistical tests work in the same way--in that they are based on examples, invoke the analogy of a model and use the size of the effect under test as a sign that the chance hypothesis is unlikely. Of existing theories of statistical inference only a weak version of Fisher's takes this into account. Aristotle anticipated Fisher by producing an argument of the form that there were too many cases in which an outcome went in a particular direction for that direction to be plausibly attributed to chance. We can therefore conclude that Aristotle would have approved of statistical inference and there is a good reason for calling this form of statistical inference classical.