# Induction, Probability and Confirmation (PHIL 357.001)

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Instructor: John Roberts. This course meets Mondays and Wednesdays from 9:30AM – 10:45AM in Caldwell 213.

This course is aimed primarily at advanced philosophy majors, but others who have had at least one philosophy course (other than a logic course) might be adequately prepared; this course is not intended to be a first course in philosophy, and it would be a bad idea to take it without having had another philosophy course first. That said, there are no specific prerequisites.

This course will be about two topics that partly overlap. The first topic isinduction: the kind of reasoning we engage in when we project patterns we have noticed into the future. For example: Water has been good for relieving first every time I’ve tried it in the past, therefore I can expect it to relieve thirst in the future; the law of conservation of energy has not been violated in any experiment performed so far, so (probably) it is never violated; 60% of the likely voters in our sample prefer candidate X, so probably, about 60% of the voters will vote for candidate X. What are the principles that govern this kind of reasoning? And more fundamentally, what makes this kind of reasoning legitimate at all? The philosopher David Hume posed a problem that appears to show that we are never justified when we reason in this way. (Roughly: We haven’t seen the future yet, so we cannot know directly that the patterns in the past will continue into the future. But in order to know it indirectly, we would have to rely on what we know about the past, and draw an inference about what will happen in the future. But whenever we do that, we implicitly assume that the patterns in the past will continue in the future — otherwise, the past could give us no information about what the future will be like. So, it seems that in order to justify our assumption that patterns will continue into the future, we have to take for granted that patterns will continue into the future — blatantly circular reasoning. So — there’s no way to justify the assumption that patterns in the past will continue into the future?) We will study this problem, as well as a companion problem posed by Nelson Goodman, and look at a wide range of attempts to solve these problems.

The second topic is probability. The mathematical theory of probability is extremely well-developed, but there are still deep problems about how to interpret probabilities — about just what probabilities really are. We’ll look at a variety of views about this, and examine some philosophical puzzles having to do with probability.

The two topics overlap because many people think that the justification of induction and the principles that govern inductive reasoning both make use of probability. We will study one way of trying to work out this idea in detail, called Bayesian Confirmation Theory.

There will be a certain amount of mathematics in this course. It will not be necessary for students to have taken a course in probability theory or statistics, though. Students should be prepared to do a certain amount of mathematics, involving a certain amount of algebra.

There will be a number of homework assignments, a paper, and a final exam.

Please note: Some seats in this class have been reserved for Philosophy majors.

This course satisfies the QI general education requirement; it does not satisfy the PH requirement.

John Roberts’s webpage