I have two questions about logic that have vexed me for a long time.

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I have two questions about logic that have vexed me for a long time. Smith has written two great books of philosophy. Now he has come out with a third book. Therefore, that book will probably be good too. Smith has flipped a coin twice, and both times it has come up tails. Now Smith will flip the coin a third time. Therefore, that flip with probably end up 'tails' too. The logical form of inductive arguments seems to contribute nothing; the premises seem to do no logical work supporting the conclusion - is that right? Smith has written two great books of philosophy. Now he has written a third. Any author that has written two great books of philosophy, and then writes a third, has probably written a third great book. Therefore, Smith has probably written a third great book. That seems a deductive argument, because the general premise was added. And if true, the premises do seem to support with conclusion with necessity, even though the conclusion is probable; it is the knowledge of the world and not the logical form that is doing the work. What about that as an argument to replace induction with strictly deductive arguments? In the coin toss example, the general premise "Anybody who flips a coin twice and gets 'tails' will probably get 'tails' on the third toss" would clearly be false, showing more clearly than inductive reasoning could why that would be a bad argument. Appreciate the continuation of the site!

I think both arguments can be analyzed as inductive arguments and still distinguished in terms of their quality. The book argument is a stronger inductive argument than the coin-toss argument for a simple reason: the probability that Smith's book C is great isn't independent of whether Smith's books A and B are great.

That is, Smith's having written great books A and B makes the probability that Smith's book C is great higher than it would be had Smith not already written two great books. Important: higher than it would be otherwise, which needn't mean higher than one-half. Even though Smith's track-record raises the probability that book C is great, the track-record needn't make it more probable than not that book C is great.

By contrast, the probability of tails on any given toss of a fair coin is independent of whether the coin came up tails twice already: that history of tosses neither increases nor decreases the probability of tails on a third toss.

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