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...
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.