One hears it said from time to time that it’s irrational to perform inductive inferences based on a single data point. Now this is sometimes irrational. For example, from the fact that Al Gore got the most votes in the last Presidential Election it would be foolish to infer that he’ll get the most votes in the next Presidential Election. But it isn’t always irrational. And this matters to some philosophical debates, and perhaps to some practical debates too.

Here’s my proof that it isn’t always irrational. Imagine on Thursday night I go and see a new movie that you’re going to go see Friday night. Friday lunchtime I tell you how the movie ended. How should you react? Most people will complain that I’ve spoiled the movie because you now know how it will end. But if induction on a single case is always bad, this is impossible. All you have is testimonial evidence of how the movie ended on a single occasion, namely Thursday night. You need to make an inferential leap to make a conclusion about how it will end Friday night. (It certainly isn’t a deductive inference because some movies have multiple endings.) That inferential leap will be induction on a single case, and will be perfectly reasonable.

That’s more or less my complete argument that induction on a single case can be perfectly rational. There is an obvious objection though. It might be argued that this isn’t _really_ induction on a single case, because it’s like underwritten by a many-case induction based on the number of previous movies that have ended the same way at multiple screenings. While that’s obviously true, it isn’t clear how much it undermines the original example.

There’s two points we could go on to debate here. First is the question of whether the inference from how the movie ended on Thursday to how it will end on Friday (the movie inference) is really an instance of induction on a single case. That looks like a relatively stale terminological debate, and I couldn’t be bothered hashing it out here. Second is the question of whether there is any way to distinguish the movie inference from what are usually taken to be bad instances of induction on a single case. This one has to be debated case by case, but I suspect the answer is in general _no_, unless there are independent reasons to dislike the particular bad instance of inductive reasoning.

Here’s a couple of illustrations of what I mean, one practical the other theoretical.

Consider the policy “Don’t start reading a blog if the first thing you read there is false.” Some might consider any application of that to be a bad instance of a single case induction – from one bad claim infer that other things the blog says are not worth reading. But just like the movie inference can be backed up by a meta-induction, this one can arguably be backed up by a claim validated by a meta-induction: that blogs which say something false the first time you open them are not worthwhile reading in the future. That claim might well be _false_, and I’m not taking sides here on whether it is true or not, but as long as the person who holds the policy believes the claim, their reasoning is no worse than the person who makes the movie inference. (Quick credit: I saw this policy defended somewhere a while ago, but Google was no help in finding where. That was more or less what inspired this post.)

Let’s take a more famous case. Why should I believe that other people have sensations? One famous answer, defended by Bertrand Russell, is that I can reason by analogy. I’m alike other people in ever so many ways, so I’m probably alike them in respect of sensations. And I know (somehow!) that I have sensations, so I know they do too.

Some people have objected that this is just induction on a single case. (E.g. Michael Rea makes that objection “here”:http://www.amazon.com/gp/reader/0199247609/ref=sib_rdr_next3_ex168/103-6891633-7112654?%5Fencoding=UTF8&keywords=ROM&p=S053&twc=14&checkSum=UUh%2B4yKxKqD3qjbFZkigaI%2BcoqguOubvU%2FiNxzZoLVA%3D#reader-page.) But it looks to me a lot like the movie inference, for it too is backed by a meta-induction. In the past, when I have tried to infer from the fact my body is a certain way to the conclusion that others are the same way, I’ve met with reasonable success. Not 100% success, but good enough for inductive purposes. Of course other people are like me in external respects – they often have two eyes, one mouth, two legs etc. But they are also like me in internal respects, at least as far as I can tell. Consider, if you aren’t too squeamish to do this, how similar the various kinds of fluids that come out of various parts of other people’s bodies are to fluids that come out of matching parts of one’s own body. X-Ray technology reveals that we are alike in even more ways than we could have previously told ‘on the inside’. So the argument _my brain states generate or constitute or correlate with phenomenal sensations, so other brains generate or constitute or correlate with phenomenal sensations_ is an instance of a schema that delivers mainly reliable instances. Just like the movie inference. And that inference can produce knowledge. So I think we can come to know about the existence of other minds with sensations on the basis of a single case, namely our own. If you don’t believe me, perhaps you don’t need to worry as much about movie spoilers as you thought you did!