Induction | Thoughts, Arguments and Rants

I got asked a question about induction earlier today, and I thought that it seemed like a nice time to look back at what I thought of the Bigelow/Pargetter line that good inductive arguments are valid. Quick summary: I don’t really believe it, though I’m still a lot more sympathetic than just about anyone not named Bigelow or Pargetter. (The original theory is in a 1996 AJP paper if you want to look it up.)

How, you might be asking, could inductive arguments be valid? Let’s look at a classic example to see the problem. (Well, the example involves a classic record.)

1. The Packers are playing at home, Brett Favre is the quarterback, and it’s below 34 degrees at kickoff.
2. When those conditions are met (as they often are in Green Bay) the Packers have never lost. (See footnote.)
C. The Packers are going to win.

Now this, you might say, is both pretty clearly a good inductive argument and pretty clearly invalid. So the Bigelow/Pargetter line is sunk.

Not so fast my friends.

Bigelow and Pargetter need three things to be true for this to not count as a counterexample.

First, they need the enthymeme claim to be true. This argument does not really have two premises, it has three, and the third is “That’s all the relevant evidence.”

Second, they need the ellipsis claim to be true. The conclusion isn’t really “The Packers will win”, it’s “The Packers will probably win.” Like other PRO terms, this ‘probably’ doesn’t get enunciated in normal statements of the inductive argument.

Third, they need a particular Keynesian claim to be true. It’s not clear exactly how strong a Keynesian claim they need, but the following will do. There’s such a thing as evidential probability (as Tim Williamson calls it) and it has the feature that if the probability of h given e is x, then necessarily the probability of h given e is x. Keynes certainly believed that (in fact he believed some even stronger claims about how x could be computed if h and e are expressed in a perfect language), and it is enough to make the argument valid, given the two earlier assumptions.

If those claims are true, and if the enthymeme and ellipsis claims are true of all other inductive arguments, which they should be if they are true here, it’s a pretty arbitrary argument, then the Bigelow/Pargetter thesis is safe. If they aren’t, it’s hard to see how to defend Bigelow/Pargetter.

What do I think of the status of these three claims?

I think the enthymeme claim is true, or at least a version of it is true. Note first that the subject matter here is not inductive arguments in the abstract, but tokens of inductive arguments. Most theorists would (I think) say inductive arguments are never good or bad in the abstract, but that those judgments only make sense in a context. So (small argumentative leap here) I think what’s at issue are arguments whose content is given by the speaker meaning of the premises and conclusion. (If this were a paper not a blog post that paragraph could do with a lot more detail. I have a bad feeling that I’m making a serious blunder here. I’m going to ignore that and press ahead.)

I think it really is tacit when presenting an inductive argument that we are presenting all the evidence. If we get the ‘extra’ evidence that the Packers starting left tackle is a 150 pound scrawny Australian philosopher, who can hardly bench press a NY size steak, we might be inclined to change our view about the Packers chances. But in that case I would say we don’t just learn a new bit of evidence, we have to throw out a previous claim, that the cold weather was a distinctively salient bit of evidence. I’m not wedded to this, but I think the enthymeme claim is defensible.

And I think the Keynesian claim is right. This is a kind of internalism about rationality. I’m using ‘rational’ here to denote a property of agents who get from evidence to conclusions in the right kind of way. I think the take home lesson of Stewart Cohen’s new evil demon is that that property is independent of the truth value of the evidence that comes in. Two creatures (not necessarily worldmates) that are disposed to draw the same conclusions from the same body of evidence are equally rational. This internalism about rationality is compatible with various kinds of externalism about evidence. (It’s certainly compatible with the claim that me and a brain in a vat never have the same evidence, the kind of position I’m drifting towards.) Indeed, I think Williamson ends up accepting this kind of claim, though he may well dispute my claim that this kind of property is a decent thing to call rationality.

Anyway, I think this kind of internalism implies necessitarianism about evidential probability. If evidential probabilities are contingent, then two creatures with the same evidence, and the same (probabilistic) conclusions, in worlds where the evidential probabilities are different, may be such that one is rational (her credences match evidential probability) and the other is not. That seems impossible to me, as it seemed impossible to Keynes. And that’s enough for the Keynesian premise needed here.

But I don’t think the ellipsis claim can be sustained. I think in an inductive argument I conclude something about the Packers, in particular that they’ll win, not about evidential probabilities about the Packers. I think Bigelow and Pargetter are right that there is a valid argument here, namely

Bigelow/Pargetter think (a) that argument is valid (that’s the Keynesian claim) and (b) it’s the argument we’re actually making when we present the earlier, shortened, version. I can buy (a), but I’m hesitant about (b), particularly the claim about the conclusion being probabilistic all along.

Footnote: The Packers are 29-0 in regular season games in these conditions. They are 6-1 in playoff games in these conditions. I’m a baseball fan more than I am a football fan, so I only count regular season records as being fully ‘real’. (‘Real’ as in Babe Ruth really hit 714 home runs.) If the game in question is a playoff game, feel free to change the example.

It’s probably relevant that when the premise involves a 35-1 record rather than a 29-0 record, it’s much easier to hear the conclusion as being tacitly probabilistic, so the ellipsis claim, at least as a claim about speaker meaning, is not entirely absurd.