In the Veltman episode on normality (46), Matt mentions the “No True Scotsman Fallacy,” in its relationship to statements of normality. I’d like to sketch out what the fallacy is just a bit more fully, and further highlight how it brings out the problem of how we falsify normality claims.
The basic idea behind the No True Scotsman Fallacy is that one can make a generalization of some sort (from the offensive ‘All Greeks are lazy’ to the more benign ‘Bears normally hibernate’), and then protect this generalization from any counterexample by claiming that it isn’t a real counterexample. But by doing so, the person making the assertion has made a contingent statement into a logically necessary statement, illegitimately. That is, ‘All Greeks are lazy’ could turn out to be either true or false until we go out, find some Greeks, and check (and quickly discover our error). But if the person who has made the assertion systematically rejects any example that undermines the generalization (‘That’s not a real Greek person.’), then it seems that the statement could never be falsified—it’s logically true. But “All Greeks are lazy” is obviously not a logical truth; it’s not a truth at all! In essence, the person who makes the ‘No True Scotsman’ move is perpetually moving the goalposts, preventing us from ever convincing her that that she made a false claim.
Now let’s see how this intersects with issues of normality with a more systematic approach. Consider an example borrowed from Veltman:
0. Women can’t play chess.
We could imagine making this claim more precise by substituting one of the three following claims:
- All women can’t play chess.
- Most women can’t play chess.
- Women normally can’t play chess.
We can get clear on the No True Scotsman Fallacy by seeing it play out in (1) and (2), and then see how it presents a problem with (3).
How might we try to refute (1)? Well, (1) might be thought of as giving us the following instruction: Find any woman in the universe and try to play a game of chess with her. And it predicts: you won’t be able to. So we can refute (1) by following the instruction and showing that the prediction doesn’t follow. Fortunately, we’ve made things pretty easy for ourselves here; we don’t need to search a whole lot of the universe to find a woman who can play chess. And because (1) is a universal claim (‘all women’), we are able to refute it by finding a single counterexample: one woman who can play chess.
But the proponent of (1) may retort: “But the ‘woman’ you’ve found who can play chess isn’t a real woman. All women can’t play chess, so all you’ve shown is that this particular person isn’t a real woman.” Such a response should strike us as logically confused (as well as misogynistic). Why? Well, because when the proponent of (1) tried to dismiss our counterexample, the core reason he gave was: “All women can’t play chess.” But this is precisely the claim in question! Effectively, what is being said is: (1) is true, because (1) is true. And this isn’t a good argument—which is what we should expect, since we’re identifying the No True Scotsman Fallacy.
So we’ve seen that ‘pulling a No True Scotsman’ (X isn’t a counterexample because X isn’t a real Y.) really comes down to assuming the claim that we’ve set out to prove when it comes to universal generalizations. For the sake of systematicity, let’s quickly work through statistical generalizations, claims like (2).
We can take (2) as providing us with the following instruction: Find a bunch of women, and try to play chess with them. And it predicts: You won’t be able to play with most of them. How do we flesh out ‘most’? Well, we’d probably say that it is some proportion of the women that we’ve played chess with, but the precise proportion will vary by context (and probably be a bit vague anyway). Let’s stipulate that most means 51% here, so (2) predicts that 51% of women won’t be able to play chess. (We’d probably also have to worry about getting the right sample population, but we’ll bracket these worries for now.)
How would we go about refuting this claim? Well, we follow the instruction and show that more than 49% of women can play chess (assuming we’ve used a ‘good’ sample population, whatever that amounts to.)
But the proponent of (2) might respond: “But the ‘women’ you’ve found who can play chess aren’t real women. Most women can’t play chess, so all you’ve show is that at least 51% of the women in your sample population aren’t real women.” But this, like the response to our refutation of (1), begs the question. So the proponent of (2) has also ‘pulled a No True Scotsman’ on us.
Now we get to statements of normality, like (3). We can see that (3) is a bit different, because the instruction we get is something like: Find a normal woman, and try to play chess with her. ‘Normal’ serves as a sort of restriction here, and it’s not quite clear what we need to do in order to find a ‘normal’ woman. But let’s press on. The prediction of (3) is similar: that woman won’t be able to play chess.
So let’s try to refute (3) by finding a woman and succeeding at playing chess with her. Or perhaps we follow our response to (2) and find a large sample of women who are able to play chess. We want to claim that we’ve refuted (3), because we’ve found women who are able to play chess.
The proponent of (3) seems to have a stronger response available than those of (1) and (2): “The women you’ve found aren’t normal women, so they don’t count as counterexamples to my claim.” This response might seem question begging: if the reason we don’t count the women we’ve found who can play chess as normal women because they can’t play chess, it seems that we’ve simply assumed (3), which we set out to prove.
But a similar line of reasoning is intuitively valid to us: If we say that Xs normally can’t do Y, and we find an X that can do Y, it seems to follow that either ‘Xs normally can’t do Y’ is false or the X we’ve found isn’t a normal X. And often, we’d be inclined to assert the latter disjunct: for example, when a car races through a red light, we imagine that this is an exception to the rule, rather than a counterexample.
So it isn’t so clear that we can accuse the proponent of (3) of pulling a No True Scotsman—we might take it as intuitively possible (on a logical, if not empirical level) that the woman we’ve found who can play chess isn’t really a normal woman (in contrast to the cases where we simply said that the woman who can play chess isn’t a real woman, full stop). That is, it isn’t clear that the proponent of (3) can’t dismiss our purported counterexample without begging the question—as we take a very similar line of reasoning to be intuitively valid. What would it take to show that we’ve refuted (3)? Well, that’s something that logicians like Veltman are currently studying; but we can surmise from the podcast that it would take an example which the proponent of (3) agrees is a normal woman, but who can also play chess. The trick, of course, is to get the proponent of (3) to agree—and this doesn’t seem to be a trivial task.