Thursday, October 06, 2005

Counterfactuals and Intuitions

Jonathan Ichikawa has a fascinating post on Tim Williamson's contention that the Gettier intuition rests on a contingent counterfactual. This is a topic Williamson spoke about at the ANU methodology conference I went to a couple of months ago, so I might as well chuck in my two cents.

The problem Williamson tackles is how to formalize the content of the Gettier intuition into logical notation. Here's a plausible first attempt:

(3*) □∀x∀p (GC(x,p) ⊃ (JTB(x,p) & ¬K(x,p)))

That is, "Necessarily, any time someone stands to a proposition as in the Gettier story, he has a case of justified true belief that isn't knowledge."

Williamson objects that the Gettier story is underdetermined in ways that leave it possible (were we to fill in the gaps in a particular way) for us to deny that the agent's belief is justified in that case, from which it follows that (3*) is false. It makes too strong a claim: what we really want to say is not that an agent satisfying the Gettier story must have JTB without knowledge, but that they would be so. It's really a counterfactual claim, Williamson suggests, which we should analyze as follows:

(3) ∃x∃p GC(x,p) □→ ∀x∀p (GC(x,p) ⊃ (JTB(x,p) & ¬K(x,p)))

That is: If it were the case that some x stood to some p as in the Gettier story, then whoever stood to a proposition in the same way would have a justified true belief that isn't knowledge.

The problem with this is that counterfactuals are contingent - depending for their truth on the location of the actual world in modal space - whereas the counterexamples yielded by thought experiments demonstrate conceptual, i.e. necessary, truths. In particular, Williamson claims that if the actual world was 'deviant' in some respect, such that the closest possible world in which the Gettier story obtains is one where the agent's belief is not in fact justified, then the Gettier story would fail to refute the JTB analysis of knowledge.

That's just plain wrong. Gettier-style thought experiments don't depend upon actual-world truth values, or our particular location in modal space. Rather, they speak to the entirety of modal space. So they shouldn't be interpreted as counterfactuals assessed from the actual world. That's not how they work at all.

Jonathan's response came at this from the perspective of truth in fiction. The key idea is that what's true in the Gettier stories is not underdetermined in the crucial respects that lead to the agent having JTB without knowledge. A deviant actual world won't affect what's true in the Gettier story, because implicit truths in fiction are better filled in by something like "collective belief worlds", i.e. what we all believe is actually true, rather than what really is true (possibly unbeknownst to any of us).

My initial reaction to Williamson's suggestion was rather similar, though I didn't see it in terms of fiction. I just thought that we should be assessing the counterfactual in (3) against normal rather than actual conditions, so as to preclude actual-world deviancy from having any effect. This amounts to the same thing as appealing to a 'collective belief worlds' analysis of truth in fiction.

So Williamson's (3) is still too strong, since thought experiments should not be held hostage to our (possibly deviant) location in modal space. I suggested to Williamson (in the "question time" after his talk) that (i) this was a problem; and (ii) we could overcome it by sticking a possibility operator in front of the whole subjunctive conditional:

(3') ◊(∃x∃p GC(x,p) □→ ∀x∀p (GC(x,p) ⊃ (JTB(x,p) & ¬K(x,p))))

That is: There is some possible world (it need not be the actual one) at which the counterfactual expressed in (3) is true.

This is a much weaker claim, since it does not depend upon actual conditions at all, but it nevertheless suffices for refuting the JTB analysis of knowledge. (I can't remember Williamson's exact response, but I think he was worried that my changes upset the logical form of his argument from the Gettier intuition to the refutation of the JTB analysis.) After all, so long as the counterfactual is true at some possible world, and the antecedent "∃x∃p GC(x,p)" is possible, then it follows that the counterexample "∃x∃p(JTB(x,p) & ¬K(x,p))" is true at some possible world also. And thus it is not a necessary truth that all cases of JTB are cases of knowledge.

So Williamson's contention, that the Gettier counterexample is merely contingent, can be refuted without relying on any particular analysis of truth in fiction. After all, it isn't really about fiction at all, but rather, what's possible. The Gettier case shows that it's possible to have JTB without knowledge. The way it shows this is not through a counterfactual anchored to the (possibly deviant) actual world, but rather, the unanchored possibility of such a counterfactual -- a possibility that does not depend upon our particular position in modal space. As such, we get the appropriate result that the success of thought experiments is not contingent on actual-world normalcy. Even if, by some bizarre coincidence, the closest realization of the Gettier story failed to constitute a counterexample to the JTB analysis, others more distant would succeed, and that's all we need for the refutation.


  1. Yeah, that's another way to go. Richard Heck suggested something similar in the question time for his talk at Brown; naturally, I pressed him on truth in fiction. We'd have to look at the modal logic more closely to make sure that it would work, and capture the intuitions.

    By the way, the collective belief version of Lewis's truth in fiction theory ("Analysis 2") *will* make truth in fiction contingent the way Williamson thinks it is -- it's a contingent fact what most people tend to believe.

  2. Oh yeah, good point. I think I'd have to say that what we'd consider 'normal' conditions is likewise contingent. But I ended up appealing to unanchored counterfactuals, rather than counterfactuals anchored at the 'normal' world, which explains the different results.

  3. (3') works (makes the Gettier argument valid), but it requires an S5 modal logic.

    It's a little weird to think that the inference involved in the Gettier counterexample requires such a strong modal logic. Then again, it's pretty weird to think it involves a contingent judgment.


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