Coherentism and Frege’s Sad Belief

Frege believed that the unrestricted comprehension axiom is true, and it is sad, since the axiom leads to paradox. If you are inclined toward coherentism, the rationality of Frege’s belief causes a problem, since it is logically inconsistent.

I’ve been working on the problem for coherentism of justified inconsistent beliefs, and this is one version of the problem. I’m tempted, though, to think it isn’t an epistemological problem, but rather a philosophy of language issue. Here’s why.

The problem concerns the problem of cognitive significance, which standard propositional theories don’t solve. They don’t, that is, give us a solution to Frege’s puzzle of how a=a can be trivial whereas a=b is substantive. The same reasons that lead Frege to appeal to sense in addition to reference should cause us to appeal to modes of presentation in addition to propositional content. This is essentially the line taken by triadic theories of intentional attitudes of the sort articulated by Nathan Salmon.

What would be helpful here is if some of the work on 2D semantics could help make more sense of the mysterious notion of a mode of presentation, but here I’m skeptical. Even the most epistemologically sensitive versions of 2D semantics focuses too much on what is knowable a priori, and such a focus won’t help with the problem of cognitive significance. To see this, notice that the information involved in apriority is information that need not be present in the noetic structure of the person in question. It may be detectable by reflection alone, but it can have that feature without being present in the noetic structure itself. So it will be more akin to the external defeaters constitutive of Gettier situations than to internal defeaters of the sort that undermine justification itself. To the extent that this diagnosis is correct, the 2D work won’t help solve the problem of Frege’s sad belief.


Coherentism and Frege’s Sad Belief — 5 Comments

  1. Hi Jon, can you say a bit more about what you take the problem to be? Do you mean the problem of giving a theory of non-ideal rationality? Certainly, by ordinary standards, Frege was a highly rational dude, but I take it that his belief in the unrestricted comprehension axiom is less than ideally rational insofar as ideal a priori reasoning shows that it leads to paradox. I think what’s throwing me off is the comparison with Gettier cases, since I take it the presence of external defeaters is not accessible even on the basis of ideal a priori reasoning.

  2. Hi Declan, I think there is a hard-hearted assessment of poor Gottlob, that this belief is irrational, but I also think there are reasons for a more compassionate assessment of the status of this belief. So, I assume, the belief is rational in addition to the believer himself being rational.

    I was thinking of your views about the closure of evidence under entailment when I fudged on exactly how the information entailed by what’s already in the noetic structure itself defeats. If evidence is closed under entailment, then of course the info in question defeats the rationality of belief. Since I’m assuming that the belief is rational, we have to reject such a closure principle (and I think we should for other reasons, anyway). If we do, then the defeaters will function more like Gettier defeaters, even though there is a difference between them and the usual Gettier-type defeaters.

  3. Hi Jon, yes – I agree that we need both compassionate and uncompromising standards of rationality. We normally use compassionate standards in our everyday assessments, as in the Frege case, but it’s plausible to suppose the compassionate standards can be reconstructed from the uncompromising standards plus further assumptions about psychological limitations. If something like this picture is right, then it might be hard to get a clean theory of the compassionate standards for rationality, since there’s going to be a lot of psychological mess in there!

    On 2D: David Chalmers makes the point that on his epistemic version of 2D, all logical and mathematical truths are a priori equivalent, so they have the same primary intensions. To capture differences in non-idealized cognitive significance, he makes a couple of suggestions: (i) appeal to compositional structure, so ‘7+3’ and ‘10’ have different primary intensions; or (ii) go hyperintensional by defining hyperintensions over a more fine-grained space of epistemic scenarios, which might include impossible worlds. We had a conference on this stuff recently at ANU and Chalmers’ slides are up on the web here:

  4. Thanks for the link, Declan. Those were the two, most obvious ideas I had in mind when I was thinking that the problem is a lang/mind problem, not an epistemology problem. There’s still the need for the coherentist to say why that saves coherentism from the inconsistency problem of Frege’s belief, but that story is pretty obvious, I think.

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