The Internality of Intuitions

In my commentary on this post, I suggested that rational intuitions not only have the properties of seeming necessary, true and justified, but that these properties must somehow be internal to the intuition itself. This kind of point is suggested in the following passage from A. C. Ewing:

Another important difference between a priori and empirical knowledge is that in the case of the former we do not see merely that something, S, is in fact P, but that it must be P and why it is P. I can discover that a flower is yellow (or at least produces sensations of yellow) by looking at it, but I cannot thereby see why it is yellow or that it must be yellow. For anything I can tell it might equally well have been a red flower. But with a truth such as that 5+7=12 I do not see merely that it is a fact but that it must be a fact. It would be quite absurd to suppose that 5+7 might have been equal to 11 and just happened to be equal to 12, and I can see that the nature of 5 and 7 constitutes a fully adequate and intelligble reason why their sum should be 12 and not some other number. (The Fundamental Questions of Philosophy, NY: MacMillan, 1953, p.26).

While I don't agree with everything Ewing says here, I am nevertheless very sympathetic to (though not in complete agreement with) his claim that he "can see that the nature of 5 and 7 constitutes a fully adequate and intelligible reason [for taking their sum to be 12]." In a genuine intuition, it is not just that we have, as it were, a sense that the proposition is necessarily true; rather it is that the conceptual content of the proposition itself seems to provide a prima facie ground for the truth of the proposition. In this sense, rational intuitions are what we might call concept-driven seemings.

Comments

[chad]

Suppose I rationally intuit the proposition p. It is one thing to say that, in that case, the "ground for the truth" of p must be some fact about the nature of the objects p is about. It is another thing to say that the "ground" must be a fact about the concepts which "make up" p. It is a third thing to say that the "ground" of *my intuiting p* is my understanding of (the natures of?) the objects p is about. It is a fourth thing to say that the "ground" of *my intuiting p* is my understanding of the concepts which "make up" p. Which one do you have in mind? It is only the fourth view which seems to me appropriately summed up by saying that rational intuitions are "concept-driven seemings."

[marc moffett]

Hi Chad. Thanks, and nicely put. I didn't have time to elaborate yesterday (I also just wanted to see what other people might say), but what I intended was the fourth suggestion.

One thing that worries me about saying this is the status of intuition-like episodes based on less-than-full mastery of the concepts. Are these genuine intuitions? I guess the answer is "yes", but there might be reasons for restricting rational intuitions to seemings that are grounded in what John and I call "reasonable conceptual mastery." Or maybe we just want to restrict the modal reliability of intuitions thesis to such intuitions.

Suppose that we allow less than full mastery. There is an interesting implication for some of Kripke's views. Historically, Carnap maintained that water might not have been H2O. The naive interpretation is that it seemed to Carnap that water might not have been H2O. But Kripke disputes this and "rephrases" the intuition: it actually seemed to him that the watery stuff might not have been H20. But on the above conept-driven-with-less-than-full-mastery proposal, it may be that the naive description is actually the right one: Carnap had a genuine, but mistaken, intuition grounded in a (to use Bealer's phrase) local conceptual misunderstanding.

There is a further reason for thinking that this is the right approach. If we accept Burge-style anti-individualism, then the naive vs. rephrasal views mimic his discussion belief-content individuation and he makes a pretty persuasive case that rephrasal is the wrong way to go there. The upshot would be that intuitions are also susceptible to anti-indvidualist effects. That is pretty funkin' cool, IMO.

I also wanted to add one other thing. I am inclined to say that on the concept-driven view tabled (sketchily) above, there is a kind of claim about the primacy of the epistemic in intuitions. I am not sure how to cash that out beyond slogan form at the moment or even that it is a good thing, but I wanted to put it on the table.

[chad]

There may be a counterexample to the fourth view I suggested. Once my naive understanding of the concept of a set is replaced with a more sophisticated understanding, my "naive comprehension intuition" persists. So my understanding of the concept of a set cannot be the "ground" of my continuing intuition.

[marc moffett]

Interesting! I wonder, does it also seem to you that the naive comprehension schema holds for, say, Zermelo-Fraenkel sets (i.e., sets as individuated by the ZF axioms)? Once I fix firmly in mind the concept of a set delineated by the ZF axioms, call it a ZF-set, I certainly don't have the intuition that every predicate defines a (ZF-)set. So it is somewhat strange that if I have really "replaced" my old, naive concept of set with a fancy, new concept, why I would continue to have the naive comprehension intuition.

But I do have it. What gives? Well, one possibility is that I haven't really replaced my old concept of a set with the new one. If I remember correctly, set theorists use the technical term "class" for something like naive sets. So maybe I just have two set concepts, one of which does (inconstently) conform to the naive comprehension schema.

Another possibility is that I don't really accept ZF set theory as the right theory of sets. I know the axiomatization and all; but I just can't really bring myself to accept that this is the correct theory of sets.

Finally, (and maybe most interestingly) it could be that there is something paradox-of-analysis-esque going on here. I am not entirely sure how to spell this out. For instance, maybe I have two competing conceptions of a set, a naive conception and a ZF conception. If I focus on the concept of a set via the ZF conception, I don't get the NCS-intuition; but if I focus on the (mistaken) naive conception of a set, then I do. If this is the right story, then maybe the right thing to say is that intuitions are conception-driven seemings. This is how I am leaning at the moment.

[NB: I updated this comment.]