I want to revisit Peacocke's response in light of our class discussion, and try to tie up some loose ends.

     P. 124:  The natural-number example is a good illustration of the dilemma I posed regarding tacitness.  The implicit conception here is an inductive definition, a sophisticated Peano-style one.  Is it supposed to be explicitly represented within an ordinary person (cf. "an ordinary person's understanding of the expression 'whole number'" (p. 55))?  I.e., there is a particular state of the person that has the propositional content (i)-(iii)?  That seems crazy.  Unless the person had actually studied at least a little number theory, and hence was not ordinary, where would such a representation have come from?  How did it get into the person's head?  (I am not here, yet, making Dorit's additional good point about rationality/justification.)<1>
     If the ordinary person does have such an implicit conception, surely it is implicit in a deeper way; the person only tacitly believes (i)-(iii), without unwittingly representing them.  And it's plausible that the person does so believe (i)-(iii).  But this is the other horn of the dilemma:  There is no good theory of nonrepresenting belief, and especially no good one that affords such belief any explanatory role.  In particular, Crimmins' theory does not.<2>
     During the last half hour of our class meeting, I'd been thinking that Peacocke's official position was the dilemma's first horn, committed to explicit representation.  But I was forgetting the passage on pp. 70-71, in which he says that "the content of the implicit conception could equally be grounded in the operation of a processor which does not involve, at the subpersonal level, explicit representation of the content of the implicit conception."  So he seems to remain uncommitted as between the two horns.

     Pp. 129-130:  Here Peacocke seems to confirm Rey's suggestion that satisfying a concept's (1992)-style possession condition often falls short of the full and clear, non-misty understanding encoded in the implicit conception underlying the concept.  (Except, remember the complication that an implicit conception may have "an incorrect content" (p. 70), which needs a good deal more explaining.)  Rey's objection is that even if (1992)-style possession conditions ground a priori knowledge, the knowledge underwritten by implicit conceptions requires a nontrivial move from possession condition to full implicit conception, and who says that step is itself warranted a priori?  If the step is not warranted a priori, then the knowledge grounded in the implicit conception would or at least need not be a priori.
     Peacocke replies, I think, in the paragraph that spans the 130-131 page break, and the paragraph following.  There he seems to be saying that at least for some concepts C, C's underlying implicit conception both individates C and serves as C's possession condition in a new, relaxed sense of "possession condition."  It's new and relaxed because it no longer requires the (1992) A(C) form.  So, ad Georges, the answer is that there is no step between possession condition and full implicit conception, because now Peacocke's view is that the implicit conception is the possession condition (in the relaxed sense).
     (The main reason I'm unsure that that's what he means is that he says only, "The treatment of implicit conceptions...is intended to be a contribution to a constitutive account of possession of the concepts in question."  And later, on p. 140, he says that an implicit conception "is meant to be part of what it is, constitutively, to possess the concept which involves having that implicit conception.")
     Then on p. 132 Peacocke argues that at least for some concepts, the simulation procedure that generates the knowledge does not in fact rely on empirical information.

     P. 136:  Peacocke's distinction here, between the "contentually" and the "judgementally" a priori, illustrates the slipperiness of the term "a priori."  Is (B) really a priori?  On some definitions yes, on others no; I don't think there's any really about it.

     Pp. 136-137:  Here Peacocke draws a distinction that may be important, though I'm not sure I understand it.  He says that "the concept limit as deployed by Newton" is distinct from the complex concept expressed by the Bolzano-Weierstrass definition; they must be distinct, because they differ cognitively.  Yet Newton's (and Leibniz') possession of the concept LIMIT consisted in their posession of the B.-W. implicit conception.  I am not sure whether, for Peacocke, "the concept limit as deployed by Newton"  =  the concept LIMIT possessed by Newton in virtue of having the B.-W. implicit conception, though that's what it sounds as though he means.

     (P. 138:  The assimilation of necessary falsehood to "unintelligibility" is something I find particularly odious, unless "unintelligible" is being used to mean something that does not imply "cannot be understood."  Of course we understand "Squares are not four-sided" and "A&B is true but A is false"; if we didn't, we wouldn't know so much as that they are necessarily false.  Peacocke would add, a priori false as well; but that doesn't make them unintelligible either.)

     P. 139:  As Peacocke says, it's common to distinguish the property designated by a term or concept from the finer-grained mode of presentation under which the term or concept does the designating.  In the example here, two people both designate the limit relation, but under distinct concepts.  However, interestingly, Peacocke seems to be saying that belief ascription goes by the common designatum (the limit relation) rather than by the finer-grained concepts: "...we may correctly predicate exactly the same predicable 'believes that the limit of such-and-such series is so-and-so' of both of them."  He adds that it's important to individuate belief contents that coarsely in order to allow for communication and transmission of knowledge.  Thus, he seems to be advocating a transparent as opposed to an opaque reading of attitude complements.  (On an opaque reading, we could not predicate the same belief of the two characters, because mode of presentation is taken as part of the attitude content.)  Yet according to the cognitive criterion of concept individuation, one must be able to have the one belief without the other; so when the criterion is applied, we must be reading the belief sentences opaquely.

     P. 140:  Here he says it: The content of an implicit conception need not be classical (need not "take the form of a definition").  It can be a prototype or whatever.  (And he emphasizes that again on p. 143.)

     P. 140:  Peacocke agrees that ANIMAL is not part of the implicit conception underlying CAT.  I'd like to see his account of that implicit conception, then, because he also agrees with Putnam that our usual perceptual-recognitional way of thinking of cats is not part of the implicit conception.  If one tried to go with Putnam's general account of natural-kind concepts, one would have to mobilize the same-species-as relation, but that seems to require thinking of cats as a(n animal) species.  (The tension is within Putnam's own diachronic overall view, I think.)

     P. 142:  So far as I follow it, the reply Peacocke makes here to Schiffer seems right.

     P. 145:  On the matter of person-level beliefs' being justified by subpersonal goings-on that are not themselves justified, Peacocke here does gesture in the direction of Reliabilism.

     P. 148:  This concise statement of the argument against Personal-Level Conceptual Role theories seems right to me.

     I'm pretty sure I'm going to regret saying this, but:  It would be a good idea for someone to go through Peacocke carefully, and re-expound his view for him (perhaps in the form of a term paper).  If we had decent pedagogy, we might then be better able to evaluate his view.
 

Footnotes

1  There is a school of thought--the school is MIT--well represented by the brilliant developmentalist Liz Spelke, according to which small children have modules in their brains that actually do embody such sophisticated principles.  The principles do not have to "get into" the ordinary person's head, but grow there naturally as a result of genetic programming.  Spelke and others come up with amazingly ingenious experiments designed to support this; but at least in my case, it will take some more convincing.

2  Irrelevant note on clause (iii) of the inductive definition:  Peacocke says that its "modality...is taken seriously."  I'm not sure what he means there.  But here's a guess.  Usually the third clause is put more simply: "Nothing else is a natural number."  Peacocke may argue that "else" has to be unpacked modally, as "other than what can be determined...."  But why?  Why can't "else" mean only: other than 0 and the successor of a natural number?  I suspect the answer is that the latter use of "natural number" would introduce vicious circularity.  But Peacocke needs to explain why his two uses of "natural number" in (iii) do not do so.  (Probbaly he has somewhere explained that and I've forgotten.)