Like Ted, I was disturbed by the tension between Peacocke's abstract Fregean notion of "concept" and his immediately very psychologistic talk about concepts' natures.  But I think I can motivate it.  (I don't say you'll be convinced.)
     If a "concept" is just a subpropositional component of a proposition, and we want to talk ontologically about it, we'd expect to talk in abstract, Fregean terms.  So, when in particular we ask how concepts in that sense are individuated, we'd expect an abstract answer.  Here's the obvious one:  Take DOG and CAT.  In virtue of what are they distinct?  Of course they differ in extension.  And they differ in the real-world properties or natural kinds they designate.  But a good Fregean semanticist will say that the real difference is in "sense" or intension, conceived as what determines the respective extensions.  A modern Fregean construes intensions as functions from possible world to extensions; DOG is a function that sucks up a world and spits out all the dogs at that world, while CAT picks out all the cats there.  Obviously distinct functions.  Duhh; end of story.
     But we must consider the phenomena of intensionality:  Frege's Puzzle(s) showed that concepts can have the same extension but differ in intension.  That's obvious for complex concepts, but almost as obviously it could happen for primitives, lexically simple concepts.  The stock example is RENATE / CORDATE, creatures with livers vs. creatures with hearts.  (Supposedly all and only creatures that have livers have hearts; I have been told that that isn't so, but I don't know a counterexample.)  So far, no problem for the Fregean, because even if RENATE and CORDATE coextend at the actual world, there are other possible worlds at which they come apart; so they determine distinct functions from worlds to extensions and are thereby different Fregean concepts, just as everyone wants.  End of story now?
     Nope.  The trouble starts when we acknowledge hyperintensionality.  Some concepts seem distinct even though they necessarily coextend.  The most obvious examples would be arithmetical (EVEN MULTIPLE OF THREE and DIVISIBLE BY SIX WITHOUT REMAINDER) and, according to the Putnamian view, natural-kind concepts (GOLD and SUBSTANCE WHOSE ATOMIC NUMBER IS 79).  This time, the distinct concepts do not differ in intension, so they are not individuated by intension.  For them, the individuation problem remains.
     Why do we think the members of such pairs are distinct?  For the reason Peacocke gives:  Beliefs and other cognitive states can differ, solely in virtue of containing one member of the pair rather than the other; the members play distinct cognitive roles.  Even Frege (who hated psychologism regarding semantics) was impressed by differences of cognitive role.
     Carnap gave us a solution to the problem of hyperintensionality:  Concepts are typically complex, built up out of smaller concepts.  And what strikes us about the two pairs aforementioned is that their members differ in structure.  EVEN MULTIPLE OF THREE has MULTIPLE and THREE as components; DIVISIBLE BY SIX WITHOUT REMAINDER doesn't.  GOLD is (arguably) primitive, while SUBSTANCE... has ATOMIC NUMBER as a component.  That is why the concepts are distinct despite necessarily coextending.  So, Carnap proposed, Fregean concepts are individuated by their intensions plus their internal structure; C1 = C2 only if C1 and C2 are, in his term, "intensionally isomorphic."
     But it is not only complex concepts that illustrate the hyperintensionality problem.  What if two primitive concepts necessarily coextend?  TRIANGULAR / TRILATERAL is the classic example here.  Then Carnap's criterion fails to slice finely enough.
     Someone might protest that TRIANGULAR and TRILATERAL aren't really primitive, but are really composed of, respectively, THREE+ANGLE and THREE+SIDE.  But I don't see why there couldn't be two genuinely primitive concepts that necessarily coextend.  Suppose there's a substance that we know as GOLD and a substance that we, or friends of ours, know as "AURIC."  Unbeknownst to us they're the same substance, the element whose atomic number is 79.  But they're both primitive concepts, and they're distinct because we can know that something is gold without knowing that the stuff is auric and vice versa.
     It's at this point that Peacocke's psychologistic turn begins to make sense.  What distinguishes AURIC from GOLD is purely psychological, that they play somewhat different roles in our thought.  And if we then ask, what are those different roles exactly?, then we might well start trying to give the kinds of characterizations that Peacocke tries to give.
     Of course, he doesn't say all or even any of this stuff about hyperintensionality, so I couldn't say whether the motivation I've given is his motivation.
     It should be noted that the original problem gets still worse.  Beyond hyperintensionality there is what I call hyperdyperintensionality.  It seems that concepts can differ even when they not only necessarily coextend but when the words that express them are synonymous.  First, there's (arguably) failure of substitutivity for synonyms in belief contexts:  Doug believes that his uncle will arrive in a fortnight, but he does not believe that his uncle will arrive in two weeks (he thinks, mistakenly, that a fortnight is ten days).  For that matter, Sue can wonder whether a fortnight is ten days or two weeks.
     Second and cognately, there's the Paradox of Analysis:  Conceptual analysis is supposed to be somehow informative or enlightening.  Yet a correct conceptual analysis is an identity statement between concepts ("BACHELOR = UNMARRIED+ADULT+MALE"); the analysis is supposed to be correct only if the analysans is synonymous with the analysandum.  How, then, can a conceptual analysis inform, if it is a correct one?  One answer is to say that the concept expressed by the analysans is not strictly the same concept as that expressed by the analysandum, even though the expressions are synonymous.
     Third, explanatory contexts distinguish otherwise identical concepts:  She got sick because she ate the carrots they served on Tuesday; she did not get sick because she ate the carrots they served on Tuesday.
     I don't know what Peacocke thinks of hyperdyperintensionality.  But his style of concept identification seems inimical to it.  I should think, though I may be wrong, that the Peacockean possession condition for FORTNIGHT would be the same as or logically equivalent to the possession condition for TWO WEEKS.  But I'm not moved to delve back into the book to try and find out.