As I mentioned before, Alejandro at "Reality Conditions" has a good review up of Nagel's The Last Word. I just wanted to say something about whether Nagel really is inflating his conclusions in order to get a "Platonic-Cartesian" theory of reason (as he calls it). I don't think he is. The gold standard for any "Platonic-Cartesian" theory of reason is Nicolas Malebranche. Malebranche's credentials in this regard are impeccable. Not only is he a Cartesian; he is perhaps the Cartesian after Descartes to whom Cartesianism most owed its dominance. (There's a letter from Hume to Ramsay, if I recall correctly, in which Hume is telling Ramsay what background he should read in order to understand Book 1 of the Treatise. In addition to Berkeley, Hume says, he should definitely read Malebranche's Search After Truth; and Descartes's Meditations -- if he can find Descartes's Meditations.) He is also a Platonist; specifically, he is explicitly an Augustinian, on all the points where Augustine is most Platonist (in our usual sense of that term). A considerable portion of Malebranche's rather hefty corpus is devoted to arguing for and developing a theory of reason of precisely the sort that Nagel calls "Platonic-Cartesian". To top it all off, he's generally regarded as having an extreme version of this: almost everyone who holds a "Platonic-Cartesian" theory of reason has a weaker version than Malebranche does.
So, let's take (in a somewhat crude form) the features of reason for which Nagel argues:
(4) Capable of exhibiting genuine necessity
(5) Capable of discerning features (e.g., in mathematics) that can only be characterized by appeal to infinites
The noteworthy thing is that, in arguing for his own theory of reason, Malebranche argues for every single one of these things. There is only one major claim that Malebranche makes that Nagel does not; Malebranche goes one more step and argues, on the basis of these characteristics, that reason is divine. Nagel doesn't go this far, and clearly starts applying the brakes once it becomes clear that he's heading in that direction. So Nagel's conclusions are fairly clearly in Platonic-Cartesian territory.
Contrast this, by the way, with the opposing theory of reason, which one finds to a limited extent in Berkeley (who, however, is partly Platonic-Cartesian himself) and to a greater extent in Hume. This is characterized (again, we are being somewhat crude) by the following:
(1) There is no strong distinction between the subjective and objective; objectivity is merely intersubjectivity.
(2) We do not know how universal reason is; we simply find it universal enough for the purposes of common life.
(3) Reason is not normative; rather, what we call the normativity of reason is just a combination of (a) the fact that we are set up so that sometimes it is difficult for us to think otherwise than we usually do; and (b) we are set up so as to approve and disapprove certain things.
(4) The so-called necessity of reason is purely verbal.
(5) Reason has no access to these supposed infinites. Berkeley in his notebooks goes so far as to deny that the Pythagorean Theorem is true; it's not the sort of thing that is true or false, being just a procedure for getting an answers (an algorithm, as we would call it) and not a truth about triangles at all. Hume doesn't, as far as I know, say this, but it can be argued that his position requires it; he denies, for instance, that geometry is a precise science -- for him it is an art, full of vagueness and imprecision, of approximation. Such positions on infinites are significant because, as both Malebranche and Nagel argue, if you accept the Platonic-Cartesian claim about infinites, you have to accept the others to at least some extent. And if you accept the claim about infinites, it becomes a genuine puzzle for the empiricist theory of reason -- a puzzle that has never been solved -- to see how you can pull genuine thought about infinity out of finite operations on finite sensory information by a finite substance. The most consistent empiricists, like Berkeley and Hume, don't even try to solve it.
So, in other words, I don't think Nagel has to inflate his claims to get a Platonic-Cartesian view. If you accept Nagel's conclusions, you are committed, whether you knew it or not, to the Platonic-Cartesian position on reason. What he is (more or less) doing in The Last Word is showing that we all tend toward such a view as it is; it's a strong view, but it's not a weird view. This can be compared to things like subjectivism and relativism, which are weak views of reason, but are weird. Of course it doesn't follow from this that all of Nagel's arguments are sufficient to support all of his claims. Rather, it's just to point out that Nagel's not really far off when it comes to arguing for the Platonic-Cartesian account of reason.