I think that all sounds pretty much right. I would say, however, that (1) needs to be a bit more general so as to include claims about stuff other than experiences like beliefs, thoughts, concepts etc. Of course, I guess I’m assuming here a relatively specific meaning of “experience” and if, instead, one is sufficiently broad about experience, the requisite generality is already built in.

Another thing, very nit-picky, forgive me:

“transcendental arguments are invalid because they imply either idealism or verificationism” doesn’t sound right. though it’s been a few months since I last read the stroud paper, I’d say that the problem here can’t hinge on invalidity. Invalidity is a formal or logical notion wheras implying idealism or verificationism isn’t. Whatever makes an argument invalid, then, can’t be that it implies some metaphysical or semantic thesis that is out of favor. Perhaps better word choice would be to replace “invalid” with “problematic” or “objectionable”.

“Some have argued that transcendental arguments imply implausible positions with respect to our understanding of the phenomena they attempt to elucidate. Barry Stroud (1968) has argued that transcendental arguments are invalid because they imply either idealism or verificationism.

The structure of a transcendental argument is
(1) A claim P about experience, the truth of which is accepted, for example, “I am a self-conscious.”
(2) The truth of a non-experiential proposition Q is a necessary condition of P, for example, “If I am self-conscious, then I must perceive myself as a physical object among physical objects.”
(3) Therefore Q, for example, “I perceive myself as a physical object among physical objects.”

Stroud argued that claims like the first claim may only appear to be true, and therefore, that the truth of Q does not follow. At best, transcendental arguments show us what we must believe about appearances, rather than showing us the layout of the nature of reality. Thus, the proponent of transcendental arguments has to show how we connect what we believe about appearances to the way that things are in reality. Stroud argues that this can only be done if the proponent accepts either idealism or verificationism. In the former case, the idealist suggests that the way that we talk or think about appearances determines the nature of reality. In the latter case, the verificationist suggests that the meaning of our terms that we apply to appearances can only be secured given there are experiential criteria that determine their application.

In response to these objections, Stroud (1994; 1999) himself has proposed that we be satisfied with more modest transcendental arguments: arguments attempt to show the indispensability of some belief, thought or concept. Such arguments have been called “belief-directed” transcendental arguments (Peacocke (1989: 4) and (Cassam 1994: 33), rather than “world-directed” transcendental arguments, because they only attempt to show that we should believe something to obviate incoherence or inconsistency. The arguments that I will employ in the dissertation should be considered “belief-directed” transcendental arguments.” (Dow, Diss MS)…

quoting myself is stupid and obnoxious…

The pivotal figures for understanding transcendental arguments are the following. Austin (1979) is the first to use the term, as far as I can tell. Taylor (1975) defines transcendental arguments as “arguments that start from some putatively undeniable facet of our experience in order to conclude that our experience must have certain features or be of a certain type, for otherwise this undeniable facet could not be” (151). Barry Stroud (1968; 1994; 1999) serves as the ground for the skepticism of transcendental arguments. Rosenberg (1975) revisits the notion of a transcendental argument given Stroud’s criticisms with particular emphasis on Kant’s use of transcendental arguments. Cassam (1987) provides an account of transcendental arguments in light of Kant’s notion of transcendental synthesis. Cassam (1994) suggests that modest transcendental arguments are all he intends to use. Anthony Brueckner (1996) argues that even modest transcendental arguments fail. Paul W. Franks (2005) provides an analysis of the role of Post-Kantian transcendental arguments and connects that structure to pivotal transcendental arguments in Anglo-American philosophy of mind, such as Putnam’s Twin Earth arguments and Burge’s anti-individualist arguments.

There is much more to be said, but again, this just a note surveying the scene…

http://branemrys.blogspot.com/2009/04/transcendental-arguments.html