On page 9, Habermas says, "A judgment can be objective if it is undertaken on the basis of a transsubjective validity claim that has the same meaning for observers and nonparticipants as it has for the acting subject himself."
This sentence explains a part of the preceding sentence, which states, "An expression satisfies the precondition for rationality if and insofar as it embodies fallible knowledge and therewith has a relation to the objective world (that is, a relation to the facts) and is open to objective judgment." Habermas is defining the "objective judgment" term that appears in that preceding sentence. In that sense, the sentence under investigation indicates that, in order to be rational, an expression must be open to objective judgment -- must, in other words, be at least undertaken on the basis of a transsubjective validity claim that has the same meaning for observer and subject alike.
In that formulation, Habermas presents what seems to be a naïve assumption that a validity claim can typically have the same meaning for two people. Also, it is not yet clear what counts as a meaning. The sentence would seem to be stronger if it eliminated the reference to meaning -- if, for example, it said, "A judgment can be objective if it is undertaken on the basis of a validity claim advanced by observer and subject alike." This would resolve the second of my two objections.
As for what constitutes a "validity claim" within this viewpoint, Habermas provides the examples of truth (regarding his hypothetical person A, who expresses a belief) and efficiency (regarding his hypothetical person B, who takes an action). Validity in these regards is seen as a matter of degree: the more strongly one can defend the claim of truth or efficiency, the more rational the belief or action from which such claim arises.
The meaning of "transsubjective" appears to be provided by the reference to a validity claim that has the same meaning for multiple persons. In this interpretation, the adjective appears superfluous: a validity claim that has such shared meaning is ipso facto transsubjective. Or if there is a desire to retain the word, the sentence might be recast as: "A judgment can be objective if it is undertaken on the basis of a validity claim that is transsubjective -- that, in other words, is held by observer and subject alike."
"Undertaken" appears to lean toward the action taken by person B, rather than the statement made by person A. To accommodate both, the term might be altered to "held or undertaken." This phrasing would make clear that the focus of objectivity is upon the judgment, not upon the verb to which the judgment gives rise. Then again, trans-subjectivity is not possible until one does take an action that brings the matter to the attention of the observer or nonparticipant. In this light, the meaning of "judgment" appears to be bound up with the action in which it is manifested. For the speaker or actor, the belief or other action orientation was such as to prompt an actual expressive (or other) behavior; but by definition, this was not the case for the observer. This interpretation seems to underscore the difficulty of the idea expressed in the quoted sentence. I wonder, however, whether that expression is a mere straw man.
On p. 10, Habermas seems to emphasize that his problem with the sentence under examination is not so much the concepts of objectivity, meaning, and so forth that I have questioned, above. Rather, his primary concern seems to lie in the immediately preceding sentence (also quoted above), in which there is a reference not only to objective judgment, but also to "fallible knowledge."
That reference to "fallible" knowledge apparently invokes a falsificationist epistemology. In my impression, that sort of epistemology is dubious in at least the senses that (a) one cannot be certain what, exactly, has shown a given statement to be false and (b) it is not clear how this formulation would exclude, say, the position of a Christian fundamentalist who bases his/her actions upon his/her interpretation of revealed truth but readily admits that his interpretation of God"s intention is prone to error. These, however, do not appear to be Habermas"s criticisms of the "proposal to base the rationality of an expression on its criticizability" (p. 10). His view seems, rather, to be that rationality does include the concept provided in the initial quote (above), but it includes other things as well, to be explored in subsequent pages.