Validity claims are not only universal but also unconditional. In fact Habermas seems at times to suggest that the unconditionality of validity claims follows from their universality. Habermas also occasionally uses the term necessity for validity claims, but the most frequently used term is unconditionality. I shall note the following:
1) Context transcendence does not imply universality. The idea of validity claims shooting each and every context is an empty and meaningless concept. Context transcendence does not mean contextlessness. Only if this were the case would one have been right to think that context transcendence implies universality, in the sense of shooting every context, and hence unconditionality.
2) Thus the concept of universality might be formulated without implying unconditionality. Even validity claims that are claims as to the universality of truth, norms etc., must be raised in a context and can be understood only in a context. And even if we accept claims about the connection between the validity of claims and universal agreement, this idealisation must remain attached to a particular context.
Thus, validity claims can be unconditional neither in the sense that they ‘shoot’ all the contexts, nor in the sense that they can be raised without being situated in a particular context. Habermas has never made the latter contention, but he does seem to have made the former. However, if what I have said above is plausible, then it seems that Habermas’ conceptions of unconditionality and universality are untenable.