Truth without Objectivity provides a critique of the mainstream view of 'meaning'. Kölbel examines the standard solutions to the conflict implicit in this view, demonstrating their inadequacy and developing instead his own relativist theory of truth. The mainstream view of meaning assumes that understanding a sentence's meaning implies knowledge of the conditions required for it to be true. This view is challenged by taste judgements, which have meaning, but seem to be neither true nor false.
Kölbel is working with the assumption that moral, aesthetic and probabilistic claims aren’t objective, and given that, he wants to see if we can still understand them as truth-evaluable, because he thinks the truth-conditional semantic project is worth saving.
I don't think Kölbel's argument against the "revisionist" (someone who thinks the content of moral, aesthetic or probabilistic claims contains an indexical element) is successful. Kölbel's revisionist claims that "Licorice is tasty" is elliptical for "I find licorice tasty". Now, Kölbel is right that there are problems with that proposal. But ellipsis is not the favored approach to dealing with context-sensitivity of content. More common is the idea that "Licorice is tasty" has a variable at the level of logical form that takes different values in different contexts. The semantic theory would represent the content of "is tasty" as a function from some contextual feature (comparison class, relevant standards, etc.) to a function from worlds to extensions (rather than just a function from worlds to extensions, as with a standard predicate). Or in Tarskian form:
If u is an utterance of "Licorice is tasty", and c is some relevant contextual feature, then u is true iff Licorice is tasty in c/according to c.
Now, Kölbel argues that revisionism has trouble accounting for how we deny someone's claim that licorice is tasty. If "Licorice is tasty" is elliptical for "I find licorice tasty", then you should be able to substitute one for the other. But denying that licorice is tasty is different than denying what is said by the utterer of "I find licorice tasty". So Kölbel concludes that the revisionist approach can't be right. Fair enough, but if you're an indexicalist, and not someone who proposes handling context-sensitivity in terms of ellipsis, this shouldn't be a problem. The predicate "is tasty" will be understood as incomplete without a value for its hidden indexical, but that doesn't mean that "I find licorice tasty" and "Licorice is tasty" will have the same truth condition:
1. If u is an utterance of "Licorice is tasty", and c is some relevant contextual feature, then u is true iff Licorice is tasty in c/according to c.
2. If u is an utterance of "I find licorice tasty", and x is the speaker of u, and c is some relevant contextual feature, then u is true iff x finds licorice tasty in c/according to c.
Since the contents of those two utterances will be different, what's involved in denying them will also be different. If I want to deny that what you say when you say "I find licorice tasty", I will have to deny that YOU find licorice tasty in c. If I want to deny what you say when you say "Licorice is tasty", I will have to deny that licorice is tasty in c. Those are different things. So there is a variety of "revisionist" who can avoid Kölbel's criticism.