What are some of the limitations of truth conditional semantics?

Here’s another limitation: speech acts. A statement of how the world is (a declarative speech act) can be true or false. A command, a promise, or a performative statement (“I hereby declare…”) cannot meaningfully be true or false: it can only be felicitous or infelicitous (that is, appropriate).

Here’s yet another, which Gary Coen already offered: Sense is not denotation, and denotation does not match de dicto references. Statements about The President Of The United States may be now statements about Barrack Obama, but come January, they won’t be. Statements about Superman may be statements about Clark Kent, but you only know that if you’re Superman or the narrator.

Yeah, truth-conditional semantics is reductionist. It’s still a starting point, and a useful one: there’s a lot of sentences that it does work for.