Ungrounded definitions of meanings have their philosophical problems. The mainstream linguistic semantics has what is called a model-theoretic definition of meaning. It is based on the truth of statements. However, you cannot simply define the meaning of a sentence as its truth value. In that case ``MIT is in Massachusetts.'' and ``Ankara is the capital of Turkey.'' would mean the same thing, both are true. So we have to be more careful. The model theoretic definition of meaning is a function which assigns a truth value to that sentence in each possible world. Thus it is equivalent to the set of possible worlds under which this sentence would be true. Putnam proved in 1981 [Putnam, 1981,Lakoff, 1987] that such a definition was inadequate to capture the concept of meaning. Putnam's theorem shows that one can always come up with two different sentences consisting of words with different meanings, that would be mapped to the same ``meaning'' according to the above definition. Attempts to patch the model-theoretic definition of meaning have not been successful. The problem seems to arise from two factors: (1) the attempt to define meaning mainly in terms of truth, and (2) the attempt to define meaning objectively, i.e. independent of the mind which assigns the meanings to the symbols in the first place.
Although Putnam's theorem may attract one's attention to the importance of including the agent side of the above picture, it is a philosophical argument. It is like Gödel's incompleteness theorem which did not stop people from using axiomatic systems to prove theorems about arithmetic. Just as a student who cannot prove some theorem in an arithmetic exam would be foolish to attribute his failure to Gödel, Putnam's argument is not, by itself, suggesting that the model-theoretic approach is inadequate in practice. We need more hard evidence for that. It does make an ironic point however, that the system founded by people whose most important criteria for success was consistency is not consistent with the basic facts of its domain.