a speaker and a hearer have to share the entire system of the meaning theory:
in the form: " 'the cat is on the mat' is true iff the cat is on the mat"
* convergence holism
a speaker and a hearer have to converge towards a common passing theory:
the hearer has to intend the intentions of the speaker, who - for instance - may intend with "cat" what hearer means with "dog" and with "mat" what the hearer means with "blanket". The corresponding inferences follow.
"cat" and "mat" are words which take their meaning from the use of these words in a context with given axioms and rules of inferences. Unless you specify the cognitive context, the words have no meaning at all.
* weak local holism
"cat" and "mat" are word which are defined in typical definitory contexts, and their basic frame structure (a set of inferences) is lifted in any context, waiting for a verification of compatibility. Changes are made afterwards.