Public Language
If you've followed this blog for a while, you'll have noticed that I'm occasionally worried about the status of shared truth-conditions in a linguistic community. Here's my current opinion.
First the problem. We can use language to communicate how things are. By saying "I have a headache" I can let you know that I have a headache roughly because it is common knowledge between us that people typically utter the words "I have a headache" only when they have a headache. In general, a sentence S can be used to convey the information that certain conditions obtain only if both speaker and hearer know that the hearer will take an utterance of S as evidence that the conditions obtain. Let's call those conditions the 'truth conditions of S'. (The name is a bit misleading because it is often used for the counterfactual conditions under which S would be true. In this sense, the truth conditions of "water isn't H2O" are nowhere satisfied. But clearly that sentence could and can be used to convey information, so these counterfactual conditions aren't the truth-conditions I'm talking of. The truth-conditions I'm talking of are the sentence's A-intensions.)
The problem is that it seems hard to find suitable truth-conditions that are known by all speakers of a language: Physicians seem to have rather different views about the conditions under which "I have arthritis" is true than non-physicians. And won't people associate different meanings with words depending on how they've learned them? Perhaps you regard "water is wet" as true iff the stuff that flows in rivers is wet, whereas I regard it as true iff the stuff that comes out of taps is wet.
My current opinion is that there is far less divergence than I used to think, and the divergence that remains is mostly harmless. First of all, the usual examples are exaggarated. Non-physicians don't believe that "I have arthritis" is true iff I have whatever physicians call arthritis. It is probably common knowledge that "arthtritis" denotes an illness (moreover, an illness different from hayfever or AIDS), and this is relevant for the truth-conditions we assign to sentences containint "arthritis". It may also be common knowledge and relevant that "arthritis" denotes a condition that is somehow causally related to the current use of the word in our community, and so on.
Secondly, and more importantly, even if the descriptions we use to characterize truth conditions vary a lot, the truth conditions may still be similar. Truth conditions aren't descriptions, they are something like functions from contexts (centered worlds) to truth values.
Finally, there is no need for the truth-conditions to coincide completely. It doesn't matter for ordinary communication if we disagree about whether a sentence is true in some bizarre situation of which we're both sure that it doesn't obtain. Is "cats are animals" true if the creatures we know as animals are all robots controlled from Mars? Suppose you think it is, whereas I think it isn't. This means that we can't use the sentence to tell each other whether or not that condition obtains. But that doesn't mean we can't use the sentence to communicate at all. If it is common knowledge that all of us take a sign S as evidence for conditions A through K, and as evidence against L-X, whereas we disagree about Y and Z, the sign can still be used to communicate that one of A-K obtains, and none of L-X. It will only be useless if we wonder about Y and Z, which usually we don't if they are far-fetched possibilities like the robots story. For many far-fetched possibilities we don't even care about how they should be correctly described.
It seems reasonable to assume that insofar as different parts of a linguistic community assign different truth-conditions to sentences, the differences will mostly concern far-fetched possibilities. Even if, unrealistically, you mean by water "the stuff that flows in rivers" and I "the stuff that comes out of taps", this doesn't harm our communication as long as we don't take seriously the possibility that the stuff that flows in rivers is not the same stuff as the stuff that comes out of taps.
It's not that linguistic communities fall into lots of subcommunities with proper language use which only understand each other by luck or by accidence. Of course there are community-wide conventions. But they aren't completely determinate. They don't settle what to say and believe in various far-fetched situations. Common knowledge of the restriction of truth-conditions to realistic contexts is enough for communication.