PHL313: Some Observations about Truth Theories

Some Observations about Truth Theories

Basic Truth Theories of Meaning

The basic intuition is straight-forward: those who advocate the truth-based theories of meaning argue that a theory of what it is for an utterance to be true in a language would also provide a theory of meaning for that language.

Recall the T-Biconditionals. The idea is that we would have a theory of truth for a language if we had a theory that could, for every sentence S in our language, produce a sentence of our theory that had the form:
"S" is true in L (at time t and place xyz) if and only if p
Where p is some kind of recursive analysis in our theory and reveals precisely the conditions under which S is true or not. Parts of language which are not themselves true or false will have their meaning then explained in terms of how they can contribute to the truth or falsity of various declarative sentences. That is, the difference in meaning between "Seagulls" and "Cats" will in part be explained by the different roles that these natural kind terms play in sentences like "Seagulls are birds" or "Cats are birds" and so on.

We discussed six problems with this basic version of the truth-based theory of meaning.
  1. Contradictions and paradoxes
  2. Vagueness and ambiguity
  3. Indexicals
  4. nondeclarative sentences
  5. possibility and other modal notions
  6. co-extensive terms or truth-conditions
We discussed Davidsonian replies to the first four. But a widely accepted way of handling the latter two is to add modal notions to our theories of meaning.

A revised tuth-based theory: the possible-worlds theory of meaning

One way that has been proposed to improve the truth-based theory is the hypothesis that meaning is not given in just truth conditions. Rather, it is given in all possible truth conditions.

On the truth-based theory, utterances S1 and S2 have the same meaning if they have the same truth conditions (in this world). This is why co-extensive terms or predicates are a problem.

On the modal-extension of the theory, utterances S1 and S2 have the same meaning if they necessarily have the same truth conditions.

Define a possible world to be a complete consistent description of how things could be. Define necessarily true as meaning true in all possible. Define possibly true as meaning true in at least one possible world.

Thus, on this view, "bachelor" and "unmarried male" are true of all and only the same things in every possible world. So, they have the same meaning.

"Has a kidney" and "Has a liver" are true of different things in some possible worlds, and so they do not have the same meaning.

Note: When we say this, we always mean to fix the use of the utterance we are describing in this the actual world. There is some possible world where the sound of the word "bachelor" means rocks or some other weird thing. But when we talk about what is necessarily or possibly true of bachelors, we use the word "bachelor" only as it is used in this world in our language, and then look at the things that we may be concerned with in various different possible worlds. This is very important. We are using our language in this world to refer to those other worlds.

This extension of the theory handles both the problem of how do we make sense of sentences like, "Lincoln could have avoided assassination" -- this means that there is a possible world in which he was not assassinated. And it makes sense of how coextensive terms can have different meaning: they may be only accidentally (and not necessarily) coextensive.

A large and ongoing program in linguistics has been to develop and analyze natural languages using what is called "Montague Grammar" or "Montague semantics." This is a formal system for describing a natural language, and named after the logician Richard Montague. The system uses modal notions along with classical logical tools. This formal system is meant to be a modal-logic that will provide a truth-based theory of meaning for a natural language.