Theories of Meaning

These are my own personal notes taken while reading "What is meaning?" by Paul H. Portner.

Semantics is the study of meaning, which begets the question "What is meaning?".

For example, what do we mean when we say the sentence "the circle is inside the square."?

A useful starting point is the observation that, given a sentence, we seem to be able to use it to classify scenarios where the sentence is true and scenarios where the sentence is false.

For example, the following scenario is compatible with the sentence being true:

Whereas the following scenario is compatible with the sentence being false:

Moreover, provided with a set of scenarios, we can classify each individual scenario where the sentence is true and where it is false.

That seems like an indication that the knowledge of meaning involves the knowledge of the conditions under which a sentence is true, and those under which it is false.

Notably, however, knowning the meaning of a sentence amounts to knowing its truth-conditions, but it has nothing to do with knowing whether it is in fact true or false (what semanticists call its truth-value). You can know the meaning of a sentence without whether it is true or false, or even having prospects for ever finding out.

For example, you know what it would take for the sentence "The third closest star to earth has six planets, one of which is inhabited by intelligent creates" to be true, but you'll probably never find out if it is actually true or not. Yet, what you know - the conditions required for it to be true, not its truth-value - seem suficient to say you know what it means.

A theory which says that all there is to the meaning of a sentence is its truth-conditions is a truth-conditional theory (broadly speaking, these can go by other names too: truth-conditional semantics, formal semantics, model-theoretic semantics, possible world semantics and situation semantics).

Formally speaking, the scenarios we used above are called possible worlds, and the meaning of a sentence is called a proposition. We say that a sentence expresses or denotes a proposition.

Thinking of meaning as truth-conditions fits into a plausible story about the utility of language in daily life.

One intuition is that language lets us pass on information about the world to one another so that we can benefit from each other's experiences and use that information to determine which actions are most likely to lead to outcomes we desire.

An action is rational to the extent that it tends to maximize the satisfaction of our desires, given our beliefs.

For example, suppose you say "There are circles and square. I want the circle to be inside the square". Out of the infinitely many possible worlds, there are the a set of possible worlds that you desire and a set of possible worlds that you believe in.

If someone tells you "there aren't any red circles", you can now revise your beliefs and have a better sense of the plausible worlds that you desire.

Another useful language phenomena that fits nicely into possible worlds and truth conditions is the imperative (and interrogatives, fwiw, but we'll cover that another time).

Like the propositional attitudes we described above (constructions that describe an attitude towards a proposition, like "I want ...", "I wish ..." or "I believe ..."), imperatives (command-like constructions) separate the possible worlds between satisfactory and unsatisfactory.

For example, in "draw a circle inside a square", here is a classification of satisfactory and unsatisfactory possible worlds:

Truth-conditional theories fit into a variety of linguistic phenomena (e.g. the imperative, interrogatives and propositional attitudes), so seems like a useful theory to denote meaning to sentences.