2 Truth
If one is to develop an explicit and precise scientific theory of meaning, the first thing one needs to do is to identify some of the data which the theory will respond to, and there is one type of data which virtually all work in semantics takes as fundamental: truth conditions. At an intuitive level, truth conditions are merely the most obvious way of understanding the meaning of a declarative sentence. If I say It is raining outside, I have described the world in a certain way. I may have described it correctly, in which case what I said is true, or I may have described it incorrectly, in which case it is false. Any competent speaker knows to a high degree of precision what the weather must be like for my sentence to count as true (a correct description) or false (an incorrect description). In other words, such a speaker knows the truth conditions of my sentence. This knowledge of truth conditions is extremely robust â far and wide, English speakers can make agreeing judgments about what would make my sentence true or false â and as a result, we can see the truth conditions themselves as a reliable fact about language which can serve as part of the basis for semantic theory.
While truth conditions constitute some of the most basic data for semantics, different approaches to semantics reckon with them in different ways. Some theories treat truth conditions not merely as the data which semantics is to deal with, but more than this as the very model of sentential meaning. This perspective can be summarized with the slogan âmeaning is truth conditionsâ, and within this tradition, we find statements like the following:
| (1) | [[ It is raining outside ]]t,s = TRUE iff it is raining outside of the building where the speaker s is located at time t, and = FALSE otherwise. |
The double brackets [[ X ]] around an expression X names the semantic value of X in the terms of the theory in question. Thus, (1) indicates a theory which takes the semantic value of a sentence to be its truth value, TRUE or FALSE. The meaning of the sentence, according to the truth conditional theory, is then captured by the entire statement (1).
Although (1) represents a truth conditional theory according to which semantic value and meaning (i.e., the truth conditions) are distinct (the semantic value is a crucial component in giving the meaning), other truth conditional theories use techniques which allow meaning to be reified, and thus identified with semantic value, in a certain sense. The most well-known and important such approach is based on possible worlds:
| (2) | a. [[ It is raining outside ]]w,t,s = TRUE iff it is raining outside of the building where the speaker s is located at time t in world w, and = FALSE otherwise. |
| b. [[ It is raining outside ]]t,s = the set of worlds {w : it is raining outside of the building where the speaker s is located at time t in world w} |
A possible world is a complete way the world could be. (Other theories use constructs similar to possible worlds, such as situations.) The statement in (2a) says virtually the same thing as (1), making explicit only that the meaning of It is raining outside depends not merely on the actual weather outside, but whatever the weather may turn out to be. Crucially, by allowing the possible world to be treated as an arbitrary point of evaluation, as in (2a), we are able to identify the truth conditions with the set of all such points, as in (2b). In (2), we have two different kinds of semantic value: the one in (2a), relativized to world, time, and speaker, corresponds to (1), and is often called the extension or reference. That in (2b), where the world point of evaluation has been transferred into the semantic value itself, is then called the intension or sense. The sense of a full sentence, for example given as a set of possible worlds as in (2b), is called a proposition. Specific theories differ in the precise nature of the extension and intension: The intension may involve more or different parameters than w, t, s, and several of these may be gathered into a set (along with the world) to form the intension. For example, in tense semantics, we often see intensions treated as sets of pairs of a world and a time.
The majority of work in semantics follows the truth conditional approach to the extent of making statements like those in (1)â(2) the fundamental fabric of the theory. Scholars often produce explicit fragments, i.e. mini-theories which cover a subset of a language, which are actually functions from expressions of a language to semantic values, with the semantic values of sentences being truth conditional in the vein of (1)â(2). But not all semantic research is truth conditional in this explicit way. Descriptive linguistics, functional linguistics, typological linguistics and cognitive linguistics frequently make important claims about meaning (in a particular language, or crosslinguistically). For example, Wolfart (1973: 25), a descriptive study of Plains Cree states: âSemantically, direction serves to specify actor and goal. In sentence (3), for instances, the direct theme sign /Ä/ indicates the noun atim as goal, whereas the inverse theme sign /ekw/ in (4) marks the same noun as actor.â
| (3) | nisÄkihÄnÄn | atim |
| scare(1p-3) | dog(3) |
| âWe scare the dog.â | |
| (4) | nisÄkihikonÄn | atim |
| scare(3-1p) | dog(3) |
| âThe dog scares us.â | |
Despite not being framed as such, this passage is implicitly truth conditional. Wolfart is stating a difference in truth conditions which depends on the grammatical category of direction using the descriptions âactorâ and âgoalâ, and using the translations of cited examples. This example serves to illustrate the centrality of truth conditions to any attempt to think about the nature of linguistic meaning.
As a corollary to the focus on truth conditions, semantic theories typically take relations like entailment, synonymy, and contradiction to provide crucial data as well. Thus, the example sentence It is raining outside entails (5), and this fact is known to any competent speaker.
| (5) | It is raining outside or the kids are playing with the water hose. |
Obviously, this entailment can be understood in terms of truth conditions (the truth of the one sentence guarantees the truth of the other), a fact which supports the idea that the analysis of truth conditions should be a central goal of semantics. It is less satisfying to describe synonymy in terms of truth conditions, as identity of truth conditions doesnât in most cases make for absolute sameness of meaning, in an intuitive sense â consider Mary hit John and John was hit by Mary; nevertheless, a truth conditional definition of synonymy allows for at least a useful concept of synonymy, since people can indeed judge whether two sentences would accurately describe the same circumstances, whereas itâs not obvious that complete intuitive synonymy is even a useful concept, insofar as it may never occur in natural language.
The truth conditional perspective on meaning is intuitive and powerful where it applies, but in and of itself, it is only a foundation. It doesnât, at first glance, say anythi...