Meaning and Truth Conditions
In this class, the meaning of a sentence is its truth condition. This is a non-obvious assertion on a number of levels, so a bit of explanation is in order. I'll begin by talking about meaning, and then move to a discussion of truth conditions, and finish with an argument for taking meanings to be truth conditions.
Sentences are valuable primarily because they are meaningful. Typically, we have little use for random strings of symbols. Such strings, no matter how complex or interesting, are regarded as at most curiosities, unless they are thought to be meaningful. To be meaningful is to have a meaning. But what is this thing, this meaning? What is the meaning of a sentence?
How can we answer this question? The first step is to notice that "meaning", as it is used in the question, suggests that we are looking for some type of thing. But where and how do we look for this thing? You can't touch it or see it, so empirical methods would appear to be useless. You might say: "Yes, I can't see it, but I know when it is there and I know when it isn't, even if this knowledge isn't observational." This response yields a hint: perhaps if we approached meaning from the perspective of our knowledge, we might be able to get a foothold. In particular, if we found something that (a) if we know it, we know a meaning, and (b) if we know a meaning, we know it, then we might discover a way of analyzing meaning. We will begin (and end) our search for this thing by examining truth conditions.
II. Truth Conditions
The truth condition of a sentence is the condition of the world under which it is true. This condition must be such that if it obtains, the sentence is true, and if it doesn't obtain, the sentence is false.
Now, whether a sentence is true or false in a given circumstance will depend on its parts. For instance, the sentence, "Snow is white," depends for its truth on snow and the property of being white. For it to be true, these things must be related in the right way; if they are not, then the sentence is false. Thus, the truth condition of a given sentence S will consist in a relation between the things in the world that correspond to the parts of S. This is often expressed in the following way:
"Snow is white" is true if and only if (or just in case) snow is white.
This seems like a platitude, but it really isn't. The first part of the sentence, "Snow is white", is a name, in this case, the name of a sentence. Thus, the sentence could be rewritten:
S is true if and only if snow is white.
This looks much less trivial. The part of the sentence on the right of the "if and only if" specifies the condition of the world that must obtain for the sentence named by the quote to be true.
This also holds for us: the truth condition of a sentence depends on the truth conditions of its parts. It is for this reason that we can use truth tables. These tables supply a group of rows that, when taken together, exhaustively describe all possible states of the world. The column under each of the sentence symbols (i.e., the Reference column) supplies the truth condition for each of those sentences, and the columns generated under the complex sentence demonstrate how to construct their truth conditions out of the truth conditions of their parts according to the rules supplied by the connectives. You wind up with a table that gives you the truth value for the complex sentence in any possible circumstance--just name a circumstance and you will be able to find the row which corresponds to it by looking at the reference columns, and then you simply move to the right to find the truth value of the complex sentence.
Recall that we were looking for something that stood in the following relation to meaning: (a) if you know it, you know a meaning, and (b) if you know a meaning, you know it. In truth conditions, we have found just what we were looking for. Consider each case in turn.
Case I: If you know the truth condition of a sentence S, then you know a condition that enables you to determine the truth value of S in any circumstance where you might evaluate it. This condition will enable you to determine when S is true and when S is false, regardless of where you happen to be evaluating it. But if you know this, certainly you must know the meaning, since the meaning must help you determine what to look for when evaluating it. (Consider: could you evaluate the sentence "Rationality requires logical consistency" without knowing the meaning of the sentence?)
Case II: If you know the meaning of a sentence S, then you know all you need to know to determine its truth value; indeed, if you are unable to determine the truth value of S in a particular context, this is usually taken to be a sign that you do not completely understand it, i.e, that you do not know its meaning.
Thus, knowing the truth condition implies knowing the meaning, and knowing the meaning implies knowing the truth condition. For our purposes, we take this to be evidence that they are identical; however, even if you do not buy this identity claim, this tight-knit association justifies basing claims about meaning on an examination of truth conditions.