We speak of three sorts of things as being true or false
But what are sentences, beliefs and propositions?And for each of these three we can ask the following:
- What is it for one to be true or false?
- Is their truth objective?
- Is their truth relative?
- And if their truth is relative, what is it relative to?
We address propositions first because they are the fundamental bearers of truth and falsity. A proposition is what is expressed by a sentence. Sentences have meanings. When a sentence admits of truth or falsity a proposition is what is meant. A sentence is true if and only if it expresses a true proposition. But a proposition’s truth or falsity is independent of whether or not a given sentence expresses it. Propositions are also the contents of our beliefs. Whether or not a belief is true depends on whether or not its propositional content is true. But the proposition’s truth or falsity is independent of whether or not it is believed.
So we appeal to propositions in characterizing the contents of beliefs and what is expressed by sentences. And for a belief or sentence to be true or false is just for its propositional content to be true or false. But what is it for a proposition to be true or false? Here we will introduce the notion of correspondence. For a proposition to be true is for it to represent the world in a way that corresponds to the way the world actually is. So, for instance, the proposition expressed by the sentence “The cat is on the mat” is true if and only the world contains the intended cat and mat and the cat is on the mat. This doesn’t sound very exciting, but there it is. Contrary to popular opinion, the notion of truth is kind of dull. We can say that the truth or falsity of a proposition is relative to the way the world is, but that’s it. The truth or falsity of a proposition is not subjective (or relative to belief). And the truth or falsity of a proposition is not open to interpretation (or relative to meaning). This last point is crucial. The truth or falsity of a proposition is not relative to what a sentence means. The truth or falsity of a sentence is relative to what proposition it expresses. But the truth or falsity of a proposition is not relative to meaning and could not be for the simple reason that propositions don’t have meanings. Rather, the proposition is what is meant.
Sentences are linguistic things made up of words that have meanings. What a sentence means depends on what its constituent words mean. A proposition is what is meant or expressed by a meaningful sentence. In principle, we can assign any meaning we like to a word. And the meanings of sentences are, in some sense, a function of the meaning of words. So, in so far as sentences are true or false, their truth is relative to meaning. More specifically, what proposition is expressed by a given sentence depends on the meanings assigned to its constituent words. For a sentence to be true or false is just for it to express a proposition that is true or false. To help see that sentences are distinct from the propositions they express, and that the propositions themselves are not relative to meanings, consider the following two sentences:
Schnei ist wiess
Snow is white
The first sentence is German for snow is white. These are distinct sentences and this is clear because they belong to different languages. But both sentences express the same thing. So, the proposition expressed must be something independent of either language. Propositions are not linguistic entities. While propositions are the meanings of sentences, they do not have meanings themselves. So, the truth of propositions is not relative to meanings the way the truth or falsity of sentences is.
Belief is a relation between a mind and a proposition. To believe a proposition is just to take it to be true. Objectively, beliefs can be true or false. From a subject’s point of view, to believe something is just to take it to be true. What is thought to be true in one belief system may well be thought false in another. But this is not to say that truth is subjective (that is, relative to subjects). To say that what is true according to one belief system is false according to another isn’t to say anything about the nature of truth. This is just a fairly obvious and mundane observation about what is held to be true according to a belief system.