Philosophy 1890d: Theories of Truth

Philosophers have been worrying about truth for just about as long as there've been philosophers. They've worried about what truth is; about what kinds of things are true; about what it is for one of these things to be true; about how its being true is related to our knowing or thinking that it is true; and so on. But why should philosophers worry about these things? This is itself a philosophical question. Some philosophers, Deflationists, think that there is nothing of philosophical interest to be said about truth. According to these philosophers, the concept of truth is boring.

There are three kinds of reasons philosophers have thought the concept of truth was interesting. First, philosophers have often concerned themselves with norms of correct reasoning (that is, with logic), and the concept of truth seems to play an important role here. Thus, a valid inference is one that is truth-preserving, whose conclusion must be true if its premises are. The concept of validity, and so that of a ‘norm of reasoning', thus seems to be tied up with the concept of truth. Second, philosophy has long concerned itself with representation, that is, with our capacity to think about, or to make claims about, the world. A fundamental feature of representations seems to be that they can be right or wrong, true or false. Moreover, it seems in some sense a primary goal of thought to acquire true rather than false beliefs. It is because thought aims at truth that valid inferences are good inferences: Being truth-preserving is a good thing for an inference to be because we infer new beliefs from old ones, and we want our beliefs to be true. Questions about truth thus appear to bear on questions about representation (or meaning). Finally, there seems to be an intimate connec­tion between truth and metaphysics. The nature of the connection is controversial, but consider, for example, the view that, for something to be true, we must be able to come to know that it is true: On this view, how things are depends upon what we are capable of knowing. That amounts to a form of Idealism, a form of the view that how the world is is in some sense or other determined, or constrained, by the mind.

We shall not discuss any of these issues directly: The course is less ambitious, the goal being that students should acquire the necessary background to appreciate contemporary discussions of truth. But we shall touch on each of them at one time or another. Indeed, a concern with these issues will shape the course in ways on which I shall comment when that seems appropriate.

The course will be structured as follows. We shall begin by looking at some famous papers on truth written in the 1950s, attempting to extract from these papers a sense of the importance of Convention T, which, so to speak, generalizes sentences of the following form:

The sentence "Snow is white" is true if, and only if, snow is white.
The sentence "Grass is green" is true if, and only if, grass is green.

I hope these sentences seem true. Convention T states that they are true, and that all sentences of the same form are true.

This principle has guided philosophical thinking about truth for over sixty years (and, indeed, for a long time before that, although less explicitly). It may seem to embody the idea that whether a sentence is true is determined by relevant features of the world: Whether the sentence "Snow is white" is true depends upon whether snow is white; whether "Grass is green" is true depends upon whether grass is green; and so forth. Indeed, some philosophers are so impressed by Convention T that they think that all that needs to be, or can be, said about truth is said by Convention T. This is one form of Deflationism, and we shall spend some time explaining and evaluating this position at the end of the course.

There is a big problem with Convention T, though: Obvious as it may seem, it is paradoxical. Among other things, Convention T tells us that:

The sentence "The sentence written in tiny type on the syllabus for Phil 1890D is not true" is true if, and only if, the sentence written in tiny type on the syllabus for Phil 1890D is not true.

But it happens that, as a matter of empirical fact, the sentence written in tiny type on the syllabus for Phil 1890D is the sentence "The sentence written in tiny type on the syllabus for Phil 1890D is not true". So, by the laws of identity, we have:

The sentence "The sentence written in tiny type on the syllabus for Phil 1890D is not true" is true if, and only if, the sentence "The sentence written in tiny type on the syllabus for Phil 1890D is not true" is not true.

That's a contradiction of the form ‘p ≡ ¬p'. This is the Liar Paradox, in one of its many versions.

One might think this is just foolish, that there is an easy solution: Isn't a sentence's referring to itself fishy? But that sentences should be able to refer to themselves in this way is essential to the proof of one of the most important mathematical theorems of this century, Gödel's incompleteness theorem. More generally, it is, roughly, a theorem of arithmetic that sentences can refer to them­selves in this way. So what the Liar Paradox shows is no less than this: That one can not, on pain of contradiction, both accept all instances of Convention T and accept all the truths of arithmetic. Something has to give.

Just what has to give is the interesting question.

Richard Heck Department of Philosophy Brown University