Truth and Disquotation Principles

By | February 17, 2015

In my previous post I talked about the correspondence theory of truth and its relation to truthmaker theory. I’m going to follow it¬†up with a series of posts on various issues concerning truth and ontology that I’ve been mulling over off-and-on over the past several years.¬†The current post concerns disquotation principles. I distinguish between sentential and propositional disquotation principles and argue that the latter is of much wider applicability than the former.

Disquotation principles

Disquotation principles comes in two main forms, (1) and (2):

  1. p” is true if and only if¬†p.
  2. <p> is true if and only if p.

I call (1) the sentential disquotation principle because in it the variable p is supposed to take the place of a sentence, and more specifically, of a declarative sentence or statement. Sentences are strings of symbols that when grammatically well-formed are capable of expressing a complete thought, one that includes both a subject and a predicate.

I call (2) the propositional disquotation principle because in it the variable p is supposed to take the place of a proposition. Unlike sentences, propositions are not strings of symbols. Rather, they are units of meaning capable of bearing a truth value. (Concepts like green are also units of meaning, but it makes no sense to suppose it is true that green.) Declarative sentences are typically used to express propositions, but they are not identical to the propositions they express. To suppose otherwise is to confuse the message (the proposition expressed) with the symbolic carrier of the message (the sentence).

Sentential disquotiation

(1) may seem like a truism, but I will argue that it is true only in very limited contexts. Consider the following examples:

  1. “Buddha was fat” is true if and only if Buddha was fat.
  2. “Janelle is a curly-haired puppy lover” is true if and only if Janelle is a curly haired puppy lover.
  3. “1 + 1 = 2” is true if and only if 1 + 1 = 2.

In each case, on the left-hand side (LHS) is a quoted declarative sentence to which is appended the predicate “is true”. On the right-hand side (RHS) the quoted sentence appears again, but without quotes.

Why are there quotes around the sentence on the LHS but not the RHS? The reason for this is because, on the LHS, we want to predicate truth¬†of a sentence, and so that sentence has to become the subject of a clause. To make it into a subject we have to refer to the sentence as a whole. Putting quotes around it¬†allows us to do this.¬†It allows us¬†to mention¬†the sentence¬†without¬†using it. The clause on the RHS, in contrast, lacks quotes because there the sentence is¬†used to describe its¬†truth conditions. The two occurrences of¬†p in (1), therefore, have very different roles. On the LHS “p” is used denotatively to single out or¬†name¬†p, whereas on the RHS p is used connotatively to¬†express¬†p.

Now, the problem with (1), the reason why it is true only in limited contexts, is because most sentences are not perfectly¬†clear and precise as to their meaning. One problem, illustrated by (3), is¬†vagueness. There is no clear line of demarcation between fat and¬†non-fat persons. Hence, the meaning, and therefore the truth conditions, of “Buddha was fat” are vague. There is no clear demarcation on the RHS between cases in which its truth conditions are fulfilled and cases in which they aren’t. Likewise, there is no clear demarcation on the LHS between cases in which “Buddha was fat” is true and cases in which it isn’t. Consequently, there is no clear demarcation between cases in which the “if and only if” comparative is satisfied and cases in which it isn’t. But then (3) isn’t true, and so neither is (1).

Another problem facing (1) is that of ambiguity. Ambiguity occurs when there are multiple distinct meanings and no clear way to choose between them. (4) is an example of ambiguity.¬†What exactly is the sentence saying about Janelle (my daughter)? Is it saying that she has curly hair and that she loves puppies? Or it it saying that she loves puppies that have curly hair? Both interpretations are grammatically admissible. Hence, there is no unique¬†set of truth conditions for (4). The “only if” part of the comparative, therefore, cannot be satisfied. But then (4) isn’t true, and so neither is (1).

We could try to save (1) by appealing to context, to speaker’s intentions, or to what a typical speaker would¬†normally mean by using a sentence in a context to fix an exact, unique, and correct¬†interpretation of the sentence. But there’s no reason to think that such appeals will, in all cases, yield an exact, unique, and correct interpretation. After all, erudite scholars who are keenly sensitive to matters of context and the nuances of language have been debating for centuries about how best to interpret certain passages of the Bible or of Shakespeare. Moreover, the moment we appeal to things like context, intentions, and common usage we are in effect admitting that¬†sentences, in and of themselves,¬†don’t have exact and unique meanings. But that’s what (1) assumes. It assumes that the meaning, and therefore the truth conditions, of any given declarative sentence are exactly fixed by the sentence. And this just isn’t so.

The least unproblematic cases for (1)¬†are cases like (5) in which the sentence in question is absolutely clear and precise. There is no vagueness or ambiguity in “1 + 1 = 2”. We can specify exactly what the sentence means and therefore what it takes for the sentence to be true. It is no accident that Tarski, the man responsible for developing and promoting (1), was a mathematical logician. Mathematical expressions are formulated in an artificial mathematical language designed for precision and logical rigor.¬†So, to the extent that (1) is true, it is true only with respect to logically rigorous contexts of this sort in which we don’t have to worry about vagueness and ambiguity.

Propositional disquotation

The angle brackets on the LHS of (2) function in the same way as the quotes in (1). They allow us to refer to or denote p without connotatively expressing p. <p> on the LHS names a proposition. p on the RHS expresses the proposition named by <p>. The reason for using angle brackets instead of quotes is to make clear that <p> is not referring to a sentence, but to a proposition.

(2) is far more plausible than (1) because propositions suffer from none of the limitations of sentences. Unlike sentences, which often have no clear meaning, a proposition is identical to its meaning. Propositions, by their very nature, exclude vagueness and ambiguity.

Propositions do have an important practical limitation, however. The difficulty is that we have no way to communicate propositions or to identify¬†which proposition we have in mind without expressing¬†our thoughts in sentential terms. And this ultimately brings vagueness and ambiguity (and figurative language etc.) back into the mix. So even if (2) is true, we often can’t know for certain whether we’ve applied it correctly, for we often can’t know for certain whether we’re all talking about the¬†same proposition.

Concluding remarks

So far I have argued that, of the two disquotation principles, (2) has much more to be said for it than (1). Indeed, many philosophers would regard (2) not only as obviously true but also as logically necessary. In my next post I will argue that this view is actually quite mistaken.

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