Now that I’ve finished Maddy’s Naturalism in Mathematics, I’ve started reading Jody Azzouni’s recent book, Deflating Existential Consequence, which apparently tries to argue that although existential claims about mathematical entities (and many other entities) may be indispensable to our best scientific theories, this doesn’t mean we’re “ontologically committed” to them. I suppose I’ll get into that stuff later, but for now I’m reading his early chapters about truth.
He suggests that we must be deflationists about truth in order to use the truth predicate the way we do. One of the important uses, he suggests, is “blind ascription”, which is when I say something like “What Mary said is true”, rather than actually exhibiting a sentence in quotation marks followed by “is true”. It’s clear that we have a reason to engage in blind ascription of truth for a variety of reasons in our scientific theorizing, either when we talk about the consequences of an infinite theory (or at least an unwieldy and large one), or when we use a simplified version of a theory to make a calculation (like replacing “sin t” by “t” in calculating the period of oscillation of a pendulum) and suggest “something in the vicinity of this result is true”. In order for blind ascription to work, he suggests, we need to have a theory of truth that endorses every Tarski biconditional of the form “‘__’ is true iff__”. But he suggests that only the deflationist about truth can really do this.
The problem is that any supplementation of deflationist (Tarski-biconditional governed) truth faces a dilemma. Either it falsifies a Tarski biconditional (and so proves unfit for blind ascription), or it fails to be a genuine supplementation of the deflationist notion of truth.
As an example, he considers the requirement one might have that a certain type of compositionality holds. That is, “snow is white” is true just in case there is some object that “snow” refers to and a predicate referred to by “white” that applies to that object. If this requirement goes beyond the requirement of the biconditional, then such a compositional notion of truth will be unfit for blind ascription. But if it doesn’t, then he says that this requirement is “toothless”, and doesn’t get us a notion of truth any different from the deflationist.
This latter seems to me to be wrong though. Both Davidson (in “Truth and Meaning”) and Field (in “Tarski’s Theory of Truth”) apply such a requirement to the truth predicate. While Davidson seems to be happy to take a deflationist account of truth, and then use the compositionality requirement to explicate the notions of reference and meaning, Field seems to do something different. Field (at least at the time of that paper, and probably into the mid-80’s) wanted a physicalist explanation of the notions of reference and meaning for individual words, and then used the notion of compositionality to define truth. Then, using the Tarski biconditionals, we can understand just what our ordinary sentences commit us to, and we have used truth as a step in the understanding of language, rather than using understanding language as a step in explaining reference as Davidson wanted.
To see that Field’s notion of truth in this case isn’t just deflationary, I point out a usage I believe Field mentions in a much later paper (“Correspondence Truth, Disquotational Truth, and Deflationism”, from 1986). This is the example that convinced me not to be a deflationist about truth, though ironically I hear that Field became one very soon afterwards. But basically, for the deflationist, the Tarski biconditionals are constitutive of the meaning of the truth predicate, so “‘Grass is white’ is true” has just the same content as “Grass is white”. Similarly, “‘Grass is white’ might have been true” is the same as “Grass might have been white”. To see the problem, we note that as a result, “If we had used our words differently, “Grass is white” might have been true” comes out the same as “If we had used our words differently, grass might have been white”. But intuitively, the former is correct and the latter not, so the deflationist must be wrong. I think the compositional account of truth gets this right, and the biconditionals are then useful only to understand how language works and to establish the the practice of blind assertion.
So I think on this point, Azzouni is not quite right, and we can have a non-deflationary position that asserts all the same biconditionals, and is thus fit for blind assertion, and thus for science. In fact, I think there’s reason to believe that this is the right sort of truth theory, but of course that’s quite hard to argue. He has a footnote that points out what I take to be the Davidsonian position, but I think he might miss the Fieldian position. Unless I’m wrong about what this footnote is supposed to mean.