Tarski, Field, and Deflationism
In "Tarski's Theory of Truth," Hartry Field (1972) contends that Tarski's theory fails to supply a definition of truth that would satisfy the demands of physicalism. Tarski's semantic theory of truth is only able to give a infinite list of propositions and tell which ones count as true. That kind of view, however, cannot explain what the concept of truth is.
Field believes that an adequate theory of truth should be able to explain what truth is in physical terms. When truth is reduced to physical terms, the reduction reveals what there is. And part of what there is is a concept of truth.
Although it might be beneficial to reduce truth in physical terms, there seems to be no reason to accept that truth is a reducible concept. Despite similarities between science and linguistics, there is no other reason to believe that truth can be explained in physicalistic terms. There seems to be good reason to believe that truth is not reducible in physical terms when we understand that truth is not a real or natural property, or a relation like correspondence or coherence. In the end, Tarskian truth is merely a formal or logical concept that fails to play any important role in metaphysical theory.
Here, I will argue that Field's physicalistic reduction of truth is suspect. I will contend that truth is not reducible to physicalist notions. First, I will review Field's main argument against Tarski's theory. Part of this section will briefly explain Tarski's theory. Then, I will offer a deflationist account of truth. Finally, I will offer a rejoinder on behalf of Field. I will conclude that a physicalistic reduction, though important for science, cannot be important for linguistic theory, especially a theory of truth, or metaphysics.
Tarski and Field on Truth
Tarski devised a criterion for a theory of truth for a given language:
T: p is true-in-L if and only if p
Call this the T-sentence. Tarski gives a list of the denotations of the names and predicates that occur in the language and all instances of T-sentences are the theorems of his proposed theory. The left side of the T-sentence is in the object language and the right side of the T-sentence gives the translation of that sentence in the metalanguage. The object language is the language you are talking about and the metalanguage is the language in which you are talking about the object language. The metalanguage translation gives you the truth conditions of the object language sentence. From the T-sentence, Tarski's theory is able to list a number of sentences:
"Grass is green" is true if and only of grass is green.
"Jacinda Ardern is Prime Minister of New Zealand" is true if and only if Jacinda Ardern is Prime Minister of New Zealand.
"The sum of 13 and 14 is 27" is true if and only if the sum of 13 and 14 is 27.
The totality of these instances define truth. A totality of instances, which may be derived from the T-sentence, fail to amount to an explanation. An explanation should tell us what about the instances make it the case that what is contained in the quotation marks is true. Tarski's theory fails to provide an explanation of truth, which is exactly what Field believes an adequate theory of truth ought to provide.
Field contends that a theory of truth must not only be able to list the sentences that are true, as Tarski's theory does very well, but also explain what truth is. Whatever Tarski's definition of truth offers in practice, it fails to give in theory.
Field wants to make truth respectable from the standpoint of physicalism. He believes that truth for natural languages can be understood through a Tarskian recursive definition. Field's version of physicalism is this:
the doctrine that chemical facts, biological facts, psychological facts, and semantical facts, are all explicable (in principle) in terms of physical facts.'' (Field 1972, pp. 357)
Field believes that truth, like chemistry, biology, etc., is reducible to physical terms. Field argues that there is an analogy between theories of language and theories of chemistry. In the late 19th Century, valence was an important concept and it was then expected that valence, like other physically important concepts, would eventually be given a physicalistically acceptable reduction. It was later given such a reduction through atomic theory. If it had begun to look like no reduction was possible, then this would have been some reason to abandon the theory of valences in spite of the usefulness of the theory and the possibility of giving an extensionally correct definition of valence.
Tarski's definition does not provide what scientific methodology demands - an acceptable reduction. Just as the usefulness of the concept of valence in chemistry is a reason to expect a physicalistic reduction for it, so with truth: the usefulness of the notion of truth is a reason to expect that it has a physicalistic reduction. In a sense, Field wants a theory of truth to have the same physicalistic standards that any other natural science may have. Field sees a theory of reference as a relation between the word and a thing. The relation between the word and a thing is just as natural as the chemical bond in valence theory. Truth is the correspondence between parts of interpreted sentences and certain objects and properties in the world. The connection between the word and a thing should be studied in the same way as valence bonds - in physical terms. Thus, we have reason to expect that truth can be given such a physicalistic reduction.
A problem for Field's theory of truth
Field expects more from a theory of truth than just a list of propositions that turn out true. An adequate theory of truth must be able to explain what truth is. Field believes that primitive semantic notions must be explained in physical terms. What I would like to call into question is whether truth is reducible in physical terms. My criticism roughly mirrors a deflationist conception of truth. According to deflationism, substantive theories, such as Field's theory, share the idea that truth has an inner nature. Truth's inner nature is analyzable in epistemic, semantic, or metaphysical terms. Deflationists deny that truth has an inner nature, and they contend that truth is not analyzable in epistemic, semantic, or metaphysical terms.
The trouble with theories of truth like Field's theory is that they presume truth is a natural property or relation. In Field's theory, there is an assumption that truth is explainable in terms of a causal-explanatory relation. Truth, then, is reducible in physicalistic terms. If a concept of truth is not a real or natural property or it is not a real or natural relation, then the notion is not reducible in physicalistic terms. In fact, the notion is not reducible - period. When we look at Tarski's theory of truth, we find that truth has no inner nature. Tarski's notion of truth is equivalent to the conjunction of all instances of T-sentences. There is no single substantive property all true statements share. Either "p" is true or "p" is false when it denotes or fails to denote something in the world, but that is to say nothing substantive about truth. The concept of truth is not a natural or real relation. It follows that truth is not reducible in physicalistic terms.
That truth is not reducible to physicalistic terms disconnects it from any philosophically interesting concepts. It seems that truth can no longer be associated with meaning, belief, translation, or synonymy. Truth no longer holds a central place in philosophical reflection. Truth is a purely formal or logical concept whose correct explanation requires far less extravagant resources than Field advocates.
Rejoinder on behalf of Field
Field's basic claim is that we need to provide a physicalistic reduction of the notion of truth. What I have called into
question is why we need such a reduction for truth. Field states, "it may well be that a detailed investigation into the purposes of the notion of truth might show that these purposes require only an approximate reduction of the notion of truth" (Field 1972,pp. 374.) Field seems to think that a theory of truth depends ona reduction or, more conservatively an approximate reduction, but I contend that there is no reason to think that even an approximate reduction relates to truth. In a Hartry Field's "Postrscript: Tarski on Truth," Field writes, ``the claim that we need to provide even an approximate physicalistic reduction of the notion of truth, or of truth conditions, is only compelling on the assumption that truth, or truth conditions, have some kind of `causal explanatory' role" (Field 2002, p. 29). Field argues that truth is a natural or real relation. By virtue of this fact, truth is reducible in physicalistic terms. He will deny the claim that truth is not a real or natural relation. Truth, according to Field, is a substantive concept that has some inner nature, which can be explained by a physicalistic reduction. Thus, Field concludes that truth is explicable in physicalistic terms.
Hartry Field's conclusion that truth can be explained by a physicalistic reduction is problematic when we discover that truth is a purely formal or logical concept. Truth, then, does not seem to play an important role in philosophical theories, especially metaphysics. No longer should we accept Field's contention that the physicalistic reduction of truth reveals what there is