Sunday, October 12, 2014
Last Post of this series of three on Tarski
In 1976, when I delivered the John Locke Lectures at Oxford, I often spent time with Peter Strawson, and one day at lunch he made a remark I have never been able to forget. He said, "Surely half the pleasure of life is sardonic comment on the passing show". This blog is devoted to comments, not all of them sardonic, on the passing philosophical show.
Philosophical morals of the preceding (presupposes Posts 1 and 2 on Tarski)
(1) Apart from §1, which ends on a massively pessimistic note, there is no attempt in Tarski(1933) to reduce any semantical notion to a non-semantical notion (unless it be a failed attempt, which is what Field thought). What there is, is a definition of a predicate (which I called "FORM(x)") that is coextensive with “true in Bob”, but one which defines a property that the sentence “snow is white” has, for example, in a possible world in which snow is white and the word “white” means black! (This is so because nothing in the definition of FORM(x) refers to the use or meaning of expressions.) As a conceptual analysis of “true”, the predicate FORM(x) fails miserably.[i] People would not have had so much difficulty in grasping this undeniable fact if Tarski had titled his conception “The Look No Semantics Conception of Truth.[ii] Of course, this is not to impugn the mathematical importance of the “material equivalence”—by which Tarski must mean the coextensiveness—of “true” (in the relevant language “Bob”) and the truth predicate (our FORM(x)), or the philosophical significance of Tarski’s work, which can only be extracted if we are clear on what it did and what it did not accomplish.
(2) “Correspondence theory of truth” is the name traditionally given to theories of the form: “a statement [or thought, or belief, or proposition, etc., depending on the particular philosopher] is true if and only if the statement [or thought, etc.] corresponds to a fact [or to reality, or to some appropriate piece of reality, depending again on the particular philosopher’s metaphysical views]”. The correspondence theory is discussed in §1 of Tarski(1933) [where the T-Schema (not Convention T!) is stated], but the section ends on a negative note about the whole project of clarifying the notion of truth in everyday language, as we noted in our previous posts. However, Convention T itself does not (as I have emphasized) contain the word “true”. FORM(x) is a one-place predicate of Meta-Bob, and we have specified that Meta-Bob does not contain any words like “true”, nor any words like “fact”. Likewise, Convention T does not contain any words like “true”, nor any words like “fact”. Thus there is no way in which Meta-Bob, or Convention T, or the “truth predicate” FORM, can even express the correspondence theory of truth.
(3) “Deflationary theory of truth” is the name given to the more recent (twentieth century) theory that the notion of truth is wholly captured by one or the other of the two following Disquotation Principles:
(D) To call a statement (or sometimes a “proposition”, rarely a “sentence” as in Tarski’s famous article) “true” is simply to affirm the statement
(D’) The statement “S is true[iii]” is equivalent to the statement S
Since Convention T does not mention truth, as I have been emphasizing, it obviously does not state either (D) or (D’). But it is plausible that it presupposes (D’) for the following reason: Tarski’s reader is supposed to see that if all of the conditionals that are required to be theorems of Meta-Bob by Convention T are theorems [and if we assume that the theorems of Meta-Bob are true![iv]], then each sentence of the form
FORM(s*) ≡ s
is true – and, implicitly using the T-Schema
true(s*) ≡ s,
it follows that
FORM(s*) ≡ true(s*).
Thus it is plausible that the disquotation principle is presupposed by Tarski’s claim that Convention T is a correct (“accurate”, in the original Polish version) condition for the “material adequacy” of a formula like FORM(x) as a truth predicate for Bob. In any case, the idea of disquotation easily arises from a study of Tarski great paper. But there is all the difference in the world between accepting a Disquotation Principle and accepting the claim that such a Principle captures completely what one has to know about truth, and the latter is the thesis of Deflationism. I conclude that Tarski is not committed to that thesis any more than he is committed to the correspondence theory of truth.
(4) Just as it is plausible to see a disquotation principle as presupposed by Convention T, even if Tarski did not state one, it is plausible to see the fact that the extension of “true in Bob” is determined by the extension of “denotes in Bob” as driving the entire strategy of defining the desired truth predicate (FORM(x)) in terms of an inductively defined predicate (in our simplified version of Tarski, above, SAT(y,x)) that is constructed to have precisely the extension of the everyday language predicate “x refers to y in Bob”.
In sum, and this is something I regard as of great importance, Tarski’s formal methods intuitively draw on and presuppose not just one property of truth, the T-Schema, or Disquotation, but on that property AND the further property that the extension of “true” depends on the extension of “refers”. The concepts of truth and of reference are intimately related, and his entire procedure exploits the relation, as Field saw in 1972.
Realism is incompatible with Deflationism
If one says “Asteroids [or daisies, or marsupials] exist”, but one’s account of what it is to understand these speech sounds (or, if one writes it instead of saying it out loud, if one’s account of what it is to understand such a string of symbols), does not mention any connection whatsoever between those ‘vocables’ (or those ‘strings’) and asteroids or daisies or marsupials, or objects and properties in terms of which such entities can be described, then I, for one, fail to see how what one says can be understood in a realist way. This is a point I have debated with Michael Devitt[v] as well as with Rorty[vi] and I will not repeat all that here. What follows is addressed to a reader who “gets it”, and agrees. Of course, a non-realist can be a Deflationist and simply refuse to understand sentences about such things in a realist way. For a logical positivist to know the meaning of a sentence is just to know its method of verification, and the method of verification is to be described in terms of tests we can perform.[vii]
Moreover, saying that certain sentences are causally connected to asteroids (or daisies, or marsupials) isn’t enough to capture the way in which truth-apt assertions about real objects relate to the world. If I say that there are marsupials in Australia, I intend my utterance to be related to marsupials and not to anything else that the event of my making that utterance may have been caused by, e.g., text books or zoos. In short, when I say it I am referring to marsupials, and that fact is not captured by pointing out that my saying it was causally connected to marsupials.
If this is often under-appreciated by “Deflationists”, it seems to me that missing it comes from missing the point with which I closed the previous section (to repeat:)
Tarski’s formal methods intuitively draw on and presuppose not just one property of truth, the T-Schema, or Disquotation, but on that property AND the further property that the extension of “true” depends on the extension of “refers” (and on the possible extensions of “refers”, if the logical vocabulary includes modal operators[viii]. Tarski did not consider such languages.) The concepts of truth and of reference are intimately interrelated.
If Deflationists regularly fail to mention the interdependence of truth and reference, they do, however, recognize the need for some account of meaning, or at least of sameness of meaning. After all, I can speak of true sentences in a language that is not properly contained in my own language. The sentence ‘‘‘Schnee ist weiss’ is true if and only if Schnee ist weiss” is not a well formed sentence in either English or German. The standard form of disquotation in this case (a generalization of Tarski’s T Schema) is to say that if I am using English (or a formalized version thereof) as a meta-language (for a part of German that is free of semantical words and includes the sentence “Schnee ist weiss”), then the appropriate T-sentence is:
“Schnee ist weiss” is true in German iff snow is white,
and more generally, for any sentence s in the part of German in question,
(T) “s” is true in German iff ...
where the three dots are to be replaced by the translation of the sentence s in English.
That the notion of translation is needed for disquotation, and therefore needed by Deflationists (since their thesis is that grasp of disquotation is all that is needed for an understanding of truth) is widely recognized. But what I have not seen discussed by Deflationists, let alone taken seriously, is the thought that translating sentences presupposes knowing what their descriptive constituents refer to. It is an illusion that disquotation does not presuppose the relation of reference.
[i] In 1953, Carnap suggested to me a way of meeting this objection. I describe Carnap’s objection (which depended on defining Bob by Bob’s “semantical rules”) and show why it fails in Representation and Reality (Cambridge, MA: MIT Press, 1988), pp. 61-67.
[ii] I put it this way in “A Comparison of Something with Something Else.”
[iii] A technical problem: in (D’) is “S” a variable over statements? Or is (D’) to be understood with some sort of systematic ambiguity? The literature discusses this problem extensively, and there are different proposals.
[iv] This cannot be taken for granted, because Meta-Bob contains significant mathematics, and a mathematical theory can contain false statements – even false arithmetical statements – without being inconsistent.
[v] See my “Comment on Michael Devitt,” in Maria Baghramian, op. cit., pp. 121-126.
[vi] See my “Richard Rorty on Reality and Justification,” in Robert Brandom, ed., Rorty And His Critics (Oxford: Blackwell, 2000), pp. 81-87.
[vii] For example, Carnap discusses the statement “If all minds (or all living beings) should disappear from the universe, the stars would still go on in their courses”, in “Testability and Meaning”, Part II, Philosophy of Science, Vol. IV, 1937, pp. 37-38, and concludes that it is both cognitively meaningful and well confirmed.
[viii] If a modal primitive is added to the language, say the symbol ◊, then the appropriate clause will read: a satisfies ◊F just in case ◊(a satisfies F). Here is a word example: take (F(x) to be (Ey)(x loves y). Interpret ◊ as physical possibility (or, alternatively, sociological possibility), and take a to be Alice. Then “a satisfies ◊F” says that Alice satisfies “it is possible x loves somebody", “◊(a satisfies F)” says that it is possible that Alice satisfies "x loves somebody" and these two formulas have the same truth condition, namely that in some possible world there is a person whom Alice loves. In mathematical jargon, “satisfies” commutes with ◊. [In my view, “in some possible world there is” means that it is possible that there is a world in which there is; modal logic does not presuppose the actual existence of possible worlds.]