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.
Hilary Putnam
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
OR SOMETIMES,
(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.]