ISSN 1393-614X Minerva - An Internet Journal of
Philosophy Vol. 10 2006
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On Why the Slingshot against
the Correspondence Theory of Truth Misfires Arhat Virdi |
Abstract
According to the correspondence
theory of truth, a statement is true just in case it corresponds to the facts.
The slingshot argument demonstrating that there can be only one fact is
understood by some philosophers to deliver a coup de grâce to the correspondence theory. Others, however, seek to
deflect the slingshot by appealling to Russell’s non-referential theory of
definite descriptions. I argue that the slingshot argument is immune to
semantical considerations concerning definite descriptions. The slingshot
argument is valid. However, I also
argue that this fails to demonstrate the untenability of the correspondence
theory of truth.
According to the correspondence theory
of truth, a statement is true just in case it corresponds to the facts. For
instance, the statement that snow is white is true just in case it corresponds
to the fact that snow is white. The theory has invited a number of criticisms
and counter-arguments. Among them is the so-called ‘slingshot argument’. This
demonstrates that (at most) there can be only one fact. In rendering the notion of fact redundant, the argument
is thereby taken to cripple the correspondence thesis in positing entia non
grata. Given that the mechanics of the argument rest on minimal logical
machinery and appears to cripple a venerable philosophical thesis in one fell
swoop, one sees why the David and Goliath metaphor has been employed. Donald
Davidson, for example, has long been convinced by all this, advocating ‘[t]here
is good reason, then, to be skeptical about the importance of the
correspondence theory of truth.’ (Davidson 1999: 106). The slingshot argument is valid, viz. there is only one fact, but it does not cripple the correspondence theory of truth. In fact, it grossly
misfires.
Many loading the slingshot take inspiration from the
Fregean view that the reference of a sentence is that sentence’s truth-value:
the True, if the sentence is true, or the False, if the sentence is false. In
demonstrating that connectives like ‘the statement that … corresponds to the
fact that …’ are truth-functional, i.e. the truth-value of sentences with these
as the governing connective depends only on the truth-value of the atoms
composing them, anti-correspondentists hope to make their case by showing that
all statements correspond to the same fact. Hence, there is at most one fact.
What prize, then, in being a correspondentist about truth? The first to develop
slingshot-type reasoning in vindication of Frege was
(S) The statement
that p corresponds to the fact that q
would be true. Clearly (S) is true when both p and q are replaced by the same sentence. However, unless facts are to be understood as mere
reflections of true sentences, there ought to be true instances of (S) when p
and q are not identical. Davidson then
observes that since (as an example) Naples satisfies
the description ‘the largest city within thirty miles of Ischia’, the statement
that Naples is farther north than Red Bluff corresponds to the fact that Red
Bluff is farther south than the largest city within thirty miles of Ischia.
Given further that
(1) The statements
replacing p and q are logically equivalent.
(2) p and q differ
only in that a singular term has been replaced by a co-extensive/co-referring
singular term.
The slingshot argument is then this:
Let
‘s’ abbreviate some true sentence. Then surely the statement that s
corresponds to the fact that s. But we may substitute for the second ‘s’
the logically equivalent ‘(the x such that x is identical with
Diogenes and s) is identical with (the x such that x is
identical with Diogenes)’. Applying the
principle that we may substitute coextensive singular terms, we can
substitute ‘t’ for ‘s’ in the last quoted sentence, provided ‘t’
is true. Finally, reversing the first step we conclude that the statement that s
corresponds to the fact that t, where ‘s’ and ‘t’ are any
true sentences. (Davidson 1969: 42) [1]
Hence, in a later paper, Davidson draws the following
moral:
… this … trivialize[s] the concept of correspondence
completely; there is no interest in the relation of correspondence if there is
only one thing to which to correspond, since…the relation may well be collapsed
into a simple property: thus, “s
corresponds to the universe”, like “s
corresponds to (or names) the True”, or “s
corresponds to the facts” can less misleadingly be read “s is true”. (Davidson 1990: 303)
The success of the slingshot is standardly taken to
depend on the semantics of the definite descriptions involved.[2] Let d represent Diogenes. Now, to let
principle (2) license the move from ‘ix(x = d & s) = ix(x = d)’ to ‘ix(x = d & t) = ix(x = d)’ one
must understand the definite descriptions employed — the iota-expressions — as singular terms that refer to the thing they
uniquely describe. If, however, one is a Russellian about descriptions then
they are not referential because they
are not singular terms. Instead they
are syncategorematic terms, defined in context rather than in isolation,
understood as belonging to the class of first-order logical expressions. For
example, the description ‘ix(x = d & s)’ is equivalent to ‘$x["y((y = d & s) « y = x) & $w("z(z = d « z = w) & x = w)]’. This is precisely what furnished
Bertrand Russell the means by which to make
expressions such as ‘the present king of
Nothing,
however, hinges on the semantics of definite descriptions. For to re-articulate
the argument in terms of set abstracts, where it is formally demonstrable that
they refer uniquely in the standard model of set theory, ensures the
slingshot’s validity. There are no iota-expressions to be concerned
with. This lends substantial credence to the suspicion Kurt Gödel once
articulated concerning the strategy of appealing to Russell’s theory of
definite descriptions in exoneration of Frege:
... I cannot help
feeling that the problem raised by Frege’s puzzling conclusion [that all true
sentences have the same reference] has only been evaded by Russell’s theory of
descriptions and that there is something behind it which is not yet completely
understood. (Gödel 1944: 215)
Following
Davidson, let s and t abbreviate true sentences. Then the following
is a valid argument:
1.
s
Premise
2.
{x: x = d & s} = {x: x = d} From 1., given substitution salva
veritate of logical equivalents
3. {x: x = d & t} = {x:
x = d} From 2., given
substitution salva veritate of co-referring terms
4. t
From 3., given substitution salva veritate of logical equivalents
Hence, there is one fact, permitting us to
speak of nothing more than a factual entirety. So, does this trivialize the
relation of correspondence, provoking no interest in it if there is only one
thing to which to correspond? No. Not if we are interested in the
correspondence theory of truth. For according to it, truth consists in the relation of correspondence; it does not consist in the relatum of
truth-maker. ‘x is true’ means that a (general) property of the
form ∃yR(x,y)
is being picked out; it does not pick out the relatum (instantiated by a, say) to which x is related. The correspondentist is saying that this property is
exactly the relation of correspondence. Now, no one denies that the truth
predicate is syntactically monadic.
But this syntactical veneer belies a latent semantics. In ‘The Thought: A
Logical Inquiry’, Frege (1911: 86) was concerned by the correspondence theory
in that, unlike ‘agrees with’ or ‘corresponds to’, the truth predicate does not
appear to signify a relation. However, can it not, nonetheless, be legitimately
compared to monadic predicates like ‘x
is a husband’ which, not appearing to signify a relation either, can only be
analysed in relational terms? In fact, this is the sine qua non in analysing such predicates. For instance, consider Colin’s
marriage to Margaret. If we were to follow Gerald Vision - another example of
those philosophers misunderstanding truth’s modus operandi - for whom ‘[t]he truth of a proposition is constituted by a state
of the world such that, were the proposition stated, it would
state the world to be that way’ (2004: 1), then Colin’s being a husband would be constituted by Margaret,
i.e. the lady to whom he is married. But this is surely incorrect. Colin’s
being a husband is constituted by his being married to some lady, who in
this case is Margaret. ‘x is a husband’ can only be correctly analysed
as ‘there is somebody to whom x is married’; husband-hood signifies a
relational property. Similarly, ‘x is true’ signifies a relational
property, and according to the correspondence theory of truth this means ‘there
is something to which x corresponds.’[3] It is vital to appreciate that it is not the
truth-maker which constitutes truth, but the relation that the
truth-bearer bears to the truth-maker which constitutes the notion.
It is, therefore, difficult to understand why the
slingshot argument has been loaded so often and seen to be of such significance
for anti-correspondentism when it so plainly misfires. Its success, or
otherwise, is independent of the correspondence theorist’s concern. Its target
is the truth-maker, not the property of truth, i.e. not what the correspondence
theory of truth is a theory of.[4]
REFERENCES
Church, A. 1943. Review of
Carnap’s Introduction to Semantics. Philosophical Review 52: 298-304.
Davidson, D. 1969. True to the
facts. In his Inquiries into Truth and Interpretation, 37-54.
Davidson,
D. 1967. Truth and meaning. In his Inquiries into Truth and
Interpretation, 17-36.
Davidson,
D. 1999. The centrality of truth. In Truth and its Nature (if any), ed.
J. Peregrin.
Etchemendy, J. 1999. The Concept of Logical Consequence.
Frege, G. 1911. The thought: a
logical inquiry. In Truth, ed. S.
Blackburn and K. Simmons. 1999.
Gödel, K. 1944. Russell’s
mathematical logic. In Philosophy of
Mathematics: Selected
Neale, S. 2001. Facing Facts.
Vision, G. 2004. Veritas: The Correspondence Theory and Its
Critics.
[2] And this is so even if we were to load the more powerful slingshot
sketched in footnote 5 of Gödel (1944: 214). The significant difference between the two is that instead of insisting
on logical equivalence, Gödel uses a tighter notion – Gödelian equivalence
– which holds between sentences like ‘Fa’ and ‘a = ix(x = a & Fx)’. For further discussion on this see chapter 9
of Neale 2001.
[3] In his chapter on
representational semantics in The Concept
of Logical Consequence, John Etchemendy expresses reservations about the
exactitude of this analogy. We need to be more precise. He writes:
‘We
often find it advantageous to explain a monadic concept in terms of a
relational one … we may find the explication of ‘x is a brother’ far more tractable if we first set out to analyze ‘x is a brother of y’. The former then reduces to an existential generalization of the
latter: brotherhood is just brother-of-someone-hood… [b]ut clearly the monadic
concept of truth … is no generalization of any … relational concepts. A
sentence can be true in some model, yet not true; a sentence can be true, yet not
be true in all models. (1999: 13-14)
If the property of truth, as a monadic term, is not a
generalization on truth-in-a-model
then it must particularize it. Etchemendy proceeds thus: ‘ …perhaps the monadic concept emerges from
the relational by fixing on a particular instance…[o]ur conceptual analogy might then run: ‘x is true in y’ stands to
‘x is true’ as ‘x is a brother of y’ stands to ‘x is Fred’s brother’.’ (p.
14) His point is well taken.
[4] I thank Colin Howson for comments, discussion
and inspiration.
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Arhat Virdi is about to complete his Doctoral
studies in Philosophy at the