ISSN 1393-614X Minerva - An Internet Journal of Philosophy Vol. 10 2006


On Why the Slingshot against the Correspondence Theory of Truth Misfires


Arhat Virdi





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 Alonzo Church (1943: 299-301), but Davidson has more famously championed it in the anti-correspondentist cause. In ‘True to the Facts’, Davidson (1969: 42) first considers when


                                  (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 Naples also satisfies the description ‘the largest city within thirty miles of Ischia, and such that London is in England’, then ‘we begin to suspect that if a statement corresponds to one fact, it corresponds to all.’ (1969: 42). This suspicion is validated as long as the following two principles are upheld:


(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 France is bald’ meaningful without having to refer. Given a Russellian reading of definite descriptions, it cannot be the case that both ix(x = d & s) = ix(x = d)’ and ix(x = d & t) = ix(x = d)’ are obtainable from each other by the substitution of co-referring terms.


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]





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. Oxford: Clarendon Press. 2001 edition.


Davidson, D. 1967. Truth and meaning. In his Inquiries into Truth and Interpretation, 17-36. Oxford: Clarendon Press. 2001 edition.


Davidson, D. 1999. The centrality of truth. In Truth and its Nature (if any), ed. J. Peregrin. Dordrecht: Kluwer.


Etchemendy, J. 1999. The Concept of Logical Consequence. Cambridge, Mass.: Harvard University Press.


Frege, G. 1911. The thought: a logical inquiry. In Truth, ed. S. Blackburn and K. Simmons. 1999. Oxford: Oxford University Press.


Gödel, K. 1944. Russell’s mathematical logic. In Philosophy of Mathematics: Selected Readings, ed. P. Benacerraf and H. Putnam. 1964. New Jersey: Prentice-Hall.


Neale, S. 2001. Facing Facts. Oxford: Clarendon Press.


Vision, G. 2004. Veritas: The Correspondence Theory and Its Critics. Cambridge, Mass.: The MIT Press.







[1] Davidson (1967: 18-20) presents a similar argument.


[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.





Copyright © 2006 Minerva


All rights are reserved, but fair and good faith use with full attribution may be made of this work for educational or scholarly purposes.




Arhat Virdi is about to complete his Doctoral studies in Philosophy at the London School of Economics. He teaches for the departments of Philosophy, Economics and Mathematics there.


 Mail to: Arhat Virdi

Return to Minerva (Volume 10) Main Page                                                      Go to Top of This Page