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| In [[logic]], a '''slingshot argument''' is one of a group of [[logical argument|argument]]s claiming to show that all [[Truth|true]] [[sentence (linguistics)|sentence]]s stand for the same thing.
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| This type of argument was dubbed the "[[slingshot]]" by [[philosopher]]s [[Jon Barwise]] and [[John Perry (philosopher)|John Perry]] (1981) due to its disarming simplicity. It is usually said that versions of the slingshot argument have been given by [[Gottlob Frege]], [[Alonzo Church]], [[W. V. Quine]], and [[Donald Davidson (philosopher)|Donald Davidson]]. However, it has been disputed by [[Lorenz Krüger]] (1995) that there is much unity in this tradition. Moreover, Krüger rejects Davidson's claim that the argument can refute the correspondence theory of [[truth]]. [[Stephen Neale]] (1995) claims, controversially, that the most compelling version was suggested by [[Kurt Gödel]] (1944).
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| These arguments are sometimes modified to support the alternative, and evidently stronger, conclusion that there is only one ''[[fact]]'', or one true ''[[proposition]]'', ''[[state of affairs|states of affairs]]'', ''[[truth condition]]'', ''[[truthmaker]]'', and so on.
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| ==The argument==
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| One version of the argument (Perry 1996) proceeds as follows.
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| '''Assumptions''':
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| # '''Substitution'''. If two terms designate the same thing, then substituting one for another in a sentence does not change the designation of that sentence.
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| # '''Redistribution'''. Rearranging the parts of a sentence does not change the designation of that sentence, provided the truth conditions of the sentence do not change.
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| # Every sentence is equivalent to a sentence of the form ''F''(''a''). In other words, every sentence has the same designation as some sentence that attributes a property to something. (For example, "All men are mortal" is equivalent to "The number 1 has the property of being such that all men are mortal".)
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| # For any two objects there is a relation that holds uniquely between them. (For example, if the objects in question are denoted by "''a''" and "''b''", the relation in question might be ''R''(''x'', ''y''), which is stipulated to hold just in case ''x'' = ''a'' and ''y'' = ''b''.)
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| Let ''S'' and ''T'' be arbitrary true sentences, designating ''Des''(''S'') and ''Des''(''T''), respectively. (No assumptions are made about what kinds of things ''Des''(''S'') and ''Des''(''T'') are.) It is now shown by a series of designation-preserving transformations that ''Des''(''S'') = ''Des''(''T''). Here, "<math>\iota x</math>" can be read as "the ''x'' such that".
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| <table align=center>
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| <tr>
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| <td>1.</td>
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| <td><math>S</math></td>
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| <td></td>
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| </tr>
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| <tr>
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| <td>2.</td>
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| <td><math>\phi (a)</math></td>
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| <td>assumption 3</td>
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| </tr>
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| <tr>
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| <td>3.</td>
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| <td><math>a = \iota x (\phi (x) \land x=a)</math></td>
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| <td>redistribution</td>
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| </tr>
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| <tr>
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| <td>4.</td>
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| <td><math>a = \iota x (\pi (x,b) \land x=a)</math></td>
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| <td>substitution, assumption 4</td>
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| </tr>
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| <tr>
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| <td>5.</td>
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| <td><math>\pi (a,b)</math></td>
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| <td>redistribution</td>
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| </tr>
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| <tr>
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| <td>6.</td>
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| <td><math> b = \iota x (\pi (a,x) \land x=b ) </math></td>
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| <td>redistribution</td>
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| </tr>
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| <tr>
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| <td>7.</td>
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| <td><math> b = \iota x (\psi (x) \land x=b )</math></td>
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| <td>substitution, assumption 3</td>
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| </tr>
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| <tr>
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| <td>8.</td>
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| <td><math> \psi (b)</math></td>
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| <td>redistribution</td>
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| </tr>
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| <tr>
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| <td>9.</td>
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| <td><math>T </math></td>
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| <td>assumption 3</td>
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| </tr>
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| </table>
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| Note that (1)-(9) is not a derivation of ''T'' from ''S''. Rather, it is a series of (allegedly) designation-preservating transformation steps.
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| == Responses to the argument ==
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| As Gödel (1944) observed, the slingshot argument does not go through if [[Bertrand Russell]]'s famous account of [[definite description]]s is assumed. Russell claimed that the proper logical interpretation of a sentence of the form "The ''F'' is ''G''" is:
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| : Exactly one thing is ''F'', and that thing is also ''G''.
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| Or, in the language of [[first-order logic]]:
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| : <math>\exists x (\forall y (F(y) \leftrightarrow y = x) \land G(x))</math>
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| When the sentences above containing <math>\iota</math>-expressions are expanded out to their proper form, the steps involving substitution are seen to be illegitimate. Consider, for example, the move from (3) to (4). On Russell's account, (3) and (4) are shorthand for:
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| <table>
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| <tr>
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| <td>3'.</td>
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| <td><math>\exists x (\forall y ((\phi(y) \land y=a) \leftrightarrow y = x) \land a = x)</math></td>
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| </tr>
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| <tr>
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| <td>4'.</td>
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| <td><math>\exists x (\forall y ((\pi (y,b) \land y=a) \leftrightarrow y = x) \land a = x)</math></td>
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| </tr>
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| </table>
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| Clearly the substitution principle and assumption 4 do not license the move from (3') to (4'). Thus, one way to look at the slingshot is as simply another argument in favor of Russell's theory of definite descriptions.
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| If one is not willing to accept Russell's theory, then it seems wise to challenge either ''substitution'' or ''redistribution'', which seem to be the other weakest points in the argument. Perry (1996), for example, rejects both of these principles, proposing to replace them with certain weaker, qualified versions that do not allow the slingshot argument to go through.
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| ==See also==
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| * [[Abstraction]]
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| * [[Logic of information]]
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| ==References==
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| {{No footnotes|date=February 2008}}
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| * Barwise, Jon, and Perry, John (1981), "Semantic innocence and uncompromising situations", ''Midwest Studies in the Philosophy of Language'', VI.
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| * Gödel, Kurt (1944), "Russell's mathematical logic", in Schilpp (ed.), ''The Philosophy of Bertrand Russell'', Evanston and Chicago: Northwestern University Press, pp. 125–53.
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| * Krüger, Lorenz (1995), "Has the correspondence theory of truth been refuted?", ''European Journal of Philosophy'', vol. 3, 157-173, repr. in Krüger, Why Does History Matter to Philosophy and the Sciences?'', ed. by Thomas Sturm, Wolfgang Carl, and Lorraine Daston. Berlin: De Gruyter, 2005, pp. 201-217.
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| * Neale, Stephen (1995), "The philosophical significance of Gödel's Slingshot", ''Mind'', vol. 104, no. 416, pp. 761–825.
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| * [[Charles Sanders Peirce|Peirce, C.S.]] (1906), "Prolegomena to an Apology for Pragmaticism", ''The Monist'', 16, 492–546 (1906). Reprinted, ''Collected Papers'', CP 4.530–572. [http://www.existentialgraphs.com/peirceoneg/prolegomena.htm Eprint].
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| * Perry, John (1996), "Evading the slingshot", in [[Andy Clark]] et al. (eds.), ''Philosophy and Cognitive Science'', The Netherlands. [http://www-csli.stanford.edu/~john/PHILPAPERS/evading.pdf PDF]
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| ==External links==
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| * [http://ndpr.nd.edu/review.cfm?id=1117 Stephen Neale's ''Facing Facts'' reviewed by John Macfarlane]
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| * [http://sprachlogik.blogspot.com/2011/09/analysis-of-davidsons-slingshot.html An Analysis of Davidson's Slingshot Argument]
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| ==Bibliography==
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| * [[Charles Sanders Peirce bibliography]]
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| [[Category:Philosophy of language]]
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| [[Category:Philosophical arguments]]
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| [[Category:Philosophical logic]]
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