In logic, a slingshot argument is one of a group of arguments claiming to show that all true sentences stand for the same thing.
This type of argument was dubbed the "slingshot" by philosophers Jon Barwise and John Perry (1981) due to its disarming simplicity. Versions of the slingshot argument have been given by Gottlob Frege, Alonzo Church, W. V. Quine, and Donald Davidson. Stephen Neale (1995) claims, controversially, that the most compelling version was suggested by Kurt Gödel (1944).
These arguments are sometimes modified to support the alternative, and evidently stronger, conclusion that there is only one fact, or one true proposition, states of affairs, truth condition, truthmaker, and so on.
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One version of the argument (Perry 1996) proceeds as follows.
Assumptions:
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, "" can be read as "the x such that".
1. | ||
2. | assumption 3 | |
3. | redistribution | |
4. | substitution, assumption 4 | |
5. | redistribution | |
6. | redistribution | |
7. | substitution, assumption 3 | |
8. | redistribution | |
9. | assumption 3 |
Note that (1)-(9) is not a derivation of T from S. Rather, it is a series of (allegedly) designation-preservating transformation steps.
As Gödel (1944) observed, the slingshot argument does not go through if Bertrand Russell's famous account of definite descriptions is assumed. Russell claimed that the proper logical interpretation of a sentence of the form "The F is G" is:
Or, in the language of first-order logic:
When the sentences above containing -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:
3'. | |
4'. |
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.
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.