Slingshot argument

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The slingshot argument ( English for "slingshot argument") is an argument for the thesis that sentences refer to truth values . It can already be found, at least hinted at, in Gottlob Frege's essay “On Sense and Meaning” from 1892. Today there are different variants of the argument, for example by Gottlob Frege, Alonzo Church, WV Quine, Donald Davidson and Kurt Gödel.

Version by Alonzo Church

The best-known version is probably the version developed by Alonzo Church ( An Introduction to Mathematical Logic , Princeton 1956). The argument is based on two principles:

A: If an expression in a sentence is replaced by another expression with the same extension , the extension of the sentence does not change.

B: Purely syntactic transformations also do not change the reference of a sentence.

An example given by Church is the following four sentences:

(1) Walter Scott is the author of Waverley.

(2) Walter Scott is the author of 29 Waverley novels.

(3) 29 is the number of Waverley novels written by Walter Scott.

(4) 29 is the number of counties in the state of Utah.

(1) and (2) have the same extension because - according to principle A - only one expression with the same extension has been substituted; (2) and (3) have the same extension, because the sentence - according to principle B - has only been restructured syntactically; (3) and (4) again have the same meaning in accordance with principle A. But if (1) and (4), which express completely different thoughts and have different truth conditions and are only characterized by the identity of the truth value, have the same extension, then - so the conclusion - the extension or reference of a sentence must be its truth value be.

Version by Donald Davidson

In Donald Davidson of the argument of Frege and Church underlying idea is then used against the correspondence theory of truth to argue. Davidson does this as follows:

It initially assumes two requirements:

(P1) The correspondence of a sentence with a fact does not change through the replacement of co-referential singular terms.

(P2) Logically equivalent sentences correspond to the same facts.

The basic idea of ​​his argument is that a series of logically equivalent sentences can be constructed for each sentence by replacing co-referential singular terms, so that in the end a completely different sentence emerges, which nevertheless would have to correspond to the same fact as the original sentence.

Explained using an example:

(1) Aristotle is wise

(2) Aristotle is not identical with Plato

(3) Plato is Greek

(1) - (3) are true, i.e. each correspond to a fact (F1, F2 and F3, respectively). Theorem (1) is logically equivalent to:

(1a) a is the only x for which the following applies: (x = a and Fx)

(Aristotle is the only object for which the following applies: it is identical to Aristotle and it is wise.)

Theorem (2) is logically equivalent to:

(2a) a is the only x for which the following applies: (x = a and x not equal to b)

(Aristotle is the only object for which the following applies: it is identical to Aristotle and it is not identical to Plato.)

Theorem (2) is also logically equivalent to:

(2b) b is the only x for which the following applies (x = b and x not equal to a)

(Plato is the only object for which the following applies: he is identical to Plato and he is not identical to Aristotle.)

Theorem (3) is logically equivalent to:

(3a) b is the only x for which the following applies: (x = b and Gx)

(Plato is the only object for which the following applies: he is identical to Plato and he is Greek.)

Since the labels "the only x for which the following applies: (x = a and Fx)" and "the only x for which the following applies: (x = a and x not equal to b)" are co-referential (both denote Aristotle), " the only x for which the following applies: (x = a and Fx) "in (2a) for" the only x for which the following applies: (x = a and x not equal to b) "are inserted. With (P1) it follows that the correspondence of (2a) does not change by this replacement. Since (1a) was converted into (2a) and both (1) and (1a) as well as (2) and (2a) are logically equivalent, it follows with (P2): F1 = F2.

Likewise, the labeling "the only x for which the following applies: (x = b and x not equal to a)" and "the only x for which the following applies: (x = b and Gx)" are co-referential (both denote Plato), consequently can these are also replaced by one another. With (P1) it follows that the correspondence of (2b) does not change by this replacement. Since (2b) has been converted into (3a) and both (2) and (2b) as well as (3) and (3a) are logically equivalent, it follows with (P2): F2 = F3.

With the equality of F1 and F2 already deduced, it follows that F1 = F2 = F3. Hence, sentences (1) - (3) all correspond to the same fact.

For a criticism of Davidson's use of the argument against the correspondence theory of truth, see p. Lorenz Krüger (1995).

supporting documents

  1. ↑ Donald Davidson: Truth and Meaning. (1967). In: Donald Davidson: Inquiries into Truth and Interpretation. 2nd edition. Clarendon Press, Oxford et al. 2001, ISBN 0-19-924629-7 , pp. 17-24, and Donald Davidson: Epistemology and Truth. (1988). In: Donald Davidson: Subjective, Intersubjective, Objective. Clarendon Press, Oxford et al. 2001, ISBN 0-19-823753-7 , pp. 177-193.

literature

  • 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.
  • Neale, Stephen (1995), "The philosophical significance of Godel's Slingshot," In Mind , vol. 104, no. 416, pp. 761-825.