Slingshot-Argument
The slingshot argument (English " slingshot " argument ) is an argument for the thesis that sets lecture on truth values . It can already be found, at least indicated, in Gottlob Frege's essay " On Sense and Reference " of 1892. Nowadays, there are various versions of the argument, for example, by Gottlob Frege, Alonzo Church, WV Quine, Donald Davidson, and Kurt Gödel.
Version of Alonzo Church
The best known is probably the version developed by Alonzo Church ( An Introduction to Mathematical Logic, Princeton 1956). The argument is based on two principles:
A: When an expression is replaced in a sentence by an extension other same expression, then the extension of the sentence does not change.
B: pure syntactic transformations also not change the reference of a sentence.
One example cited by Church example, the following four sets:
( 1) Walter Scott is the author of Waverley.
( 2) Walter Scott is the author of 29 Waverley novels.
(3 ) 29 is the number of written by Walter Scott Waverley novels.
(4 ) 29 is the number of counties of the State of Utah.
( 1) and (2) have the same extension, because - was substituted by only one extension of the same expression - according to principle A; (2 ) and ( 3) have the same extension, because the sentence - according to Principle B - was restructured only syntactically; (3) and ( 4) have, in turn, in accordance with Principle A has the same meaning. But if (1 ) and ( 4) that express completely different thoughts and have different truth conditions and are distinguished only by the identity of truth-value, have the same extension, then - so the conclusion - would the extension or reference of a sentence whose truth value be.
Version of Donald Davidson
In Donald Davidson thought the argument of Frege and Church based is then used to argue against the correspondence theory of truth. This does Davidson as follows:
He is initially based on two conditions:
(P1 ) The correspondence of a sentence with a fact is not altered by the replacement koreferentieller singular terms.
(P2 ) Logically equivalent sentences correspond to the same facts.
The basic idea of his argument is now that it is possible to construct a set of logically equivalent sentences for each sentence by replacing koreferentieller singular terms, so in the end comes out a completely different set, but still correspond to the same fact would like the output set.
An example explains:
( 1) Aristotle is wise
( 2) Aristotle is not identical with Plato
( 3) Plato 's Greek
(1) - (3) are true, that each correspond to a fact (F1, F2, and F3, respectively ). Set (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:. It is identical with Aristotle, and he is wise )
Sentence (2) is logically equivalent to:
( 2 ) A is the only x for which the following applies: ( X = a and x equal to b)
( Aristotle is the only object for which:. It is identical with Aristotle, and he is not identical with Plato )
However, rate ( 2) is logically equivalent to:
(2b ) b is the only x for which valid (x = b and x not equal to a)
(Plato is the only object for which:. It is identical with Plato and he is not identical with Aristotle )
Set (3 ) is logically equivalent to:
(3a ) b is the only x, applies: (x = b and Gx)
(Plato is the only object for which:. It is identical with Plato and he's Greek)
Since the markings " the only x for which the following applies: (x = a and Fx )" and " the only x, applies: (x = a and x is not equal b ) " are koreferentiell (both denote Aristotle ), can " 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 used. By (P1 ), it follows that the correspondence of (2a ) does not change by this replacement. Since it (1a) was converted to (2a ), and both (1) and ( 1a) and (2) and (2a) are logically equivalent, it follows with (P2): F1 = F2.
Similarly, the marking " the only x for which the following applies: (x = b and x is not equal a) " and " the only x for which the following applies: (x = b and Gx) " koreferentiell (both refer to Plato ), hence can these are replaced with each other. By (P1 ), it follows that the correspondence of (2b ) does not change by this replacement. Since it (2b) was converted to (3a ), and both (2) and (2b ) and (3) and (3a) are logically equivalent, it follows with (P2): F2 = F3.
With the already derived equality between F1 and F2 so follows: F1 = F2 = F3. Consequently, the sets of (1) correspond to - (3 ) all having the same fact.
For a critique of Davidson's use of the argument against the correspondence theory of truth, see Lorenz Krüger ( 1995).