Slingshot Argument - The Argument

The Argument

One version of the argument (Perry 1996) proceeds as follows.

Assumptions:

  1. Substitution. If two terms designate the same thing, then substituting one for another in a sentence does not change the designation of that sentence.
  2. 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.
  3. 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".)
  4. 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.)

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.

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