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Hi I am trying to understand Davidson's Slingshot argument. Apparently it is said that Russell's Theory of Definite Descriptions does not face the problem that Davidson highlights.

For instance, if we have two statements: "Snow is white" which can be translated as (βˆ€x)(Sx βŠƒ Wx)

AND

"the thing which is Socrates if and only if snow is white is Socrates" (I am not sure how to translate this)

The move that Davidson carries out in equating one fact like "Snow is white" to its equivalent statement such as "the thing that is Socrates if and only if snow is white is Socrates" is not legitimate given Russell's Theory of Definite Descriptions. This was recognised by Godel.

  • A minor comment: your formalization of "snow is white" is wrong. It should be "βˆ€π‘₯(𝑆π‘₯β†’π‘Šπ‘₯)," or "all things which are snow are white." What you've written translates instead to "some snow is white." We get an existential quantifier out front (according to Russell anyways) in statements of the form "the unique F is G," such as "Socrates is a philosopher;" these statements get translated as "There is a thing x such that [(x is the unique thing with property F) and x has property G]." In "Socrates is a philosopher," F is "is Socrates" and G is "is a philosopher." (cont'd) – Noah Schweber Nov 24 '20 at 15:48
  • The clause "x is the unique thing with property F" can be formalized in a couple different ways. I'd differ slightly from the wikipedia formalization and go with "𝐹π‘₯∧(βˆ€π‘¦(𝐹𝑦→π‘₯=𝑦))," which I think is clearer (they are equivalent though). So my choice of formalization of the whole statement "The unique F is G" would be "βˆƒπ‘₯((𝐹π‘₯βˆ§βˆ€π‘¦(𝐹𝑦→π‘₯=𝑦))∧𝐺π‘₯)," although there are variants. – Noah Schweber Nov 24 '20 at 15:51
  • So we can just translate "the thing which is Socrates if and only if snow is white" in the same manner as "the thing Socrates that has the property 'snow is white'"? – Cherry Blossom Bomb Nov 25 '20 at 5:49

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