"First problem" -- '[the] representation of a false existential statement' as 'a theorem'

by J. L. Speranza
for the Grice Club.

After stating the eight 'natural inclinations', Grice notes two problems. The first involves the result that '[the] representation of a false existential statement ('Pegasus exists') will be a theorem' (Grice, p. 119).

Why?

How Grice proceeds:

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The seventh natural inclination is the 'law of identity' qua theorem:

1. LAW OF IDENTITY:
(x)x=x

Now, if, by the sixth natural inclination, we allow unrestricted use of UI and EG we get the paradox:

2. a=a (From 1, and UI)

Third step:

3. (Ex)x=a (From 2, and EG)

Grice notes: "It is natural to take [(3)] as a representation of 'a exists'. So, given the second and third natural inclinations, 'a representation of a false existential statement ('Pegasus exists') will be a theorem'. Grice's system, with the aid of scope dominance, aims at solving this problem.