Definition of existential commitment

Grice wants to define 'existential commitment' on p. 128 of "Vacuous Names".

He has already defined the 'important related notion' of dominance so that he can read:

'a dominates phi'.

There are then two scenarios:

First scenario: the existential commitment scenario:

If a dominates phi, for any interpretation Z,

phi will be correlated with 1 on Z only if

a is non-vacuous.

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The second scenario is trickier:

if a does NOT dominate phi, it may still,

but it may still NOT be the case that

phi is correlated with 1 oly if a

is non-vacuous.

Grice gives two cases here:

phi may be true if phi is

~4~3F1a2

phi may also be true if phi is

F1a2 \/3 G1a2.

HOWEVER,

phi will NOT be correlated with 1 if

phi is, for example,

F1a2 )3 G1a2.

The important point, as Grice notes, is that "whehter or not it is the case [that a dominates phi or not] is formally decidable".

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He sets to define 'existential commitment recursively.