Recursive definition of existential commitment

Grice proposes to abbreviate:

'phi is true only if a is non-vacuous'

by

'phi is E-commital for alpha'.

----

He is then able to provide a six-rule recursive definition of 'existential commitment'.

First case:

If a dominates phi, phi is E-committal for alpha.

Second case:

Double Negation:

"If

a. phi is

~n~n-mpsi

and

b. psi is e-commital for a

phi is e-commital for alpha.

---

third case:

/\

if

a. phi is

psi /\n khi

and

b. either psi or khi are

e-commital for a,

phi is e-commital for alpha.

----

Fourth case:

\/

If

1. phi is

si \/n ki

and

2. BOTH psi and khi are e-commital for a,

phi is e-commital for alpha.

----

Fifth scenario: the horseshoe

If

a. phi is

psi )n khi

and

2. both psi and khi are e-commital for a,

phi is e-commital for a.

----

sixth and last case:

if

a. phi is

Aonpsi or Ewnpsi

and

2. psi(beta/omega) is e-commital for a,

phi is e-commital for a.

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