[lit-ideas] The Alltogether Girl and the One-At-A-Time Boy
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Mon, 25 Jun 2012 01:19:04 -0400 (EDT)
-- and disputable metaphysics.
"Every boy loves some girl" (R. Paul)
"Every girl destests some boy" (Grice).
Grice's Altogether Boy and One-At-A-Time
R. Paul was mentioning some substitutional quantificational problem which
reminded me of ... Grice.
In "Reply to Richards" (R. Grandy/R. Warner, PGRICE, Oxford, 1986), Grice
writes:
"To the epithet, 'boy', it will be assigned not
only boys, but also such SPECIAL objects
as the altogether boy and the
one-at-a-time boy."
"The altogether boy satisfies a
given predicate 'boy', just in case
every nonspecial item associated
with the special altogether boy
satisfies the predicate in question."
"The one-at-a-time boy satisfies
a given predicate 'boy' just in
case AT LEAST ONE of the associated
nonspecial objects associated with that
special object satisfies the predicate in question".
The altogether boy is smart just in case EVERY individual boy is smart.
The one-at-a-time boy is smart just in case at least one individual boy is
smart.
"We can take this pair of statements about special boys ('the
one-at-a-time boy' and 'the altogether boy') as providing with the logical form
of the
assertion that some boy is smart and the statement that all boys are smart".
"This apparatus", Grice notes, "as it stands, will not be adequate to
provide a comprehensive treatment of quantification."
We need "to be able to cope with the well-known examples arising from
features of multiple quantification".
One then sees why Grice never spent much time with (x) and (Ex) which he
does list in the opening sentence of "Logic and Conversation" as providing
the logical form for 'all' and 'some' (Never mind 'the').
Grice goes on: we need a System that "will deliver for us distinct logical
forms for the two notorious readings of "Every girl detests some boy"".
"In one reading," Grice writes, "the universal quantifier, 'every girl',
is dominant with respect to scope."
"In the other reading, it is the existential quantifier which is dominant".
In the first reading, "we attribute a property to the altogether girl." In
the second reading, "we attribute a property to the one-at-a-time boy".
"Exportation WILL affect truth-value when it is applied to sentences about
special objects like the altogether girl and the one-at-a-time boy".
Grice considers an objection: "Some may find these objects -- the
altogether girl and the one-at-a-time boy as metaphysically disreputable."
Not me.
-- i.e., in logical form (or better 'symbols'): "Not I".
Grice says, we are looking for "a subject-predicate account of
quantification".
Grice then goes on to propose the account of ontological correlates in
terms of "at least a second order" set theory.
Grice goes on:
"A dozen years or so ago, I devoted a good deal
of time to this proposal, and I convinced
myself that it offered a powerful instrument
which was capable of handing not only
indefinitely long sequences of mixed quantificational
phrases, but also some other less obviously tractable
problems."
--- such as, "Where is my hat?"
---
Grice goes on:
"As I envisage it, a proposition will be regarded as a family of
propositional complexes".
"Now, the propositional complex directly associated with
----- Some boys are smart.
"will be both logically equivalent -- yet numerically distinct from the
propositional complex
----- Not every boy is not smart.
".
Grice goes on: "Indeed, for any given propositional complex there will be
indefinitely many propositional complexes, which are both logically
equivalent and also numerically distinct from the original complex."
---- And so on.
Cheers,
Speranza
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