Subject: Re: [lojban] Re: [jboske] Quantifiers, Existential Import

From: [email-masked]
Date: Wed, 6 Mar 2002 14:32:25 EST

In a message dated 3/6/2002 12:46:11 PM Central Standard Time, [email-masked] 
writes:

> All S is P (A): SP = S
> Some S is P (I): SP /= 0
> No S is P (E): SP = 0
> Some S is not P (O): SP /= S
> 
> Then existential import is simply the assertion that S /= 0, and we can
> understand I- as asserting that S, which may be null, has a non-null
> intersection with P. But plainly no set P can have a non-null intersection
> with 0, and so from SP /= 0 we can deduce that S /= 0. Therefore I-
> is false if S = 0, and to assert anything useful we need I+.
> 
I- is "SP/=0 OR S=0" on this reading, so, while, when S=0 the SP part drops 
out, when SP/=0 (and hence a fortiori S/=0) then an number (1 or greater) of 
Ss may be Ps. So, I- is compatible with any number (0 or greater) of Ss 
being Ps. To be sure, the useful part is I+, but that can't be derived from 
"not both SP=0 and S/=0". You might expect E+ to be pretty useless, too, but 
it seems quite normal.