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

[pycyn@aol.com]

In a message dated 3/6/2002 12:46:11 PM Central Standard Time, cowan@ccil.org 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.