lo/le definition

[Bob LeChevalier-Logical Language Group <lojbab@lojban.org>]

Nora observes that since the ultimate definition of lo broda and le broda 
pertains to things that fill the x1 of broda, and since for various broda, 
the x1 place is expressed as individuals, sets, masses, and what have you, 
then le/lo manifestly MUST be ambiguous amongst those meanings, regardless 
of the specified default quantifiers and what people have deduced from the 
assignment of such quantifiers.

What this does to the supposed equivalence of lo broda and da poi broda, I 
leave to someone else, since da poi ke'a broda implicitly says that da also 
has to have the implicit quantification implied by the x1 of broda.

(In writing this, I think I now remember where the phrase "default 
quantifier" came from, though I need to check. In normal quantificational 
logic, the variables would all be quantified in the prenex. We are taking 
a shortcut by not using a prenex; the default quantifiers are therefore an 
attempt to set up rules to establish what the prenex would be if it were 
explicit. I believe that it was found that this is an intractable problem, 
but that general defaults could be assumed, with the option of being 
explicit in the prenex if necessary. This implies that when a sumti need 
not be quantified in the prenex in order to be well-formed notationally, it 
does not need a default quantifier. Thus a system of logic that does not 
use quantifiers, or that uses different defaults, is perfectly acceptable 
under loglan/lojban, meeting And's needs to talk about things using a 
different logic than "John's conservative, everything-quantified ..." version.)

lojbab

--
lojbab lojbab@lojban.org
Bob LeChevalier, President, The Logical Language Group, Inc.
2904 Beau Lane, Fairfax VA 22031-1303 USA 703-385-0273
Artificial language Loglan/Lojban: http://www.lojban.org