Message-Id: <m0scdfw-0000ZHC@xiron.pc.helsinki.fi>
Date:         Sun, 30 Jul 1995 12:02:00 -0700
Reply-To:     Gerald Koenig <jlk@NETCOM.COM>
Sender:       Lojban list <LOJBAN@CUVMB.BITNET>
From:         Gerald Koenig <jlk@NETCOM.COM>
Subject:      Re: quantifiers
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 2972
Lines: 59

pc said:


        Even though sets are the individuals that Lojban deals with most
naturally (I'll get back to that one), I think that subset quantification
should be dealt with by the other standard method, a cover device relating
the variable of the original quantifier to a new variable with the new
quantifier.  The set approach is inherently more complex and less natural,
even in Lojban, where the variable, if not the other terms, still refer to
individuals.  The requantification approach is conceptually confused, trea
ting a variable at once as for ordinary individuals and for a set.  But,
more importantly, requantification with open scopes means that we cannot
easily get back to the original quantifier once the new is introduced and
such return is often something we do want to do. The only problem for
explicit connection is to find the right predicate to use (attached by poi
or syntactically to the new quantifier).  None of the "obvious" choices
works well literally, since they also would result in taking variables as
sets and individuals equivocally.  So, since the form in logic is an
artifical term made up for the purpose (and partially defined in most
particular cases), I suggest we use a new artifical term (temporarily
xu'u, since almost all the other experiemntal terms are probably already
up in the air) for the purpose.  Yes, hitting cmavo space yet again to
solve a problem!

end pc
___________

        Could you clarify the nature of "the new artifical term" cmavo
        with an example?  Am I correct in asuming that it is the "Z"
        variable which stood for w,v,u in the 3-men 3-dogs conundrum?

        When I posted my last 3 sentences I did so with the objective
        in mind of contrasting the set and non-set characterization of
        number.  I believed that [ro] lo ci nanmu was shorthand for the
        full E!3 expression of identities and disjunctions together
        with the assertion that each remna existed. I thought that this
        [descriptor-quantifier-selbri] form was the remnant in lojban
        of the Russell/Whitehead version of exact numerical claims. I
        thought that this exact numerical claim clothed in identities,
        disjunctions, and predications was neither a cardinal nor an
        ordinal number, but a very primitive number concept which does
        not call upon either of these abstractions.  Now it appears
        from your posts that there is no such remnant in lojban and
        that all number is cardinal or ordinal. That there is virtually
        no difference between "ci lo broda" and "lo ci broda", except
        perhaps the convention that "lo ci broda" claims only ci broda
        exist.

        Where are we, anyway?


1. ro lo ci nanmu ku goi da ci lo gerku ku goi de zo'u tu'e da pencu de
2. ro lo ci nanmu ku goi da ci lo so gerku ku goi de zo'u tu'e da pencu
de
3. ro lo ci nanmu ku goi da ci lo ci gerku ku goi de zo'u tu'e da pencu
de

djer