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Re: [lojban] A Simpler Quantifier Logic (blog article)

On 10.10.2016 02:08, Jorge Llambías wrote:

On Sun, Oct 9, 2016 at 12:23 PM, selpahi <seladwa@gmx.de
<mailto:seladwa@gmx.de>> wrote:


    What I really want is for the existential quantifier to become
    distinct from the "at least n" operator. In my preferred version of
    cekitauj (the cmavo swap dialects) the existential quantifier is
    spelled {su} and the "at least" operator is spelled {su'o}. This
    split is not possible in official Lojban, unfortunately, but it
    would keep the symmetry intact.


That makes sense. One difference with the singular version is that
plural "su'e" (and plural "me'i") will have existential import: "su'e re
no tadni cu sruri lo dinju" with plural "su'ereno" would mean "there are
some students, who are at most twenty, surrounding the building".

How do we say the old singular "su'e mu broda cu brode" (which allows
the possibility that "no broda cu brode") with the new system?


How about {na ku za'u mu broda cu brode}?
(And when existential import isn't a problem, {ru'o broda cu su'e mu mei} (or {lo broda cu su'e mu mei}) are options). 


        Would "no" become "no'oi" as well?

    Yes, I believe it must and should.


And singular "no" is then "no pa", right?


Yes, I would say so.


    So I would say that

       ru'o da poi jbopre zo'u so'e de poi menre da cu banka'e lo .inglico
       "All [the] Lojbanists taken together are such that most of them
    speak English."

    is a better (intermediate) expansion. (Getting rid of {so'e}
    entirely is possible, but I'm too lazy to type it out. The
    proportion is >0.5)


I think the expansion should be:

 PA broda cu brode -> su'oi da poi PA mei lo broda cu brode

which I think would work for all the numeric quantifiers:
[da'a][su'o|su'e|me'i|za'u|ji'i] n; so'V; du'e, mo'a, rau; and also for
ru'o.


This seems to be pretty much the same as the {ru'o} expansion.
But I think it's only equivalent if you subscribe to {lo}'s maximality. (It wouldn't be the first expansion that presupposes maximality even though we never decided that {lo} must have maximality) 

So, I take it, you do subscribe to maximality? (I do)


    But {me'i} and {za'u} can be considered prefixes. I had thought
    {me'i PA da} would mean {su'oi da poi me'i PA mei}. A definition in
    terms of {ru'o} would also be possible, but I'm not sure that it
    would be better. It would mean allowing prefixes (like "<" and ">")
    to turn non-{ru'o} numerical quantifiers into {ru'o}-type
    quantifiers, and this requires a good justification.


What do you mean by non-ru'o numerical quantifiers? su'oi, ro'oi, no'oi,
me'oi are non-ru'o, in the sense that they don't expand to a "su'oi da
poi PA mei" form. (I don't even know what "PA mei" would mean for them.)
Sorry if I wasn't clear. I meant "non-{ru'o}" in a {noi} way. All numerical quantifiers are of the non-{ru'o} type. Your prefixes turn them into {ru'o} types. 

~~~mi'e la solpa'i


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