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Subject: Re: [lojban] A Simpler Quantifier Logic (blog article)
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Date: Sun, 9 Oct 2016 17:23:17 +0200
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On 08.10.2016 00:37, Jorge Llamb=C3=ADas wrote:
> Have you thought about "su'e"? Presumably it should pattern with "ru'o",
> not with "ro'oi", so the su'o/su'e symmetry would be broken if su'o
> becomes su'oi.

What I really want is for the existential quantifier to become distinct=20
from the "at least n" operator. In my preferred version of cekitauj (the=20
cmavo swap dialects) the existential quantifier is spelled {su} and the=20
"at least" operator is spelled {su'o}. This split is not possible in=20
official Lojban, unfortunately, but it would keep the symmetry intact.

(There is also another problem it would deal with: for some reason some=20
people want {su'o} without a following number to be the same as {su'o=20
xo'e} rather than a guaranteed {su'o pa}. With a distinct {su} this=20
wouldn't be as much of a problem)

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

Yes, I believe it must and should.

{no} should be {na ku su'oi} so that a claim like {no da jmaji} has the=20
proper strength.

> We should also have explicit definitions for me'i, za'u, da'a, so'a,
> so'e, etc since they all admit more than one pluralification, but I'm
> guessing they would all follow the "ru'o" pattern as well.

Yes.

{so'e jbopre cu banka'e lo .inglico} ("Most Lojbanists speak English")=20
cannot be expanded like a normal numerically quantified statement:

    ? su'oi da poi jbopre gi'e so'e mei cu banka'e lo .inglico
      "Some xx that are Lojbanists and most in number speak English." [1]

Quantifiers like {so'e}, {so'a}, ..., so-called proportional=20
quantifiers, require there to be something they are proportional to. The=20
number of broda in e.g. {so'e broda cu brode} is compared to the number=20
of (all) broda that brode. "Out of all the Lojbanists, most of them=20
speak English."

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=20
speak English."

is a better (intermediate) expansion. (Getting rid of {so'e} entirely is=20
possible, but I'm too lazy to type it out. The proportion is >0.5)

But {me'i} and {za'u} can be considered prefixes. I had thought {me'i PA=20
da} would mean {su'oi da poi me'i PA mei}. A definition in terms of=20
{ru'o} would also be possible, but I'm not sure that it would be better.=20
It would mean allowing prefixes (like "<" and ">") to turn non-{ru'o}=20
numerical quantifiers into {ru'o}-type quantifiers, and this requires a=20
good justification.

~~~mi'e la solpa'i

--
[1]: I don't think arguing that mei2 could save this expansion is all=20
that helpful.


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