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Date: Fri, 2 Dec 2011 19:01:24 -0500
From: Martin Bays <mbays@sdf.org>
To: jboste <lojban@googlegroups.com>
Subject: [lojban] some critics admire only one another
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(being the "Geach-Kaplan" sentence, a classic example of
a "nonfirstorderizable" natlang sentence)

I thought it would be amusing whether or not worthwhile to catalogue our
ways of translating this (and generally, our ways of doing monadic
second-order quantification).

I'll use {xaurpai} to translate 'critic(s)', and {sinma} for 'admire'.


(i) using sets - this is the obvious boring way of dodging the issue:
{da poi selcmi ku'o ro de poi cmima da zi'e noi xaurpai zo'u ro di
se sinma de gi'o cmima da} ^1
                                                                                                                                                                       (ii) using {bu'a}:
{bu'a zo'u ro da poi bu'a cu xaurpei .i je ro de se sinma da gi'o bu'a}

This is essentially the same as (i), but using our (not overly pleasant)
explicit second-order quantification facility.

(iii) using a plural existential quantifier - let's call it {su'oi},
though I'm not sure we shouldn't call it {piza'u}:
{su'oi xaurpei goi xy zo'u ro me xy cu sinma ro da .i jo da me xy}

(which may or may not be the same as
{ro me su'oi xaurpei goi xy cu sinma ro da .i jo da me xy})

Or to parallel the english's vague "only" and lack of an "each":
{su'oi xaurpei goi xy cu sinma xy po'o}
(but that's probably too vague in lojban to count as a translation)

(iv) making up a predicate for it:
e.g. one possibly plausible semantics of the tanru {jimte simxu} is such
that
{su'oi xaurpei cu jimte simxu}
is as desired.


Any other ideas?

Martin


^1 making use of {noi} in a way which may or may not be legitimate

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