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Date: Sat, 3 Dec 2011 14:09:23 -0800 (PST)
From: John E Clifford <kali9putra@yahoo.com>
Subject: Re: [lojban] some critics admire only one another
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I reasonably certain that Dave knew about Lesniewski (since UC-LA/-B was a 
regular stop for Polish logicians in the  60s) and I suppose seach did, too.  
But the relevance was not obvious and, in the first case, Left-Coast logicians 
were averse to any dose of Quinine.  But with the present system it seems fairly 
straightforward:  there is a bunch of [individually] critics who are such that 
for each of them who admires somebody (and that somebody is a critic?)(and that 
somebody is not the admirer?),  the admiree is in the bunch (and is not the 
admirer?).  Now putting this into Lojban or even FOPL iis not a trivial matter, 
of course, but there is no obvious need to go to second order, unless you reify 
bunches, which you don't need to do.  There may be some nonobvious reason, but I 
don't see it now.


----- Original Message ----
From: Martin Bays <mbays@sdf.org>
To: jboste <lojban@googlegroups.com>
Sent: Fri, December 2, 2011 6:01:24 PM
Subject: [lojban] some critics admire only one another

(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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