Date: Wed, 14 Dec 1994 02:46:14 -0500
From: Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Subject: Re: reply: (1) veridicality
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>Can you write me the proposition grammatically encoded by
>"la lojbab cilre lo cukta" in predicate calculs form, without there
>being a bound variable? I think not.
 
No.  I can't write predicate calaculus for much of anything - I'm the LOjban
Centralist who flunked Logic in college, remember %^) (actually it was a
D/incomplete on a self-paced course, but I admit to be hopeless in formal logic)
 
I have long been of the opinion that much of Lojban is not encodable as
predicate logic in its standard forms.  Certainly the moment that you stick
an indicator on, formal logic breaks down.  Before the current go-round,
it was implicit to the definition of "lo" that it could not be expressed
in predicate logic since it neither climed existence nor made claims about
the empty set (respectively false and true regardless of the content of
the predicate - or is that vacuously true and false - whatever it 1s 230 AM
and I'm still sick).
 
At the time we previously debated "lo", PC basically said that there were
several traditions of predicate logic that contracdicted on how to deal with
"lo unicorn" type statements, so we chose the one which was most useful and
he said it could be defended.  But people who want unambiguous formal
logic representations need to explicitly use "da"-like variables and prenexes.
This is not the norm for conversation.  The logic will work for "lo" no
matter how we define it, but the manipulation necessary is non-trivial and
peculiar to certain conventions of logic that are not universal.
 
(Another more well known convention is the LOjban definition of a question
being true if the supplied answer is a true statement - this is accepted by some
schools of logic byut not by all.  I got that one out of the Brittanica in
what was probably my apex of logical understanding during this project (then
checked with pc to see if I was right).)
 
In any event, even if lo cukta turns out to be a DA+POI semantic equivakent,
it is not a grammatical equivalent.  And this is likely to lead to incompati
biklities in the conversions to a prenex form.  And in any case the implicit
DA is not "da", but "daxitu'o" some unspecified member of the bound variables.
 
And per my other post, i would not be surprised if we have to define a
convention for prenexing that differs from "da poi" in the same location.
 
lojbab