From mark@xxx.xxx Wed Aug 25 06:08:27 1999
X-Digest-Num: 221
Message-ID: <44114.221.1197.959273825@eGroups.com>
Date: 25 Aug 1999 13:08:27 -0000
From: mark@xxx.xxx
Subject: Re: Anselmisms and gadro
>From: Pycyn@aol.com
>Date: Wed, 25 Aug 1999 05:18:57 EDT
>
>From: Pycyn@aol.com
>
>In logic, the article-like objects function like quantifiers, with variables.
> The stock form is "the x such that Fx." The corresponding Lojban would be
>"le da da broda" then (maybe with a separator between the das). But Lojban,
>of course, does not exactly replicate this version but drops the das
>altogether, "le broda." With more complicated predicates, the variable
>becomes more important, "the x such that Fyx" can be handled in Lojban with
>conversion, "le se broda y," say. But what about genuine and functioning
>complexity? Though there are several intervening levels of complexity, the
>one I am now working with and can not make any headway on is
>"the x such that it is not possible that someone conceive that there is a y
>greater than x" conversions and collapsed or permuted tanru cannot be used
>here as the scopes of the various operators (possibility, conception,
>quantifiers) are crucial in the argument this leads up to. Suggestions (and,
>best of all, citations from the Red Book on how to do it legally) would be
>most welcome.
I hope I'm answering the right question...
The thing to remember about all this is that {lo broda} is the same,
semantically, as {da poi [ke'a] broda}, with the exception that the latter
also asserts the existence of such a thing, while the former doesn't. ({le
broda} is correspondingly {da voi broda}). Similarly, "the x such that
Fyx" is {da poi de se broda da[/ke'a]} in {da poi} syntax, and {lo se broda
be de} as a gadrified sumti (note the necessity for the link with {be};
also note I'm glossing over the implicit existential quantifier on {de} as
well).
Given this parity between {lo broda} and {da poi broda}, you can easily see
how to create something of any complexity:
da poi le nu rode rodi zo'u de krici lenu di zmadu da kei kei cu na cumki
X which-is-such-that: (the-event-that: for-all Y, for-all Z: Y believes
(the-event-that: Z exceeds X ) ) is not possible
(my grouping above may not show off the Lojban grouping perfectly, but I
think it's right in Lojban). The only thing less than gadri-like about
this phrasing is the fact that without some sort of quantification it
implicitly quantifies this {da} with existence: at least one of these
things is claimed to exist. But you can probably fix that too, with
appropriate quantification.
pc, I hope I didn't miss something obvious; I know of your expertise in
formal logic.
~mark