Re: Anselmisms and gadro

[mark@xxx.xxx]

>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