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Date: Wed, 26 Dec 2012 16:32:51 +0100
From: v4hn <me@v4hn.de>
To: lojban@googlegroups.com
Subject: Re: [lojban] Some weirdness in how mathematicians work with quantifiers
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Hey Ian,

you hopefully are aware of the fact that you posted your question
on Christmas Eve... Why do you wonder why no one replied within 24 hours?

On Wed, Dec 26, 2012 at 08:37:53AM -0500, Ian Johnson wrote:
> (Also, you needed a ku or a cu after kei :))
>=20
> On Wed, Dec 26, 2012 at 5:33 AM, v4hn <me@v4hn.de> wrote:
> > .uesai lonu tavla fi la'o gy. convolution .gy vecu'u le mriste kei spaj=
i mi

Thanks, I didn't notice this was necessary.

> The weirdness in the original post is that we don't know how exactly we're
> going to relate e1 and d1 to e2 and d2 in advance. In this case the
> relationship turns out to be basically trivial; in complicated cases it c=
an
> be much less trivial. In either case, the way the analysis actually
> happens, you wind up introducing e1 and d1, introducing e2 and d2, and th=
en
> doing some work to see what the latter have to do with the former. You can
> go back afterward and introduce e1 and d1, define e2 and d2 relative to
> them immediately (knowing how they will be related), and then obtain the
> desired result, but that's not the way the reasoning happens the first
> time, and there should be a "logical" way of showing the initial reasonin=
g.

Hm, I'm not sure this "initial motivation" text really is "logical" (as in
predicate logic) the way people normally write it down. Category Theory
(and implicitly also Skolemization) serve as a much better basis for formul=
ating
these arguments.

> You point out the ability to Skolemize the statement P. I'm familiar with
> this, and am pretty fond of it as well, but in practice (at least in
> analysis) this style is quite atypical.

I wouldn't say so for category theoretical arguments.

> Indeed, even the style of
> subscripting quantified variables as I did here is pretty unusual;
> typically people just don't write out their quantified statements, and ju=
st
> "use the continuity of g to get delta ... such that ... < epsilon/3" or
> such things. I think the Skolemized style may be the better choice for
> adapting this idea into Lojban style (or indeed for eventually writing
> mathematics in Lojban).

I think that as well, also one reason these arguments are often hard to und=
erstand
is because the are not structured in a very logical way.


mi'e la .van. mu'o

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