Re: tech: logic matters

[Iain Alexander <ia@stryx.demon.co.uk>]

In message <823137063.24801.0@cunyvm.cuny.edu> pcliffje@CRL.COM writes:

> i,n:
> McCawley admits that in
> this case, "all [his] bills" includes the possibility of
> "no bills".
> pc:
> Sorry, I was reading this in the light of an earlier case.  Yes, English
> "all" is the most uncertain of the universal forms, which is why
> logicians, when they are careful, use "every" and "any."  But the
> habit of using "all" in logic, even when "every" is meant, is fairly
> firmly fixed (alas).

So, we are agreed that the natural language quantifier "all"
can in some cases include the possibility of "none", i.e. lack
existential import.  And that the natural language quantifier
"any" regularly does.  And that it would be appropriate to be
able to use the natural language form "<quantifier> <predicate>"
in Lojban for such a situation (e.g. "all [his] bills").
And therefore that we ought to have a Lojban <quantifier> which
means "any and all".  But ...

> i,n:
> I'm talking about
> numbers and you're talking about expressions.
> pc:
> Gee, it looks like expressions to me: how to say thus and so, with
> various suggestions about how to do it, both old and new.  What
> have I missed?

(where I said "number" rather than "quantifier")
... you want {ro} to have existential import, disapprove of my
suggestion of {ro su'o no}, and generally don't appear to
understand the point.  Is that any clearer?

> i,n
> .  It tells you how to convert
> {naku Q} to {naku Q'}, but it doesn't tell you how to interpret
> {Q naku}.
> pc:
> Actually it is from _naku Q_ to _Q'_, since the quantifiers have
> inherent negations or not, e.g. from _naku su'o_ to _no_

Sorry, that's what I meant to say.

> The other problem is the exact way to deal with the
> collapsed forms of unrestricted quantifiers

Do you mean e.g. {(naku) roda (naku) broda}?

> (once we decide which
> those are), since the nature of the implict connection between
> subject and predicate changes with the passage of the quantifier.

You lost me here.

> Well, if the universe could be empty, then a whole bunch of
> theorems of standard logic would be false -- all those which started
> off with an existential quantifier at least

Could you give an example, please.

> (and I would say the ones
> that start with universals as well, but that is controversial, to put it
> mildly) -- and many rules of inference would be invalid as they stand
> (again, with some variations about which ones).

> i,n:
> I certainly can't claim
> to be aware of _all_ the text, and I (no disrespect) doubt that
> you are either, to the extent of spotting whether someone used
> {ro} with the intention of allowing the zero option.
> pc:
> True.  But it has been my experience that anyone who is seriously
> claiming -- or saying something that involves the claim -- that the
> universe (of discourse, remember) even MIGHT be empty, makes a
> big todo about, and I have not seen that todo nor has anyone else
> mentioned it.  So, I suspect it hasn't happened.  And, again, it really
> is a very unlikely (I am frequently tempted to say "contradictory")
> position for anyone to want to take up and talk about.

Well ... as far as the empty universe (of discourse or otherwise)
goes ... there's something I can't quite put my finger on here -
I need to go away and think about it.

But here I'm principally talking about restricted quantification,
where someone might have used {ro <broda>} to mean "any <whatnot>",
which wouldn't necessarily have caused any great todo.

> i,n:
> ro da poi te janta fi ro de nagi'a pleji pu li pamu po ro masti
> cu jerna panoce'i me'ardi'a be ro lo vo'a selpapri
> Is _that_ what you want us to say?
> pc:
> Beats the Hell outta me!  What might that be in English or symbols?  So, I
> guess it is NOT what I want you to say, though I might wish you to espouse
> some claim of the same content, said in one of my languages.
> pc>|83

Something like

(Ax: ((Ay) receives-bill(x, y) -> pays [by 15th of the month] (x, y)))
deserves(x, 15% discount on all publications)
--
Iain Alexander                    ia@stryx.demon.co.uk
                    I.Alexander@bra0125.wins.icl.co.uk