Message-Id: <m0qq9XZ-00005JC@xiron.pc.helsinki.fi>
Date:         Wed, 28 Sep 1994 18:19:15 EDT
Reply-To:     jorge@PHYAST.PITT.EDU
Sender:       Lojban list <LOJBAN%CUVMB.bitnet@FINHUTC.hut.fi>
From:         Jorge Llambias <jorge@PHYAST.PITT.EDU>
Subject:      Re: any
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 4963
Lines: 115

la veion cusku di'e

>   Our natural language habits (though languages disagree with each
>   other in the usages) make us feel that we must be able to make an
>   (inherently) opaque claim in a transparent situation.

I think you are equating 'opaque' with 'non-specific', otherwise I
don't understand your assertion. Most claims are not opaque.


>   Pragmatics (Zipf) makes us use language
>   (at least a natural one) inaccurately.

I was in a physics seminar the other day, when to my joy and surprise
the speaker mentioned Zipf's law. Unfortunately, it turns out that it
had nothing to do with what I had learned about it from lojbanic lore.
According to this guy, Zipf discovered that if you plot on a log-log
graph the frequency of a word vs its position in order of frequency,
you get a straight line (of slope 1, I think). This is a very
interesting result, and apparently it works for any language, but has
nothing at all to do with lengths of words. Of course, I'm not
advocating that we lower Our Lord Zipf from his pedestal, but I
thought I'd just mention it.


> I decided to approach the problem from a different angle:
>
>   Given a sentence AND ONLY THE INFORMATION CONTAINED THEREIN write
>   a program which performs the requested action.

A sentence is not a requested action, unless it contains {ko}.

A sentence is a claim about the world (be it the real world, or any other
that we take as real for the purposes of evaluating the truth value).
To determine the truth value of the claim you examine that world, and
see whether the claim holds. In most cases, us poor inhabitants of that
world are unable to determine the truth value of most statements, but
fortunately, we can talk about those truth values.

> Now, of course, it turns out that it is impossible to derive any but
> the opaque case from a blanket statement like 'mi nitcu re tanxe'

To derive? We examine the world (from an omniscient perspective). We know
who {mi} is. We look at all tanxe. Are there exactly two in relationship
{nitcu} with {mi}? If yes, the statement is true. If not, it is false.

Of course, the purpose of language is to transmit information, not to
provide sentences for truth value evaluation. From the point of view of
the listener of the sentence, the sentence is assumed true, and the
information obtained is that there exist two tanxe in relationship {nitcu}
with {mi}.

> To get anything else but 'any two boxes' requires you to supply
> information about any mental reservations you have or any preconditions
> the boxes have to satisfy.

You can add as much information as you want, to help the listener
identify the two boxes, but this doesn't mean that the claim would
be true for any two boxes you pick.

> So the whole question about outer quantifiers boils down to
>
>   do we want an outer quantifier to be a 'pure' quantifier
>   (opaque, 'any') or do we allow it to be 'hazy' in the
>   sense that there always maybe some hidden reservation?

Why is the 'pure' quantifier the opaque one? The normal logical quantifier
is the transparent one, and there's nothing hazy about it. If you say in
mathematics: "For all y, there exists an x, such that x + y = 0", then you
don't mean "any x". You don't give any clue as to which x you are refering
to, but it certainly is not any whatsoever.

In Lojban, informally this would be:

        li no sumji roda de
        0 is the sum of each y with some x

and you clearly don't mean any x. You don't specify which x, you don't
have to specify x for the claim to be true. All you need is that x exists.


> In the first case we have either to mark the transparent case or
> supply at least part of the reservations/conditions, in the
> second case we have to mark the opaque case with {xe'e}.
>
> The consequences in each case would be
>
>   (1) opaque interpretation: logically sound but in everyday
>       usage either ambiguous (does he really mean 'any' or
>       just 'use your common sense'?) or requiring marking/
>       supplying the conditions explicitly.

This one is logically UNsound, with the usual interpretation of logics.
The everyday usage would be what we expect for nitcu and family (where
the opaque form is the norm in English), but crazy claims for most other
predicates.

>   (2) transparent interpretation: convenient (though ambiguos
>       in the NL way) in everyday usage but beyond logics
>       unless marked, and probably even then.

On the contrary, this is the one that logics requires. It is not ambiguous
in the NL way if the "any" case is required to be marked.

> This is a policy question. I'd choose (1) and require that the
> existence of the hidden conditions is at least acknowledged
> with a marker or a vague restriction,

Are you aware that with interpretation (1), {li no sumji roda de} means
"Zero is the sum of each x and any y (the first you can find)"?

How do you say "Zero is the sum of each x with some y" using
interpretation (1)?

Jorge