Re: quantifiers

[jorge@PHYAST.PITT.EDU]

> pc:
> While the meaning of quantifiers embedded in simple sentence matrices
> is open to some interpretation, once we get the quantifiers into prenex
> position, we are in the notation of standard logic and so its rules apply,
> not merely by definition or guess (remember, this is how Lojban was
> designed).  And the rules say that the two orders are provably equivalent.
> So, by xorxes rule about what "means the same" means, they mean the same.
> QED

Ok, that's fair enough, I guess.

If I understand correctly then, standard logic notation dictates that:

(1)     reda su'ode zo'u da broda de

must necessarily correspond to:

(2)     Ex Ey Ez ( broda(x,z) & broda(y,z)  &  x=/=y &
                   Aw ( broda(w,z) -> (w=x V w=y) ) )

and cannot possibly correspond to:

(3)     Ex Ey ( Ez broda(x,z) & Ez broda(y,z) & x=/=y &
                Aw ( Ez broda(w,z) -> (w=x V w=y) ) )


I must admit that I am not familiar with standard logic notation
other than the basic stuff so I accept that. But then is there no
standard shorthand for (3)?  The shorthand expressed by (1) must
necessarily be for (2)?

What would this be:

(4)     reda zo'u su'ode zo'u da broda de

I suspect this should be more like (3). Maybe using two prenexes like
that is the answer? My initial reaction to that is a heartfelt "ptui",
but maybe that's how it is.

> xorxes:
> 1) ci da poi nanmu ku ci de poi gerku zo'u da pencu de
> 2) ci da poi nanmu ku ci de poi gerku ku pencu
pc:
> However, whatever the underlying structure is in any grammatical system I
> can think of (and I admit that there are a few gross I have not kept up
> on but would love to hear about), 1 and 2 (and so 3) have marked
> different structures and not structures that are interderivable in
> meaning-preserving ways.

I always assumed they were equivalent in Lojban. (I believe that so does
the teaching material, although I can't say for sure without looking
at it again.)

> I also disagree that ci da poi nanmu, etc. do not mean anything on their
> own, although they do not assert anything, of course but only delineate
> areas of reference.

Well, I agree with that, but they should mean the same in the prenex or
in the body of the expression. (Indeed, selbri-less sentences are grammatical.
I interpret them with an implicit {co'e}, just as unfilled sumti places
have an implicit {zo'e}.)

> Now along with this, xorxes does have a point : in the underlying logical
> representation, all quantified expressions must be prenex, since logical
> notation has no means of representing quantifiers in argument places (not
> quite literally true, but near as makes no nevermind).  So, putting Lojban
> quantified sumti (which is damned near all of them) in Lojban prenex
> position rather than embedded is a clarifying notational device.  That
> does not mean, however, that the clarifying device has to consist simply
> in taking the sumti out of the matrix and putting it in prenex position
> and putting an appropriate anaphora sumti in its old place.

Nor does it necessarily mean that it has to be something more complicated
than that!

> To be
> genuinely clarifying, something more may well be required and in this case
> -- prenexing the quantifiers in 2 or 3 -- I think actually is, else the
> order of the two quantifiers would be irrelevant (as it is in 1) and we
> have agreed that it is not.

I await impatiently the general theory, then. I hope that for the simple
quantifiers (ro, su'o) it will still be the case that simply moving them
to the prenex is enough.

> xorxes:
> Well, I would use "and" to explain the second possible meaning, as I believe
> I did. When we started discussing this with And, I favoured the "and"
> reading, but then I changed to the And reading which seemed more useful.
> You say that we don't have a choice, and that one of the readings is forced
> by some prior rule, but I don't see it.
> pc:
> Xorxes actually put the "and" (e) in his Lojban version, which got into a
> conflict with a general rule about how to expand logically joined sumti.
> I just meant that "and"  worked better in the English translation (see
> above) than the "with respect to which" or whatever that introduced
> visions of relative selections that were not there.

Here you misunderstood me. By "and" I did not mean my {.e} proposal,
I meant the same that you did. I did use "and" to clarify one of the
two possible meanings, and "for which" for the other.

Somewhat as an aside, one has to be careful with the "general rule"
about how to expand {e}. For example:

        lo prenu cu prami la djan e la meris

does not expand to:

        lo prenu cu prami la djan
        ije lo prenu cu prami la meris

but rather to:

        lo prenu cu prami la djan
        ije py prami la meris

The same person loves each of them. So I am not sure what general
rule my {e}-proposal violates, since quantifiers must be taken
into account when expanding.

> To be sure, the "and"
> is not there either but, since it is coordinating rather than
> subordinating, it gives a less misleading impression while also making the
> English more readable than "for three men, for three dogs," or some such
> literal bit.

Well, that's the whole point, isn't it? Logically, there is a coordinating
and a subordinating case. You say that standard logical notation favours
the coordinating case in this instance, but the subordinating case is
real as well, and since it is arguably the most common, perhaps it should
get the more convenient notation.

> As for xorxes or And's rules, I have less than two years of this material
> at hand since I started reading and of that I lost a large chunk in the
> process of changing computers.  I am sorry if I have misrepresented their
> views, but I do not have records of any systematic interpretations of
> these issues.

I don't have And's proposal at hand, maybe he would like to re-post it?
It involved markers precisely for the coordinating and subordinating
cases, as well as for the "superordinating" case (my word for backwards
nesting). It also had other markers that I never fully understood, but
those three were, I think, the most interesting.

> I cannot find, for example, the rule which xorxes claims to
> be general, unless it is that changing surface order and subordination have
> no affect on meaning, which is general but clearly wrong, so probably not
> what he meant.

No, I didn't mean that, but I'm not sure what is the rule we are talking
about here. All I might have said is that it would be equally general
to take {reda rede} always as coordinating or always as subordinating.

("Superordianting" would be counter-lojbanic, even though it happens
sometimes in English, e.g. "I gave an apple to each of them", where
"an apple" comes first but is subordinate to "each of them".)

>  I hope soon to present a coherent
> (logically and lojbanically) reconstruction of quantifiers and gadri,
> along with some justification for the form it takes.

Great! Something like that is certainly much needed.

> I cannot, at this point -- and
> can't imagine that there was a time when I could -- explain to someone
> who does not seem the difference between referring directly to an
> individual and making a general claim about all or some individuals of a
> certain kind what that difference is,

Ah, but you are changing the question! Referring directly to an individual
is not the same as referring directly to several individuals. Lojban's
claim that it doesn't distinguish between plural and singular falls apart
if you limit descriptions to singular reference.

What you never explained is how something like {le re gerku} can be
different if taken as a universal quantification or as a direct reference
to two individuals.

You said that the two interpretations of {le pa gerku}, universal
quantification and singular reference, were at least equipollent
(if I got the word right). Why not the same for {le re gerku}?

Jorge