[lojban] Re: xorlo and the expansion of bridi

[Jorge Llambías <jjllambias@gmail.com>]

2009/10/29 Roman Naumann <roman_naumann@fastmail.fm>:
>
> In {ci da poi mlatu cu blaci .ije re da cu barda} [according to your (more
> mathematical) use of logic, not the CLL use], is {da} only to be considered
> an independent variable, because there is a leading PA before it?

There's also the possible problem of ".ije". This one would be unproblematic:

ci da poi mlatu zo'u ge da blabi gi da barda
"There are three cats x such that: both x is white and x is big."

This does not preclude there being any number of white cats that are
not big or any number of big cats that are not white.

If what you want to say is that there are three cats that are white,
and that all the cats that are white are big, then that will be
something different. And if you want to say that there are three cats
that are white, and that all and only the cats that are white are big,
that will be different again.

> (If not:) If reusing a variable in a connected bridi generally introduces a
> new, independend variable, expressions like {lo gerku cu vasxu gi'e bajra},
> which expand to {da poi gerku zo'u da vasxu ije da bajra} would mean {da poi
> gerku zo'u da vasxu ije de poi gerku zo'u de bajra}, which means, we could
> be talking about different dogs. That would collide with my understanding of
> {gi'e}.

The correct expansion is:

da poi gerku cu vasxu gi'e bajra
= da poi gerku zo'u da vasxu gi'e bajra
= da poi gerku zo'u ge da vasxu gi da bajra

so your understanding of "gi'e" is correct.

"da poi gerku zo'u da vasxu ije de poi gerku zo'u de bajra" is
actually ungrammatical, because "ije" cannot connect two bridi with
prenexes. The first prenex is in fact a prenex for the whole thing,
and you can't have a second prenex after "ije". This is quite
unintuitive and was a bad choice, in my opinion, I think there even is
an example in CLL that violates this, but that's how it was defined in
the formal grammar. If you stick to forethough connectives "ge ... gi
...", there can be no doubt about the scopes of the different
prenexes, so it is better to use those for clarifications. The
relative scopes in that case are transparent.

>>> The appearance of ``ci da'' quantifies ``da''
>>> as referring to three things, which are restricted by the relative clause
>>> to be cats.
>>
>> The way I would say it is that the variable "da" takes values from the
>> things that are cats, and (exactly) three of those values satisfy the
>> predicate "blabi" (which also means all but three of those values
>> don't satify it). If there is any reference going on here at all it is
>> to all cats, not just to the three that do satisfy the predicate
>> "blabi". If we were to say "no da poi mlatu cu blabi" then "da" again
>> takes values from the same set of referents, but now the number of
>> them that are said to satisfy blabi is zero. Would we say that "da"
>> doesn't refer to anything in this case?
>
> That's an interesting question. I would say it refers to all referents in
> the set, but the bridi is negated. At least the statement still has an
> implication on all referents in the set, your explanation includes that, the
> CLL one does not. (..or was that a rethorical question of yours..?)

Yes, it was sort of a rhetorical question to show why I wouldn't say
that da refers to three things in the case of "ci da". If da refers to
anything, it refers to all the values that the quantifier ranges over,
not just to those that make the bridi true.

[...]
> I understood that now. The inner quantifier is just incidential information
> about the cardinality of the set-of-things we are talking about.

Exactly.

[...]
> Well explained.

Thank you! The usual situation is that nobody understands what I'm
saying when I try to explain these things. :)

> By the way, is there any document about lojban logic on the
> web which sticks closer to what you explaned/to logic than the CLL?

Nothing I can think of. The CLL is correct for the most part, but it
has some glitches here and there.

mu'o mi'e xorxes


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