any? (response to Desmond)

[Logical Language Group <lojbab>]

Talking through my hat here.  I don't claim to know what I am talking
about, but am just feeling my way.  We are now solidly into non-solid
logics, which is pc's specialty.  I defer to him to say what I/we REALLY
mean in Lojban $^)

From: Jorge Llambias <jorge@PHYAST.PITT.EDU>
>Desmond:
>> A feature of dr is the fundamental role in it of what I call
>> *indeterminates*.  For example, if a and b are indeterminates of the sort
>> number, then the *unquantified* sentence
>>         a^2 - b^2 = (a-b)(a+b)
>> is true.  a and b are *potential entities* of the sort number.  This may be
>> the only information we have about them, or we may have total information
>> about them (such as that a=5 and b=3) or we may have partial information
>> about them (such as that a is positive).  In each case our sentence remains
>> true: it is true by virtue solely of the fact that a and b are numbers.
>
>This is not the case for Lojban {lo}.
>
>For example:
>
>        lo remna cu mamta mi
>        A human being is mother to me
>
>is true.  Not by virtue of the fact that {lo remna} is a human being,
>but because of the fact that there is one human being that is in
>relationship {mamta} with {mi}.

We may be dealing with the idiosyncracies of individual predicates here.
Replace mammta with "se bersa" and the answer is probably indeterminate,
since you (probably) do not know whether you (will) have a son in a
time-free sense.

>> On
>> the other hand, in the absence of specific information about a and b, the
>> sentence
>>         a^2 - b^2 = (a-b)^2
>> (though a perfectly acceptable sentence) is neither true nor false.

I think that this claim is a definition and not a given.  You know they
are numbers, and you know that there is at least one number assignment
that could make it true (b=0).  You lack specific information as to
whether that (or any other specific value) is a permissible value of
"b".

Pragmatic usage of "lo" has incomplete specification of necessary
restrictions.

>Sentences with {lo} in Lojban are usually true or false.

Is "mi nitcu lo [unikorn]' true or false?  "In the absence of specific
information" applies much more often to mathematical problems than to
linguistic ones.

>For example:
>
>        lo remna cu kalte lo remna
>        A human hunts a human
>
>is true only if there really is at least one human that hunts at least
>one human.  It's not a matter of giving values to each {lo remna}.

Umm.  Let me hedge this a bit.  Remember that we have some modals that
have significant truth-functional import, and some of them involve
potentiality.  We can translate "inflammable" by "jelca", not requiring
explicit use of "ka'e".  Is "lo remna cu jelca" true or false? - depends
on the modalities.

In your example, there are no less than 3 predicates that could be
potentials. make them explicitly so, and you have a truth-functional
mess":

         lo ka'e remna cu ka'e kalte lo ka'e remna
         A potential-human potentially can hunt a potential-human


>If "a" and "b" were replaced by {lo namcu} = "a number" in your
>sentence, it would be a true sentence in Lojban, because there indeed
>exists at least one "a" and at least one "b" that make it true.

"'a' number" in the same sense as "I need 'a' box"???

>> It
>> becomes true in the presence of the information that b=0, and it becomes
>> false in the presence of the information that a=5 and b=3.
>
>That sounds like it might be more or less equivalent (at least for some
>purposes) to Lojban {le}
>
>        le remna cu mamta mi
>        The human is mother to me.
>
>is true if by {le remna} I mean the human who is my mother.  In that
>sense, you can say that it's neither true nor false in the absence of
>information of what {le remna} is referring to, but that information is
>at least in principle always obtainable (by asking the speaker who they
>meant by it).  >From what I understand, your "a" need not have a value
>obtainable even in principle.

Ask Shakespeare what he means by various passages in his plays.

>> I believe that indeterminates in this sense play a fundamental role in
>> everyday reasoning as well as in mathematical reasoning.  Ordinary language
>> accomodates indeterminates nicely.  The use of 'a box' in the sentence "I
>> need a box." is an example.  It is a way of referring to something whose
>> type is known, but about which we have no other information.
>
>I think something like that is what I meant by my proposal of {xe'e},
>although I don't have it that clear in my mind.

I think that pragmatically, "lo" is used as a non-specific categorizer.
I like the word "indeterminate" better than "non-specific", now that
Desmond has brought it into the jargon.

If I say "lo [unikorn] cu klama lo zarci", you do not know what unicorn
I am talking about (much less what store).  You only know that it is
veridically a member of the class of unicorns, if such a member exists.
"Unicorn" is serving as a 'type' for the sumti.

Change the example from "lo [unikorn]" to "lo nanmu" and you may have
the same situation.  If you require that "lo zarci" refer to a specific
one store that merely hasn't been specified, rather than 'any' store in
your "xe'e" sense, then you do not know the truth value of the sentence
unless you can say that for EVERY possible value of "lo zarci", it is
true that at least one man goes there.  (This is how djer. ends up with
universals in trying to analyze this problem.)

Alternatively, you can say that (assuming that the sets exist), the
statement means merely

"su'oda poi nanmu ku'o su'ode poi zarci zo'u da klama de"
There exists at least one man X, and at least one market Y such that:  X
goes to Y

But this really doesn't track with your "mamta" example above.  Yeah, it
works since there is indeed at least one human that is your mother, but
there really is a little implication of specificity or you wouldn't
argue so comfortably that it is true.

But how do you evaluate a story:

"lo nanmu cu klama co jibni lo ninmu .i le nanmu cu cpedu le ninmu lenu
kansa klama le dansu nunsalci"

"A man goes near a woman.  And the man asks the woman to
accompanyingly-go to the dance-celebration."

Now what do you make of this?  Is the first sentence inherently true
because at least one man has at some time gone near a woman?  If so, it
makes "lo" rather useless.  I think that there may indeed be a 'typing'
going on here, and the 2nd sentence "le" is an instantiation that tells
us that the first sentence WAS referring to a specific man and a
specific woman.

>> Additional
>> information that may be given serves to pin down what is meant:
>>
>> "I need a box."
>> "You mean a cardboard box?"
>> "Yes."
>> "Here's one from the attic."
>> "Great."
>> "What are you going to do with the box?"
>> >
>> The dialogue starts with a total indeterminate (a potential entity of the
>> sort box) and concludes with an entity that instantiates it.
>
>The first two mentions of "box" are indeterminate (one of the sort
>"box", the other of the sort "cardboard box").  The last one is an
>actual box.
>
>In my opinion, as things stand now, we can only refer to the first type
>in Lojban within abstractions.
>
>> I do not think that classical logic accomodates or is even compatible with
>> this notion --- I am going out on a limb here, and might be persuaded
>> otherwise.  Indeterminates are not constants, and they are not variables,
>> they require a *typed* language and they do away with the need for
>> universal quantification.
>
>I wouldn't know if they do away with it, but it would be nice to have them.
>
>> It would be disappointing to me if lojban did not admit indeterminates in a
>> simple way, but that's what the debate seems to suggest.  Am I wrong about
>> this?
>
>I think you're right. But maybe it's just me  :)

hypothetical mode:

IFF Desmond's concept turns out to be what we (want to) mean by "lo"
(and by extension "loi" and "lo'i", though the standard quantification
values attached to those may tend to make them a little less
problematical), would this resolve the issues of "I need a box"?  What
new issues can you see it introducing?  In particular, what actual
Lojban usages that you can think of are incorrect and which are
uncertain.

lojbab