Re: quantifiers and existence

[Gerald Koenig <jlk@NETCOM.COM>]

>>=djer, first post
>=xorxes, reply

>
>djer:
>> I think what pc means here is that something of the form:
>>
>> E(x)[A(x)broda(x)]. has a scope that asserts the second x exists.
>
>I don't think pc would accept that as a well formed expression. You can't
>quantify the same variable twice.

I know. I was also trying to show the so called "clash of variables" in
the ill formed expression.  When the lojban is ill-formed, so is the
FOL.

>
>> pc has said that "re broda" means the standard  Russell expression
>> which I take to be:
>>
>> ExEy[(x\=y & Az(z=x v z=y)) & broda(x) & broda(y)].
>
>This is not quite right. {re broda} is an argument, it is not a claim.

I take it you mean it is a sumpti.  I consulted the Oracle at PARSER on
this and she returned the following:
re broda
text_0(terms_80(quantifier_300(PA(re),boi(boi)),selbri_130(broda),ku(ku)),
vau(vau)).
Then I asked her about de broda:
de broda
text_0(terms_80(de),bridi_tail_50(selbri_130(broda),tail_terms_71(vau))).

"de broda"  is clearly a sumti-selbri expression. Yet PARSER doesn't see
"re broda"  with the same parse. Actually she sees "re broda" identically to
"su'o broda", which makes sense as they are each [PA]. I think "su'o broda"
makes a claim. It claims existence for at least one broda. I think that
"re broda" claims existence for exactly two broda.

>
>But you are still missing something there.  Az(z=x v z=y) should be replaced
>by Az(broda(z) -> (z=x v z=y)). Otherwise, you are claiming that there are
>only two things in the universe.

Yes, I am. And the form you prefer claims that there are only 2 brodas
in the universe. You don't really intend, at least Russell and Whitehead
didn't, that these forms be taken literally. There is always an implied
restriction, set by the universe of discourse.

>> What does it mean now to say "lo re broda"?
>
>{lo re broda} is not constructed from {re broda}. Remember that {re broda}
>is only a shorthand for {re lo ro broda}. (Or maybe it is something else,
>as pc proposes, but in any case it is not the inside part of {lo re broda}.
>
>In {lo re broda}, the "re broda" part cannot stand alone.

If "re broda" is equivalent to "re lo ro broda", then "lo re broda" is
equivalent to "lo re lo ro broda". Is this really necessary to say
2 broda? If we are going to create monstrous idomatic expressions in
lojban, I don't think the quantifier scheme is the place to do it.
It is really time we started calling a set a set with these quantifiers,
and stop calling a Russell expression a set, or a quantifier expression
an ordinary sumti. How else can we improve on these meaningless mantras
composed of implicit and explicit quantifier strings?

>
>> lo by itself claims existence
>> for the broda it modifies.
>
>No, the article only says that we are talking about individuals. The existence
>comes from its default quantifier. {lo broda} stands for {su'o lo ro broda},
>but you can override the default by giving another explicit quantifier.

 lo        LE       the really is                             veridical
 descriptor: the one(s) that really is(are) ...


>{lo re broda} means {su'o lo re broda} = "at least one of the two broda
>that there are in all". It claims nothing by itself because it is a sumti,
>not a bridi.

It is neither an ordinary sumti nor an  ordinary  bridi. But it does
claim something.

>> lo is also a determiner.
>
>"Determiner" is very ambiguous, but the key difference between {lo}
>and {le} is that {lo} is indeterminate or nonspecific and {le} is
>determinate or specific. {lo} does not tell you _which_ broda you
>are talking about. {le} does.

"Le" may be perfectly clear to the speaker, but the listener is at
sea.

>> Now what does "pa lo re broda" mean?
>
>"Exactly one of the two broda that there are in all."
>
>> In exploring this we find that the
>> lo has yet another function. It separates the pa and re from merging
>> into one number, pare, or 12. But there is no difference between
>>
>> "pa ti lo ci broda"  and
>> "pa ti ci broda".
>
>Both of those expressions are two sumti: {pa ti} and {lo ci broda}
>or {ci broda} respectively.
>
>{pa ti} means "one of these". The second part is a separate sumti.

As I outlined above with the parser output," [PA] broda" is not just your
ordinary sumti. It makes an existence claim; with the possible exception
of a "ro" in the first clause of a material implication.
>
>Jorge
>


djer