Re: Can We Quantify over Everything?

On May 23, 1:12 pm, LauLuna <laureanol...@xxxxxxxx> wrote:
You seem to think that (1) is a proposition, since you consider it
tautologous and hence (I assume) true.

I thank you FOR QUOTING ME ACCURATELY
so that everybody can see how to rebut that.
You requested:
Consider

(1) all propositions not about themselves are propositions

If (1) quantifies over (1),

I replied (and YOU QUOTED me replying!)
Well, whether 1 quantifies over 1 (or not)
DEPENDS on whether
1 is (or is not) a proposition.
IF IT IS, then OF COURSE it quantifies
over itself. It is also clearly tautologous. It is NOT, however,
clearly ABOUT itself. Nor is it clearly NOT about itself,
for that matter.
That, however, simply has nothing to do with whether it is a
proposition.

My point is that my reply CLEARLY shows that I do NOT
think that 1 is a proposition (or that it isn't).
It shows that I consider that
question to be under debate.

Moreover, I continued:

You have 3 SEPARATE questions to answer about 1.
1. Is 1 a proposition?
2. Does 1 quantify over itself?
3. Is 1 about itself?

There is no paradox unless ALL 8
of the universes this puts us into are paradoxical.


So, again, *I* have not ANSWERED any of these
questions or claimed a side for any of them.
Moreover, I have DENIED THE IMPORTANCE of
answering any of these questions, because
YOU ARE ALLEGING PARADOX!
Therefore,
IT DOES NOT MATTER
what the answers to any of these questions may be!
If what you have stated is really a paradox, then it needs to
come up paradoxical under ALL 8 combinations of POSSIBLE
answers to these questions! If it comes up "possible" under
ANY combination, then the "resolution" of the paradox is
simply to insist that your framework of inquiry forces these
3 questions to be answered in the "possibilitating" combination!

You might then only object that
I have not clearly defined what 'being about' is.

I am sure you will do that later, but the problem is,
that may not matter either. In any case, since you
(as you already concede) haven't defined it yet,
you do NOT have a paradox YET.


I achieve this in a reasonable way
(IMHO) later in my post

Probably.

and the paradoxes is reproduced.

No, produced for the FIRST time.
The existence of paradox DEPENDS on "about"
being defined that way. Which is unusual.
Paradoxes normally DON'T depend on the content
of the terms. Since you are talking about Thomson's theorem
(which you Should Not; that is just the denial of Russell's
Paradox, and Russell's Paradox is old), you know that
Ay[Rry<->~Ryy]
is paradoxical because it is false
for ALL R and ALL r, REGARDLESS of what
they mean or are interpreted to. If this winds up depending
on a definition of R then the proper thing to say is simply
that R does not exist, and that that definition therefore
simply fails. You cannot, for example, define r to MEAN
"the smallest element of the empty set". The empty set
doesn't have any elements, so if you try to make r mean
this, you fail; r doesn't mean anything. Aboutness may mean
something but if this were REALLY a paradox then it simply
shouldn't matter what. The only way it does matter is if
some statement that does NOT appear to be "in this form"
(when you phrase it with "about"), DOES turn into an
instance of this form AFTER YOU EXPAND THE DEFINITION
of "about".






As for your opinion that no
single proposition can really quantify,
well I don't understand your point.

It's a point about first-order languages.
My point is that (first-order) quantification belongs to the
first-order paradigm AS A WHOLE and that every first-
order sentence (if it that quantifies) quantifies IN THE SAME
way using THE SAME first-order quantifers, so the
ACTION of quantifying would be PROPERLY located
in the quantifiers and the paradigm AND NOT in any
individual sentence.

would say that:

'all horses are mammals'

does quantify by itself.

No, "all" quantifies, and all sentences that
use it in that way do it in the same way.
The fact that 'all horses are mammals'
quantifies is not SEPARABLE from the fact
that 'all bees are insects' quantifies.
They are in a shared language with shared
rules and shared QUANTIFIERS.
They share an attitude toward the domain of
quantification. ALL THESE THINGS CAN CHANGE
if you go to a DIFFERENT first-order language (and
worse, you are not even in formal language anyway;
you are in natural language -- that is bad).


For all I know Aristotle would say it quantifies universally.

Aristotle is old and dead.

Excuse me if I misunderstand you.

It is I who should beg your pardon. I am nitpicking.

And finally, the only principled way I can
figure out to escape the
paradox is that no proposition
can quantify over itself even if a
proposition can quantify at all.

Please don't introduce the paradox prematurely.
If you don't have a CLEAR PRIOR definition of
"about" then you have no paradox.
And you should NOT presume to leave DOUBT
in anyone's mind about whether anything
is or isn't a proposition. Just give CLEAR DEFINITIONS,
in advance, of what a proposition is, and what it means
for one proposition to be about another (or itself).
Then anyone can easily check whether they do or don't
lead to paradox. More likely they lead to exposure of
some hidden assumption (don't make me channel Phil!).



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