Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

On 5/11/2024 9:38 AM, Ross Finlayson wrote:

On 05/11/2024 01:18 AM, Jim Burns wrote:

Date: Tue, 7 May 2024 15:16:27 -0400.

Are there differences in syntax between
'for.any' 'for.each' 'for.every' 'for.all' ?

>
If your answer, if it ever comes, is "no",
then I do not know what is meant by

quantifier comprehension artifacts of the extra sort

That looks to me like
quantifiers used in several domains, full stop.
>
If your answer, if it ever comes, is "yes",
then I would like to know different how.
Syntax is pretty intimately entangled with semantics.
>
If your answer never comes,
why don't I just balk and clam up, because,
without it, I don't have much to say.

Now of course such a notion or idea or concept or
pensee or thought didn't just erupt fully-formed,
like Conrad from the tin of corned beef,
that it starts rather more like 'for-any, or, for-all',
about things like "for-any well-founded set, it's a set in
the well-founded universe", then, "for-all well-founded
or non-well-founded sets, they are sets in the set-theoretic
universal set".
 Then, it's not necessary to invoke the entire universe of
sets, the entire domain of discourse that is anything that
is a set, though is reasonably brief when in a theory with
only logical sets, logically, sets of sets.
 I.e., it applies as closely to "sets of sets", and the n'th order
about quantification, and comprehension.
  Let's be clearly understood that I am a formalist,
if though not a nominalist yet a platonist,
because mathematics its truths are discovered
not invented, while our language and terms and
derivations are as yet technique.
 So, constructivism is regarded as the rulial in
the standard, and intutionism is that which
revolves in the abductive inference, as what
makes for embracing the fuller dialectic.
 Thusly, the "standard" is "our standard",
while what's of interest in the fuller dialectic
is the "extra-ordinary" or "super-standard",
that the "non-standard", must be in these
classes of classes, yet formalist, and rulial
again, in the competing regularities, which
comprise "it", the thing, the universe of the
mathematical and logical objects, a theory,
to which we attain, "A Theory", the theory,
of the things, the theory of every thing.
 So, just saying, there's a greater mathematics
than "our standard", with "R, standard", and
modern mathematics as it's usually known,
a paleo-classical post-modern mathematics,
which mathematics owes physics for the
greater context of continuity, convergence,
and the laws of large numbers.
 I'm a formalist: and in natural language.

Date: Tue, 7 May 2024 15:16:27 -0400.

Are there differences in syntax between
'for.any' 'for.each' 'for.every' 'for.all' ?

If your answer, if it ever comes, is "no",
then I do not know what is meant by

quantifier comprehension artifacts of the extra sort

That looks to me like
quantifiers used in several domains, full stop.
If your answer, if it ever comes, is "yes",
then I would like to know different how.
Syntax is pretty intimately entangled with semantics.
If your answer never comes,
why don't I just balk and clam up, because,
without it, I don't have much to say.
So, it's door number 3.