On 05/11/2024 07:40 AM, Jim Burns wrote:
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.
>
>
In the logical, syntax "is" semantics.
Of course, above that is called higher-order and
variously non- or properly logical, when the elements
of the theory, that are elementary, thusly model,
embody a model, descriptively, thusly, what makes
for descriptive model theory, for example, with
regards to that being the default meta-theory and
the theory, descriptive set theory.
So, logic, then with regards to: terms, predicates,
and relations, have variously which one of those
is primary, or elementary, the others being expressed
in it. It's similar with mathematical objects like
sets, which of course define relations, where the only
relation in set theory usually is elt, which is "any-to-1",
and members, which is "1-to-any", is not included,
for the most usual sort of "class/set distinction",
as what results from quantifier ambiguity and impredicativity.
I.e., the group nouns, as was mentioned, the groups nouns
result a sort of, "group noun game", whether classes are
sets and sets are classes and this and that and the other.
It's quite most so in all sorts the most, "fundamental",
theories, of the objects, whether sets or classes or
parts or particles or substance or essence or atoms or
molecules or waves or particles or what results as for:
number theory
geometry
arithmetic
algebra
topology
function theory, "functionalogy", "functionimetry",
as with regards to all sorts usual concerns where the
objects of mathematics and also logic are primary and
fundamental and _all fit in one theory_.
So, in the logical, syntax "is" semantics.
"A Theory"
Here then, for the formalism, there are terms, or,
predicates, or, relations, and relations are richest,
for the symmetrical as after the inverse, where the
axiom is "inverse".
Then all their inner and outer products exist, what
for the usual planar and direct and natural products,
have of course in all ways their generalized inverses,
that they are and so model each other, where of course
model-theory and proof-theory are thusly equi-interpretable
as they model each other, according to proof-theory,
formally, thus provably, in model theory, faithfully.
So, the syntax, as soon as it introduces schemes or
orders, of comprehension, of quantification, either
remains logical, or, introduces the extensionality,
the non- or properly-logical, thusly, semantics,
whether fully modeled or not.
In the logical, the purely logical, the syntax "is" the semantics.
And, the semantics "is" the syntax.
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