On 05/11/2024 01:18 AM, Jim Burns wrote:
On 5/10/2024 8:17 PM, Ross Finlayson wrote:
On 05/10/2024 03:26 PM, Jim Burns wrote:
On 5/10/2024 4:12 PM, Ross Finlayson wrote:
On 05/10/2024 03:59 AM, Jim Burns wrote:
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[...]
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I'd like to suggest a reading from
Dehaene's "The Number Sense",
in Chapter 9 "Of Neurons and Numbers",
in the section
"When Intuition Outruns Axioms".
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I found a copy online from
the International Cognition and Culture Institute,
and about page 238.
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He explains that there _are_
non-standard models of integers.
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Is "When Intuition Outruns Axioms" concerned with
other.than.standard.issue quantifiers?
[1]
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If so,
since you are currently holding the talking.stick,
you could use the opportunity to expound on
what Dehaene has to say.
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Maybe I should clarify:
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I don't say that there aren't non.standard objects.
That's not the same as saying that
there aren't non.standard quantifiers.
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I also don't say that there aren't
non.standard quantifiers.
There might not be.
Quantifiers are live near the roots of our logic.
There might be.
Mathematicians are smart.
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What I say is
I don't know yet what sort of
non.standard.quantification scheme
you introduced at your "universal quantification"
post.
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If you wish I had more to say about your posts
(a big IF, not everyone does)
helping me to understand your posts seems like
an effective strategy for bringing that about.
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Just saying.
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Again, what correspondence of yours I see,
which is any in response to me, I've replied.
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If you have used ∀? ∀+ ∀* ∀$ in sentences,
I have overlooked them.
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Surely, it would only be a very small favor to me
to repeat those sentences.
By doing so, you would increase the chances
of me NOT balking and clamming up.
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Could you please do so again?
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[1]
By other.than.standard.issue quantifiers, I mean
other than those such that:
| ∀x:B(x) ⇒ B(t)
| ∀x:(B⇒C(x)) ⇒ (B⇒∀x:C(x))
| B(x) ⊢ ∀x:B(x)
| ∃x:B(x) ⇔ ¬∀x:¬B(x)
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">
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Well, first of all, it's after pondering that there
is quantifier comprehension artifacts of the extra sort,
as of a set of all sets, order type of ordinals, a universe,
set of sets that don't contain themself, sets that contain
themselves, and so on.
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Then, English affords "any, "each, "every, "all".
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The -any means for example that "it's always a fragment".
So in this sense the usual universal quantifier is for-each.
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Then, for-each, means usual comprehension, as if an enumeration,
or a choice function, each.
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Then, for-every, means as a sort of comprehension, where it
so establishes itself again, any differently than -each,
when -each and -every implies both none missing and all gained.
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Then, "for-all", sort of is for that what is so "for-each"
and "for-every" is so, "for-all", as for the multitude as
for the individual.
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Then, I sort of ran out of words, "any", "each", "every", "all",
then that seems their sort of ordering, about comprehension,
in quantification, in the universals, of each particular.
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About sums it up, ...." -- Monday
>
Date: Tue, 7 May 2024 15:16:27 -0400.
Are there differences in syntax between
'for.any' 'for.each' 'for.every' 'for.all' ?
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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.
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If your answer, if it ever comes, is "yes",
then I would like to know different how.
Syntax is pretty intimately entangled with semantics.
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If your answer never comes,
why don't I just balk and clam up, because,
without it, I don't have much to say.
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I'd like to think of my internet production as
carefully.curated stretches of silence
artfully.punctuated with non.silences,
something in the direction of John Cage's 4'33"
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I try to indicate not.having something to say
by not.saying it.
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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.
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