Re: Mathematics and the singularity, let's discuss it

On 04/10/2020 03:11 PM, Ross A. Finlayson wrote:

On Friday, April 10, 2020 at 10:55:46 AM UTC-7, Mostowski Collapse wrote:

Its gibberish, since most of your
sentences lack a verb. Whats is this
pile of words:
>
"structure, in sets, for of course all the formality
of all the structure of the sets **usually** "mechanically",
then what a "reality" embodies for a "mathematical universe"
a model of a universe of ZF set theory."
>
Do you mean **usually** **is**?
Since when is it chick to drop verbs
in english sentences?
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On Friday, April 10, 2020 at 7:06:20 PM UTC+2, Mostowski Collapse wrote:

Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
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LoL
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On Friday, April 10, 2020 at 5:51:35 PM UTC+2, Ross A. Finlayson wrote:

On Friday, April 10, 2020 at 3:34:05 AM UTC-7, Mostowski Collapse
wrote:

Corr.:
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
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A theory of anything, is not really
a theory of something. Calling ZFC a model
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of reality is pretty crank.

No, it's the same as "there exists causality"
(there exists a theory, there exists A-Theory),
then that the model universe, ZF's, sees in other
theories that "the universe of ZF is its own powerset",
encompassing all relation.
>
The "Pure" part of set theory is two things:
structure, in sets, for of course all the formality
of all the structure of the sets usually "mechanically",
then what a "reality" embodies for a "mathematical universe"
a model of a universe of ZF set theory.
>
Then this "mechanically pure" and "totally pure",
help to reflect that applied set theory is descriptive.
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Applied set theory is descriptive.  The "naive" set
theory is often best - for where it's true.
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"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
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I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
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Results in theorem proving?

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The "Pure" part of set theory is two things:
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
>
then what a "reality" embodies
for a "mathematical universe" :
(2) a model of a universe of ZF set theory.
>
>
Verb?  This is:  "is" a structure and "is" a model.
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The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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About the universe being its own powerset,
a similar result of Russell's made Frege
abandon his completeness results, which is
important because Goedel's both "completeness"
and "incompleteness" results about arithmetization
of structure reflect truisms.
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So, ..., "gibberish" here is only as received -
i.e. you're a very excellent English speaker
and apparently quite fluent in the concepts,
it's too bad that some idiomatic grammar
leaves you at a loss.  Don't get me wrong -
I'm not perfect.
>
>
Also of course there's an importance of context,
and a usual coherency and constancy in narrative.
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Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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To your question of "what universe of ZF?  V?  L?",
it's appreciated.  Here of course you already know
that there's Cantor's, Russell's, and Burali-Forti's
results with that of course the universe of ZF is in
a theory that is extra-ZF (here "stronger/weaker",
in the results/axiomatics).
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Then, even just looking at ordinals and as that
"powerset is order type is successor" and that
for example "diagonalizing the finite ordinals
makes an infinite one", notes that Russell would
have to apply a resolution to the paradox that
there's an infinite ordinal at all, consistently
(as for example is defined as the second constant
in the language of ZF besides empty:  omega,
or an inductive set, those two sets, the rest
following expansion and restriction of comprehension).
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I.e., ZF to be accepted _does_ have "truly infinite" things.
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