Discussion:
Mathematics and the singularity, let's discuss it
(too old to reply)
David Petry
2020-04-08 07:15:45 UTC
Permalink
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?

Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.

So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?

What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?

We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.

So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.

Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.

As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.

People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.

So like I said, I'd like to encourage people to discuss this topic.
FromTheRafters
2020-04-08 10:59:03 UTC
Permalink
Post by David Petry
But what mathematicians have chosen to be the foundation of their own subject
(ie ZFC) is quite deficient as a foundation for AI, and the mathematicians
now seem to be very opposed to the idea of even considering alternate
foundations that might have great practical value.
What do you think is deficient about the current mathematics and why do
you think having a different choice as 'foundation' would help?
Ganzhinterseher
2020-04-08 12:21:33 UTC
Permalink
Post by FromTheRafters
What do you think is deficient about the current mathematics and why do
you think having a different choice as 'foundation' would help?
An endsegment of |N is E(k) = {k, k+1, k+2, ...} .
∀k ∈ ℕ: ∩{E(1), E(2), ..., E(k)} = E(k) with |E(k)| = ℵo
So every definable E(x) can be omitted from
∩{E(x), E(x+1), E(x+2), ...} = { } .
Therefore undefinable natnumbers are needed in ZFC. But there are no undefinable natnumbers in ZCFC. That is deficient.

Regards, WM
Dan Christensen
2020-04-10 18:03:36 UTC
Permalink
Post by Ganzhinterseher
Post by FromTheRafters
What do you think is deficient about the current mathematics and why do
you think having a different choice as 'foundation' would help?
An endsegment of |N is E(k) = {k, k+1, k+2, ...} .
∀k ∈ ℕ: ∩{E(1), E(2), ..., E(k)} = E(k) with |E(k)| = ℵo
So every definable E(x) can be omitted from
∩{E(x), E(x+1), E(x+2), ...} = { } .
Therefore undefinable natnumbers are needed in ZFC. But there are no undefinable natnumbers in ZCFC. That is deficient.
Still flogging that dead horse, Mucke? You need nothing more than ZFC and a suitable definition of arbitrary intersection (not included in the axioms) to understand why

∩{E(x), E(x+1), E(x+2), ...} = { }

and
∩{ } = { }

You don't need "definable" anything here. You also don't need "dark numbers." As usual, you are barking up the wrong tree. When will you learn?


Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Ganzhinterseher
2020-04-10 19:04:34 UTC
Permalink
Am Freitag, 10. April 2020 20:03:44 UTC+2 schrieb Dan Christensen:

t of |N is E(k) = {k, k+1, k+2, ...} .
Post by Dan Christensen
Post by Ganzhinterseher
∀k ∈ ℕ: ∩{E(1), E(2), ..., E(k)} = E(k) with |E(k)| = ℵo
So every definable E(x) can be omitted from
∩{E(x), E(x+1), E(x+2), ...} = { } .
Therefore undefinable natnumbers are needed in ZFC. But there are no undefinable natnumbers in ZCFC. That is deficient.
∩{ } = { }
First that is wrong in ZFC, second ZFC claims that nonempty endsegments for

∩{E(x), E(x+1), E(x+2), ...} = { }

exist.

Regards, WM
Dan Christensen
2020-04-10 20:22:00 UTC
Permalink
Post by Ganzhinterseher
t of |N is E(k) = {k, k+1, k+2, ...} .
Post by Dan Christensen
Post by Ganzhinterseher
∀k ∈ ℕ: ∩{E(1), E(2), ..., E(k)} = E(k) with |E(k)| = ℵo
So every definable E(x) can be omitted from
∩{E(x), E(x+1), E(x+2), ...} = { } .
Therefore undefinable natnumbers are needed in ZFC. But there are no undefinable natnumbers in ZCFC. That is deficient.
Still flogging that dead horse, Mucke? You need nothing more than ZFC and a suitable definition of arbitrary intersection (not included in the axioms) to understand why
∩{E(x), E(x+1), E(x+2), ...} = { }
and
∩{ } = { }
First that is wrong in ZFC,
Wrong again, Mucke. Arbitrary intersection is defined as follows:

∩ M = {a| a in U M & Ax:[x in M => a in x]}

So it is vacuously true that ∩{ } = { }

See: https://en.wikipedia.org/wiki/Intersection_(set_theory)#Nullary_intersection
Post by Ganzhinterseher
second ZFC claims that nonempty endsegments for
∩{E(x), E(x+1), E(x+2), ...} = { }
exist.
Pure gibberish! There is no element common to each of the sets E(x), E(x+1), E(x+2), .... So ∩{E(x), E(x+1), E(x+2), ...} = { }.

When will you learn???


Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Ganzhinterseher
2020-04-11 13:03:05 UTC
Permalink
Post by Dan Christensen
Post by Ganzhinterseher
Post by Ganzhinterseher
∩{E(x), E(x+1), E(x+2), ...} = { }
and
∩{ } = { }
First that is wrong in ZFC,
Nonsense, but irrelevant.
Post by Dan Christensen
Post by Ganzhinterseher
second ZFC claims that nonempty endsegments for
∩{E(x), E(x+1), E(x+2), ...} = { }
exist.
There is no element common to each of the sets E(x), E(x+1), E(x+2), .... So ∩{E(x), E(x+1), E(x+2), ...} = { }.
Nevertheless there must be a first endsegments E(x). But it cannot be defined.

Regards, WM
Dan Christensen
2020-04-11 14:21:19 UTC
Permalink
Post by Ganzhinterseher
Post by Dan Christensen
Post by Ganzhinterseher
Post by Ganzhinterseher
∩{E(x), E(x+1), E(x+2), ...} = { }
and
∩{ } = { }
First that is wrong in ZFC,
∩ M = {a| a in U M & Ax:[x in M => a in x]}
So it is vacuously true that ∩{ } = { }
See: https://en.wikipedia.org/wiki/Intersection_(set_theory)#Nullary_intersection
Nonsense, but irrelevant.
More of your wishful thinking, Mucke.
Post by Ganzhinterseher
Post by Dan Christensen
Post by Ganzhinterseher
second ZFC claims that nonempty endsegments for
∩{E(x), E(x+1), E(x+2), ...} = { }
exist.
There is no element common to each of the sets E(x), E(x+1), E(x+2), .... So ∩{E(x), E(x+1), E(x+2), ...} = { }.
Nevertheless there must be a first endsegments E(x). But it cannot be defined.
Wrong again, Mucke. The first end-segment is E(1). You yourself have defined it here as E(1) = {1, 2, 3, ... }. And E(2) = {2, 3, 4, ...}, etc.


Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Ganzhinterseher
2020-04-12 11:54:27 UTC
Permalink
Post by Dan Christensen
Post by Ganzhinterseher
Post by Dan Christensen
Post by Ganzhinterseher
∩{E(x), E(x+1), E(x+2), ...} = { }
exist.
There is no element common to each of the sets E(x), E(x+1), E(x+2), .... So ∩{E(x), E(x+1), E(x+2), ...} = { }.
Nevertheless there must be a first endsegments E(x). But it cannot be defined.
The first end-segment is E(1).
We look for the first endsegment E(x) that cannot be oitted without changing the result.

Regards, WM
Dan Christensen
2020-04-12 15:50:30 UTC
Permalink
Post by Dan Christensen
Post by Ganzhinterseher
Post by Dan Christensen
Post by Ganzhinterseher
∩{E(x), E(x+1), E(x+2), ...} = { }
exist.
There is no element common to each of the sets E(x), E(x+1), E(x+2), .... So ∩{E(x), E(x+1), E(x+2), ...} = { }.
Nevertheless there must be a first endsegments E(x). But it cannot be defined.
The first end-segment is E(1).
We look for the first endsegment E(x) that cannot be omitted [?] without changing the result.
Again, the answer is E(1). We have

∩{E(1), E(2), E(3), ...} = { }

since there is no element common to each of the E(i)'s.

Omitting only E(1) (if that is what you mean), the result is still...

∩{E(2), E(3), E(4), ...} = { }

since there is still no element common to each of the remaining E(i)'s.

Omitting all of E(i)'s, the result is still...

∩{ } = { }

What part don't you get, Mucke?


Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Julio Di Egidio
2020-04-12 16:43:54 UTC
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Post by Dan Christensen
Post by Dan Christensen
Post by Ganzhinterseher
Post by Dan Christensen
Post by Ganzhinterseher
∩{E(x), E(x+1), E(x+2), ...} = { }
exist.
There is no element common to each of the sets E(x), E(x+1), E(x+2), .... So ∩{E(x), E(x+1), E(x+2), ...} = { }.
Nevertheless there must be a first endsegments E(x). But it cannot be defined.
The first end-segment is E(1).
We look for the first endsegment E(x) that cannot be omitted [?] without
changing the result.
Again, the answer is E(1). We have
∩{E(1), E(2), E(3), ...} = { }
since there is no element common to each of the E(i)'s.
The answer is none: you must have missed the double negative, "we look for
the first endsegment E(x) that *can* be omitted [i.e. removed] *to change*
the result".

Why that should be an interesting question at all I just cannot see: removing
any finite number of E's from that sequence is not going to change the result.
While removing all E(i)'s s.t. i >= x of course changes the result to E(i-1).
In either case, can you guess where dark numbers might pop out of? Or even
how is this at all related to the OP?
Post by Dan Christensen
Omitting only E(1) (if that is what you mean), the result is still...
∩{E(2), E(3), E(4), ...} = { }
since there is still no element common to each of the remaining E(i)'s.
Omitting all of E(i)'s, the result is still...
∩{ } = { }
What part don't you get, Mucke?
That's void of content. In this case you'd have to prove that there in no
E(i) such that /\{E(i+1),...} =/= {}: how would you actually prove it? Your
last line is the thesis, not the proof.

Julio
Dan Christensen
2020-04-12 21:35:43 UTC
Permalink
Post by Julio Di Egidio
Post by Dan Christensen
Post by Dan Christensen
Post by Ganzhinterseher
Post by Dan Christensen
Post by Ganzhinterseher
∩{E(x), E(x+1), E(x+2), ...} = { }
exist.
There is no element common to each of the sets E(x), E(x+1), E(x+2), .... So ∩{E(x), E(x+1), E(x+2), ...} = { }.
Nevertheless there must be a first endsegments E(x). But it cannot be defined.
The first end-segment is E(1).
We look for the first endsegment E(x) that cannot be omitted [?] without
changing the result.
Again, the answer is E(1). We have
∩{E(1), E(2), E(3), ...} = { }
since there is no element common to each of the E(i)'s.
The answer is none: you must have missed the double negative, "we look for
the first endsegment E(x) that *can* be omitted [i.e. removed] *to change*
the result".
Oooops! You are right. If you remove any individual end-segment, or you remove all of them, the intersection will remain unchanged { }.
Post by Julio Di Egidio
Why that should be an interesting question at all I just cannot see: removing
any finite number of E's from that sequence is not going to change the result.
It wasn't meant to be "interesting." It was meant to be confusing and a diversion from the fact that WM has failed once again to demonstrate any inconsistency in ZFC.

If he can remain sufficiently vague and obscure and just keep talking, WM must figure that, maybe, just maybe some naive student with wander in and think there must be something to all this heated debate, and that there is a non-zero chance that they will randomly side with him in this "epic" struggle against the "establishment." What are the chances of that? Very close to zero, but it's all that WM has left.
Post by Julio Di Egidio
While removing all E(i)'s s.t. i >= x of course changes the result to E(i-1).
Yes.
Post by Julio Di Egidio
In either case, can you guess where dark numbers might pop out of?
Out of WM's ass?
Post by Julio Di Egidio
Or even
how is this at all related to the OP?
It has nothing to do with the OP, of course, but WM must keep his numbers up.
Post by Julio Di Egidio
Post by Dan Christensen
Omitting only E(1) (if that is what you mean), the result is still...
∩{E(2), E(3), E(4), ...} = { }
since there is still no element common to each of the remaining E(i)'s.
Omitting all of E(i)'s, the result is still...
∩{ } = { }
What part don't you get, Mucke?
That's void of content. In this case you'd have to prove that there in no
E(i) such that /\{E(i+1),...} =/= {}: how would you actually prove it?
Suppose i in N.

Suppose x in N.

Case 1: x < i+1

x ~in E(i+1), so x is not common to all elements of {E(i+1),...}

Case 2: x >= i+1

E(x+1) in {E(i+1),...} and x ~in E(x+1), so x is not common to all elements of {E(i+1),...}

Conclusion: No x in N is common to all elements of {E(i+1),...}, so /\{E(i+1),...} = { }

Conclusion: For all i in N, /\{E(i+1),...} = {}


Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Mitch Raemsch
2020-04-12 23:23:18 UTC
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In mathematical science the first point to exist was the mathematical
hypersphere-closed universe. The singularity was a math of itself...

Mitchell Raemsch
Julio Di Egidio
2020-04-14 14:30:30 UTC
Permalink
<snip>
Post by Dan Christensen
Post by Julio Di Egidio
Post by Dan Christensen
We look for the first endsegment E(x) that cannot be omitted [?] without
changing the result.
Again, the answer is E(1). We have
∩{E(1), E(2), E(3), ...} = { }
since there is no element common to each of the E(i)'s.
The answer is none: you must have missed the double negative, "we look for
the first endsegment E(x) that *can* be omitted [i.e. removed] *to change*
the result".
While removing all E(i)'s s.t. i >= x of course changes the result to E(i-1).
Yes.
Correction: the last one should be E(x-1).
Post by Dan Christensen
Post by Julio Di Egidio
In either case, can you guess where dark numbers might pop out of?
Out of WM's ass?
Post by Julio Di Egidio
Or even
how is this at all related to the OP?
It has nothing to do with the OP, of course, but WM must keep his numbers up.
Indeed, as much as you are playing his game...
Post by Dan Christensen
Post by Julio Di Egidio
Post by Dan Christensen
Omitting only E(1) (if that is what you mean), the result is still...
∩{E(2), E(3), E(4), ...} = { }
since there is still no element common to each of the remaining E(i)'s.
Omitting all of E(i)'s, the result is still...
∩{ } = { }
What part don't you get, Mucke?
That's void of content. In this case you'd have to prove that there in no
E(i) such that /\{E(i+1),...} =/= {}: how would you actually prove it?
Suppose i in N.
Suppose x in N.
Case 1: x < i+1
x ~in E(i+1), so x is not common to all elements of {E(i+1),...}
Case 2: x >= i+1
E(x+1) in {E(i+1),...} and x ~in E(x+1), so x is not common to all elements
of {E(i+1),...}
Conclusion: No x in N is common to all elements of {E(i+1),...}, so /\{E(i+1),...} = { }
Conclusion: For all i in N, /\{E(i+1),...} = {}
So, by induction, no x in /\{E(1),...}, that is /\{E(1),...} = {}.

Then, a fortiori, no i s.t. /\( {E(1),...} \ {E(i)} ) =/= {}.

QED.

Julio
Eram semper recta
2020-04-11 14:27:11 UTC
Permalink
Post by Ganzhinterseher
Post by Dan Christensen
Post by Ganzhinterseher
Post by Ganzhinterseher
∩{E(x), E(x+1), E(x+2), ...} = { }
and
∩{ } = { }
First that is wrong in ZFC,
Nonsense, but irrelevant.
Post by Dan Christensen
Post by Ganzhinterseher
second ZFC claims that nonempty endsegments for
∩{E(x), E(x+1), E(x+2), ...} = { }
exist.
There is no element common to each of the sets E(x), E(x+1), E(x+2), .... So ∩{E(x), E(x+1), E(x+2), ...} = { }.
Nevertheless there must be a first endsegments E(x). But it cannot be defined.
I think they are working around the clock to cure this serious problem with set theory. You can expect a decision from Donald Trump very soon! Chuckle.
Post by Ganzhinterseher
Regards, WM
Ross A. Finlayson
2020-04-08 19:29:38 UTC
Permalink
Post by FromTheRafters
Post by David Petry
But what mathematicians have chosen to be the foundation of their own subject
(ie ZFC) is quite deficient as a foundation for AI, and the mathematicians
now seem to be very opposed to the idea of even considering alternate
foundations that might have great practical value.
What do you think is deficient about the current mathematics and why do
you think having a different choice as 'foundation' would help?
A spiral space-filling curve is a singularity for
singularity theory - other usual example are asymptotes.

ZF of course is quite perfectly regular under definition.

A usual addendum of "univalency" (a.k.a. domain principle)
sees a more "fundamental" framework (of some axiomless
system of natural deduction that's arrived at via for
example an axiomless system of natural deduction, and
all its usual inductive and deductive inferences).

This has questions of reference and self-reference
in front instead of on top (of the theory).

Line-drawing: now in remedial.


"Mechanized reasoning" isn't necessarily that complicated.
Ross Finlayson
2024-07-28 16:03:15 UTC
Permalink
Post by Ross A. Finlayson
Post by FromTheRafters
Post by David Petry
But what mathematicians have chosen to be the foundation of their own subject
(ie ZFC) is quite deficient as a foundation for AI, and the mathematicians
now seem to be very opposed to the idea of even considering alternate
foundations that might have great practical value.
What do you think is deficient about the current mathematics and why do
you think having a different choice as 'foundation' would help?
A spiral space-filling curve is a singularity for
singularity theory - other usual example are asymptotes.
ZF of course is quite perfectly regular under definition.
A usual addendum of "univalency" (a.k.a. domain principle)
sees a more "fundamental" framework (of some axiomless
system of natural deduction that's arrived at via for
example an axiomless system of natural deduction, and
all its usual inductive and deductive inferences).
This has questions of reference and self-reference
in front instead of on top (of the theory).
Line-drawing: now in remedial.
"Mechanized reasoning" isn't necessarily that complicated.
David Petry
2020-04-09 12:48:58 UTC
Permalink
Post by FromTheRafters
Post by David Petry
But what mathematicians have chosen to be the foundation of their own subject
(ie ZFC) is quite deficient as a foundation for AI, and the mathematicians
now seem to be very opposed to the idea of even considering alternate
foundations that might have great practical value.
What do you think is deficient about the current mathematics and why do
you think having a different choice as 'foundation' would help?
It's deficient as a foundation for artificial intelligence because an artificial intelligence would need to distinguish between reality and make believe, and that distinction cannot be made within ZFC.
Mostowski Collapse
2020-04-09 13:38:10 UTC
Permalink
Why can you not make this distinction in ZFC?
You could introduce a couple of modal operators:

reality(X): X is true in reality.
believe(A,X): X is believed by agent A.

Works fine for me. See also:

Multiagent Systems - 15. Logics for Multiagent System
B. Nebel, C. Becker-Asano, S. Wölfl
Albert-Ludwigs-Universität Freiburg - July 25, 2014
http://gki.informatik.uni-freiburg.de/teaching/ss14/multiagent-systems/mas15-handout4.pdf
Post by David Petry
It's deficient as a foundation for artificial intelligence because an artificial intelligence would need to distinguish between reality and make believe, and that distinction cannot be made within ZFC.
Mostowski Collapse
2020-04-09 13:43:37 UTC
Permalink
You could introduce reality as a seperate
agent R, then you only need

believe(A,X): X is believed by agent A.

In economics roughly this agent is sometimes
refered to as externality.

https://en.wikipedia.org/wiki/Externality

Now guess what the agent R believes.

LMAO!
Post by Mostowski Collapse
Why can you not make this distinction in ZFC?
reality(X): X is true in reality.
believe(A,X): X is believed by agent A.
Multiagent Systems - 15. Logics for Multiagent System
B. Nebel, C. Becker-Asano, S. Wölfl
Albert-Ludwigs-Universität Freiburg - July 25, 2014
http://gki.informatik.uni-freiburg.de/teaching/ss14/multiagent-systems/mas15-handout4.pdf
Post by David Petry
It's deficient as a foundation for artificial intelligence because an artificial intelligence would need to distinguish between reality and make believe, and that distinction cannot be made within ZFC.
Mostowski Collapse
2020-04-09 14:02:23 UTC
Permalink
You could then go on and modell
artificial intelligence and natural
stupidity, like for example:

believe(Boris, Dick_Not_Rotten => Super_Immune)

https://nymag.com/intelligencer/2019/12/boris-johnson-brexit.html
Post by Mostowski Collapse
You could introduce reality as a seperate
agent R, then you only need
believe(A,X): X is believed by agent A.
In economics roughly this agent is sometimes
refered to as externality.
https://en.wikipedia.org/wiki/Externality
Now guess what the agent R believes.
LMAO!
Post by Mostowski Collapse
Why can you not make this distinction in ZFC?
reality(X): X is true in reality.
believe(A,X): X is believed by agent A.
Multiagent Systems - 15. Logics for Multiagent System
B. Nebel, C. Becker-Asano, S. Wölfl
Albert-Ludwigs-Universität Freiburg - July 25, 2014
http://gki.informatik.uni-freiburg.de/teaching/ss14/multiagent-systems/mas15-handout4.pdf
Post by David Petry
It's deficient as a foundation for artificial intelligence because an artificial intelligence would need to distinguish between reality and make believe, and that distinction cannot be made within ZFC.
FromTheRafters
2020-04-10 09:02:54 UTC
Permalink
Post by David Petry
Post by FromTheRafters
Post by David Petry
But what mathematicians have chosen to be the foundation of their own
subject (ie ZFC) is quite deficient as a foundation for AI, and the
mathematicians now seem to be very opposed to the idea of even considering
alternate foundations that might have great practical value.
What do you think is deficient about the current mathematics and why do
you think having a different choice as 'foundation' would help?
It's deficient as a foundation for artificial intelligence because an
artificial intelligence would need to distinguish between reality and make
believe, and that distinction cannot be made within ZFC.
Why not let AI decide for itself whether or not it even needs a
foundation for the mathematics it 'knows' works, and what that
foundation would be? We have math. derived directly from our
observations and we 'desire' to have a foundation we all can agree on
for the sake of argument. Do you insist on a top down approach?
Sergio
2020-04-10 16:20:44 UTC
Permalink
Post by David Petry
Post by FromTheRafters
Post by David Petry
But what mathematicians have chosen to be the foundation of their own subject
(ie ZFC) is quite deficient as a foundation for AI, and the mathematicians
now seem to be very opposed to the idea of even considering alternate
foundations that might have great practical value.
What do you think is deficient about the current mathematics and why do
you think having a different choice as 'foundation' would help?
It's deficient as a foundation for artificial intelligence because an artificial intelligence would need to distinguish between reality and make believe, and that distinction cannot be made within ZFC.
artificial intelligence = *artificial* intelligence
Eram semper recta
2020-04-08 12:10:45 UTC
Permalink
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
What is the singularity you are talking about? None here are mind-readers. Chuckle, most of them can't even read!
Post by David Petry
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
Nope. That is not at all what happened. Too much to tell here, but your interpretation is wrong.
Post by David Petry
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
There are NO axioms in sound mathematics. I stop here.

<PLONK>
Post by David Petry
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
Julio Di Egidio
2020-04-08 13:01:33 UTC
Permalink
Post by David Petry
Since most of us are locked in our homes with little to do, this might be
a good time to have a discussion about the future.
There is no future with a basket of rotten apples.
Post by David Petry
The so called "singularity" is probably not far off, maybe just a few
decades.
We have never been farther from AI proper. It's just statistics all over
the place and the bullshit that goes with it: indeed, it's the triumph of
the lying with numbers.

<snipped the rest of the usual stupidities and lies: troll>

Julio
Julio Di Egidio
2020-04-08 17:58:04 UTC
Permalink
Post by Julio Di Egidio
Post by David Petry
Since most of us are locked in our homes with little to do, this might be
a good time to have a discussion about the future.
There is no future with a basket of rotten apples.
Post by David Petry
The so called "singularity" is probably not far off, maybe just a few
decades.
We have never been farther from AI proper. It's just statistics all over
the place and the bullshit that goes with it: indeed, it's the triumph of
the lying with numbers.
<snipped the rest of the usual stupidities and lies: troll>
In fact, if there is a singularity we are quickly approaching, that is the
average human being become *dumber than a toaster*.

How fucking pathetic...

(EOD.)

Julio
Eram semper recta
2020-04-09 15:14:27 UTC
Permalink
Post by Julio Di Egidio
Post by David Petry
Since most of us are locked in our homes with little to do, this might be
a good time to have a discussion about the future.
There is no future with a basket of rotten apples.
Post by David Petry
The so called "singularity" is probably not far off, maybe just a few
decades.
We have never been farther from AI proper. It's just statistics all over
the place and the bullshit that goes with it: indeed, it's the triumph of
the lying with numbers.
You got this one right!
Post by Julio Di Egidio
<snipped the rest of the usual stupidities and lies: troll>
Julio
Randy
2020-04-09 15:16:16 UTC
Permalink
Shut up idiot.
Julio Di Egidio
2020-04-10 00:46:36 UTC
Permalink
Post by Julio Di Egidio
Post by David Petry
The so called "singularity" is probably not far off, maybe just a few
decades.
We have never been farther from AI proper. It's just statistics all over
the place and the bullshit that goes with it: indeed, it's the triumph of
the lying with numbers.
"Exploring an intelligence beyond intellect":

Technologies of the Future, Sadhguru and Michio Kaku (2018)


Memory, Consciousness & Coma, Sadhguru at Harvard Medical School


Enjoy,

Julio
sobriquet
2020-04-09 13:34:54 UTC
Permalink
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.

It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.

I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.

So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
Ross A. Finlayson
2020-04-10 00:58:06 UTC
Permalink
Post by sobriquet
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.
It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.
I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.
So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
In "pure set theory" ZF's universe of sets is
just kind of a "model" of reality.

I.e. all the physical objects are mathematical objects
and also all their relations are physical and mathematical
objects, as are theirs "ad infinitum" (or, "to a singularity"),
a universe of mathematical objects. Then, where ZF's objects
are well-founded, but, this universe object _would be its own
powerset_, Cantor's "Paradox", gets into why regular ZF
is a fragment of ZF.

Otherwise "just the axioms about sets" and defining relation
(for example, functions), in sets, can for example use all
the axioms of the sets while for example not employing uncountability
for anything.

Or, for example, employing inequalities in uncountability quite regularly.

Because, for the finite case, those are just "score".

"AI" is really quite too general compared to "omniscience",
for example, where "AI" is "lowering the thermostat after
it gets warm". "Pervasive centralized distributed algorithms",
is, not "AI", it's a bee-hive. (AI: The Hive Mind.)

"Foundations in Mathematics" is for humans
and they really do include some excellent reasoners.

Mine these days, "Foundations in Mathematics", is, ..., mine.

Which I well expect could be the same for anybody.


(As it is.)

Maybe you should quit worrying about AI and learn mathematics.
Mostowski Collapse
2020-04-10 10:23:43 UTC
Permalink
No its not. ZFC is not a model of reality.
For example real numbers are not directly
represented, you need first to construct
them, also in ZFC. Whats wrong with you?

ZFC is just a framework to have extensional
concepts of type 1, type 2, type 3, etc...
or something that is even more monstrous
than Russell ranks. Example:

type 1: A set X
type 2: A set like funtion space f : X -> X,
its again a set, i.e. the set X^X
Etc..

then:

type 1: C : Coronainfected in USA
type 2: f : C -> C, daily increase
Post by Ross A. Finlayson
Post by sobriquet
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.
It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.
I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.
So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
In "pure set theory" ZF's universe of sets is
just kind of a "model" of reality.
I.e. all the physical objects are mathematical objects
and also all their relations are physical and mathematical
objects, as are theirs "ad infinitum" (or, "to a singularity"),
a universe of mathematical objects. Then, where ZF's objects
are well-founded, but, this universe object _would be its own
powerset_, Cantor's "Paradox", gets into why regular ZF
is a fragment of ZF.
Otherwise "just the axioms about sets" and defining relation
(for example, functions), in sets, can for example use all
the axioms of the sets while for example not employing uncountability
for anything.
Or, for example, employing inequalities in uncountability quite regularly.
Because, for the finite case, those are just "score".
"AI" is really quite too general compared to "omniscience",
for example, where "AI" is "lowering the thermostat after
it gets warm". "Pervasive centralized distributed algorithms",
is, not "AI", it's a bee-hive. (AI: The Hive Mind.)
"Foundations in Mathematics" is for humans
and they really do include some excellent reasoners.
Mine these days, "Foundations in Mathematics", is, ..., mine.
Which I well expect could be the same for anybody.
(As it is.)
Maybe you should quit worrying about AI and learn mathematics.
Mostowski Collapse
2020-04-10 10:25:56 UTC
Permalink
Corr.:

type 1: C : #of Coronainfected in USA at some day
type 2: f : C -> C, daily increase
Etc..
Post by Mostowski Collapse
No its not. ZFC is not a model of reality.
For example real numbers are not directly
represented, you need first to construct
them, also in ZFC. Whats wrong with you?
ZFC is just a framework to have extensional
concepts of type 1, type 2, type 3, etc...
or something that is even more monstrous
type 1: A set X
type 2: A set like funtion space f : X -> X,
its again a set, i.e. the set X^X
Etc..
type 1: C : Coronainfected in USA
type 2: f : C -> C, daily increase
Post by Ross A. Finlayson
Post by sobriquet
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.
It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.
I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.
So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
In "pure set theory" ZF's universe of sets is
just kind of a "model" of reality.
I.e. all the physical objects are mathematical objects
and also all their relations are physical and mathematical
objects, as are theirs "ad infinitum" (or, "to a singularity"),
a universe of mathematical objects. Then, where ZF's objects
are well-founded, but, this universe object _would be its own
powerset_, Cantor's "Paradox", gets into why regular ZF
is a fragment of ZF.
Otherwise "just the axioms about sets" and defining relation
(for example, functions), in sets, can for example use all
the axioms of the sets while for example not employing uncountability
for anything.
Or, for example, employing inequalities in uncountability quite regularly.
Because, for the finite case, those are just "score".
"AI" is really quite too general compared to "omniscience",
for example, where "AI" is "lowering the thermostat after
it gets warm". "Pervasive centralized distributed algorithms",
is, not "AI", it's a bee-hive. (AI: The Hive Mind.)
"Foundations in Mathematics" is for humans
and they really do include some excellent reasoners.
Mine these days, "Foundations in Mathematics", is, ..., mine.
Which I well expect could be the same for anybody.
(As it is.)
Maybe you should quit worrying about AI and learn mathematics.
Mostowski Collapse
2020-04-10 10:31:44 UTC
Permalink
Well this aint working as a good model,
you would need to make a SIR model or
something else to get a better model.

But pretty sure ZFC is postulating
some reality here. Unless you are that
much drunk, that you confuse frameworks

with what is built. Foundation with
the cathedral that sits on top. Wood
material with the kitchen furniture.

Etc..
Post by Mostowski Collapse
type 1: C : #of Coronainfected in USA at some day
type 2: f : C -> C, daily increase
Etc..
Post by Mostowski Collapse
No its not. ZFC is not a model of reality.
For example real numbers are not directly
represented, you need first to construct
them, also in ZFC. Whats wrong with you?
ZFC is just a framework to have extensional
concepts of type 1, type 2, type 3, etc...
or something that is even more monstrous
type 1: A set X
type 2: A set like funtion space f : X -> X,
its again a set, i.e. the set X^X
Etc..
type 1: C : Coronainfected in USA
type 2: f : C -> C, daily increase
Post by Ross A. Finlayson
Post by sobriquet
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.
It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.
I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.
So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
In "pure set theory" ZF's universe of sets is
just kind of a "model" of reality.
I.e. all the physical objects are mathematical objects
and also all their relations are physical and mathematical
objects, as are theirs "ad infinitum" (or, "to a singularity"),
a universe of mathematical objects. Then, where ZF's objects
are well-founded, but, this universe object _would be its own
powerset_, Cantor's "Paradox", gets into why regular ZF
is a fragment of ZF.
Otherwise "just the axioms about sets" and defining relation
(for example, functions), in sets, can for example use all
the axioms of the sets while for example not employing uncountability
for anything.
Or, for example, employing inequalities in uncountability quite regularly.
Because, for the finite case, those are just "score".
"AI" is really quite too general compared to "omniscience",
for example, where "AI" is "lowering the thermostat after
it gets warm". "Pervasive centralized distributed algorithms",
is, not "AI", it's a bee-hive. (AI: The Hive Mind.)
"Foundations in Mathematics" is for humans
and they really do include some excellent reasoners.
Mine these days, "Foundations in Mathematics", is, ..., mine.
Which I well expect could be the same for anybody.
(As it is.)
Maybe you should quit worrying about AI and learn mathematics.
Mostowski Collapse
2020-04-10 10:33:57 UTC
Permalink
Corr.:
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that

A theory of anything, is not really
a theory of something. Calling ZFC a model

of reality is pretty crank.
Post by Mostowski Collapse
Well this aint working as a good model,
you would need to make a SIR model or
something else to get a better model.
But pretty sure ZFC is postulating
some reality here. Unless you are that
much drunk, that you confuse frameworks
with what is built. Foundation with
the cathedral that sits on top. Wood
material with the kitchen furniture.
Etc..
Post by Mostowski Collapse
type 1: C : #of Coronainfected in USA at some day
type 2: f : C -> C, daily increase
Etc..
Post by Mostowski Collapse
No its not. ZFC is not a model of reality.
For example real numbers are not directly
represented, you need first to construct
them, also in ZFC. Whats wrong with you?
ZFC is just a framework to have extensional
concepts of type 1, type 2, type 3, etc...
or something that is even more monstrous
type 1: A set X
type 2: A set like funtion space f : X -> X,
its again a set, i.e. the set X^X
Etc..
type 1: C : Coronainfected in USA
type 2: f : C -> C, daily increase
Post by Ross A. Finlayson
Post by sobriquet
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.
It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.
I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.
So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
In "pure set theory" ZF's universe of sets is
just kind of a "model" of reality.
I.e. all the physical objects are mathematical objects
and also all their relations are physical and mathematical
objects, as are theirs "ad infinitum" (or, "to a singularity"),
a universe of mathematical objects. Then, where ZF's objects
are well-founded, but, this universe object _would be its own
powerset_, Cantor's "Paradox", gets into why regular ZF
is a fragment of ZF.
Otherwise "just the axioms about sets" and defining relation
(for example, functions), in sets, can for example use all
the axioms of the sets while for example not employing uncountability
for anything.
Or, for example, employing inequalities in uncountability quite regularly.
Because, for the finite case, those are just "score".
"AI" is really quite too general compared to "omniscience",
for example, where "AI" is "lowering the thermostat after
it gets warm". "Pervasive centralized distributed algorithms",
is, not "AI", it's a bee-hive. (AI: The Hive Mind.)
"Foundations in Mathematics" is for humans
and they really do include some excellent reasoners.
Mine these days, "Foundations in Mathematics", is, ..., mine.
Which I well expect could be the same for anybody.
(As it is.)
Maybe you should quit worrying about AI and learn mathematics.
Ross A. Finlayson
2020-04-10 15:51:26 UTC
Permalink
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
of reality is pretty crank.
Post by Mostowski Collapse
Well this aint working as a good model,
you would need to make a SIR model or
something else to get a better model.
But pretty sure ZFC is postulating
some reality here. Unless you are that
much drunk, that you confuse frameworks
with what is built. Foundation with
the cathedral that sits on top. Wood
material with the kitchen furniture.
Etc..
Post by Mostowski Collapse
type 1: C : #of Coronainfected in USA at some day
type 2: f : C -> C, daily increase
Etc..
Post by Mostowski Collapse
No its not. ZFC is not a model of reality.
For example real numbers are not directly
represented, you need first to construct
them, also in ZFC. Whats wrong with you?
ZFC is just a framework to have extensional
concepts of type 1, type 2, type 3, etc...
or something that is even more monstrous
type 1: A set X
type 2: A set like funtion space f : X -> X,
its again a set, i.e. the set X^X
Etc..
type 1: C : Coronainfected in USA
type 2: f : C -> C, daily increase
Post by Ross A. Finlayson
Post by sobriquet
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.
It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.
I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.
So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
In "pure set theory" ZF's universe of sets is
just kind of a "model" of reality.
I.e. all the physical objects are mathematical objects
and also all their relations are physical and mathematical
objects, as are theirs "ad infinitum" (or, "to a singularity"),
a universe of mathematical objects. Then, where ZF's objects
are well-founded, but, this universe object _would be its own
powerset_, Cantor's "Paradox", gets into why regular ZF
is a fragment of ZF.
Otherwise "just the axioms about sets" and defining relation
(for example, functions), in sets, can for example use all
the axioms of the sets while for example not employing uncountability
for anything.
Or, for example, employing inequalities in uncountability quite regularly.
Because, for the finite case, those are just "score".
"AI" is really quite too general compared to "omniscience",
for example, where "AI" is "lowering the thermostat after
it gets warm". "Pervasive centralized distributed algorithms",
is, not "AI", it's a bee-hive. (AI: The Hive Mind.)
"Foundations in Mathematics" is for humans
and they really do include some excellent reasoners.
Mine these days, "Foundations in Mathematics", is, ..., mine.
Which I well expect could be the same for anybody.
(As it is.)
Maybe you should quit worrying about AI and learn mathematics.
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.

Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.

"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.

I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.

Results in theorem proving?
Mostowski Collapse
2020-04-10 17:06:12 UTC
Permalink
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.

LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
Mostowski Collapse
2020-04-10 17:12:42 UTC
Permalink
Which model of ZF do you want to "make"
a reality? Gödels L? von Neumanns V?

And whats real about it? Does the ordinal
3 have a distinct smell from ordinal 4?

LMAO!
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
Mostowski Collapse
2020-04-10 17:55:39 UTC
Permalink
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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
Mitch Raemsch
2020-04-10 17:58:55 UTC
Permalink
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
Point particles are sub finite or unlimited small.
Sergio
2020-04-10 18:13:05 UTC
Permalink
Post by Mitch Raemsch
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
Point particles are sub finite or unlimited small.
show me your point particle....
Mitch Raemsch
2020-04-10 18:20:25 UTC
Permalink
Post by Sergio
Post by Mitch Raemsch
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
Point particles are sub finite or unlimited small.
show me your point particle....
It is an aether energy point...
Look at the unlimited small...
It has its own God creating quantum gravity
it is a fundamental mathematical point
as is the BH singluarity's sameness...

Mitchell Raemsch
Ganzhinterseher
2020-04-10 19:03:47 UTC
Permalink
Post by Mitch Raemsch
Look at the unlimited small...
There is no unlimited small. The smallest possibe is the wavelength of a photon containing the enery of the whole universe.

Regards, WM
Sergio
2020-04-10 19:40:22 UTC
Permalink
Post by Ganzhinterseher
Post by Mitch Raemsch
Look at the unlimited small...
There is no unlimited small. The smallest possibe is the wavelength of a photon containing the enery of the whole universe.
Regards, WM
why a photon ? why not a coconut ?
Mitch Raemsch
2020-04-10 22:30:13 UTC
Permalink
Post by Sergio
Post by Ganzhinterseher
Post by Mitch Raemsch
Look at the unlimited small...
There is no unlimited small. The smallest possibe is the wavelength of a photon containing the enery of the whole universe.
Sure there is. It is the first quantity after zero math...
Post by Sergio
Post by Ganzhinterseher
Regards, WM
why a photon ? why not a coconut ?
Light is a wave.
Waves absorbs particles can't.
Ganzhinterseher
2020-04-11 12:58:36 UTC
Permalink
Post by Sergio
Post by Ganzhinterseher
Post by Mitch Raemsch
Look at the unlimited small...
There is no unlimited small. The smallest possibe is the wavelength of a photon containing the enery of the whole universe.
why a photon ?
Light is use to measure distances.
Post by Sergio
why not a coconut ?
If you like. But can a coconut contain all eneregy of the universe?

Regards, WM
Mitch Raemsch
2020-04-10 22:32:30 UTC
Permalink
Post by Ganzhinterseher
Post by Mitch Raemsch
Look at the unlimited small...
There is no unlimited small. The smallest possibe is the wavelength of a photon containing the enery of the whole universe.
Regards, WM
A photon is a point particle unlimited small...
how is it absorbed?
No. Only the light wave is real.

Mitchell Raemsch
Ross A. Finlayson
2020-04-10 22:11:31 UTC
Permalink
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
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.

The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.

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.

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.

Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".

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).

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).

I.e., ZF to be accepted _does_ have "truly infinite" things.
Mostowski Collapse
2020-04-11 08:18:01 UTC
Permalink
I have never heard or seen written
somebody about "pure" sets.

I guess this is pure nonsense. Also
"machanical" structure,

is utter gibberish.
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
Mostowski Collapse
2020-04-11 08:24:41 UTC
Permalink
Adding too much verbs to a sentence
doesn't improve your gibberish either.

"powerset is order type is successor"

WTF? Why not:

"then powerset in order type for successor"

Or why not:

"for powerset is quite order type _does_ have successor"

Its all similarly incomprehensible.
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
I guess this is pure nonsense. Also
"machanical" structure,
is utter gibberish.
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
Mostowski Collapse
2020-04-11 08:42:41 UTC
Permalink
And no, you dont need extra-ZF to show
for example this here:

P(V) = V

You can show it inside ZF, just note that
you need to use classes:

V is a class, not a set
P(_) need then to be a class operator

Classes emerge by this simple FOL syntactic
sugar rule for the class builder, for A
some formula:

x e { y | A(y) } <=> A(x)

Since the e is ovderloaded in the above,
it is the e with as class argument, you
might even go that far

and claim you don't need any set theory
at all for classes. Sets and classes are
then linked by a transfer theorem:

{ y | y e x } = x
Post by Mostowski Collapse
Adding too much verbs to a sentence
doesn't improve your gibberish either.
"powerset is order type is successor"
"then powerset in order type for successor"
"for powerset is quite order type _does_ have successor"
Its all similarly incomprehensible.
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
I guess this is pure nonsense. Also
"machanical" structure,
is utter gibberish.
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
Mostowski Collapse
2020-04-11 08:57:16 UTC
Permalink
An extra-ZF is for example ZFC, this
is ZF with the axiom of choice. The axiom
of choice talks about the set relation

e and not the class relation e. It has the
effect that in a model of ZFC more sets
certainly exist, than in a model of ZF.

They might also exist in a model of ZF,
but since the axiom of choice is missing,
its not mandatory. You can think of it:

ZF

+-----+---+---------+
| Set | ? | |
+-----+---+---------+

ZFC

+---------+----------+
| Set | |
+---------+----------+

But I currently don't know how
to relate this to classes. Axiom
of choice is not a class builder

shaped axiom. Many axioms of ZF
are just class builder shaped axiom,
that simply say a certain class

is also a set.
Post by Mostowski Collapse
And no, you dont need extra-ZF to show
P(V) = V
You can show it inside ZF, just note that
V is a class, not a set
P(_) need then to be a class operator
Classes emerge by this simple FOL syntactic
sugar rule for the class builder, for A
x e { y | A(y) } <=> A(x)
Since the e is ovderloaded in the above,
it is the e with as class argument, you
might even go that far
and claim you don't need any set theory
at all for classes. Sets and classes are
{ y | y e x } = x
Post by Mostowski Collapse
Adding too much verbs to a sentence
doesn't improve your gibberish either.
"powerset is order type is successor"
"then powerset in order type for successor"
"for powerset is quite order type _does_ have successor"
Its all similarly incomprehensible.
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
I guess this is pure nonsense. Also
"machanical" structure,
is utter gibberish.
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
Ross A. Finlayson
2020-04-12 04:23:37 UTC
Permalink
Post by Mostowski Collapse
And no, you dont need extra-ZF to show
P(V) = V
You can show it inside ZF, just note that
V is a class, not a set
P(_) need then to be a class operator
Classes emerge by this simple FOL syntactic
sugar rule for the class builder, for A
x e { y | A(y) } <=> A(x)
Since the e is ovderloaded in the above,
it is the e with as class argument, you
might even go that far
and claim you don't need any set theory
at all for classes. Sets and classes are
{ y | y e x } = x
Post by Mostowski Collapse
Adding too much verbs to a sentence
doesn't improve your gibberish either.
"powerset is order type is successor"
"then powerset in order type for successor"
"for powerset is quite order type _does_ have successor"
Its all similarly incomprehensible.
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
I guess this is pure nonsense. Also
"machanical" structure,
is utter gibberish.
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
It's so, classes over sets and class-set distinction
makes for comprehension, but both are defined by their
elements (in their structure that their model must have).

It's not, "anti-foundational", extra-ZF, introducing classes,
but is it not? Otherwise there exist the sets so much
larger as like "the equivalence class of finite-automata
of a certain size", to be "foundational" and reflect in
their model the structure, going to classes left off this
required fact in the model and its structure, about
that introducing classes, to set theory, IS, extra-ZF.
Ross A. Finlayson
2020-04-12 04:50:19 UTC
Permalink
Post by Ross A. Finlayson
Post by Mostowski Collapse
And no, you dont need extra-ZF to show
P(V) = V
You can show it inside ZF, just note that
V is a class, not a set
P(_) need then to be a class operator
Classes emerge by this simple FOL syntactic
sugar rule for the class builder, for A
x e { y | A(y) } <=> A(x)
Since the e is ovderloaded in the above,
it is the e with as class argument, you
might even go that far
and claim you don't need any set theory
at all for classes. Sets and classes are
{ y | y e x } = x
Post by Mostowski Collapse
Adding too much verbs to a sentence
doesn't improve your gibberish either.
"powerset is order type is successor"
"then powerset in order type for successor"
"for powerset is quite order type _does_ have successor"
Its all similarly incomprehensible.
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
I guess this is pure nonsense. Also
"machanical" structure,
is utter gibberish.
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
It's so, classes over sets and class-set distinction
makes for comprehension, but both are defined by their
elements (in their structure that their model must have).
It's not, "anti-foundational", extra-ZF, introducing classes,
but is it not? Otherwise there exist the sets so much
larger as like "the equivalence class of finite-automata
of a certain size", to be "foundational" and reflect in
their model the structure, going to classes left off this
required fact in the model and its structure, about
that introducing classes, to set theory, IS, extra-ZF.
https://groups.google.com/forum/#!topicsearchin/sci.math/powerset$20AND$20order$20AND$20type$20AND$20successor$20AND$20authorname$3AFinlayson

Hundred results?


An idiomatic response when asked a question without an answer: "Search, me."

"One way to look at the powerset result is that with a different
definition of ordinal, than the standard von Neumann construction, that
the powerset is order type is successor. Then, in terms of a universal
set or maximal ordinal, as are tossed about in various discussions,
that gets into the natural numbers being the continuum and universe and
basically sufficient for their purpose as there are in that sense thus
completed infinities, in that way."

2006?

"Platonism seems worthwhile.

There's only one theory with no axioms. Nothing, zero, is obvious,
then nothing or not nothing, or not, ad infinitum, with ubiquitous
ordinals, and powerset as order type as successor, with binary
representation being more than a number."

2006.


When I use words I wonder that you would
have the same terms in different words,
(in the same language), besides,
keeping them, for finding them.

This way when we talk about "set" or "class",
they are definitely the same thing.


That is: when we talk about Cantor space it's 2^w.


The language of words of 2^w is all the different
infinite words of 0's and 1's, zeroes and ones.

Half of them have equal 0-1 density. <-- Finlayson

Here it's the "them" that needs about twenty words:
to make clear that of all the 0's and 1's, thus that
there exists _any_ string of 0's and 1's "in a row",
all the 0's and 1', that half of those, 1/2, result
from that there are "columns", that might as well be "rows".

I.e., to write a theorem about why there can be
a countable continuity when the reals of the
complete ordered field is countable, one of
those things is "half of them have equal 0-1 density".

I call this "Borel vs. combinatorics",
now also "Banach vs. combinatorics".

2003
Mostowski Collapse
2020-04-12 08:58:33 UTC
Permalink
Trump the Stump and Ross the Floss, what
do the have in common?

If they open their mouth, its just
clown gibberish.

LoL
Post by Ross A. Finlayson
Post by Ross A. Finlayson
Post by Mostowski Collapse
And no, you dont need extra-ZF to show
P(V) = V
You can show it inside ZF, just note that
V is a class, not a set
P(_) need then to be a class operator
Classes emerge by this simple FOL syntactic
sugar rule for the class builder, for A
x e { y | A(y) } <=> A(x)
Since the e is ovderloaded in the above,
it is the e with as class argument, you
might even go that far
and claim you don't need any set theory
at all for classes. Sets and classes are
{ y | y e x } = x
Post by Mostowski Collapse
Adding too much verbs to a sentence
doesn't improve your gibberish either.
"powerset is order type is successor"
"then powerset in order type for successor"
"for powerset is quite order type _does_ have successor"
Its all similarly incomprehensible.
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
I guess this is pure nonsense. Also
"machanical" structure,
is utter gibberish.
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
It's so, classes over sets and class-set distinction
makes for comprehension, but both are defined by their
elements (in their structure that their model must have).
It's not, "anti-foundational", extra-ZF, introducing classes,
but is it not? Otherwise there exist the sets so much
larger as like "the equivalence class of finite-automata
of a certain size", to be "foundational" and reflect in
their model the structure, going to classes left off this
required fact in the model and its structure, about
that introducing classes, to set theory, IS, extra-ZF.
https://groups.google.com/forum/#!topicsearchin/sci.math/powerset$20AND$20order$20AND$20type$20AND$20successor$20AND$20authorname$3AFinlayson
Hundred results?
An idiomatic response when asked a question without an answer: "Search, me."
"One way to look at the powerset result is that with a different
definition of ordinal, than the standard von Neumann construction, that
the powerset is order type is successor. Then, in terms of a universal
set or maximal ordinal, as are tossed about in various discussions,
that gets into the natural numbers being the continuum and universe and
basically sufficient for their purpose as there are in that sense thus
completed infinities, in that way."
2006?
"Platonism seems worthwhile.
There's only one theory with no axioms. Nothing, zero, is obvious,
then nothing or not nothing, or not, ad infinitum, with ubiquitous
ordinals, and powerset as order type as successor, with binary
representation being more than a number."
2006.
When I use words I wonder that you would
have the same terms in different words,
(in the same language), besides,
keeping them, for finding them.
This way when we talk about "set" or "class",
they are definitely the same thing.
That is: when we talk about Cantor space it's 2^w.
The language of words of 2^w is all the different
infinite words of 0's and 1's, zeroes and ones.
Half of them have equal 0-1 density. <-- Finlayson
to make clear that of all the 0's and 1's, thus that
there exists _any_ string of 0's and 1's "in a row",
all the 0's and 1', that half of those, 1/2, result
from that there are "columns", that might as well be "rows".
I.e., to write a theorem about why there can be
a countable continuity when the reals of the
complete ordered field is countable, one of
those things is "half of them have equal 0-1 density".
I call this "Borel vs. combinatorics",
now also "Banach vs. combinatorics".
2003
Ross A. Finlayson
2020-04-12 17:49:26 UTC
Permalink
Post by Mostowski Collapse
Trump the Stump and Ross the Floss, what
do the have in common?
If they open their mouth, its just
clown gibberish.
LoL
Post by Ross A. Finlayson
Post by Ross A. Finlayson
Post by Mostowski Collapse
And no, you dont need extra-ZF to show
P(V) = V
You can show it inside ZF, just note that
V is a class, not a set
P(_) need then to be a class operator
Classes emerge by this simple FOL syntactic
sugar rule for the class builder, for A
x e { y | A(y) } <=> A(x)
Since the e is ovderloaded in the above,
it is the e with as class argument, you
might even go that far
and claim you don't need any set theory
at all for classes. Sets and classes are
{ y | y e x } = x
Post by Mostowski Collapse
Adding too much verbs to a sentence
doesn't improve your gibberish either.
"powerset is order type is successor"
"then powerset in order type for successor"
"for powerset is quite order type _does_ have successor"
Its all similarly incomprehensible.
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
I guess this is pure nonsense. Also
"machanical" structure,
is utter gibberish.
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
It's so, classes over sets and class-set distinction
makes for comprehension, but both are defined by their
elements (in their structure that their model must have).
It's not, "anti-foundational", extra-ZF, introducing classes,
but is it not? Otherwise there exist the sets so much
larger as like "the equivalence class of finite-automata
of a certain size", to be "foundational" and reflect in
their model the structure, going to classes left off this
required fact in the model and its structure, about
that introducing classes, to set theory, IS, extra-ZF.
https://groups.google.com/forum/#!topicsearchin/sci.math/powerset$20AND$20order$20AND$20type$20AND$20successor$20AND$20authorname$3AFinlayson
Hundred results?
An idiomatic response when asked a question without an answer: "Search, me."
"One way to look at the powerset result is that with a different
definition of ordinal, than the standard von Neumann construction, that
the powerset is order type is successor. Then, in terms of a universal
set or maximal ordinal, as are tossed about in various discussions,
that gets into the natural numbers being the continuum and universe and
basically sufficient for their purpose as there are in that sense thus
completed infinities, in that way."
2006?
"Platonism seems worthwhile.
There's only one theory with no axioms. Nothing, zero, is obvious,
then nothing or not nothing, or not, ad infinitum, with ubiquitous
ordinals, and powerset as order type as successor, with binary
representation being more than a number."
2006.
When I use words I wonder that you would
have the same terms in different words,
(in the same language), besides,
keeping them, for finding them.
This way when we talk about "set" or "class",
they are definitely the same thing.
That is: when we talk about Cantor space it's 2^w.
The language of words of 2^w is all the different
infinite words of 0's and 1's, zeroes and ones.
Half of them have equal 0-1 density. <-- Finlayson
to make clear that of all the 0's and 1's, thus that
there exists _any_ string of 0's and 1's "in a row",
all the 0's and 1', that half of those, 1/2, result
from that there are "columns", that might as well be "rows".
I.e., to write a theorem about why there can be
a countable continuity when the reals of the
complete ordered field is countable, one of
those things is "half of them have equal 0-1 density".
I call this "Borel vs. combinatorics",
now also "Banach vs. combinatorics".
2003
I invented an "natural/unit equivalency function"
long before I heard of: trans-finite cardinals.

Understanding that the major result of trans-finite
cardinals result from there not being an "natural/
unit equivalency function" between the natural integers
and [0,1], so I went about understanding how they are.

So, with f(0) = 0 and f(oo) = 1, that looks like a rising
line of some constant rise, here that it's an "infinitesimal
constant rise", between 0 and 1, that f(0) = 0 and f(oo) = 1.
Then it would look like a triangle, or f(x) = x from zero to one,
one notes that has area 1/2, half of the area of the unit square.

But, the point of the equivalency function I found was that
the area under this function, is 1, not 1/2.

"The integral of this discrete function only defined on
all the integers a) exists and b) equals one, not one half." <-- Finlayson


(Burse: "clown gibberish".)


What this means for singularity theory is that the theoretical
study resulted in a notion of a spiral space-filling curve (from
the origin), that is a _singularity_ in the mathematical singularity
theory from mathematical physics. The "Kurzweil singularity"
(or "doomsday theory") here then is a usual modeling of
asymptotes about usual expected things in, for example,
supply-and-demand, for example if sand turned to gold
and everybody on Earth was suddenly rich.

For this singularity theory it's a mathematical foundations.
Ross A. Finlayson
2020-04-12 04:19:36 UTC
Permalink
Post by Mostowski Collapse
Adding too much verbs to a sentence
doesn't improve your gibberish either.
"powerset is order type is successor"
"then powerset in order type for successor"
"for powerset is quite order type _does_ have successor"
Its all similarly incomprehensible.
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
I guess this is pure nonsense. Also
"machanical" structure,
is utter gibberish.
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
Actually, that's the point, it's just: "is".

Mach principle is more than one thing.

Point, local, global, total: Mach principle.

Zero is _not_ infinity.
FredJeffries
2020-04-11 16:00:55 UTC
Permalink
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
https://en.wikipedia.org/wiki/Hereditary_set

https://ncatlab.org/nlab/show/pure+set

https://www.google.com/search?q=pure+set
Mostowski Collapse
2020-04-11 16:17:56 UTC
Permalink
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no

Ross Finlayson halucinated:
"The "Pure" part of (ZF) set theory"

Thats like WM saying there are dark
numbers. LMAO!
Post by FredJeffries
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
https://en.wikipedia.org/wiki/Hereditary_set
https://ncatlab.org/nlab/show/pure+set
https://www.google.com/search?q=pure+set
Mostowski Collapse
2020-04-11 16:19:36 UTC
Permalink
And then WM calling out to look
at the light numbers only. LoL
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Thats like WM saying there are dark
numbers. LMAO!
Post by FredJeffries
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
https://en.wikipedia.org/wiki/Hereditary_set
https://ncatlab.org/nlab/show/pure+set
https://www.google.com/search?q=pure+set
Mostowski Collapse
2020-04-11 16:28:40 UTC
Permalink
If you want impure sets, just use ZFU
or ZFCU, still no model of reality.
I guess the problem is rather the

meaning of the word universe of discourse
in logic,and a leaning towards a confusion
that universe implies something like

a physical or mechanically universe.
Post by Mostowski Collapse
And then WM calling out to look
at the light numbers only. LoL
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Thats like WM saying there are dark
numbers. LMAO!
Post by FredJeffries
Post by Mostowski Collapse
I have never heard or seen written
somebody about "pure" sets.
https://en.wikipedia.org/wiki/Hereditary_set
https://ncatlab.org/nlab/show/pure+set
https://www.google.com/search?q=pure+set
FredJeffries
2020-04-11 16:31:40 UTC
Permalink
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Because of your rude habit of top posting, it is impossible for anyone to know the referent of your inane comments.
Mostowski Collapse
2020-04-11 16:36:45 UTC
Permalink
Seems you are stupid.
Post by FredJeffries
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Because of your rude habit of top posting, it is impossible for anyone to know the referent of your inane comments.
Mostowski Collapse
2020-04-11 16:38:19 UTC
Permalink
Stupid to the extend that you don't
understand the typography of quoting?

Right?
Post by Mostowski Collapse
Seems you are stupid.
Post by FredJeffries
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Because of your rude habit of top posting, it is impossible for anyone to know the referent of your inane comments.
Mostowski Collapse
2020-04-11 16:48:16 UTC
Permalink
The full quote, not using short " " for quote
Post by Ross A. Finlayson
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.
https://groups.google.com/d/msg/sci.math/RvV4IVTsOoM/521YLeorCgAJ

Still the above phrase by Ross Finlayson
is hardly comprehensible. Even if "pure" has
some legitimate use elsewhere. Its still
doesn't make so much sense? What does

Ross Finlayson say? That we should elevate
universes of discourse to realities? And
why is this stance an integral two part
thing of set theory? Mostlikely most

mathematicians will be careful enough to
not conflate reality with universes of
discourse.
Post by Ross A. Finlayson
Stupid to the extend that you don't
understand the typography of quoting?
Right?
Post by Mostowski Collapse
Seems you are stupid.
Post by FredJeffries
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Because of your rude habit of top posting, it is impossible for anyone to know the referent of your inane comments.
Mostowski Collapse
2020-04-11 16:57:36 UTC
Permalink
Since there exists model theory, and
in model theory a model and an universe of
discourse is kind of synonymous,

aready this here "a model of a universe of ZF
set theory." in Ross Finlayson quote makes
no sense. A model of ZF is an universe of

discourse of this signature:

<V, e>

V : The universe of sets, the "things"
in the universe

e : A relation between two "things"
of the universe.

What "a model **of** an universe" should be
I don't know. Really, I have no clue.
Post by Mostowski Collapse
The full quote, not using short " " for quote
Post by Ross A. Finlayson
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.
https://groups.google.com/d/msg/sci.math/RvV4IVTsOoM/521YLeorCgAJ
Still the above phrase by Ross Finlayson
is hardly comprehensible. Even if "pure" has
some legitimate use elsewhere. Its still
doesn't make so much sense? What does
Ross Finlayson say? That we should elevate
universes of discourse to realities? And
why is this stance an integral two part
thing of set theory? Mostlikely most
mathematicians will be careful enough to
not conflate reality with universes of
discourse.
Post by Ross A. Finlayson
Stupid to the extend that you don't
understand the typography of quoting?
Right?
Post by Mostowski Collapse
Seems you are stupid.
Post by FredJeffries
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Because of your rude habit of top posting, it is impossible for anyone to know the referent of your inane comments.
Mostowski Collapse
2020-04-11 17:18:19 UTC
Permalink
Somehow I have the feeling that Ross
Finlayson uses "pure" in another sense
than what FredJeffries was digging

from the internet. Because impure
theories like ZFU or ZFCU also have
models. You just get a wider bottom:

ZF(C):

\ /
\ /
\/
{}

https://imgbin.com/png/USvuEyJk/von-neumann-universe-set-theory-axiom-png

ZF(C)U:


\ /
\ /
\___/
U
Post by Mostowski Collapse
Since there exists model theory, and
in model theory a model and an universe of
discourse is kind of synonymous,
aready this here "a model of a universe of ZF
set theory." in Ross Finlayson quote makes
no sense. A model of ZF is an universe of
<V, e>
V : The universe of sets, the "things"
in the universe
e : A relation between two "things"
of the universe.
What "a model **of** an universe" should be
I don't know. Really, I have no clue.
Post by Mostowski Collapse
The full quote, not using short " " for quote
Post by Ross A. Finlayson
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.
https://groups.google.com/d/msg/sci.math/RvV4IVTsOoM/521YLeorCgAJ
Still the above phrase by Ross Finlayson
is hardly comprehensible. Even if "pure" has
some legitimate use elsewhere. Its still
doesn't make so much sense? What does
Ross Finlayson say? That we should elevate
universes of discourse to realities? And
why is this stance an integral two part
thing of set theory? Mostlikely most
mathematicians will be careful enough to
not conflate reality with universes of
discourse.
Post by Ross A. Finlayson
Stupid to the extend that you don't
understand the typography of quoting?
Right?
Post by Mostowski Collapse
Seems you are stupid.
Post by FredJeffries
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Because of your rude habit of top posting, it is impossible for anyone to know the referent of your inane comments.
Mostowski Collapse
2020-04-12 21:05:02 UTC
Permalink
The problem with Ross the Floss equality
ZF model = reality, is as follows. To use
ZF to model physics or something,

you need to make definitions, and circle
outs certain sets which make up your model.
So inside the whole ZF universe/model,

you have to identify a submodel. You
can think of a submodel 1 having light
velocity c1, and submodel 2 having light

velocity c2, so basically what happens with
a ZF universe/model:

ZF(C):

\ /
\ /
\ /
\ /
\/
{}

Your physics is just some subset:

ZF(C) and physics X: (one pocket)

\ /
\ ()/ <-- Your physic X
\ /
\ /
\/
{}

Or if you have alternative physics X and physics
Y, they might still fit into the same ZF univers/model,
just occupying different subsets:

ZF(C), physics X and physics Y: (two pockets)

\ /
\ ()/ <-- physic X
physic Y ->\() /
\ /
\/
{}

Etc..

Such a multiverse model that embraces multiple physics
seems be the current model of reality anyway. Some
of the driving forces are string theory, dark matter

and eternal inflation. See also:

{DOKU} UNIVERSUM oder MULTIVERSUM !HD!

Post by Mostowski Collapse
Somehow I have the feeling that Ross
Finlayson uses "pure" in another sense
than what FredJeffries was digging
from the internet. Because impure
theories like ZFU or ZFCU also have
\ /
\ /
\/
{}
https://imgbin.com/png/USvuEyJk/von-neumann-universe-set-theory-axiom-png
\ /
\ /
\___/
U
Post by Mostowski Collapse
Since there exists model theory, and
in model theory a model and an universe of
discourse is kind of synonymous,
aready this here "a model of a universe of ZF
set theory." in Ross Finlayson quote makes
no sense. A model of ZF is an universe of
<V, e>
V : The universe of sets, the "things"
in the universe
e : A relation between two "things"
of the universe.
What "a model **of** an universe" should be
I don't know. Really, I have no clue.
Post by Mostowski Collapse
The full quote, not using short " " for quote
Post by Ross A. Finlayson
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.
https://groups.google.com/d/msg/sci.math/RvV4IVTsOoM/521YLeorCgAJ
Still the above phrase by Ross Finlayson
is hardly comprehensible. Even if "pure" has
some legitimate use elsewhere. Its still
doesn't make so much sense? What does
Ross Finlayson say? That we should elevate
universes of discourse to realities? And
why is this stance an integral two part
thing of set theory? Mostlikely most
mathematicians will be careful enough to
not conflate reality with universes of
discourse.
Post by Ross A. Finlayson
Stupid to the extend that you don't
understand the typography of quoting?
Right?
Post by Mostowski Collapse
Seems you are stupid.
Post by FredJeffries
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Because of your rude habit of top posting, it is impossible for anyone to know the referent of your inane comments.
Ross A. Finlayson
2020-04-12 21:52:51 UTC
Permalink
Post by Mostowski Collapse
The problem with Ross the Floss equality
ZF model = reality, is as follows. To use
ZF to model physics or something,
you need to make definitions, and circle
outs certain sets which make up your model.
So inside the whole ZF universe/model,
you have to identify a submodel. You
can think of a submodel 1 having light
velocity c1, and submodel 2 having light
velocity c2, so basically what happens with
\ /
\ /
\ /
\ /
\/
{}
ZF(C) and physics X: (one pocket)
\ /
\ ()/ <-- Your physic X
\ /
\ /
\/
{}
Or if you have alternative physics X and physics
Y, they might still fit into the same ZF univers/model,
ZF(C), physics X and physics Y: (two pockets)
\ /
\ ()/ <-- physic X
physic Y ->\() /
\ /
\/
{}
Etc..
Such a multiverse model that embraces multiple physics
seems be the current model of reality anyway. Some
of the driving forces are string theory, dark matter
{DOKU} UNIVERSUM oder MULTIVERSUM !HD!
http://youtu.be/rohACRRTP8w
Post by Mostowski Collapse
Somehow I have the feeling that Ross
Finlayson uses "pure" in another sense
than what FredJeffries was digging
from the internet. Because impure
theories like ZFU or ZFCU also have
\ /
\ /
\/
{}
https://imgbin.com/png/USvuEyJk/von-neumann-universe-set-theory-axiom-png
\ /
\ /
\___/
U
Post by Mostowski Collapse
Since there exists model theory, and
in model theory a model and an universe of
discourse is kind of synonymous,
aready this here "a model of a universe of ZF
set theory." in Ross Finlayson quote makes
no sense. A model of ZF is an universe of
<V, e>
V : The universe of sets, the "things"
in the universe
e : A relation between two "things"
of the universe.
What "a model **of** an universe" should be
I don't know. Really, I have no clue.
Post by Mostowski Collapse
The full quote, not using short " " for quote
Post by Ross A. Finlayson
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.
https://groups.google.com/d/msg/sci.math/RvV4IVTsOoM/521YLeorCgAJ
Still the above phrase by Ross Finlayson
is hardly comprehensible. Even if "pure" has
some legitimate use elsewhere. Its still
doesn't make so much sense? What does
Ross Finlayson say? That we should elevate
universes of discourse to realities? And
why is this stance an integral two part
thing of set theory? Mostlikely most
mathematicians will be careful enough to
not conflate reality with universes of
discourse.
Post by Ross A. Finlayson
Stupid to the extend that you don't
understand the typography of quoting?
Right?
Post by Mostowski Collapse
Seems you are stupid.
Post by FredJeffries
Post by Mostowski Collapse
In ZF there is only one sort, so
pure ZF is a pleonasm. There is no
"The "Pure" part of (ZF) set theory"
Because of your rude habit of top posting, it is impossible for anyone to know the referent of your inane comments.
ZF's always a fragment /
there's no standard model?

I think I read Burse's current model,
I don't know if he's read mine,
and he tells me he doesn't,
when he does.

I read the current model.


Actually, it's, he reads then
tells you that you don't.

Or, here, just tries to invoke
multiple-worlds-interpretation of
quantum mechanics when there's a
single-world-interpretation of a
mathematical universe.

Quantum mechanics is really above
particle statistics in waves and
resonances, these days, for resonances
in particles over waves in particles.
(And their waves.) This point-local-
global-total in the quantum and gravity
is these days a current model in the
potential theory of the physics.

Then when I talk about ZF the fragment
and its embedding in the universe, and,
the standard model (and that it exists),
"in ZF" and "of ZF", and why that's in and
of a theory, it is to remind you if you already
read or introduce if you have not read, several
long discussions I gave that now might make
a lot more sense, given what was said.

I think that a lot I put forward as deliberative
will eventually just seem elementary.

Even trite....


This is laudable.
Mostowski Collapse
2020-04-12 23:38:00 UTC
Permalink
I take von Neuman V, the ZF model
is then this here:

\ /
\ /
\/
{}

https://imgbin.com/png/USvuEyJk/von-neumann-universe-set-theory-axiom-png

Rumors have it that Ross the Floss,
aka Herpes Boy, has a fragment

of V in his rectum .
Post by Ross A. Finlayson
ZF's always a fragment /
there's no standard model?
I think I read Burse's current model,
I don't know if he's read mine,
and he tells me he doesn't,
when he does.
I read the current model.
Actually, it's, he reads then
tells you that you don't.
Or, here, just tries to invoke
multiple-worlds-interpretation of
quantum mechanics when there's a
single-world-interpretation of a
mathematical universe.
Quantum mechanics is really above
particle statistics in waves and
resonances, these days, for resonances
in particles over waves in particles.
(And their waves.) This point-local-
global-total in the quantum and gravity
is these days a current model in the
potential theory of the physics.
Then when I talk about ZF the fragment
and its embedding in the universe, and,
the standard model (and that it exists),
"in ZF" and "of ZF", and why that's in and
of a theory, it is to remind you if you already
read or introduce if you have not read, several
long discussions I gave that now might make
a lot more sense, given what was said.
I think that a lot I put forward as deliberative
will eventually just seem elementary.
Even trite....
This is laudable.
Mostowski Collapse
2020-04-12 23:42:22 UTC
Permalink
And since the fragment doesn't get out of
his rectum, he is the first person infected

by COVID-19 bottomly.
Post by Mostowski Collapse
I take von Neuman V, the ZF model
\ /
\ /
\/
{}
https://imgbin.com/png/USvuEyJk/von-neumann-universe-set-theory-axiom-png
Rumors have it that Ross the Floss,
aka Herpes Boy, has a fragment
of V in his rectum .
Post by Ross A. Finlayson
ZF's always a fragment /
there's no standard model?
I think I read Burse's current model,
I don't know if he's read mine,
and he tells me he doesn't,
when he does.
I read the current model.
Actually, it's, he reads then
tells you that you don't.
Or, here, just tries to invoke
multiple-worlds-interpretation of
quantum mechanics when there's a
single-world-interpretation of a
mathematical universe.
Quantum mechanics is really above
particle statistics in waves and
resonances, these days, for resonances
in particles over waves in particles.
(And their waves.) This point-local-
global-total in the quantum and gravity
is these days a current model in the
potential theory of the physics.
Then when I talk about ZF the fragment
and its embedding in the universe, and,
the standard model (and that it exists),
"in ZF" and "of ZF", and why that's in and
of a theory, it is to remind you if you already
read or introduce if you have not read, several
long discussions I gave that now might make
a lot more sense, given what was said.
I think that a lot I put forward as deliberative
will eventually just seem elementary.
Even trite....
This is laudable.
Ross Finlayson
2024-07-28 16:04:31 UTC
Permalink
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
Ross Finlayson
2025-01-01 18:09:22 UTC
Permalink
Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb? This is: "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
Mild Shock
2025-01-27 08:09:14 UTC
Permalink
Hi,

Mostowski Collapse has left the building, his successor
is Mild Shock. But you might be interested in:

What if Singularities DO NOT Exist?


Bye

P.S.: Not to be confused with this singularity, but
maybe nevertheless the same creative motivation?

AI Scientist Ben Goertzel Explains the Singularity

Post by Ross A. Finlayson
Post by Mostowski Collapse
Its gibberish, since most of your
sentences lack a verb. Whats is this
"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?
Post by Mostowski Collapse
Gibberish makes ZFC being a model of
reality? Yeah if your reality is brain cancer.
LoL
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
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.
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.
Applied set theory is descriptive.  The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
(1) structure, in sets,
for of course all the formality
of all the structure of the sets
usually "mechanically",
then what a "reality" embodies
(2) a model of a universe of ZF set theory.
Verb?  This is:  "is" a structure and "is" a model.
The diagrammatical sentence diagram, you'll find in
my style, is often both explicit, and encompassing
parenthetical reference.
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.
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.
Then, "pure mathematics" in "philosophy of mathematics"
and for "foundations of mathematics" is quite "mathematics".
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).
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).
I.e., ZF to be accepted _does_ have "truly infinite" things.
Mostowski Collapse
2020-04-14 12:46:49 UTC
Permalink
Well descriptive set theory helps defining
pockets in the multiverse of set theory:

ZF:

\ ()/ <-- A Pocket
\ /
\/
{}

Or as this author puts it:

"Mathematicians in the early 20th century
discovered that the Axiom of Choice implied
the existence of pathological subsets of the
real line lacking desirable regularity
properties (for example nonmeasurable sets).
This gave rise to descriptive set theory, a
systematic study of classes of sets where
these pathologies can be avoided, including,
in particular, the definable sets."
https://faculty.math.illinois.edu/~anush/Teaching_notes/dst_lectures.pdf

In descriptive set theory you might
find use of determinacy axiom which

you dont find in ZFC, since it is
incompatible with the axiom of choice:

Incompatibility of the axiom of determinacy with the axiom of choice
https://en.wikipedia.org/wiki/Axiom_of_determinacy
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
of reality is pretty crank.
Post by Mostowski Collapse
Well this aint working as a good model,
you would need to make a SIR model or
something else to get a better model.
But pretty sure ZFC is postulating
some reality here. Unless you are that
much drunk, that you confuse frameworks
with what is built. Foundation with
the cathedral that sits on top. Wood
material with the kitchen furniture.
Etc..
Post by Mostowski Collapse
type 1: C : #of Coronainfected in USA at some day
type 2: f : C -> C, daily increase
Etc..
Post by Mostowski Collapse
No its not. ZFC is not a model of reality.
For example real numbers are not directly
represented, you need first to construct
them, also in ZFC. Whats wrong with you?
ZFC is just a framework to have extensional
concepts of type 1, type 2, type 3, etc...
or something that is even more monstrous
type 1: A set X
type 2: A set like funtion space f : X -> X,
its again a set, i.e. the set X^X
Etc..
type 1: C : Coronainfected in USA
type 2: f : C -> C, daily increase
Post by Ross A. Finlayson
Post by sobriquet
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.
It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.
I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.
So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
In "pure set theory" ZF's universe of sets is
just kind of a "model" of reality.
I.e. all the physical objects are mathematical objects
and also all their relations are physical and mathematical
objects, as are theirs "ad infinitum" (or, "to a singularity"),
a universe of mathematical objects. Then, where ZF's objects
are well-founded, but, this universe object _would be its own
powerset_, Cantor's "Paradox", gets into why regular ZF
is a fragment of ZF.
Otherwise "just the axioms about sets" and defining relation
(for example, functions), in sets, can for example use all
the axioms of the sets while for example not employing uncountability
for anything.
Or, for example, employing inequalities in uncountability quite regularly.
Because, for the finite case, those are just "score".
"AI" is really quite too general compared to "omniscience",
for example, where "AI" is "lowering the thermostat after
it gets warm". "Pervasive centralized distributed algorithms",
is, not "AI", it's a bee-hive. (AI: The Hive Mind.)
"Foundations in Mathematics" is for humans
and they really do include some excellent reasoners.
Mine these days, "Foundations in Mathematics", is, ..., mine.
Which I well expect could be the same for anybody.
(As it is.)
Maybe you should quit worrying about AI and learn mathematics.
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
Mostowski Collapse
2020-04-14 13:01:30 UTC
Permalink
There seems to be also some model L(R).
But I don't know whether this can be called
a pocket. Maybe better compare it to ZF and ZFU:

ZF: ZFU:
\ / \ /
\ / \ /
\/ \___/
{} Urelements

And then Gödels L, and Mycielski/Steinhaus L(R):

L: L(R):
\ / \ /
\ / \ /
\/ \___/
{} Reals

https://en.wikipedia.org/wiki/L%28R%29
Post by Mostowski Collapse
Well descriptive set theory helps defining
\ ()/ <-- A Pocket
\ /
\/
{}
"Mathematicians in the early 20th century
discovered that the Axiom of Choice implied
the existence of pathological subsets of the
real line lacking desirable regularity
properties (for example nonmeasurable sets).
This gave rise to descriptive set theory, a
systematic study of classes of sets where
these pathologies can be avoided, including,
in particular, the definable sets."
https://faculty.math.illinois.edu/~anush/Teaching_notes/dst_lectures.pdf
In descriptive set theory you might
find use of determinacy axiom which
you dont find in ZFC, since it is
Incompatibility of the axiom of determinacy with the axiom of choice
https://en.wikipedia.org/wiki/Axiom_of_determinacy
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
of reality is pretty crank.
Post by Mostowski Collapse
Well this aint working as a good model,
you would need to make a SIR model or
something else to get a better model.
But pretty sure ZFC is postulating
some reality here. Unless you are that
much drunk, that you confuse frameworks
with what is built. Foundation with
the cathedral that sits on top. Wood
material with the kitchen furniture.
Etc..
Post by Mostowski Collapse
type 1: C : #of Coronainfected in USA at some day
type 2: f : C -> C, daily increase
Etc..
Post by Mostowski Collapse
No its not. ZFC is not a model of reality.
For example real numbers are not directly
represented, you need first to construct
them, also in ZFC. Whats wrong with you?
ZFC is just a framework to have extensional
concepts of type 1, type 2, type 3, etc...
or something that is even more monstrous
type 1: A set X
type 2: A set like funtion space f : X -> X,
its again a set, i.e. the set X^X
Etc..
type 1: C : Coronainfected in USA
type 2: f : C -> C, daily increase
Post by Ross A. Finlayson
Post by sobriquet
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.
It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.
I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.
So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
In "pure set theory" ZF's universe of sets is
just kind of a "model" of reality.
I.e. all the physical objects are mathematical objects
and also all their relations are physical and mathematical
objects, as are theirs "ad infinitum" (or, "to a singularity"),
a universe of mathematical objects. Then, where ZF's objects
are well-founded, but, this universe object _would be its own
powerset_, Cantor's "Paradox", gets into why regular ZF
is a fragment of ZF.
Otherwise "just the axioms about sets" and defining relation
(for example, functions), in sets, can for example use all
the axioms of the sets while for example not employing uncountability
for anything.
Or, for example, employing inequalities in uncountability quite regularly.
Because, for the finite case, those are just "score".
"AI" is really quite too general compared to "omniscience",
for example, where "AI" is "lowering the thermostat after
it gets warm". "Pervasive centralized distributed algorithms",
is, not "AI", it's a bee-hive. (AI: The Hive Mind.)
"Foundations in Mathematics" is for humans
and they really do include some excellent reasoners.
Mine these days, "Foundations in Mathematics", is, ..., mine.
Which I well expect could be the same for anybody.
(As it is.)
Maybe you should quit worrying about AI and learn mathematics.
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
Mitch Raemsch
2020-04-14 19:30:38 UTC
Permalink
Post by Mostowski Collapse
There seems to be also some model L(R).
But I don't know whether this can be called
\ / \ /
\ / \ /
\/ \___/
{} Urelements
\ / \ /
\ / \ /
\/ \___/
{} Reals
https://en.wikipedia.org/wiki/L%28R%29
Post by Mostowski Collapse
Well descriptive set theory helps defining
\ ()/ <-- A Pocket
\ /
\/
{}
"Mathematicians in the early 20th century
discovered that the Axiom of Choice implied
the existence of pathological subsets of the
real line lacking desirable regularity
properties (for example nonmeasurable sets).
This gave rise to descriptive set theory, a
systematic study of classes of sets where
these pathologies can be avoided, including,
in particular, the definable sets."
https://faculty.math.illinois.edu/~anush/Teaching_notes/dst_lectures.pdf
In descriptive set theory you might
find use of determinacy axiom which
you dont find in ZFC, since it is
Incompatibility of the axiom of determinacy with the axiom of choice
https://en.wikipedia.org/wiki/Axiom_of_determinacy
Post by Ross A. Finlayson
Post by Mostowski Collapse
But pretty sure ZFC is **not** postulating
some reality here. Unless you are that
A theory of anything, is not really
a theory of something. Calling ZFC a model
of reality is pretty crank.
Post by Mostowski Collapse
Well this aint working as a good model,
you would need to make a SIR model or
something else to get a better model.
But pretty sure ZFC is postulating
some reality here. Unless you are that
much drunk, that you confuse frameworks
with what is built. Foundation with
the cathedral that sits on top. Wood
material with the kitchen furniture.
Etc..
Post by Mostowski Collapse
type 1: C : #of Coronainfected in USA at some day
type 2: f : C -> C, daily increase
Etc..
Post by Mostowski Collapse
No its not. ZFC is not a model of reality.
For example real numbers are not directly
represented, you need first to construct
them, also in ZFC. Whats wrong with you?
ZFC is just a framework to have extensional
concepts of type 1, type 2, type 3, etc...
or something that is even more monstrous
type 1: A set X
type 2: A set like funtion space f : X -> X,
its again a set, i.e. the set X^X
Etc..
type 1: C : Coronainfected in USA
type 2: f : C -> C, daily increase
Post by Ross A. Finlayson
Post by sobriquet
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
So far in the development of AI we've seen the creation of
artificial neural networks with an ability to process information
and to (learn to) recognize patterns, but we have not reached the
point yet where these artificial neural networks develop their own
concepts or language allowing them to communicate in a population
of neural networks or enabling communication between humans and
artificial neural networks.
Maybe it's because language is mostly a social phenomenon that
takes place at the level of populations of information processing
units rather than at the level of an individual information
processing unit.
It's a question to what degree we really need a rigorous conceptual
foundation to transcend from artificial intelligence to artificial
consciousness. We can have intuitive ideas about concepts as
sets or categories and connections as relationships or associations
and we might render such foundations in successive iterations where
we go back and forth between modifying the foundations and exploring
to what degree this foundation enables one to conceptualize a model
of reality that allows us to capture the essential aspects.
As we explore the range of patterns we encounter in reality, we might
run into situations that motivate us to go back to the fundamental
principles to make some modifications there to expand the range of
patterns we're able to characterize.
Just like humans gradually developed more detailed and elaborate
conceptual frameworks in math/science.
I think a game like go provides a nice test-case to see if we
can go from an AI that is able to learn the skill of playing go
to an AI that is able to develop the skill of understanding or
teaching go.
So the AI should be able to come up with concepts and be able to
formulate ideas in terms of such concepts in order to capture
the essentials and providing people or other AI's with principles
that enable them to improve their skill level rapidly.
In "pure set theory" ZF's universe of sets is
just kind of a "model" of reality.
I.e. all the physical objects are mathematical objects
and also all their relations are physical and mathematical
objects, as are theirs "ad infinitum" (or, "to a singularity"),
a universe of mathematical objects. Then, where ZF's objects
are well-founded, but, this universe object _would be its own
powerset_, Cantor's "Paradox", gets into why regular ZF
is a fragment of ZF.
Otherwise "just the axioms about sets" and defining relation
(for example, functions), in sets, can for example use all
the axioms of the sets while for example not employing uncountability
for anything.
Or, for example, employing inequalities in uncountability quite regularly.
Because, for the finite case, those are just "score".
"AI" is really quite too general compared to "omniscience",
for example, where "AI" is "lowering the thermostat after
it gets warm". "Pervasive centralized distributed algorithms",
is, not "AI", it's a bee-hive. (AI: The Hive Mind.)
"Foundations in Mathematics" is for humans
and they really do include some excellent reasoners.
Mine these days, "Foundations in Mathematics", is, ..., mine.
Which I well expect could be the same for anybody.
(As it is.)
Maybe you should quit worrying about AI and learn mathematics.
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.
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.
Applied set theory is descriptive. The "naive" set
theory is often best - for where it's true.
"The proof strength of ZFC", is where, these days,
univalency, as an example, is basically a naive
universal.
I.e. "for theorems in mathematics" "the proof
strength of ZFC" suffices for quite a work.
Results in theorem proving?
Zero isn't a mathematical point.
Sergio
2020-04-10 02:41:58 UTC
Permalink
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
what singularity ? you/0 ?
Post by David Petry
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
not any human player...

and chess can be reduced to tables
Post by David Petry
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
nope, can't get rid of the heat.
Post by David Petry
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives,
what does this singularity arrive in ? a Car or PokieBall ?


then what they are doing will never have any benefit for humanity; an
advanced AI will be able to reproduce that the mathematicians' life work
in just a few hours, and will even go far beyond that in a few more
hours. And then what the mathematicians have been doing for all these
years will be mostly consigned to the dustbin of history. That's
something to think about, is it not?

not really, go code in AI for a while and you will find out its not that
big a deal.
Post by David Petry
We might also discuss what mathematicians could be doing to bring about the singularity.
hire a magician ?

I like to point out that mathematics has a very close connection to
artificial intelligence.

AI is written in Math.
Post by David Petry
We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
too general.
Post by David Petry
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI.
Dork, human write the code for AI.


Again, that's something that would be of enormous value to humanity, in
the long run.
Post by David Petry
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
paranoid ? realize that AI is just a computer program, alway has been.
Post by David Petry
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
you are the one making stuff up, go on ahead.....
Dan Christensen
2020-04-10 18:15:21 UTC
Permalink
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
I don't know that chess and mathematics are comparable in this way. It is easy for a computer to tell if a chess game is won or lost. Not so easy for a computer that is entirely cut off from reality to tell which line of enquiry might be useful or "interesting." It would also have to have the ability to construct its own systems of axioms and definitions, to make up its own rules.


Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Jan
2020-04-11 01:07:45 UTC
Permalink
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades.
I consider this pseudoscience.

--
Jan
Mitch Raemsch
2020-04-11 02:00:59 UTC
Permalink
Post by Jan
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades.
I consider this pseudoscience.
--
Jan
You are going to find out you are not science Jan.

Mitchell Raemsch
Jan
2020-04-11 03:48:52 UTC
Permalink
Post by Mitch Raemsch
Post by Jan
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades.
I consider this pseudoscience.
--
Jan
You are going to find out you are not science Jan.
Mitchell Raemsch
It's just a bit of New Age nonsense.

--
Jan
Mitch Raemsch
2020-04-11 04:19:13 UTC
Permalink
Post by Jan
Post by Mitch Raemsch
Post by Jan
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades.
I consider this pseudoscience.
--
Jan
You are going to find out you are not science Jan.
Mitchell Raemsch
It's just a bit of New Age nonsense.
--
Jan
You are just as bad...
Mostowski Collapse
2020-04-12 17:32:41 UTC
Permalink
Ray Kurzweil define the concept in terms of the
technological creation of super intelligence.
Maybe singularity is just repetition of the same

on a higher level. Like here:

Life in Life


For the lower level, it might deserive the
attribute "super". Although its the same intelligence,
only a different scale.
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
Mostowski Collapse
2020-04-12 17:55:44 UTC
Permalink
So this super intelligence would again use
ZFC, only it might be on steroids.

Like the markets recently, never seen a price
crash that fast. What does it mean?

Those who needed cash sold their stocks? So
markets where helpful in the covid crises?
Post by Mostowski Collapse
Ray Kurzweil define the concept in terms of the
technological creation of super intelligence.
Maybe singularity is just repetition of the same
Life in Life
http://youtu.be/xP5-iIeKXE8
For the lower level, it might deserive the
attribute "super". Although its the same intelligence,
only a different scale.
Post by David Petry
Since most of us are locked in our homes with little to do, this might be a good time to have a discussion about the future. The so called "singularity" is probably not far off, maybe just a few decades. So what impact will this have on mathematics, and what impact will mathematics have one the singularity?
Here's one thing to consider. It was just a few years ago that Google's AlphaZero program did something rather remarkable. It was given the rules of chess, and then just by playing against itself and learning as it played, within four hours of this process it learned to play chess at a level far exceeding the abilities of any human player, and even surpassed the abilities of any computer player that had come before it.
So, does this not suggest that when the singularity arrives, and we have computers that may be millions of times more intelligent than humans, that these artificially intelligent computers will be able to start from the axioms of mathematics and little more, and then within a few hours, develop mathematics far beyond the level that humans have been able to develop it?
What this suggests is that if mathematicians are not doing something that will have a benefit for humanity before the singularity arrives, then what they are doing will never have any benefit for humanity; an advanced AI will be able to reproduce that the mathematicians' life work in just a few hours, and will even go far beyond that in a few more hours. And then what the mathematicians have been doing for all these years will be mostly consigned to the dustbin of history. That's something to think about, is it not?
We might also discuss what mathematicians could be doing to bring about the singularity. I like to point out that mathematics has a very close connection to artificial intelligence. We can think of mathematics as a rigorous conceptual framework for reasoning about the real work, and likewise, a computer will be intelligent when it can reason about the real world. It would be reasonable to say that mathematics is a rigorous theory of inteligence.
So what I have been arguing is that mathemticians could be developing a rigorous foundation for artificial intelligence. That's something I have always wanted to do. But what mathematicians have chosen to be the foundation of their own subject (ie ZFC) is quite deficient as a foundation for AI, and the mathematicians now seem to be very opposed to the idea of even considering alternate foundations that might have great practical value.
Something else the mathematicians could be doing is to develop a language that facilitates communication between humans and AI. Again, that's something that would be of enormous value to humanity, in the long run.
As I see it, the AI that is being developed is being built on a deficient theoretical foundation, and what is being produced will be unavailable to all but a few members of an elite priestly class of experts. Again, as I see it, AI itself holds out enormous potential for the benefit of humanity, but the AI that is currently being produced will likely be a flawed AI, with its enormous power resting in the hands of the elites, and then the dystopic nightmares that guys like Elon Musk and others are concerned about will very possibly come to fruition.
People with mathematical talent could be doing something to smooth out the transition to a post-singularity world.
So like I said, I'd like to encourage people to discuss this topic.
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