Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 11 Jun 2018, at 18:08, John Clark  wrote:
> 
> On Mon, Jun 11, 2018 at 5:16 AM, Bruno Marchal  > wrote:
> 
> ​> ​why in the world did you say " With mechanism, obviously a soul, or a 
> first person experience can be duplicated from a third person pov. But not 
> from a first person pov”?
> 
> ​> ​I think this has ben explained many times,
> 
> I think the internet must have failed many times because it failed to deliver 
> any of those explanations to me.
> 
> > With mechanism we can duplicate you, in W and M, say. For an external 
> > observer who accept mechanism, there is a you conscious in W and there is a 
> > you conscious in M. In that sense (the 3-1 sense) your soul has been 
> > duplicated relatively to the external observer.
> 
> OK, I have no problem with any of that.
> 
> > But let us ask both the you in M and the you in W: both confirms that from 
> > their point of view, they have not felt any duplication, [...] at no moment 
> > do they have a FIRST PERSON experience of a split.
> 
> Exactly! If the copy had noticed the duplication that would mean the 
> duplication process was imperfect and caused a large enough difference 
> between the copy and the original that the copy noticed a discontinuous 
> change the instant the copy button was pressed but the original noticed no 
> change; however this is NOT what happened, if there was any imperfections in 
> the copy process at all the change was too small for the copy to notice that 
> anything unusual happened when the copy button was pressed. 
> 
> > and the other copy is no more attached to their personal experience. It is 
> > a doppelgänger. They might feel intimate with their   dippelganger in some 
> > intellectual way, but without magic or telepathy, despite they re both the 
> > “H-guy”, they have become independent person,
> 
> Forget telepathy! If 2 identical grandfather clocks are running properly and 
> set to the same time and you come back an hour later and notice they still 
> show the same time you don’t need to invoke telepathy to explain it, indeed 
> if they DIDN’T show the same time then you’d need to resort to some new 
> spooky action at a distance effect previously unknown to science.
> 
> > Their soul has been maintained private and integral: no soul duplication in 
> > the soul’s first personal view.
> 
> Stating something is not the same as proving something. You start with the 
> axiom that the “soul” can’t be duplicated, and end your “proof” by claiming 
> you’ve proven it.


I start from the fact that any exact prediction is refuted in both copies’ 
diary/memory. 





> 
> > See above
> 
> Why?
> 
> >>There is nothing indeterminate about that, its all 100% predictable.
> 
> >Ok, what is your algorithm in Helsinki?
> 
> Seeing Moscow will turn the Helsinki man into the Moscow man and seeing 
> Washington will turn the Helsinki man into the Washington man with 100% 
> certainty and no indeterminacy whatsoever.

That fails to give the prediction made in Helsinki about the immediate future 
experience. The H-guy know that he will survive in both place, but also but 
that in both places he will felt like surviving in only one place from its 
first person point of view.
That is the reason why it cannot predict which one will be lived in particular, 

Again, you fail to address the first experience lived by the two copies.

Bruno


> 
> > how the H-person, when still in Helsinki could predict who he will feel to 
> > be?
> 
> A prediction can’t be made until it is clear exactly who Mr. He is. Forget 
> people duplicating machines, if Mr. He means the man experiencing Helsinki on 
> June 11 2018 at 14:36:09 Coordinated Universal Time then Mr. He will 
> experience no city and no nothing tomorrow because by definition Mr. He will 
> not exist then. However if Mr. He means the person who remembers experiencing 
> Helsinki on June 11 2018 at 14:36:09 Coordinated Universal Time and if Mr. He 
> is duplicated then the fact that there are 2 answers to your question is no 
> more metaphysical or indeterminate or profound than the fact that there and 2 
> correct answers to the question “What is the value of X in this quadratic 
> equation X^2=4 ?”. Don’t you think it would be silly to demand to know the 
> one and only one true answer?
> 
> > You ignore the work of Theaetetus,
> 
> Theaetetus wasn’t a person, Theaetetus was one of Plato’s dialogs. And the 
> time reading Plato is time spent not reading FAR more important things.
> 
> > and apparently even Diophantus, who founded Algebra
> 
> If this list existed one thousand eight hundred years ago I’d be talking a 
> lot about Diophantus too, but there have been a few interesting developments 
> since the days of Diophantus, such as the far more recent discovery made in 
> 1530 on how to solve cubic equations, something Diophantus had no idea how to 
> do.
> 
> >>why would anybody working on modern scientific problems be interested in 
> >>

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Mon, Jun 11, 2018 at 5:16 AM, Bruno Marchal  wrote:

​> ​
>> why in the world did you say " With mechanism, obviously a soul, or a
>> first person experience can be duplicated from a third person pov. But not
>> from a first person pov”?
>
>
> ​> *​*
> *I think this has ben explained many times,*
>

I think the internet must have failed many times because it failed to
deliver any of those explanations to me.

*> With mechanism we can duplicate you, in W and M, say. For an external
> observer who accept mechanism, there is a you conscious in W and there is a
> you conscious in M. In that sense (the 3-1 sense) your soul has been
> duplicated relatively to the external observer.*


OK, I have no problem with any of that.

*> But let us ask both the you in M and the you in W: both confirms that
> from their point of view, they have not felt any duplication, [...] at no
> moment do they have a FIRST PERSON experience of a split.*


Exactly! If the copy had noticed the duplication that would mean the
duplication process was imperfect and caused a large enough difference
between the copy and the original that the copy noticed a discontinuous
change the instant the copy button was pressed but the original noticed no
change; however this is NOT what happened, if there was any imperfections
in the copy process at all the change was too small for the copy to notice
that anything unusual happened when the copy button was pressed.

*> and the other copy is no more attached to their personal experience. It
> is a doppelgänger. They might feel intimate with their   dippelganger in
> some intellectual way, but without magic or telepathy, despite they re both
> the “H-guy”, they have become independent person,*


Forget telepathy! If 2 identical grandfather clocks are running properly
and set to the same time and you come back an hour later and notice they
still show the same time you don’t need to invoke telepathy to explain it,
indeed if they DIDN’T show the same time then you’d need to resort to some
new spooky action at a distance effect previously unknown to science.

*> Their soul has been maintained private and integral: no soul duplication
> in the soul’s first personal view.*


Stating something is not the same as proving something. You start with the
axiom that the “soul” can’t be duplicated, and end your “proof” by claiming
you’ve proven it.

*> See above*


Why?

>>There is nothing indeterminate about that, its all 100% predictable.
>
>
> >*Ok, what is your algorithm in Helsinki?*


Seeing Moscow will turn the Helsinki man into the Moscow man and seeing
Washington will turn the Helsinki man into the Washington man with 100%
certainty and no indeterminacy whatsoever.

*> how the H-person, when still in Helsinki could predict who he will feel
> to be?*


A prediction can’t be made until it is clear exactly who Mr. He is. Forget
people duplicating machines, if Mr. He means the man experiencing Helsinki
on June 11 2018 at 14:36:09 Coordinated Universal Time then Mr. He will
experience no city and no nothing tomorrow because by definition Mr. He
will not exist then. However if Mr. He means the person who remembers
experiencing Helsinki on June 11 2018 at 14:36:09 Coordinated Universal
Time and if Mr. He is duplicated then the fact that there are 2 answers to
your question is no more metaphysical or indeterminate or profound than the
fact that there and 2 correct answers to the question “What is the value of
X in this quadratic equation X^2=4 ?”. Don’t you think it would be silly to
demand to know the one and only one true answer?

*> You ignore the work of Theaetetus,*


Theaetetus wasn’t a person, Theaetetus was one of Plato’s dialogs. And the
time reading Plato is time spent not reading FAR more important things.

*> and apparently even Diophantus, who founded Algebra*


If this list existed one thousand eight hundred years ago I’d be talking a
lot about Diophantus too, but there have been a few interesting
developments since the days of Diophantus, such as the far more recent
discovery made in 1530 on how to solve cubic equations, something
Diophantus had no idea how to do.

>>why would anybody working on modern scientific problems be interested in
>> what they ancient Greeks had to say about anything?
>
>
> > *Because in theology* [...]


I don’t give a tinkers damn what is in theology nor should anyone who is
interested in modern scientific problems.

* > I use theology in the original sense, which is almost the opposite
> sense than the one used by any religious institution*


And why would Bruno deliberately cause confusion by giving familiar words
like “theology” and “God” very unfamiliar meanings that are the very
opposite of the meanings used by billions of people today? For the same
reason Bruno sprinkles personal pronouns around so liberally in thought
experiments, if your idea is bad precise language is not your friend. It is
better to be thought of as being unclear than to be thought of as being
stu

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 11 Jun 2018, at 03:56, John Clark  wrote:
> 
> On Sun, Jun 10, 2018 at 6:49 AM, Bruno Marchal  > wrote:
> 
> ​>>​that is one (of many) problems with your “proof”. You start off by 
> assuming a physical mechanism can duplicate everything
>  
> ​>​False. I start from the assumption that I can survive from a digital 
> emulation of my brain at some level.
> 
> Then why in the world did you say " With mechanism, obviously a soul, or a 
> first person experience can be duplicated from a third person pov. But not 
> from a first person pov”?


?

I think this has ben explained many times, and that the duplication thought 
experiment illustrates so well, like also the non feeling of the split in 
Everett.

With mechanism we can duplicate you, in W and M, say. For an external observer 
who accept mechanism, there is a you conscious in W and there is a you 
conscious in M. In that sense (the 3-1 sense) your soul has been duplicated 
relatively to the external observer. But let us ask both the you in M and the 
you in W: both confirms that from their point of view, they have not felt any 
duplication, and the other copy is no more attached to their personal 
experience. It is a doppelgänger. They might feel intimate with 
theirdippelganger in some intellectual way, but without magic or telepathy, 
despite they re both the “H-guy”, they have become independent person, and at 
no moment do they have a FIRST PERSON experience of a split. Their soul has 
been maintained private and integral: no soul duplication in the soul’s first 
personal view.






>  
> ​>>​EXCEPT for ​the​ first person pov,
> 
> ​>​EXCEPT *from*, not for.
> 
> ​I​ don't see why mechanism can't duplicate experience *from* the first 
> person pov, but its "obvious" to you so you should have no difficulty 
> explaining why with clear precise words, and in English not Brunospeak.  

See above, but that has been explained already many time, and you are using it 
implicitly when you say that the observer does not feel the split, or the 
differentiation, in Everett measurement theory.



> 
> ​>​Mechanism cannot duplicate or do something.
> 
> I won't say that's the silliest thing you've ever said but its in the top 10.​


? (You made  an obvious category error, or just a grammar error). Mechanism is 
a principle, a doctrine. That does not belong to the category of things capable 
to do something. It only makes people able to do something.




>  
> ​>>​observers will feel things after both the Everett type split and the 
> duplicating machine type split, and if the environments they are put into are 
> different then what they feel will be different and they will become 
> different people from that point on, although both will remember being the 
> same person before the split (or walking into the copying machine).
> 
> ​>​OK then, but that entails the first person indeterminacy for the 
> self-duplication.
> 
> There is nothing indeterminate about that, its all 100% predictable.


Ok, what is your algorithm in Helsinki? If you agree that after the 
duplication, the W-person and the M-person  become different people, but still, 
by mechanism, keeping they H-people identity, how the H-person, when still in 
Helsinki could predict who he will feel to be? If that is 100% predictable, 
just give the method of prediction.



> ​ 
> 
> ​>>​​l​ike most of the wise men you recommend on this list the guy who 
> dreamed up Theaetetus would flunk a freshman algebra test
> 
> ​>​No. He was a great mathematician. He proved the irrationality of all 
> square root of non perfect square.
> 
> We've known how to solve cubic equations since 1530, but not one of your 
> ancient Greeks could,


You ignore the work of Theaetetus, and apparently even Diophantus, who founded 
Algebra, and is responsible for many findings there. It is weird. Fermat knew 
only Diophantus. The rebirth of mathematics comes from the translation of greek 
mathematics, etc.




> and in physics astronomy and biology they were even more ignorant than in 
> mathematics.

Eratosthene knew that the earth was spheric, and has measured its diameter. 
Yes, that will be forgotten, but has help for the coming back. 




> So why would anybody working on modern scientific problems be interested in 
> what they ancient Greeks had to say about anything?

Because in theology, they were rationalist and formulate the problem 
scientifically. So, they are still in advance. We have lost the track due to 
the use of violence, terror and other argument-per-authority. Then, computer 
science shows that they were very close to the scientific and mathematical 
theology, discovered by Gödel, Löb and made complete at the propositional level 
by Solovay. Again I use theology in the original sense, which is almost the 
opposite sense than the one used by any religious institution, which prevent 
the research instead of promoting it, for special private interest.

Bruno





>  
> 
> 
> 
> ​​

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 11 Jun 2018, at 01:44, Russell Standish  wrote:
> 
> On Sun, Jun 10, 2018 at 12:49:17PM +0200, Bruno Marchal wrote:
>> 
>>> On 8 Jun 2018, at 16:26, John Clark  wrote:
>>> 
>> 
>>> and didn't even know where the sun went at night. You've recommended many 
>>> many books on this list but only a very small number of them were written 
>>> by authors who have been dead for less than a century, but even those books 
>>> are unable to calculate 2+2.
> 
> ISTM, the bulk of the books Bruno cites are 20th century, mostly
> mid-20th C. This is not surprising: a) because the 20th C was an
> explosion of human knowledge, and most of the key concepts Bruno
> relies on were elucidated in the early-mid 20th C; b) like most of us,
> Bruno did most of his formative reading in his teens and twenties,
> which corresponds to the 1960-70s in his case, and c) it is bloody hard
> keeping up with 21st century literature, there's so much of it.
> 
> I enjoy Bruno's inclusion of ancient texts, both for the colour, and
> for the feeling of hubris you get when you realise someone living 2000
> years ago got surprisingly close to the mark. But his arguments do not
> depend on those texts at all.

Right. Except for Lao-Ze, and a bit of Plato and Plotinus, it is only thanks to 
computer science that I realise those people where close to the mark.

If mechanism is true, that is hardly a coincidence. Mechanism, or even just the 
self-reference theory, explains all what a machine can discover when reasoning 
about itself without prejudice (except classical logic, which is something 
discovered by Aristotle). So, it would be astonishing that the humans reasoning 
about themselves would not have been close to the machine. That would have an 
indication that mechanism is wrong. But I did not expect at all that Plotinus, 
and perhaps even more so Moderatus of Gades, would that close.

Cheers!

Bruno



> 
> 
> -- 
> 
> 
> Dr Russell StandishPhone 0425 253119 (mobile)
> Principal, High Performance Coders
> Visiting Senior Research Fellowhpco...@hpcoders.com.au
> Economics, Kingston University http://www.hpcoders.com.au
> 
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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Sun, Jun 10, 2018 at 6:49 AM, Bruno Marchal  wrote:

​>>​that is one (of many) problems with your “proof”. You start off by
>> assuming a physical mechanism can duplicate everything
>
>

*​>​False. I start from the assumption that I can survive from a digital
> emulation of my brain at some level.*
>

Then why in the world did you say " With mechanism, obviously a soul, or a
first person experience can be duplicated from a third person pov. But not
from a first person pov"?


> ​>>​
>> EXCEPT for
>> ​the​
>>  first person pov,
>
>
> *​>​EXCEPT *from*, not for.*
>

​I​
 don't see why mechanism can't duplicate experience *from* the first person
pov, but its "obvious" to you so you should have no difficulty explaining
why with clear precise words, and in English not Brunospeak.

*​>​Mechanism cannot duplicate or do something.*


I won't say that's the silliest thing you've ever said but its in the top
10.​


> ​>>​observers will feel things after both the Everett type split and the
>> duplicating machine type split, and if the environments they are put into
>> are different then what they feel will be different and they will become
>> different people from that point on, although both will remember being the
>> same person before the split (or walking into the copying machine).
>
>
> *​>​OK then, but that entails the first person indeterminacy for the
> self-duplication.*
>

There is nothing indeterminate about that, its all 100% predictable. ​


​>>​
>> ​l​ike most of the wise men you recommend on this list the guy who
>> dreamed up Theaetetus would flunk a freshman algebra test
>
>
> *​>​No. He was a great mathematician. He proved the irrationality of all
> square root of non perfect square.*
>

We've known how to solve cubic equations since 1530, but not one of your
ancient Greeks could, and in physics astronomy and biology they were even
more ignorant than in mathematics. So why would anybody working on modern
scientific problems be interested in what they ancient Greeks had to say
about anything?

<*sigh*>
>

​​

​ John K Clark​

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Russell Standish]

On Sun, Jun 10, 2018 at 12:49:17PM +0200, Bruno Marchal wrote:
> 
> > On 8 Jun 2018, at 16:26, John Clark  wrote:
> > 
> 
> > and didn't even know where the sun went at night. You've recommended many 
> > many books on this list but only a very small number of them were written 
> > by authors who have been dead for less than a century, but even those books 
> > are unable to calculate 2+2.

ISTM, the bulk of the books Bruno cites are 20th century, mostly
mid-20th C. This is not surprising: a) because the 20th C was an
explosion of human knowledge, and most of the key concepts Bruno
relies on were elucidated in the early-mid 20th C; b) like most of us,
Bruno did most of his formative reading in his teens and twenties,
which corresponds to the 1960-70s in his case, and c) it is bloody hard
keeping up with 21st century literature, there's so much of it.

I enjoy Bruno's inclusion of ancient texts, both for the colour, and
for the feeling of hubris you get when you realise someone living 2000
years ago got surprisingly close to the mark. But his arguments do not
depend on those texts at all.


-- 


Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 8 Jun 2018, at 16:26, John Clark  wrote:
> 
> On Fri, Jun 8, 2018 at 6:31 AM, Bruno Marchal  > wrote:
> 
> >>  I said information was as close as you can get to the traditional 
> >> religious concept of the soul and still remain within the scientific 
> >> method. In the past I pointed out exactly what those similarities and 
> >> differences were, I will repeat them now:
> 
> * The soul is non material and so is information.
> * It's difficult to pin down a unique physical location for the soul, and the 
> same is true for information.
> *The soul is the essential, must have, part of consciousness, exactly the 
> same situation is true for information.
>  
> *The soul is immortal and so, potentially, is information.  
>  
> > Well. Thanks. Brent was quoting me, but your answer is not too bad.
>  
> >>But there are important differences too.
> 
> *A soul is unique but information can be duplicated.
> 
> >  With mechanism, obviously a soul, or a first person experience can be 
> > duplicated from a third person pov. But not from a first person pov,
> 
> And that is one (of many) problems with your “proof”. You start off by 
> assuming a physical mechanism can duplicate everything


False. I start from the assumption that I can survive from a digital emulation 
of my brain at some level. From this I have deduced many years ago the 
non-cloning theorem (without assuming quantum mechanics nor even an ontological 
 physical universe).




> EXCEPT for ​the​ first person pov,


EXCEPT *from*, not for.



> and then at the end you conclude you have proven mechanism can duplicate 
> everything EXCEPT for ​the​ first person pov .


Mechanism cannot duplicate or do something. Your phrasing is non sensical, and 
as often, you don’t seem to listen to what I say, and attribute me non sense 
that I have never asserted.



> 
> > you say that with Everett the observer does not feel the split.
> 
> Yes, but observers will feel things after both the Everett type split and the 
> duplicating machine type split, and if the environments they are put into are 
> different then what they feel will be different and they will become 
> different people from that point on, although both will remember being the 
> same person before the split (or walking into the copying machine).

OK then, but that entails the first person indeterminacy for the 
self-duplication. You make my point.



> 
> >> *The soul is and will always remain unfathomable, but information is 
> >> understandable, in fact, information is the ONLY thing that is 
> >> understandable.
> 
> > Theaetetus is *the* counterexample to this,
> 
> That is of course Bullshit, and like most of the wise men you recommend on 
> this list the guy who dreamed up Theaetetus would flunk a freshman algebra 
> test


No. He was a great mathematician. He proved the irrationality of all square 
root of non perfect square.

And his definition of knowledge is one of the main improvement in theology for 
that period.



> and didn't even know where the sun went at night. You've recommended many 
> many books on this list but only a very small number of them were written by 
> authors who have been dead for less than a century, but even those books are 
> unable to calculate 2+2.




Bruno



> 
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> 
> 
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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Fri, Jun 8, 2018 at 6:41 AM, Bruno Marchal  wrote:

​>>​
>> Today "you" means the man who is currently experiencing H, tomorrow "you"
>> means the man who is currently experiencing W and remembers experiencing H
>> yesterday; and tomorrow "you" also means the man who is currently
>> experiencing M and remembers experiencing H yesterday. And please don't
>> rebut with your standard "from the 1p" rubber stamp reply unless it is made
>> clear which "THE 1p" is being referred to.
>
>
> *​>​That is simply not true. The first person “I” means always the H-guy,*
>

​OK, but what do you mean by "the H-guy"? I can tell you exactly what I
mean by "the H-guy", somebody who remembers being in Helsinki yesterday.
Can you be as precise?

> ​>>
>>> ​>>​
>>> ​
>>> so which ONE is Mr. You??
>>
>>
>> *​>​>>​ ​If I could answer that question, there would, of course, no be
>> any first person indeterminacy. *
>>
>
> ​
> ​>>​
> If Bruno can not answer that question then Bruno has absolutely no
> business ever using the word "you" in any thought experiment and all the
> grand sounding term "
> first person indeterminacy
> ​" means is that gibberish questions have no answers.   ​
>
> *​>​No, you are only setting up a trap. If I could answer your question in
> one word, then and only then the first person indeterminacy would be
> gibberish. *
>

​So in a world that contains people duplicating machines Bruno is unable to
say what the personal pronoun "You" means, therefore in Brunospeak we could
replace the question "what will you see?" with "what will flobkneegob see?"
because both "you" and "flobkneegob" have exactly the same meaning in
Bruno's native language, and that would be none at all.

​
>> ​>>​
>> What the M-guy says or doesn't say is irrelevant.
>
>
> *​>​Why?*
>

​Because if the W-guy is seeing Washington, and if the W-guy remembers
being the H-guy yesterday, and if "the H-guy" means remembering being in
Helsinki yesterday, then that's the end of the story; the H-guy ended up
seeing Washington just as I predicted. The fact that the M-guy (who is also
the H-guy) saw something different will not change what the W-guy is seeing
right now nor what he remembers seeing yesterday. And if something is
copied that means there are 2 of them, and there is nothing contradictory
about 2 things seeing 2 things.

John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Fri, Jun 8, 2018 at 6:31 AM, Bruno Marchal  wrote:

>>  I said information was as close as you can get to the traditional
> religious concept of the soul and still remain within the scientific
> method. In the past I pointed out exactly what those similarities and
> differences were, I will repeat them now:
>
> * The soul is non material and so is information.
>
> * It's difficult to pin down a unique physical location for the soul, and
> the same is true for information.
>
> *The soul is the essential, must have, part of consciousness, exactly the
> same situation is true for information.



*The soul is immortal and so, potentially, is information.



> *Well. Thanks. Brent was quoting me, but your answer is not too bad.*


> >>But there are important differences too.
>
> *A soul is unique but information can be duplicated.
>
> >  *With mechanism, obviously a soul, or a first person experience can be
> duplicated from a third person pov. But not from a first person pov,*


And that is one (of many) problems with your “proof”. You start off by
assuming a physical mechanism can duplicate everything EXCEPT for
​the​
 first person pov, and then at the end you conclude you have proven
mechanism can duplicate everything EXCEPT for
​the​
 first person pov .

*> you say that with Everett the observer does not feel the split.*


Yes, but observers will feel things after both the Everett type split and
the duplicating machine type split, and if the environments they are put
into are different then what they feel will be different and they will
become different people from that point on, although both will remember
being the same person before the split (or walking into the copying
machine).

>> *The soul is and will always remain unfathomable, but information is
>> understandable, in fact, information is the ONLY thing that is
>> understandable.
>
>
> >* Theaetetus is *the* counterexample to this,*


That is of course Bullshit, and like most of the wise men you recommend on
this list the guy who dreamed up Theaetetus would flunk a freshman algebra
test and didn't even know where the sun went at night. You've recommended
many many books on this list but only a very small number of them were
written by authors who have been dead for less than a century, but even
those books are unable to calculate 2+2.

 John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 7 Jun 2018, at 19:40, John Clark  wrote:
> 
> On Thu, Jun 7, 2018 at 10:23 AM, Bruno Marchal  > wrote:
> 
> ​> ​I know perfectly well what the personal pronoun “you” will mean, as its 
> meaning will not change.
> 
> Of course it will change. Today "you" means the man who is currently 
> experiencing H, tomorrow "you" means the man who is currently experiencing W 
> and remembers experiencing H yesterday; and tomorrow "you" also means the man 
> who is currently experiencing M and remembers experiencing H yesterday. And 
> please don't rebut with your standard "from the 1p" rubber stamp reply unless 
> it is made clear which "THE 1p" is being referred to.


That is simply not true. The first person “I” means always the H-guy, even when 
his experience differentiates into two histories. Or you cannot say “I will 
survive with an artificial brain”, and computationalism is made senseless.



> 
> ​>> ​so which ONE is Mr. You??
> 
> ​> ​If I could answer that question, there would, of course, no be any first 
> person indeterminacy. 
> 
> ​If Bruno can not answer that question then Bruno has absolutely no business 
> ever using the word "you" in any thought experiment and all the grand 
> sounding term "first person indeterminacy​" means is that gibberish questions 
> have no answers.   ​

No, you are only setting up a trap. If I could answer your question in one 
word, then and only then the first person indeterminacy would be gibberish. 
Well tried!




>> ​>​>>​ One will say “oh, I am the H-guy having survived in W” and he is right
>> 
>> ​>>​​I agree.​​ ​So what is the probability the H-​guy will see W? 100% 
> 
> ​> ​No,
> 
> ​No? So you think the H-guy will see W ​no question about it,

?



>  ​but there is not a 100% chance the H-guy will see W​. This is logic?​

?

I explain this later … Let us see.


> 
>  
> ​> ​because if that is the prediction made in Helsinki, as asked, it will be 
> refuted by the M-guy.
> 
> ​What the M-guy says or doesn't say is irrelevant.


Why?



> ​If the W-guy is the H-guy and the W-guy sees W then that's the end of the 
> story, the H guy will see W with absolute certainty.


Oh, just to evacuate the counter-example. That is not valid.





> Yes the H-guy is no longer unique ​but that is to be expected because that's 
> what "being copied" means.​

But that enforce you to listen to the M-guy. Simply enough.



> 
> ​> ​We want the prediction be correct for both copies
> 
> ​What you want is contradictory, its ridiculous!

Obviously not. If the H-guy, when still in H, predicts W v M, that prediction 
is verified, when all the others are contradicted by one of the copies, if not 
both.




> If they are dropped into different environments, like in different cities, 
> then they can't have the same fate so no one prediction can be correct about 
> what will happen to both of them; and that is all utterly predictable. So 
> where is the indeterminacy?

It is on the first person that the H-guy will live *from its first person point 
of view*.





> The only grand mystery in all this is what does the word "you" mean when 
> Bruno asks "What one and only one city will YOU see after YOU step out of a 
> YOU duplicating machine?”


The “you” is an indexical. If you were genuinely interested, you would study 
the translation in arithmetic. The 3-you is mathematically defined with 
Kleene’s second recursion theorem, and the 1p-you is defined with applying 
Theaetus’s definition on it. 

Bruno


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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 7 Jun 2018, at 16:44, John Clark  wrote:
> 
> On Wed, Jun 6, 2018 at 3:15 PM, Brent Meeker  > wrote:
> 
> ​> ​I don't want to get into arguments about pronouns,
> 
> Then you don't want to talk about Bruno's ideas because personal pronouns are 
> vitally important to it, they are the rug that Bruno uses to cover the gaping 
> holes in Bruno's logic.

That you have not succeeded to debunk, without changing the question asked, and 
the definitions used.



>  
> ​> ​ you've explicitly admitted that you believe there is soul
>  
> No. I said information was as close as you can get to the traditional 
> religious concept of the soul and still remain within the scientific method. 
> In the past I pointed out exactly what those similarities and differences 
> were, I will repeat them now: 
> 
> * The soul is non material and so is information.
> * It's difficult to pin down a unique physical location for the soul, and the 
> same is true for information. 
> *The soul is the essential, must have, part of consciousness, exactly the 
> same situation is true for information. 
> *The soul is immortal and so, potentially, is information.  

Well. Thanks. Brent was quoting me, but your answer is not too bad.



>  
> 
> But there are important differences too. 
> 
> *A soul is unique but information can be duplicated.

With mechanism, obviously a soul, or a first person experience can be 
duplicated from a third person pov. But not from a first person pov, in the 
sense that each duplicated soul will still feel unique from its first person 
pov. You have used this when you say that with Everett the observer does not 
feel the split. Likewise, I could duplicate you during the light, you wold not 
be aware of this.




> *The soul is and will always remain unfathomable, but information is 
> understandable, in fact,information is the ONLY thing that is 
> understandable.

Theaetetus is *the* counterexample to this, an doubly so when translated in 
arithmetic, in the 3p way.




> *Information unambiguously exists, I don't think anyone would deny that, but 
> if the soul exists it will never be proven scientifically.

Using Theatetus’ definition, and using “provable” as “believable” (the modesty 
enforce by incompleteness), it becomes a theorem of arithmetic that all 
universal machines have a soul

That is important. Incompleteness enforces []p to have a logic distinct of the 
logic of knowledge (S4 like) and the distinction of the logic of []p and of []p 
& p, which last one do acts as a logic of knowledge. So a first person knower 
is canonically attached to any machine, and its logic is close to the epistemic 
interpretation of intuitionism, brought by Brouwer in his attempts to found 
mathematics on (first person) intuition.

Bruno




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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Thu, Jun 7, 2018 at 10:23 AM, Bruno Marchal  wrote:

​> *​*
> *I know perfectly well what the personal pronoun “you” will mean, as its
> meaning will not change.*
>

Of course it will change. Today "you" means the man who is currently
experiencing H, tomorrow "you" means the man who is currently experiencing
W and remembers experiencing H yesterday; and tomorrow "you" also means the
man who is currently experiencing M and remembers experiencing H yesterday.
And please don't rebut with your standard "from the 1p" rubber stamp reply
unless it is made clear which "THE 1p" is being referred to.

​>> ​
>> so which ONE is Mr. You??
>
>
> *​> ​If I could answer that question, there would, of course, no be any
> first person indeterminacy. *
>

​If Bruno can not answer that question then Bruno has absolutely no
business ever using the word "you" in any thought experiment and all the
grand sounding term "
first person indeterminacy
​" means is that gibberish questions have no answers.   ​

> ​>
>>> ​>>​
>>> * One will say “oh, I am the H-guy having survived in W” and he is right*
>>
>>
> ​>>​
>> ​I agree.​
>> ​
>> ​So what is the probability the H-​guy will see W? 100%
>>
>
> *​> ​No,*
>

​No? So you think the H-guy will see W ​
no question about it,
​but there is not a 100% chance
the H-guy will see W
​. This is logic?​



> ​>* ​*
> *because if that is the prediction made in Helsinki, as asked, it will be
> refuted by the M-guy.*
>

​What the M-guy says or doesn't say is irrelevant. ​If the W-guy is the
H-guy and the W-guy sees W then that's the end of the story, the H guy will
see W with absolute certainty. Yes the H-guy is no longer unique

​but that is to be expected because that's what "being copied" means.​

​> ​
> *We want the prediction be correct for both copies*
>

​
What you want is contradictory, its ridiculous! If they are dropped into
different environments, like in different cities, then they can't have the
same fate so no one prediction can be correct about what will happen to
both of them; and that is all utterly predictable. So where is the
indeterminacy? The only grand mystery in all this is what does the word
"you" mean when Bruno asks "What one and only one city will YOU see after
YOU step out of a YOU duplicating machine?"

John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Wed, Jun 6, 2018 at 3:15 PM, Brent Meeker  wrote:

>
​> ​
> I don't want to get into arguments about pronouns,


Then you don't want to talk about Bruno's ideas because personal pronouns
are vitally important to it, they are the rug that Bruno uses to cover the
gaping holes in Bruno's logic.


> ​> *​*
> * you've explicitly admitted that you believe there is soul*


No. I said information was as close as you can get to the traditional
religious concept of the soul and still remain within the
scientific method. In the past I pointed out exactly what those
similarities and differences were, I will repeat them now:

* The soul is non material and so is information.
* It's difficult to pin down a unique physical location for the soul, and
the same is true for information.
*The soul is the essential, must have, part of consciousness, exactly the
same situation is true for information.
*The soul is immortal and so, potentially, is information.

But there are important differences too.

*A soul is unique but information can be duplicated.
*The soul is and will always remain unfathomable, but information is
understandable, in fact,information is the ONLY thing that is
understandable.
*Information unambiguously exists, I don't think anyone would deny that,
but if the soul exists it will never be proven scientifically.

 John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 6 Jun 2018, at 21:15, Brent Meeker  wrote:
> 
> 
> 
> On 6/6/2018 3:04 AM, Bruno Marchal wrote:
>> 
>> But in Helsinki, as a computationalist, you know in advance that whatever 
>> you will live is a definite unique experience, of W or of M. You lost 
>> unicity in the 3p view, indeed, but as human survivor, you keep it, and feel 
>> to be only one of the two copies. In all diaries obtained, the results are 
>> either W and M. This can be predicted, and indeed is verified by the two 
>> copies, independently.  Just take the 3p and 1p distinction into account, 
>> which is part of the question in that thought experience.
>> 
>> Bruno
> 
> I don't want to get into arguments about pronouns, but now that you've 
> explicitly admitted that you believe there is soul and the brain is only a 
> kind interface whereby the soul interacts with a physical world, doesn't that 
> imply that this soul in not duplicated and only one of the W and M bodies has 
> THE soul of the Helsinki man?

I have given two definition of the soul, or first person, so far. 

In the Universal Dovetailer Argument (UDA), the soul is well approximated by 
the owner of the personal diary. As such it is not duplicated from its personal 
perspective, but of course it is duplicated for the 3p observer who did not 
enter the box.

In the abstract translation of the UDA in arithmetic, The soul looks vey much 
to what you have defended many times: it is the machine and its memory 
(translated by the Gödel provability predicate in the case of ideally correct 
machine (which is why we need to get the “correct physics” with the meachniast 
assumption) conjuncted to either the truth, or consistency, or both, that is 
the 

[]p & p
[]p & <>p
[]p & <>p & p

That is akin to your desire to consider the environment in the picture, 
formally. And you are right, as consciousness is more in p, <>p and <>p v p 
than in the “machine” ([]p).

There is a sort of paradox, as the universal machine’s soul will NOT say “yes” 
to the doctor. 
Machines when correct will instinctively say “no” to the doctor, until they 
understand this, and, for some reason, do the act of faith of the 
computationalist.

This undermines only the position of those who believe that computationalism is 
obvious and does not require some act of faith. It does. That is why it is more 
a theology than a psychology, notably.

Bruno





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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 7 Jun 2018, at 00:39, John Clark  wrote:
> 
> 
> On Wed, Jun 6, 2018 at 6:04 AM, Bruno Marchal  > wrote:
> 
> ​>​ in Helsinki, as a computationalist, you know in advance that whatever you 
> will live is a definite unique experience
> 
> ​But as a ​computationalist​ YOU don't know today what the goddamn personal 
> pronoun "YOU​" will mean tomorrow if YOU are going to be duplicated today. 


Why? I know perfectly well what the personal pronoun “you” will mean, as its 
meaning will not change.

What is true is that in Helsinki, I don’t know today if tomorrow I will 
interpret it (as usual) in Moscow or in Washington. 

What you say is equivalent by acknowledging the first person indeterminacy, 
once you take into account that you survive (by computationalism) and that all 
first person obtained in such experience remains unique from their first person 
view.




> 
> ​>>​I couldn't eliminate the personal memories and experiences of Mr. You 
> even if I wanted to because I don't know which one is Mr. YOU, and even Mr. 
> YOU doesn't know that.
> 
> ​> ​That contradicts you statement that each “you” obtained are accepted 
> continuation of the “you” in Helsinki.
> 
> Then answer the question I've been asking for 5 years, forget prediction, 
> after it was all over which ONE turned out to be Mr.You, was​ he​ in in 
> Moscow or Washington?


I will give the same answer: both are, in the 3p outsider picture, and only one 
will be, in the first person picture, but I cannot know which one in advance. 
It is well definite, but non predictable, which is the point.



> If that question can't be answered with ONE word then that proves it was 
> never a question, it was nothing but gibberish and a question mark.
> 
> ​> ​And both of them know very well who they are from their first person 
> point of view.
> 
> ​So both must know what THE ONE and only answer is​, so which ONE is Mr. 
> You?? 

If I could answer that question, there would, of course, no be any first person 
indeterminacy. 



> 
> ​> ​One will say “oh, I am the H-guy having survived in W” and he is right
> 
> ​I agree.​ ​So what is the probability the H-​guy will see W? 100% 

No, because if that is the prediction made in Helsinki, as asked, it will be 
refuted by the M-guy.




> 
> ​> ​the other will say “oh, I am the H-guy having survived in M”, and he is 
> right too.
>  
> ​I agree.​ ​So what is the probability the H-​guy will see M? 100% ​.


No, because if that is the prediction made in Helsinki, as asked, it will be 
refuted by the M-guy.

We want the prediction be correct for both copies, and, trivially, only “W v M” 
will work.

Bruno



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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Brent Meeker]

Just wondering, John.  Did you learn capitalization at the Wharton 
School of Business?


Brent

On 6/6/2018 3:39 PM, John Clark wrote:


On Wed, Jun 6, 2018 at 6:04 AM, Bruno Marchal > wrote:


​>​
/in Helsinki, as a computationalist, you know in advance that
whatever you will live is a definite unique experience/


​But as a ​
computationalist
​ YOU don't know today what the goddamn personal pronoun "*YOU*​" will 
mean tomorrow if *YOU *are going to be duplicated today.



​>>​
I couldn't eliminate the personal memories and
experiences of Mr. You even if I wanted to because I don't
know which one is Mr. YOU, and even Mr. YOU doesn't know that.


​> ​
/That contradicts you statement that each “you” obtained are
accepted continuation of the “you” in Helsinki./


Then answer the question I've been asking for 5 years, forget 
prediction, after it was all over which *ONE* turned out to be Mr.You, 
was

​ he​
in in Moscow or Washington? If that question can't be answered with 
*ONE* word then that proves it was never a question, it was nothing 
but gibberish and a question mark.


​> ​
/And both of them know very well who they are from their first
person point of view./


​So both must know what THE ONE and only answer is​, so which ONE is 
Mr. You??


/
​> ​
One will say “oh, I am the H-guy having survived in W” and he is
right/


​I agree.​
​So what is the probability the H-​guy will see W? 100%

/
​> ​
the other will say “oh, I am the H-guy having survived in M”, and
he is right too./


​I agree.​
​So what is the probability the H-​guy will see M? 100%
​.

John K Clark​





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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Wed, Jun 6, 2018 at 6:04 AM, Bruno Marchal  wrote:

​>​
>  *in Helsinki, as a computationalist, you know in advance that whatever
> you will live is a definite unique experience*
>

​But as a ​
computationalist
​ YOU don't know today what the goddamn personal pronoun "*YOU*​" will mean
tomorrow if *YOU *are going to be duplicated today.


​>>​
>> I couldn't eliminate the personal memories and experiences of Mr. You
>> even if I wanted to because I don't know which one is Mr. YOU, and even Mr.
>> YOU doesn't know that.
>
>
> ​> ​
> *That contradicts you statement that each “you” obtained are accepted
> continuation of the “you” in Helsinki.*
>

Then answer the question I've been asking for 5 years, forget prediction,
after it was all over which *ONE* turned out to be Mr.You, was
​ he​
in in Moscow or Washington? If that question can't be answered with *ONE*
word then that proves it was never a question, it was nothing but gibberish
and a question mark.

​> ​
> *And both of them know very well who they are from their first person
> point of view.*
>

​So both must know what THE ONE and only answer is​, so which ONE is Mr.
You??


*​> ​One will say “oh, I am the H-guy having survived in W” and he is right*
>

​I agree.​

​So what is the probability the H-​guy will see W? 100%


*​> ​the other will say “oh, I am the H-guy having survived in M”, and he
> is right too.*
>

​I agree.​

​So what is the probability the H-​guy will see M? 100%

​.

John K Clark​

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Brent Meeker]

On 6/6/2018 3:04 AM, Bruno Marchal wrote:


But in Helsinki, as a computationalist, you know in advance that 
whatever you will live is a definite unique experience, of W or of M. 
You lost unicity in the 3p view, indeed, but as human survivor, you 
keep it, and feel to be only one of the two copies. In all diaries 
obtained, the results are either W and M. This can be predicted, and 
indeed is verified by the two copies, independently.  Just take the 3p 
and 1p distinction into account, which is part of the question in that 
thought experience.


Bruno


I don't want to get into arguments about pronouns, but now that you've 
explicitly admitted that you believe there is soul and the brain is only 
a kind interface whereby the soul interacts with a physical world, 
doesn't that imply that this soul in not duplicated and only one of the 
W and M bodies has THE soul of the Helsinki man?


Brent

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 4 Jun 2018, at 17:04, John Clark  wrote:
> 
> On Mon, Jun 4, 2018 at 6:14 AM, Bruno Marchal  > wrote:
> 
> ​>>​There is absolutely nothing unique about that silly personal diary of 
> yours and there is nothing unique about your memories either because  because 
> YOU HAVE BEEN DUPLICATED and that is what the word "duplicated" means. 
> 
> ​> ​Sure, but as you say just above, you differentiate just after the 
> duplication, when opening the box
> 
> ​Yes.​ 
>  
> ​> ​and it is because there is only once consciousness before the opening of 
> the door that just before the differentiation,
> 
> ​Yes.​ 
>  
> ​> ​you cannot predict the unique experience that you will live after the 
> duplication.
> 
> YOU can predict that seeing W will turn YOU into the W man and seeing M will 
> turn YOU into the M man.  However YOU can not predict what unique experience 
> YOU will have if YOU is no longer unique,


But in Helsinki, as a computationalist, you know in advance that whatever you 
will live is a definite unique experience, of W or of M. You lost unicity in 
the 3p view, indeed, but as human survivor, you keep it, and feel to be only 
one of the two copies. In all diaries obtained, the results are either W and M. 
This can be predicted, and indeed is verified by the two copies, independently. 
 Just take the 3p and 1p distinction into account, which is part of the 
question in that thought experience.

Bruno


> and not only is prediction impossible there is no way to know what that 
> personal pronoun should have meant even after the experiment is long over. 
> Therefore by examining "What​ ​unique experience will YOU have after “YOU" is 
> no longer unique?" we have an existence proof that not every string of ASCII 
> characters is a question even if it has a question mark at the end.
> 
> ​>>>​Tell me if you get this.
> 
> ​>> ​I don't because there is nothing to get.
> 
> ​> ​Either you fake this,
> 
> ​Generally people pretend to understand scientific points when they really 
> don't, they don't understand them and pretend they don't. ​ 
>  
> ​> ​and are just acting like a bullying
> 
> ​Bullying? So much for being a professional logician. ​ ​If you ​can't stand 
> the heat get out of the logical kitchen.
>  
> ​> ​troll,
> 
> I've been on this list almost as long as you have and I've been expressing 
> similar views elsewhere on the internet for well over 25 years. If I'm a 
> troll I should get a certificate from the Guinness book of world records 
> people as the world's longest living troll who spent more than a quarter of a 
> century expressing views he did not believe. 
> ​
> ​> ​or you just eliminate the personal memories and experience of the 
> subject(s) involved.
> I couldn't eliminate the personal memories and experiences of Mr. You even if 
> I wanted to because I don't know which one is Mr. YOU, and even Mr. YOU 
> doesn't know that.
> 
> 

That contradicts you statement that each “you” obtained are accepted 
continuation of the “you” in Helsinki. And both of them know very well who they 
are from their first person point of view. One will say “oh, I am the H-guy 
having survived in W” and he is right (we assume Mechanism), and the other will 
say “oh, I am the H-guy having survived in M”, and he is right too. Both, when 
repeating the experience understand what is going on, and it is isomorphic as 
throwing a coin.

Bruno


>  John K Clark
> 
>  
> 
> 
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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Mon, Jun 4, 2018 at 6:14 AM, Bruno Marchal  wrote:

​>>​
>> There is absolutely nothing unique about that silly personal diary of
>> yours and there is nothing unique about your memories either because
>>  because YOU HAVE BEEN DUPLICATED and that is what the word "duplicated"
>> means.
>
>
> ​> ​
> *Sure, but as you say just above, you differentiate just after the
> duplication, when opening the box*
>

​Yes.​



> ​>* ​*
> *and it is because there is only once consciousness before the opening of
> the door that just before the differentiation,*
>

​Yes.​



> ​>* ​*
> *you cannot predict the unique experience that you will live after the
> duplication.*
>

YOU can predict that seeing W will turn YOU into the W man and seeing M
will turn YOU into the M man.  However YOU can not predict what unique
experience YOU will have if YOU is no longer unique, and not only is
prediction impossible there is no way to know what that personal pronoun
should have meant even after the experiment is long over. Therefore by
examining "What
​ ​
unique experience will YOU have after “YOU" is no longer unique?" we have
an existence proof that not every string of ASCII characters is a question
even if it has a question mark at the end.

*​>>>​Tell me if you get this.*
>>
>>
> ​>> ​
>> I don't because there is nothing to get.
>
>
> ​>* ​*
> *Either you fake this,*
>

​Generally people pretend to understand scientific points when they really
don't, they don't understand them and pretend they don't. ​



> ​> ​
> *and are just acting like a bullying*
>

​Bullying? So much for being a professional logician. ​

​If you ​can't stand the heat get out of the logical kitchen.


> ​> *​*
> *troll,*
>

I've been on this list almost as long as you have and I've been expressing
similar views elsewhere on the internet for well over 25 years. If I'm a
troll I should get a certificate from the Guinness book of world records
people as the world's longest living troll who spent more than a quarter of
a century expressing views he did not believe.
​

> ​> ​
> or you just eliminate the personal memories and experience of the
> subject(s) involved.
>
I couldn't eliminate the personal memories and experiences of Mr. You even
if I wanted to because I don't know which one is Mr. YOU, and even Mr. YOU
doesn't know that.

 John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 3 Jun 2018, at 22:36, John Clark  wrote:
> 
> On Sun, Jun 3, 2018 at 9:33 AM, Bruno Marchal  > wrote:
> 
> >> If you believe that is not possible then you must believe the most 
> >> important part of us is supernatural and can not be duplicated because it 
> >> is not amenable to the scientific method or even to logic. In other words 
> >> you believe in the soul. If I believed in crap like that I’d burn all my 
> >> scientific books get some saffron robes and join a monastery or something. 
> >>  
>  
> > No. It means that you have a criteria to distinguish undistinguishable state
>  
> You actually want me to tell you my criteria for distinguishing between a 
> un-distinguishable state and a distinguishable one? Very well, in one I can 
> tell a difference because that's what "distinguishable" means, and in the 
> other I can't because the prefix "un" means the opposite.
> 
> > You said your self that two identical brains located at two places 
> > simultaneously will process one consciousness. 
> If the environment is identical yes, they evolve in lockstep at least for a 
> while until random quantum variations and the butterfly effect cause them to 
> diverge.  
> 
> > Yes, I believe in the soul, because it is defined by the conscious owner of 
> > the unique personal diary, or memories.
> There is absolutely nothing unique about that silly personal diary of yours 
> and there is nothing unique about your memories either because  because YOU 
> HAVE BEEN DUPLICATED and that is what the word "duplicated" means. 
> 

Sure, but as you say just above, you differentiate just after the duplication, 
when opening the box, and it is because there is only once consciousness before 
the opening of the door that just before the differentiation, you cannot 
predict the unique experience that you will live after the duplication.

Bruno




> > The soul is the greek [blah blah blah]
> Greeks Greeks Greeks,  with you its always the goddamn imbecilic no nothing 
> Greeks! Hasn't anything of interest happened a little more recently, like in 
> the last 2000 years? I hereby issue a challenge, when you respond to this 
> post see if you can write the entire thing without the words "Greeks" or 
> "diary".  
> 
> > You said yourself very recently in this thread, and also before, that when 
> > the door of the reconstitution box, is not open, the consciousness is unique
> I said when the two boxes were closed the Helsinki man (that is to say the 
> man who remembers being in Helsinki) had 2 brains but only one consciousness 
> experience, but when box was opened and he saw different things and started 
> forming different memories the Helsinki Man had 2 different conscious 
> experiences. Do you disagree with what I just said?   
> 
> > You are avoiding the though experience. Let us consider that “1” 
> > corresponds to “I measure where I feel to be, and see Washington” and “0” 
> > if not. The H-guy survives in both cities, but once they both open the 
> > door, one of them has to write  1 is the diary, and the other one has to 
> > write 0.
> From day one I have clearly stated that for the thought experiment I accept 
> that everybody involved is telling the truth so if one on they says I see 
> city X   I believe him and that's why I get so impatient with that moronic 
> diary, it serves no purpose and just needlessly clutters up a already 
> convoluted thought   experiment. I get it, they are in different environments 
> and so formed different memories I don't need the damn diary to figure that 
> out.  
> 
> > By consulting their diaries, or their personal memories
>  Can we PLEASE drop the idiot diaries? I am perfectly willing to accept that 
> their personal memories are true. 
> 
> >  I don’t see how you don’t see that.
> And I see perfectly well, as I have from day one, that if they are placed in 
> environments that are not identical, and Moscow and Washington are not 
> identical, then they will start to diverge and form different memories. I 
> don't understand why you keep mentioning that as if its a revolutionary new 
> discovery. 
> 
> > In helsinki, the guy knows that he will open the door, and get a definite 
> > result. He just cannot be sure of which one. 
> Bruno,  not only is the Helsinki guy unable to predict that "definite result" 
> he will never ever EVER know what that "definite result" turned out to be. 
> Doesn't that fact make you suspect that maybe just maybe you're just a little 
> bit confused about what "definite result" means? The Helsinki man can't see 
> one definite result if there is no longer one definite Helsinki man, and 
> there no longer is because the Helsinki man HAS BEEN DUPLICATED and that is 
> what "duplicated" means. What did you think it meant?  
> 

Then you eliminate the first person experience, or the first person report. 
Because when I ask the W-guy, he tell me that he did obtained a definite 
result, and the same with the M-guy.




>

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Sun, Jun 3, 2018 at 9:33 AM, Bruno Marchal  wrote:

> >> If you believe that is not possible then you must believe the most
>> important part of us is supernatural and can not be duplicated because it
>> is not amenable to the scientific method or even to logic. In other words
>> you believe in the soul. If I believed in crap like that I’d burn all
>> my scientific books get some saffron robes and join a monastery or
>> something.
>
>

> No. It means that you have a criteria to distinguish undistinguishable
> state


You actually want me to tell you my criteria for distinguishing between
a un-distinguishable state and a distinguishable one? Very well, in one I
can tell a difference because that's what "distinguishable" means, and in
the other I can't because the prefix "un" means the opposite.
>
>
> *> You said your self that two identical brains located at two places
> simultaneously will process one consciousness. *

If the environment is identical yes, they evolve in lockstep at least for a
while until random quantum variations and the butterfly effect cause them
to diverge.

> *> Yes, I believe in the soul, because it is defined by the conscious
> owner of the unique personal diary, or memories.*

There is absolutely nothing unique about that silly personal diary of yours
and there is nothing unique about your memories either because  because YOU
HAVE BEEN DUPLICATED and that is what the word "duplicated" means.

> *> The soul is the greek [blah blah blah]*

Greeks Greeks Greeks,  with you its always the goddamn imbecilic no nothing
Greeks! Hasn't anything of interest happened a little more recently, like
in the last 2000 years? I hereby issue a challenge, when you respond to
this post see if you can write the entire thing without the words "Greeks"
or "diary".

> *> You said yourself very recently in this thread, and also before, that
> when the door of the reconstitution box, is not open, the consciousness is
> unique*

I said when the two boxes were closed the Helsinki man (that is to say the
man who remembers being in Helsinki) had 2 brains but only one
consciousness experience, but when box was opened and he saw different
things and started forming different memories the Helsinki Man had 2
different conscious experiences. Do you disagree with what I just said?

> *> You are avoiding the though experience. Let us consider that “1”
> corresponds to “I measure where I feel to be, and see Washington” and “0”
> if not. The H-guy survives in both cities, but once they both open the
> door, one of them has to write  1 is the diary, and the other one has to
> write 0.*

>From day one I have clearly stated that for the thought experiment I accept
that everybody involved is telling the truth so if one on they says I see
city X   I believe him and that's why I get so impatient with that moronic
diary, it serves no purpose and just needlessly clutters up a already
convoluted thought   experiment. I get it, they are in different
environments and so formed different memories I don't need the damn diary
to figure that out.

> *> By consulting their diaries, or their personal memories*

 Can we PLEASE drop the idiot diaries? I am perfectly willing to accept
that their personal memories are true.

> *>  I don’t see how you don’t see that.*

And I see perfectly well, as I have from day one, that if they are placed
in environments that are not identical, and Moscow and Washington are not
identical, then they will start to diverge and form different memories. I
don't understand why you keep mentioning that as if its a revolutionary new
discovery.

> *> In helsinki, the guy knows that he will open the door, and get a
> definite result. He just cannot be sure of which one. *

Bruno,  not only is the Helsinki guy unable to predict that "definite
result" he will never ever EVER know what that "definite result" turned out
to be. Doesn't that fact make you suspect that maybe just maybe you're just
a little bit confused about what "definite result" means? The Helsinki man
can't see one definite result if there is no longer one definite Helsinki
man, and there no longer is because the Helsinki man HAS BEEN DUPLICATED
and that is what "duplicated" means. What did you think it meant?

> *> Washington and Moscow seem to me rather different environments. *

Yes, and so they will form different memories, but information is physical
so that means the arrangement of atoms in the two will be different.
Identical arrangements of atoms will produce identical conscious
experiences, different arrangements will produce different conscious
experiences. So what's your point?

> *>  it is impossible to predict among the answers W and M, or 1 and 0,
> which one will occur,*

The reason its impossible to get the answer is because its impossible to
state the question.

> *> at both place, the survivor feels to be unique in one place *

Yes and that fact is 100% predicable, one unique feeling survivor feels
he’s in Washington and another uni

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 1 Jun 2018, at 19:52, John Clark  wrote:
> 
> On Fri, Jun 1, 2018 at 4:09 AM, Bruno Marchal  > wrote:
> 
> >>> The 1p-you is defined by the sequence of memories personally accessible​
> 
> >> That does not define a unique object if the world contains 1p-you 
> >> duplicating machines as it does in your thought experiment ,
> 
> >How could that be possible?
> That is a very odd question for a scientifically minded person to ask, very 
> odd indeed. If you believe that is not possible then you must believe the 
> most important part of us is supernatural and can not be duplicated because 
> it is not amenable to the scientific method or even to logic. In other words 
> you believe in the soul. If I believed in crap like that I’d burn all my 
> scientific books get some saffron robes and join a monastery or something.  
> 
> 


No. It means that you have a criteria to distinguish undistinguishable state. 
You said your self that two identical brains located at two places 
simultaneously will process one consciousness. 

Yes, I believe in the soul, because it is defined by the conscious owner of the 
unique personal diary, or memories. The soul is the greek original way to point 
on the first person experience. 




> > After iterating 10 times the duplication, each 1p person is unique, 
> They would only be unique if the duplication machine was bad or if the 
> environments they were in was different and there was sufficient time for 
> then to diverge.
> 
> 

Not at all. The diverge when they open the door nd see in which city they are. 
You said yourself very recently in this thread, and also before, that when the 
door of the reconstitution box, is not open, the consciousness is unique




> > with its definite history in the diary (like 1000110110). 
>  
> If I can be duplicated then 1000110110 can be too,

Of course.




> hell technology is good enough to to that right now. That’s why the entire 
> diary business you keep talking about is so dumb.


You are avoiding the though experience. Let us consider that “1” corresponds to 
“I measure where I feel to be, and see Washington” and “0” if not.

The H-guy survives in both cities, but once they both open the door, one of 
them has to write  1 is the diary, and the other one has to write 0. Then they 
come back by usual plane, still with their diary, and do the experience again. 
After that we have 4 “H-Guys”, one with the history 11 in his diary, one with 
10, one with 01, and one with 00. The H-guy could have guess that this is what 
happen, and that any attempt to predict a certain definite outcome of that 
sequence of self-localisation would be refuted by all the others. 



> 
> >> therefore it is nonsensical to ask what one and ony one thing will "you" 
> >> see or feel. If you claim the 1p-you can not be duplicated then there must 
> >> be some subjective difference between the two, but we know there is not 
> >> because they can't ever tell which one they are, the copy or the original.
> 
> > They can each tell who they are among the 2^10.
> 
> I don't see how.
> 

?

By consulting their diaries, or their personal memories. I don’t see how you 
don’t see that.



>  In fact if the duplicating machine was working properly and the environments 
> were the same then there wouldn’t even be a “they”, there wouldn’t be 2^10 
> conscious beings, they would all be identical so there would only be one.
> 
> 

In helsinki, the guy knows that he will open the door, and get a definite 
result. He just cannot be sure of which one. 


> 
> > They have become different but they are all the original. 
> Then time must have passed and you must of put them in different environments.
> 

Washington and Moscow seem to me rather different environments. 




> Either that or you haven't been performing proper maintenance on the 
> duplicating machine and it is malfunctioning. 
> 
> > Of course the diary can be duplicated. That is the whole point
> Then I’ll be damned if I know what “the whole point” is.
> 
> 


To show that in a self-duplication experience of the type described, it is 
impossible to predict among the answers W and M, or 1 and 0, which one will 
occur, despite with computationalism we strive at both places. The thereupon is 
that at both place, the survivor feels to be unique in one place (or mechanism 
is wrong, or the door did not choose the right level, etc.).





> > but it contains different strings of 0 and 1
> 
> Then the diary is saying different things from the original and you r  
> duplicating machine is malfunctioning.
> 

No. The guy enter with for example 000 in the diary. Then in both cities, he is 
reconstitute with the same 000. But then he opens the door, and obviously, the 
one in Washington complete the diary into 0001, and the one in Moscow complete 
the diary into . Then they come back in Helsinki, by train or plane, and do 
the experience again. The content of the diary is well duplicated, but 

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Fri, Jun 1, 2018 at 4:09 AM, Bruno Marchal  wrote:

> >>>
>>> *The 1p-you is defined by the sequence of memories personally
>>> accessible​*
>>
>>
> >> That does not define a unique object if the world contains 1p-you
>> duplicating machines as it does in your thought experiment ,
>
>
> >*How could that be possible?*

That is a very odd question for a scientifically minded person to ask, very
odd indeed. If you believe that is not possible then you must believe the
most important part of us is supernatural and can not be duplicated because
it is not amenable to the scientific method or even to logic. In other
words you believe in the soul. If I believed in crap like that I’d burn all
my scientific books get some saffron robes and join a monastery or
something.

> *> After iterating 10 times the duplication, each 1p person is unique, *

They would only be unique if the duplication machine was bad or if the
environments they were in was different and there was sufficient time for
then to diverge.

> *> with its definite history in the diary (like 1000110110). *


If I can be duplicated then 1000110110 can be too, hell technology is good
enough to to that right now. That’s why the entire diary business you keep
talking about is so dumb.

>> therefore it is nonsensical to ask what one and ony one thing will "you"
>> see or feel. If you claim the 1p-you can not be duplicated then there must
>> be some subjective difference between the two, but we know there is not
>> because they can't ever tell which one they are, the copy or the original.
>
>
> > *They can each tell who they are among the 2^10.*


I don't see how. In fact if the duplicating machine was working properly
and the environments were the same then there wouldn’t even be a “they”,
there wouldn’t be 2^10 conscious beings, they would all be identical so
there would only be one.

*> They have become different but they are all the original. *

Then time must have passed and you must of put them in different
environments. Either that or you haven't been performing proper maintenance
on the duplicating machine and it is malfunctioning.

> *> Of course the diary can be duplicated. That is the whole point*

Then I’ll be damned if I know what “the whole point” is.

> *> but it contains different strings of 0 and 1*

Then the diary is saying different things from the original and you r
 duplicating machine is malfunctioning. And if a copy the diary  is made
with a Xerox machine and the copy says something different from the
original then the Xerox machine is malfunctioning.

> >> A thing like a unbridgeable wall between Washington and Moscow is
> tantamount to postulating a new law of physics,
> ​
>
​
>
> > *That makes no sense, as your use of “tantamount” illustrates.*

Get a dictionary, it means equivalent.

> >> and there is no evidence such a law exists or any reason to even
>> suspect that it does in order to explain experimental results.
>
>
>
> >* But it is enough we could build it.*

You can’t build it because you can’t make the laws of physics be anything
you want them to be.

John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 30 May 2018, at 21:56, John Clark  wrote:
> 
> 
> 
> On Wed, May 30, 2018 at 12:31 PM, Bruno Marchal  > wrote:
> 
> 
> ​> ​The 1p-you is defined by the sequence of memories personally accessible
> 
> ​That does not define a unique object if the world contains 1p-you 
> duplicating machines as it does in your thought experiment​,


How could that be possible? After iterating 10 times the duplication, each 1p 
person is unique, with its definite history in the diary (like 1000110110). 


>  therefore it is nonsensical to ask what one and ony one thing will "you" see 
> or feel. If you claim the ​1p-you​ can not be duplicated then ​there must be 
> some subjective difference between the two, but we know there is not because 
> they can't ever tell which one they are, the copy or the original.

They can each tell who they are among the 2^10. They have become different, but 
they are all the original. We have already agreed that personal identity is not 
transitive, nor euclidian, etc.



> 
>  
> ​> ​like the personal diary
> 
> ​If the 1p-you can be duplicated ( and can be because there is no way to know 
> if "you" are the copy or the original because both have identical subjective 
> experiences) then it can certainly duplicate a  diary. That's why the entire 
> diary business is so dumb.  

Of course the diary can be duplicated. That is the whole point, but it contains 
different strings of 0 and 1, which specifies for each resulting person who 
they have become.




>  
> ​> ​I remind you that your argument that in the two situations the 
> doppelgängers have different chance to meet, is not relevant, or just add in 
> the thought experience that someone has build a an unbridgeable wall between 
> Washington and Moscow.
> 
> ​If the laws of physics work the way we think they do then I can never meet 
> my Everett style doppelganger even in principle, but I can if my doppelganger 
> was made in a 1p-you duplicating machine as it was in your thought experiment.


If QM is slightly not linear, as shown by Weinberg and Plaga (cf this list), 
the doppelgänger are accessible, but that does not change the probabilities. 
Anyway, the meeting has no relevance for the immediate probabilities at all.





> A thing like a unbridgeable wall between Washington and Moscow is tantamount 
> to postulating a new law of physics,

That makes no sense, as your use of “tantamount” illustrates.



> and there is no evidence such a law exists or any reason to even suspect that 
> it does in order to explain experimental results.


But it is enough we could build it. Or you introduce non Turing emulable 
element in the mind implicitly, and we can no more say “yes” to the doctor, at 
least through Mechanism. You need Mechanism + some non Turing emulable magic. 



> So in summary if physics were different ​then​ you could be right, but it 
> isn't and you're not.  


Like anticipated, you avoid the reasoning without saying anything relevant. Why 
does people do that. I met a lot of people like you on Facebook, but always on 
the subject of drugs, or on Israel, or similar, but almost never on scientific 
matter. 

If someone else can defend your point, let him/her speak.

Bruno






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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Wed, May 30, 2018 at 12:31 PM, Bruno Marchal  wrote:


​> ​
> The 1p-you is defined by the sequence of memories personally accessible
>

​
That does not define a unique object if the world contains 1p-you
duplicating machines as it does in your thought experiment
​, therefore it is nonsensical to ask what one and ony one thing will "you"
see or feel. If you claim the ​
1p-you
​ can not be duplicated then ​there must be some subjective difference
between the two,
but we know there is not because they can't ever tell which one they are,
the copy or the original.



> ​> ​
> like the personal diary
>

​
If the 1p-you can be duplicated ( and can be because there is no way to
know if "you" are the copy or the original because both have identical
subjective experiences) then it can certainly duplicate a  diary. That's
why the entire diary business is so dumb.


> ​> ​
> *I remind you that your argument that in the two situations the
> doppelgängers have different chance to meet, is not relevant, or just add
> in the thought experience that someone has build a an unbridgeable wall
> between Washington and Moscow.*
>

​
If the laws of physics work the way we think they do then I can never meet
my Everett style doppelganger even in principle, but I can if my
doppelganger was made in a 1p-you duplicating machine as it was in your
thought experiment. A thing like a unbridgeable wall between Washington and
Moscow is tantamount to postulating a new law of physics, and there is no
evidence such a law exists or any reason to even suspect that it does in
order to explain experimental results. So in summary if physics were
different
​then​
 you could be right, but it isn't and you're not.

​ ​
John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

Others,

I thanks John Clark for giving me the opportunity to sum up the basics.

Of course anyone can ask for a precision.

I train my pedagogy.

Grayson, don’t hesitate to read my sum up here:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html

Download the slides, and read the argument in 8 steps. 

I mean, it seems you want to understand, OK?

I am a teacher. I am aware that when people want to not understand, they can be 
quite gifted in the task. 





> On 30 May 2018, at 15:26, John Clark  wrote:
> 
> 
> 
> On Wed, May 30, 2018 at 5:46 AM, Bruno Marchal  > wrote:
> 
> ​> ​Just try to refute step 3 without eliminating the distinction between 
> first and third person view,
>  
> Just try explaining what unique thing the personal pronoun “you” refers to in 
> a world that contains first person view duplicating machines. Until you do 
> that step 3 isn't even wrong, its gibberish and only a fool keeps reading a 
> proof after gibberish is found.


It means exactly the same as the one used informally by Everett in his short 
and long texts. 

The 1p-you is defined by the sequence of memories personally accessible, like 
the personal diary taken by the candidate for some duplication, or the person 
in the superposition state seeing a dead cat + seeing a cat alive. In both 
case, after the result of the experience, the 1p-you have multiplied (in the 3p 
“reality”) and each assess a precise sharp results of the measurement (like 
“Washington”, or “cat alive”, etc.).

I remind you that your argument that in the two situations the doppelgängers 
have different chance to meet, is not relevant, or just add in the thought 
experience that someone has build a an unbridgeable wall between Washington and 
Moscow.

The 1p-you are associated to series of machine states, and it is the sequence 
of memorised measurements, or local input readings building your personal 
history. The 1p-you is always unique from the 1p-you point of view. After a 10 
times iterated duplication, each resulting persons surviving that experience, 
among 2^10, have a unique precise personal history given by a precise sequence, 
like say 10100111011. As the 1p-you is defined by that sequences.

The 3p-you is given by your body, up to some local representation with respect 
to some universal number/machine/combinator or more general.

The only difference is that Everett does that in a universal quantum universal 
machine, the “universal” wave. I do it in arithmetic, or in any Turing 
universal machinery (phi_i)

I recall that phi_i is the sequence of partial recursive/computable function, 
that you can enumerate by enumeration all programs in any presentation of a 
programming language or computer, in the sense of Church, Post, ...

All I say is that if computationalism is true, the quantum universal 
dovetailing, the wave, the unitary rotation,  has to be justified by some 
precise intensional variant of Gödel’s arithmetical (and sigma_1 complete) 
predicate of provability/believability.

It is not a matter of choice, or you can always invoke some magic to stop the 
reasoning.

If you study a bit of math, and what is a universal machinery (the phi_i and 
w_i), you will understand that I introduce 

(4 + 4 * infinity ) nuances of “you” and “me”. 

Each one having a precise definition either in first order arithmetic, or in in 
term of such arithmetical relations.

I understand it is shocking for the strong believer in a primitively material 
universe(s), or in physicalism, as you can sum it all by it is in the head of 
the universal (church-Turing-Post-Kleene) machine.

The universal machine is not a theory of everything, it is a door to the 
unknown. It is a baby god, which can become a terrible child, also. 

Bruno




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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Wed, May 30, 2018 at 5:46 AM, Bruno Marchal  wrote:

​> ​
> *Just try to refute step 3 without eliminating the distinction between
> first and third person view,*
>

Just try explaining what unique thing the personal pronoun “you” refers to
in a world that contains first person view duplicating machines. Until you
do that step 3 isn't even wrong, its gibberish and only a fool keeps
reading a proof after gibberish is found.

​ ​
John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 29 May 2018, at 17:34, John Clark  wrote:
> 
> On Tue, May 29, 2018 at 10:48 AM, Bruno Marchal  > wrote:
> 
> ​> ​You, Sir, are definitely a troll. Your answer here is just a bunch of 
> begging the question, and of spreading misinformations, + blatant 
> inconsistencies, on the very subject of computability. Whatever I would 
> answer would be used to aggravate this. You are a liar, as many said already, 
> and a troll. 
> 
> ​Translation from the original Brunospeak:
> "I can find no logical response to the points you raised against my ideas so 
> I’m afraid to continued this debate because I'd only end up looking even 
> worse."
> 
> 


Just try to refute step 3 without eliminating the distinction between first and 
third person view, then we can talk again.

Bruno






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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Tue, May 29, 2018 at 10:48 AM, Bruno Marchal  wrote:

​> ​
> *You, Sir, are definitely a troll. Your answer here is just a bunch of
> begging the question, and of spreading misinformations, + blatant
> inconsistencies, on the very subject of computability. Whatever I would
> answer would be used to aggravate this. You are a liar, as many said
> already, and a troll. *
>

​
*Translation from the original Brunospeak:*

*"I can find no logical response to the points you raised against my ideas
so I’m afraid to continued this debate because I'd only end up looking even
worse."*
John K Clark


*​*

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 28 May 2018, at 18:09, John Clark  wrote:
> 
> On Sun, May 27, 2018 at 6:15 AM, Bruno Marchal  > wrote:
> 
> > You ask me examples of computations?
> No, I did not ask you that. I asked you for an example of a computation made 
> WITHOUT THE USE OF MATTER THAT OBEYS THE LAWS OF PHYSICS.
> 
> > OK, that is fair enough.
> Let me give you some example. In the Turing formalism, with combinators, and 
> with elementary arithmetic, and an informal one with Diophantine 
> polynomial.1) With Turing machine, which are set of quadruple q_i S_j S_k q_r 
> [blah blah]​ ​So, a computation, which is an abstract sequence of  [wow wow] 
> First of all that's not an example, that's just another goddamn definition. 
> And second of all if its abstract that means it exists in the form of a 
> thought not a physical structure, but you can't give me an example (although 
> I'm sure you could dig up many definitions) of a thought exiting WITHOUT THE 
> USE OF MATTER THAT OBEYS THE LAWS OF PHYSICS.
> 
> > Example 
> SS(KI)(KK)(SS)
> S(KK)(KI(KK)))(SS)
> S(KK)I(SS)
> KK(SS)(I(SS)
> KK(SS)(SS)
> K(SS)
> What the hell do you think that proves? Those are symbols computed by your 
> physical brain typed by your physical computer transmitted to my physical 
> computer by physical means and then interpreted by my physical brain. If 
> computations are not subject to the limitation of physics then tell me, what 
> is the seventieth non-Mesmer prime that is larger than 2^77,232,917 − 1 ?  
> Since you're not limited by trivialities like the speed of light, quantum 
> mechanics, energy considerations , the nature of space and time or any other 
> physical factor I expect to see your answer by tomorrow morning at the 
> latest.
> 
> > He important point is that the definition of computation [blah blah]
> To hell with definitions, definitions can’t compute
> 
> > The definition can be done with [...]
>  
> OK Bruno sit down and let me explain to you something about definitions. All 
> your definitions are made of mathematical symbols, and those symbols have 
> there own definitions that consist of more mathematical symbols. You only 
> have a finite number of mathematical symbols in your toolbox so eventually 
> you’re going to have the definition of symbol X needing symbol Y and the 
> definition of symbol Y needing symbol X.  The only way to break out of that 
> meaningless circularity and put some meat on the bone is not with more 
> definitions but with examples, in particular examples from the PHYSICAL 
> world. Without physical examples a mountain full of dictionaries wouldn’t 
> help and the English language would just be meaningless noise and the 
> Mathematical language just a game played with squiggles of no more profundity 
> that a crossword puzzle.  
> 
> 
> >>I want an EXAMPLE not another silly definition. But you can't provide one 
> >>nor can anyone else.
> 
> > I just did.
> BULLSHIT!   
> 
> > Both examples can be translated into pure number theoretical relation
> 
> ​Nothing can be translated into anything without matter that obeys the laws 
> of physics.
> 
> 
> > x + 0 = x
> x + s(y) = s(x + y)
> Try to compute s(0) + (s0).
> Again the key point is that Logic + the axioms:
> 0 ≠ s(x)
> s(x) = s(y) -> x = y
> x = 0 v Ey(x = s(y))
> x+0 = x
> x+s(y) = s(x+y)
> x*0=0 x*s(y)=(x*y)+x
> Provides a Turing-complete (but not Löbian) theory, that is, a universal 
> machinery and machine.
> As you can see, no assumption on a physical reality is made
> True, no assumption of physical reality has been made and no computation made 
> without the use of matter that obeys the laws of physics has been made 
> either. If I'm wrong about that then the simplest way to prove I’m wrong is 
> to make a calculation that physics could never do even in theory. The  7918th 
> Busy Beaver number is large but finite and if all the Real Numbers exist (I 
> have my doubts but I'm sure you don't) then the 7918th Busy Beaver number 
> exists, so tell me what it is. If you are not limited by the boundaries of 
> the merely physical this task should be easy.
> 
> > This is needed only to ensure the existence of a physical computation, 
> > which is a much more particular concept.
> I maintain physical computation is the only type of computation there is, and 
> you can't prove me wrong by dreaming up yet another definition. And I don't 
> want to see another computation made with your physical brain, show me a 
> computation made with your non-physical brain, and the best way to prove it 
> was done non-physically is to compute something physics can't, like finding 
> the 7918th Busy Beaver number, its finite but too big for physics to handle.  
> In your last post you claim you've already made a small non-physical 
> computation, but size is a mere physical thing so making a calculation that 
> is a little bit larger should be no barrier to you. So the second number I 
> expect to hear from you by tomo

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Sun, May 27, 2018 at 6:15 AM, Bruno Marchal  wrote:

> *> You ask me examples of computations?*

No, I did not ask you that. I asked you for an example of a computation
made WITHOUT THE USE OF MATTER THAT OBEYS THE LAWS OF PHYSICS.

>
> *> OK, that is fair enough.Let me give you some example. In the Turing
> formalism, with combinators, and with elementary arithmetic, and an
> informal one with Diophantine polynomial.1) With Turing machine, which are
> set of quadruple q_i S_j S_k q_r [blah blah]​ ​So, a computation, which is
> an abstract sequence of  [wow wow] *

First of all that's not an example, that's just another goddamn definition.
And second of all if its abstract that means it exists in the form of a
thought not a physical structure, but you can't give me an example
(although I'm sure you could dig up many definitions) of a thought exiting
WITHOUT THE USE OF MATTER THAT OBEYS THE LAWS OF PHYSICS.

>
>
>
>
>
>
> *>
> Example SS(KI)(KK)(SS)S(KK)(KI(KK)))(SS)S(KK)I(SS)KK(SS)(I(SS)KK(SS)(SS)K(SS)*

What the hell do you think that proves? Those are symbols computed by your
physical brain typed by your physical computer transmitted to my physical
computer by physical means and then interpreted by my physical brain. If
computations are not subject to the limitation of physics then tell me,
what is the seventieth non-Mesmer prime that is larger than 2^77,232,917 −
1 ?  Since you're not limited by trivialities like the speed of light,
quantum mechanics, energy considerations , the nature of space and time or
any other physical factor I expect to see your answer by tomorrow morning
at the latest.

> *> He important point is that the definition of computation [blah blah]*

To hell with definitions, definitions can’t compute

> *> The definition can be done with [...]*


OK Bruno sit down and let me explain to you something about definitions.
All your definitions are made of mathematical symbols, and those symbols
have there own definitions that consist of more mathematical symbols. You
only have a finite number of mathematical symbols in your toolbox so
eventually you’re going to have the definition of symbol X needing symbol Y
and the definition of symbol Y needing symbol X.  The only way to break out
of that meaningless circularity and put some meat on the bone is not with
more definitions but with examples, in particular examples from the
PHYSICAL world. Without physical examples a mountain full of dictionaries
wouldn’t help and the English language would just be meaningless noise and
the Mathematical language just a game played with squiggles of no more
profundity that a crossword puzzle.


>>I want an EXAMPLE not another silly definition. But you can't provide one
>> nor can anyone else.
>
>
> > *I just did.*

BULLSHIT!

> *> Both examples can be translated into pure number theoretical relation*

​Nothing can be
 translated into anything without matter that obeys the laws of physics.



>
>
>
>
>
>
>
>
>
>
> *> x + 0 = xx + s(y) = s(x + y)Try to compute s(0) + (s0).Again the key
> point is that Logic + the axioms:0 ≠ s(x)s(x) = s(y) -> x = yx = 0 v Ey(x =
> s(y))x+0 = xx+s(y) = s(x+y)x*0=0 x*s(y)=(x*y)+xProvides a
> Turing-complete (but not Löbian) theory, that is, a universal machinery and
> machine.As you can see, no assumption on a physical reality is made*

True, no assumption of physical reality has been made and no computation
made without the use of matter that obeys the laws of physics has been made
either. If I'm wrong about that then the simplest way to prove I’m wrong is
to make a calculation that physics could never do even in theory.
The  7918th Busy Beaver number is large but finite and if all the Real
Numbers exist (I have my doubts but I'm sure you don't) then the 7918th
Busy Beaver number exists, so tell me what it is. If you are not limited by
the boundaries of the merely physical this task should be easy.

> *> This is needed only to ensure the existence of a physical computation,
> which is a much more particular concept.*

I maintain physical computation is the only type of computation there is,
and you can't prove me wrong by dreaming up yet another definition. And I
don't want to see another computation made with your physical brain, show
me a computation made with your non-physical brain, and the best way to
prove it was done non-physically is to compute something physics can't,
like finding the 7918th Busy Beaver number, its finite but too big for
physics to handle.  In your last post you claim you've already made a small
non-physical computation, but size is a mere physical thing so making a
calculation that is a little bit larger should be no barrier to you. So the
second number I expect to hear from you by tomorrow morning is the 7918th
Busy Beaver number.

> *> It will of course be defined only after*

Bruno, no finite number of definitions are going to be enough to allow you
to break out of the meaningless logical loop you’ve gotten yourself into.

> >> and that is 

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 26 May 2018, at 01:43, John Clark  wrote:
> 
> On Thu, May 24, 2018 at 1:18 PM, Bruno Marchal  > wrote:
> 
> > I have provided definition of computations, and explicit examples,
> 
> I’m not interested in your definitions, examples are VASTLY more important.  
> Definitions can't conjure anything into existence except for more 
> definitions. 

You ask me examples of computations? OK, that is fair enough.

Let me give you some example. In the Turing formalism, with combinators, and 
with elementary arithmetic, and an informal one with Diophantine polynomial.

1) With Turing machine, which are set of quadruple q_i S_j S_k q_r. (The qs are 
state, the Ss are symbols tape).

The computation start from some instantaneous tape description, with the 
machine in state q_1, and this can be written

q_1S_nS_mS_l …. S_h. (It means that the machine is scanning the first element 
of its tape containing S_n, and it looks if it has a quadrupent beginning with 
q_1 S_n, and operates accordingly (see my preceding post on this).

So, a computation, which is an abstract sequence of instantaneous description 
of the machine enforced by its quadruplet. It will looks like:

q1S2S0S5S3
S2q1S0S5S3
S2S0q1S5S3
S2S0S5q2S5
S2S0q3S5S5

More on this in Davis little book “Computability and unsolvability”. See 
especially the chapter 4 which explains in all details how this is entirely 
translatable in Arithmetic, using Gödel’s numbering ¨*and* computational 
isomophism.

2) with combinators. I recall that S and K are combinators, and that if x and y 
are combinators so is (x y), abbreviated by xy (we suppress all left 
parentheses for reason of readability (aaa(bbb)aaa must be read as if it is 
a a) a)((b b) b))((a a ) a)).
The axioms of reduction aare Kxy => x and Sxyz => xz(yz).
In this case, it happens that a computation is a sequence of combinators, each 
resulting from the preceding one by the application of the axioms of reduction.

Example 

SS(KI)(KK)(SS)
S(KK)(KI(KK)))(SS)
S(KK)I(SS)
KK(SS)(I(SS)
KK(SS)(SS)
K(SS)

The computations should be identified with their description, but only with 
their abstract sequence when a universal number, like the combinators axioms, 
related them.

Amazingly, it can be shown that Turing machine can mimic exactly the 
combinators, and that the combinators can mimic exactly the Turing machine 
computations, and that a universal number cannot distinguish its base 
computations by introspection.




> Definitions of computation without the use of matter

That is not the interesting or relevant point. He important point is that the 
definition of computation, including their existence do not *assume* the 
existence of anything physical. The definition can be done with our without 
matter, but what is important is that the computation themselves does not 
require the assumption of a physical reality. Eventually, with mechanism, it is 
the physical reality which is emergent from the first person statistics on all 
computation (and this is conformed by the fact that []p & p, []p & <>t, and []p 
& <>t & p, obeys to quantum logics when p is restricted to the sigma_1 
sentences (which correspond to the computable states by Kleene Normal Form 
theorem).


> that obeys the laws of physics exist, but that certainly doesn't means 
> computations without the use of matter that obeys the laws of physics exists; 
> that's why I want an EXAMPLE not another silly definition. But you can't 
> provide one nor can anyone else.

I just did. Both examples can be translated into pure number theoretical 
relation, preserving the computational isomorphism that Gödel discovered 
between partial computability and the arithmetic reality, although this will be 
made utterly precise by Kleene’s normal form theorem.

I let you give a computation with  elementary arithmetic, or just with the 
addition axioms:

x + 0 = x
x + s(y) = s(x + y)

Try to compute s(0) + (s0).

Again the key point is that Logic + the axioms:

0 ≠ s(x)
s(x) = s(y) -> x = y
x = 0 v Ey(x = s(y))
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x


Provides a Turing-complete (but not Löbian) theory, that is, a universal 
machinery and machine.

As you can see, no assumption on a physical reality is made. This is needed 
only to ensure the existence of a physical computation, which is a much more 
particular concept. It will of course be defined only after we have derived the 
sum on all computations.


>  
> 
>   >  and explicit examples, with the combinators, (may be you were not yet in 
> this list), with numbers, with LISP and lambda-expressions,
> 
> That is an excellent example of something that has never calculated a goddamn 
> thing and never will. It is a description of how matter that obeys the laws 
> of physics can make a calculation if it is organized in a certain way. 
> Specifically a structure made of matter can calculate if and only if its 
> logical operational structure in its simplest most essential form 

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Thu, May 24, 2018 at 1:18 PM, Bruno Marchal  wrote:

*> I have provided definition of computations, and explicit examples,*


I’m not interested in your definitions, examples are VASTLY more
important.  Definitions can't conjure anything into existence except for
more definitions.  Definitions of computation without the use of matter
that obeys the laws of physics exist, but that certainly doesn't means
computations without the use of matter that obeys the laws of physics
exists; that's why I want an EXAMPLE not another silly definition. But you
can't provide one nor can anyone else.

  *>  and explicit examples, with the combinators, (may be you were not yet
> in this list), with numbers, with LISP and lambda-expressions,*


That is an excellent example of something that has never calculated a
goddamn thing and never will. It is a description of how matter that obeys
the laws of physics can make a calculation if it is organized in a certain
way. Specifically a structure made of matter can calculate if and only if
its logical operational structure in its simplest most essential form is a
Turing Machine. And yes I know, the authors of many computational papers
never specifically mention matter or the laws of physics, they take that as
a given too obvious to mention, and that is exactly why numbers, with LISP
and lambda-expressions by themselves can't calculate a goddamn thing . I
mean, do the programers at Microsoft really have to constantly remind their
bosses that for the computer code they’ve just written to actually do what
they claim it can do it must first be run on a computer??

*> I am not inclined to repeat this,*


Thank god!

*>  Let me quote Gödel What matter in a computation is that at some
> (relative )instant, some proposition are true, like “the content at place 3
> of the register R is 5” ,*


For that to be relevant to our topic Godel would first have to establish
that "register R" actually exists independently of atoms that obey the laws
of physics, and that register R had at least 3 places in it, and the
contents of the third place in that register is 5. And Godel did not do any
of that, he just made a definition, nobody has ever done that and nobody
has ever done anything even a little bit like that and nobody ever will.
And it may be true that Godel gave definitions of things without referring
to physics but definitions alone don't automatically cause things to spring
into existence.

JK Rowling defined Harry Potter as a boy wizard and gave a detailed
description of him in 7 books, but Rowling did not prove that Harry Potter
actually exists. Just as with the English language both fiction and
nonfiction can be written in the language of mathematics. Just as with
English fiction mathematical fiction may be very interesting and it may
sometimes provide poetic insights and hints about the real world, but that
doesn’t change the fact that Harry Potter doesn’t exist.



> *> John, if you don’t buy some book and study, you will just look like a
> liar. Buy the Dover book by Davis “The Undecidable”*


Stop talking down to me, I’ve been listening and from everything I've heard
I must conclude that I have a deeper understanding of mathematical logic
than you do. I make no claim of being particularly smart but I have done
something you have not, I've avoided a fundamental blunder, the same
blunder any good freshman student would be able to avoid by his second day
studying the subject, I understand that defining X is not the same thing as
proving X exists independently of matter that obeys the laws of physics.

> you will just look like a liar


At least I haven't been educated beyond my intelligence. I don't know much
but what little I do know I know in some depth.

*> Apple would not exist if Turing and other mathematician did not
> discovered the universal machineries and machines.*


True, we need mathematicians to describe to us how to organize matter so it
can calculate. It is also true that Apple would not exist if physicists
like Brattain, Shockley and Bardeen hadn't invented the transistor because
a description of a computation is just not good enough to get the job done,
you've got to actually make the calculation, you’ve got to get an answer,
and that can't be done without matter and physics.

> *The “theology” of the machine is* [...]


Sorry, I haven’t been updated so I don’t know what the word “theology”
means in Brunospeak today, so I can’t comment.

*> Let me quote Gödel (footnote 9) of its 1931 paper “In other words the
> above described procedure provides an isomorphic image of PM (principal
> mathematical) in the domain of arithmetic, and all metamathematical
> arguments can equally well be conducted in this isomorphic image”.*


Principal mathematical? I assume you mean " Principia Mathematica " the
massive book by Russell and Whitehead, as Godel mentions it in the very
title of his famous 1931 paper that you're talking about, and Russell said
that as far as he knew there we

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 24 May 2018, at 01:05, John Clark  wrote:
> 
> On Wed, May 23, 2018 at 8:59 AM, Bruno Marchal  > wrote:
> 
> >  You were changing the mathematical definition of computations given 
> > independently by Church, Post, Turing, Markov 
>> ​>​I don't know what definition you're referring to
> 
> ​> ​See any (serious) textbook in logic.
> 
> ​In other words YOU DON'T KNOW.​ 


?



> ​Nobody says "the proof you are wrong is in some unspecified ​book" if they 
> have the ability to provide a better retort.


I did answer this many times. I have provided definition of computations, and 
explicit examples,  with the combinators, (may be you were not yet in this 
list), with numbers, with LISP and lambda-expressions, …

I am not inclined to repeat this, because it is long to explain, rather subtle 
(it needs to prove the intensional Church-Turing thesis), and, as we need all 
the time to describe the computations, someone who want to fake 
non-understanding will have plenty of word-play to use, so, I prefer to invite 
you into studying the subject. 

By the normal form theorem of Kleene all computations can be transformed into 
the search of solutions of a degree 4 diophantine polynomial. All the 
subtleties between proof and computations will come from the association of 
computations with proof of sigma_1 proposition (basically ExP(x, y) with P 
decidable/total-computable).

Then “provable” has been famously translated in arithmetic. Each time I use 
“[]” it can be seen as an abbreviation of Gödel arithmetical Beweisbar 
predicate.

Note that, with t the boolean constant “true” and f the boolean constant 
“false”, the non provability of the false, consistency is ~Bewesibar(“f”), or 
~Bewesibar(“0 = s(0)”), with the “ “  “ playing the role of Gödel numbers. 

The Gödel numbering is only the faithful *representation*, and is only one half 
of the arithmetization (of metamathematics). What you need to understand, is 
that at the digital substitution level, the arithmetical truth supports 
*semantically” the relation making some number relation into computations.

The people needs to read only one paper, really, which is the Gödel 1931 paper 
(it exists in Dover Edition). 
The arithmetisation is done. I might say more if people are interested in the 
details.

Let me quote Gödel 

What matter in a computation is that at some (relative )instant, some 
proposition are true, like “the content at place 3 of the register R is 5” , 
and Gödel show that the truth value making a computation what it is did not 
exceed sigma_1, as “[]” is itself sigma_1, and sigma_1 complete, and with 
induction: it is Löbian: by which I mean Turing universal (sigma1 complete) and 
knowing it, in the weak sense of proving p -> []p for all p sigma_1.







> 
>  ​>> ​but if it doesn't have something about actually obtaining an answer 
> then its idiotic, but neither Church, Post, Turing nor Markov were idiots.
> 
> ​>​Contradiction.
> 
> Yes, and therefore we have an indirect proof by contradiction that when 
> Church, Post, Turing or Markov was talking about computation they were 
> talking about actually getting an answer.  


You lost me.






>  
> ​> ​we know since about a century, are not physical notion, but purely 
> arithmetical one.
> 
> ​BULLSHIT.​ 


Gödel missed it, actually, but it was anticipated by Post, who, actually 
anticipated both Church’s thesis, or better Kleene’s discovery that Church made 
an incredible thesis which would, unlike provability resists diagonalisation. 

Gödel confessed it, and made this point clear. For him, it is a miracle that 
the enumeration of the partial computable functions is closed for 
diagonalization. I have explained the “prize” of, which is that machine 
impredictiblity, and its ability to refute all complete theories made of itself.

John, if you don’t buy some book and study, you will just look like a liar. Buy 
the Dover book by Davis “The Undecidable”, which contains the main staring 
point of Mathematical logic. Buy also the thin book by Tarski “Undecidable 
Theories”.











>> ​>​>>​​Of course not. I point to some book and paper which provides a 
>> counter-example.
> 
>  
>> ​​>> ​LIKE HELL IT DOES! The damn book can't calculate 2+2
> 
> 
> ​> ​That joke again.
>  
> Then please let me in on the joke because I don't get it, I don’t see the 
> humor. Far from being funny I think its a tragedy that in the 21st century 
> somebody, who no doubt considers himself an intellectual, believes the 
> ancient Greeks reached the absolute pinnacle of human achievement and that 
> calculations can be made without matter that obey the laws of physics even 
> though there is OVERWHELMING evidence to the contrary because Plato said it 
> could and the authority of Plato is absolute.   
>  
> ​> ​You also confuse book and its content.
> 
> OK forget the book we'll just deal with its contents. If one day Apple 
> decided to put the contents of a book about compu

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 23 May 2018, at 16:31, Lawrence Crowell  
> wrote:
> 
> On Monday, May 21, 2018 at 7:42:50 PM UTC-5, spudb...@aol.com wrote:
> The answer is right in front of us. Quantum collapse indicates that a photon 
> must pass through a slit, and become either a wave or a particle.  But the 
> answer gets more complex, with Wigner's 4 body solution, with the photons 
> becoming either Yanny or Laurel, as opposed to Alice and Bob. 
> 
> 
> The two slits do not force the dichotomy. The wave function does pass through 
> both openings which impose a topology on the wave function, or better thought 
> of as the set of paths in the sum over histories or path integral. However, 
> without a detecting screen the electron wave function carries on along its 
> merry path. It is the detection by a screen, photoplate CCD or what ever is 
> place in the background that reduces the wave function to appear as a 
> particle.

Or, with MW, It is the detection by a screen, photoplate CCD or what ever is 
place in the background that makes the observers localising themselves in the 
branches where there the particles is localised, given it the impression that 
the measurement has reduced the wave function as to appear as being one 
particle. The SWE implies that the observer just get entangled, and 
self-multiplied by all possible outcome for the measurement, weighed by the 
Born rules (deducible from Gleason theorem).
Here, you seemed to imply a physical collapse.

Bruno



> 
> LC
> 
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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Wed, May 23, 2018 at 8:59 AM, Bruno Marchal  wrote:

*>  You were changing the mathematical definition of computations given
>>> independently by Church, Post, Turing, Markov *
>>
>> ​>​
>> I don't know what definition you're referring to
>
> ​> ​
> *See any (serious) textbook in logic.*
>

​In other words YOU DON'T KNOW.​

​Nobody says "the proof you are wrong is in some unspecified ​book" if they
have the ability to provide a better retort.


>> ​>> ​
>> but if it doesn't have something about actually obtaining an answer then
>> its idiotic, but neither Church, Post, Turing nor Markov were idiots.
>
>
> *​>​Contradiction.*
>

Yes, and therefore we have an indirect proof by contradiction that
when Church, Post, Turing or Markov was talking about computation they were
talking about actually getting an answer.


> ​> ​
> we know since about a century, are not physical notion, but purely
> arithmetical one.
>

​BULLSHIT.​


> ​>
>>> ​>>​
>>> ​Of course not. I point to some book and paper which provides a
>>> counter-example.
>>
>>

​
> ​>> ​
> LIKE HELL IT DOES! The damn book can't calculate 2+2
>
>
> ​> ​
> That joke again.
>

Then please let me in on the joke because I don't get it, I don’t see the
humor. Far from being funny I think its a tragedy that in the 21st
century somebody, who no doubt considers himself an intellectual, believes
the ancient Greeks reached the absolute pinnacle of human achievement and
that calculations can be made without matter that obey the laws of physics
even though there is* OVERWHELMING* evidence to the contrary because Plato
said it could and the authority of Plato is absolute.


> ​> ​
> *You also confuse book and its content.*
>

OK forget the book we'll just deal with its contents. If one day Apple
decided to put the contents of a book about computational theory into their
next iPhone instead of a microprocessor do you think Apple's stock price
would go up or down the next day?


> ​> ​
> you confuse computations and description of computations,
>

I think a microprocessor can perform a calculation but a description of a
computation such as one in a book, can not. You believe the opposite. I ask
anyone who is reading this to explain why I am the one who is confused
about the difference between a computation and a description of a
computation and not Bruno.   ​


> ​> ​
> *Read Gödel 1931. *
>

Godel's 1931 paper is one of the greatest achievements in thought in the
20th century, but there is no evidence Godel's 1931 paper can calculate
2+2. And Godel's 1931 paper only exists because the matter between Godel's
ears obeyed the laws of physics back in 1931.


> ​>* ​*
> *physics emerge from the numbers.*
>

You've got it backwards, numbers emerge from physics.

>
> ​> ​
> *You need only a physical reality to get a physical answer*
>

​So you admit it, physics can do something pure mathematics can't.​



> ​> ​
> explain me what is primary matter
>

​I think you should have asked somebody what "primary matter" is many years
ago before you started insisting in almost ever post that "primary matter"
didn't exist.


> ​> ​
> and how it makes a physical computations conscious
>

​
Turing (maybe you've heard of him) explained how to arrange atoms in such a
way that the laws physics force atoms to make computations and behave
intelligently. And if Charles Darwin was right then consciousness must be a
unavoidable byproduct of intelligent behavior.


> ​> ​
> On the contrary, you are using Deutsch idea that computation are physical,
> which is not the standard definition given by the Church-Turing original
> thesis.
>

You are incorrect. The ​
Church-Turing thesis
​ says a human or anything else can compute something if and only if a
Turing Machine can calculate it; and I think that's true.


​>>
 ​>>​
 ​
 it would be easy to prove me wrong; just calculate 2+2, you are free to
 use the contents of that paper you were talking about or any other paper or
 anything else, the only restrictions I place is that you are not allowed to
 use matter or energy or to increase entropy when you perform the
 calculation, other than that anything goes. If you successfully accomplish
 my little task I will publicly declare that I have been wrong all these
 years and you have been totally right and is a genius. So what do you say,
 do you accept my challenge?
>>>
>>>
>>> *​>​>>​ ​You ask me again something impossible.*
>>>
>>
>> ​>> ​
>> Obviously, but ask yourself a question "Exactly why is it ​impossible?".
>> Because physics can do something that mathematics can’t.
>>
>
> ​>* ​*
> *Assuming Aristotle theology.*
>

​They I guess you are assuming that "Aristotle theology" (whatever the hell
that is) is true because you just said "You ask me again something
impossible"..


> ​>>​
>> You may have reasons why physics can do something that mathematics can't
>> and they may be good reasons or they may be bad reasons it really doesn't
>> matter because for whatev

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Lawrence Crowell]

On Monday, May 21, 2018 at 7:42:50 PM UTC-5, spudb...@aol.com wrote:
>
> The answer is right in front of us. Quantum collapse indicates that a 
> photon must pass through a slit, and become either a wave or a particle.  
> But the answer gets more complex, with Wigner's 4 body solution, with the 
> photons becoming either Yanny or Laurel, as opposed to Alice and Bob. 
>
>
The two slits do not force the dichotomy. The wave function does pass 
through both openings which impose a topology on the wave function, or 
better thought of as the set of paths in the sum over histories or path 
integral. However, without a detecting screen the electron wave function 
carries on along its merry path. It is the detection by a screen, 
photoplate CCD or what ever is place in the background that reduces the 
wave function to appear as a particle.

LC

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 22 May 2018, at 01:37, John Clark  wrote:
> 
> On Mon, May 21, 2018 at 7:33 AM, Bruno Marchal  > wrote:
> 
> >  You were changing the mathematical definition of computations given 
> > independently by Church, Post, Turing, Markov ,
> 
> I don't know what definition you're referring to


See any (serious) textbook in logic.




>  but if it doesn't have something about actually obtaining an answer then its 
> idiotic, but neither Church, Post, Turing nor Markov were idiots.


Contradiction.




>  
> ​> ​which are not dependent of any assumption in physics, to a definition
> 
> ​Definition​ ​be damned! I don't want a definition I want an answer, I want 
> an answer to the question "How much is 2+2?" and there is absolutely 
> positively no way to obtain that answer without using matter that obeys the 
> laws of physics.

Proof?

You seem unable to doubt that the physical reality may be don’t exist 
“ontologically”. But that was the point of *all* theologian (being aware that 
seeing is not proving) until the religious institution enforce the existence of 
matter as a dogma, notably 1500 years ago.

That helps me to understand what is your problem. 




> ​
> 
> ​> ​You are right. A definition cannot do a calculation. Only a 
> machine/number/combinator can do that. But there are plenty of such entities 
> in arithmetic.
> 
> Well for gods sake stop wasting your time on this list and tell INTEL about 
> this revolutionary new discovery and then watch as the world is transformed 
> beyond recognition overnight!!
> 
> ​> ​My belief are private.
> 
> Mine aren't but then I am in a different situation than you,  I am not 
> ashamed by my philosophical beliefs.
>  
> ​>> ​you are saying you don't think matter soul and shape are separate things,
> 
> ​> ​?
> ​!​ 
>  
> ​>> ​they can not be separated, you think secondary matter is the only sort 
> of matter that there is. And that would make your beliefs far more matter 
> orientated than mine because although I don't believe in the soul  I  do 
> believe in shape ,  although I prefer to say information .  I think 
> information and matter, although related, are 2 different things and I think 
> Leibniz was right, matter that has not been organized by information is just 
> a chaotic high entropy lump that can’t produce work or make calculations or 
> do anything else. 
> 
> ​> ​No problem here.
> 
> Leibniz, who invented the term,


It came from Aristotle’s metaphysics. Leibniz, like basically everyone, believe 
in this, but as I show, it is inconsistent with indexical digital mechanism 
(the idea that my body is physically Turing emulable).


> said all "primary matter" brought to the table was continuity, soul and shape 
> were separate things. So if you mix in soul and shape with "primary matter" 
> you end up with "secondary matter" and that's the stuff that we observe and 
> that can actually do things. You have made no secret in showing your contempt 
> for "primary matter", but if it doesn't exist that means soul and shape can 
> not be separated from matter, so "secondary matter" is the only type of 
> matter there is.


Right. But its existence is phenomenological. It is not made of a mixing of 
form and soul. Both soul and form come from computations, which, as we know 
since about a century, are not physical notion, but purely arithmetical one.




> And that is why I say it would make you more matter orientated than I am. And 
> that is also why I said you don't know what "primary matter" means. 
> 
> ​>> ​​I'm not joking I'm dead serious!! Ever time I say nothing can be 
> calculated without matter that obeys the laws of physics and even then only 
> if that matter is in the form of a Turing Machine you point to some book or 
> paper as a counterexample,
> 
> ​>​Of course not. I point to some book and paper which provides a 
> counter-example.
> 
> ​LIKE HELL IT DOES! The damn book can't calculate 2+2

That joke again.





> nor can the book tell me the answer to the question "How much is​ ​2+2?" 
> without using matter that obeys the laws of physics​
> 
> ​> ​You fake to see so to make your joke
> 
> ​It's not funny and I'm not joking. 


Yes you are. You also confuse book and its content. You confuse book and 
machine, you confuse computations and description of computations, etc.


>  
> ​> we both know that a book is not a machine.
> 
> Exactly, a book is not a machine. And only a machine of the general type 
> described by Turing can make a calculation.

Yes, and those Turing equivalent to it, like very elementary arithmetic. Read 
Gödel 1931. 



>  
> ​> ​arithmetic contains both the description of the machine, and the machine 
> itself. It contains both the description of the computation, and the 
> computations themselves.
> 
> And yet without the help of physics arithmetic is totally unable to answer 
> the question "How much is 2+2?”.

Not at all. If mechanism is true, physics emerge from the numbers. Y

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[spudboy100 via Everything List]

The answer is right in front of us. Quantum collapse indicates that a photon 
must pass through a slit, and become either a wave or a particle.  But the 
answer gets more complex, with Wigner's 4 body solution, with the photons 
becoming either Yanny or Laurel, as opposed to Alice and Bob. 



-Original Message-
From: John Clark 
To: everything-list 
Sent: Mon, May 21, 2018 7:37 pm
Subject: Re: Is the Continuum Hypothesis a) really true or really false, or b) 
something else ?



On Mon, May 21, 2018 at 7:33 AM, Bruno Marchal  wrote:




>  You were changing the mathematical definition of computations given 
> independently by Church, Post, Turing, Markov ,


I don't know what definition you're referring to  but if it doesn't have 
something about actually obtaining an answer then its idiotic, but neither 
Church, Post, Turing nor Markov were idiots.
 



 
​> ​
which are not dependent of any assumption in physics, to a definition





​Definition​
 
​be damned! I don't want a definition I want an answer, I want an answer to the 
question "How much is 2+2?" and there is absolutely positively no way to obtain 
that answer without using matter that obeys the laws of physics. ​







​> ​
You are right. A definition cannot do a calculation. Only a 
machine/number/combinator can do that. But there are plenty of such entities in 
arithmetic.




Well for gods sake stop wasting your time on this list and tell INTEL about 
this revolutionary new discovery and then watch as the world is transformed 
beyond recognition overnight!!




​> ​
My belief are private.




Mine aren't but then I am in a different situation than you,  I am not ashamed 
by my philosophical beliefs. 
 





​>> ​
you are saying you don't think matter soul and shape are separate things, 





​> ​
?


​!​
 

 



​>> ​
they can not be separated, you think secondary matter is the only sort of 
matter that there is. And that would make your beliefs far more matter 
orientated than mine because although I don't believe in the soul  I  do 
believe in shape ,  although I prefer to say information .  I think information 
and matter, although related, are 2 different things and I think Leibniz was 
right, matter that has not been organized by information is just a chaotic high 
entropy lump that can’t produce work or make calculations or do anything else. 






​> ​
No problem here.




Leibniz, who invented the term, said all "primary matter" brought to the table 
was continuity, soul and shape were separate things. So if you mix in soul and 
shape with "primary matter" you end up with "secondary matter" and that's the 
stuff that we observe and that can actually do things. You have made no secret 
in showing your contempt for "primary matter", but if it doesn't exist that 
means soul and shape can not be separated from matter, so "secondary matter" is 
the only type of matter there is. And that is why I say it would make you more 
matter orientated than I am. And that is also why I said you don't know what 
"primary matter" means. 







​>> ​
​I'm not joking I'm dead serious!! Ever time I say nothing can be calculated 
without matter that obeys the laws of physics and even then only if that matter 
is in the form of a Turing Machine you point to some book or paper as a 
counterexample, 




​>​
Of course not. I point to some book and paper which provides a counter-example.




​LIKE HELL IT DOES! The damn book can't calculate 2+2 nor can the book tell me 
the answer to the question "How much is​
 
​2+2?" without using matter that obeys the laws of physics​





​> ​
You fake to see so to make your joke





​It's not funny and I'm not joking. 

 


​> 
we both know that a book is not a machine.




Exactly, a book is not a machine. And only a machine of the general type 
described by Turing can make a calculation.
 

 
​> ​
arithmetic contains both the description of the machine, and the machine 
itself. It contains both the description of the computation, and the 
computations themselves.




And yet without the help of physics arithmetic is totally unable to answer the 
question "How much is 2+2?". So like the word "God" the word "computation" has 
a meaning in the Brunospeak language that is unrelated to the English meaning 
of the word, but I don't know what those meanings are because only one person 
on the planet is fluent in Brunospeak and I'm not him

 





​>> ​
it would be easy to prove me wrong; just calculate 2+2, you are free to use the 
contents of that paper you were talking about or any other paper or anything 
else, the only restrictions I place is that you are not allowed to use matter 
or energy or to increase entropy when you perform the calculation, othe

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Mon, May 21, 2018 at 7:33 AM, Bruno Marchal  wrote:

*>  You were changing the mathematical definition of computations given
> independently by Church, Post, Turing, Markov ,*


I don't know what definition you're referring to  but if it doesn't have
something about actually obtaining an answer then its idiotic, but neither
Church, Post, Turing nor Markov were idiots.


> *​> ​which are not dependent of any assumption in physics, to a definition*
>

​Definition​

​be damned! I don't want a definition I want an answer, I want an answer to
the question "How much is 2+2?" and there is absolutely positively no way
to obtain that answer without using matter that obeys the laws of physics.
  ​

*​> ​You are right. A definition cannot do a calculation. Only a
> machine/number/combinator can do that. But there are plenty of such
> entities in arithmetic.*
>

Well for gods sake stop wasting your time on this list and tell INTEL about
this revolutionary new discovery and then watch as the world is transformed
beyond recognition overnight!!

*​> ​My belief are private.*
>

Mine aren't but then I am in a different situation than you,  I am not
ashamed by my philosophical beliefs.


> ​>> ​
>> you are saying you don't think matter soul and shape are separate things,
>
>
> ​>* ​*
> *?*
>
*​!​ *


> ​>> ​
>> they can not be separated, you think secondary matter is the only sort of
>> matter that there is. And that would make your beliefs far more matter
>> orientated than mine because although I don't believe in the soul  I  do
>> believe in shape ,  although I prefer to say information .  I think
>> information and matter, although related, are 2 different things and I
>> think Leibniz was right, matter that has not been organized by information
>> is just a chaotic high entropy lump that can’t produce work or make
>> calculations or do anything else.
>
>
> ​> ​
> *No problem here.*
>

Leibniz, who invented the term, said all "primary matter" brought to the
table was continuity, soul and shape were separate things. So if you mix in
soul and shape with "primary matter" you end up with "secondary matter" and
that's the stuff that we observe and that can actually do things. You have
made no secret in showing your contempt for "primary matter", but if it
doesn't exist that means soul and shape can not be separated from matter,
so "secondary matter" is the only type of matter there is. And that is why
I say it would make you more matter orientated than I am. And that is also
why I said you don't know what "primary matter" means.

​>> ​
>> ​I'm not joking I'm dead serious!! Ever time I say nothing can be
>> calculated without matter that obeys the laws of physics and even then only
>> if that matter is in the form of a Turing Machine you point to some book or
>> paper as a counterexample,
>
>
> *​>​Of course not. I point to some book and paper which provides a
> counter-example.*
>

​LIKE HELL IT DOES! The damn book can't calculate 2+2 nor can the book tell
me the answer to the question "How much is​

​2+2?" without using matter that obeys the laws of physics​

​> ​
> *You fake to see so to make your joke*
>

​It's not funny and I'm not joking.


> ​>
> we both know that a book is not a machine.
>

Exactly, a book is not a machine. And only a machine of the general type
described by Turing can make a calculation.

>
> ​> ​
> arithmetic contains both the description of the machine, and the machine
> itself. It contains both the description of the computation, and the
> computations themselves.
>

And yet without the help of physics arithmetic is totally unable to answer
the question "How much is 2+2?". So like the word "God" the word
"computation" has a meaning in the Brunospeak language that is unrelated to
the English meaning of the word, but I don't know what those meanings are
because only one person on the planet is fluent in Brunospeak and I'm not
him


> ​>> ​
>> it would be easy to prove me wrong; just calculate 2+2, you are free to
>> use the contents of that paper you were talking about or any other paper or
>> anything else, the only restrictions I place is that you are not allowed to
>> use matter or energy or to increase entropy when you perform the
>> calculation, other than that anything goes. If you successfully accomplish
>> my little task I will publicly declare that I have been wrong all these
>> years and you have been totally right and is a genius. So what do you say,
>> do you accept my challenge?
>
>
> *​> ​You ask me again something impossible.*
>

Obviously, but ask yourself a question "Exactly why is it ​impossible?".
Because physics can do something that mathematics can't. You may have
reasons why physics can do something that mathematics can't and they may be
good reasons or they may be bad reasons it really doesn't matter because
for whatever reason the undeniable FACT remains physics can do something
that mathematics can't. Of course not just any old arrangement of matter
can perform calculatio

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 18 May 2018, at 21:02, John Clark  wrote:
> 
> On Fri, May 18, 2018 at 7:36 AM, Bruno Marchal  > wrote:
>  
> ​>​ a Turing Machine knows nothing excepts what state it should go into, if 
> it should write a 1 or a 0, and if it should move left or right or halt. 
> That's it. And yet it can calculate anything that can be calculated provided 
> that it just follows the laws of physics when it moves and it uses a minimum 
> amount of energy (that can also be calculated) and produces entropy whenever 
> it changes one symbol to another. 
> 
> ​> ​You change the definition.
> 
> ​Huh?? I change the definition of what from what to what”

You were changing the mathematical definition of computations given 
independently by Church, Post, Turing, Markov , which are not dependent of any 
assumption in physics, to a definition of the physical implementation of such a 
machine, which indeed assume a physical realm, although not necessarily a 
primary one.




>  
> ​> ​And you seem to ignore that the notion of computation and implementation 
> are definable in arithmetic
> 
> ​Definitions can't make calculations, only matter that obeys the laws of 
> physics can.

You are right. A definition cannot do a calculation. Only a 
machine/number/combinator can do that. But there are plenty of such entities in 
arithmetic.



> 
> ​> ​You assume a primary matter​ ​for which there has never been evidence for
> You keep saying that over and over and over again but I don't think you even 
> know what primary matter means.  Leibniz  invented the term
> 
It cames with Aristotle. But Leibniz use a similar idea. 



> and it means matter in itself in bulk. Leibniz  said primary matter was not a 
> complete substance because it is missing some key things, soul and shape, and 
> therefore by itself primary matter is passive and can't do anything; if you 
> mix those things in with primary matter then you get what Leibniz called 
> secondary matter, and that is complete and that is active and can do things.
> 
But that moves is what my argument shows inconsistent.




> When you say you don't believe in primary matter
> 

My belief are private. I have never said that I don’t believe in primary 
matter. I have “only” proven that primary matter makes no sense at all once we 
assume computationalism. 



> you are saying you don't think matter soul and shape are separate things,
> 

?

On the contrary, I explain why the machine can only separate those things, 
despite truth does not.

I refer you to the two facts:

G1* proves p <-> []p <-> ([]p & p) <-> ([]p & <>t) <-> ([]Øp & <>t & p)

But G1 loves none of them.

With G1 = G + (p -> []p), and G1* is the “starification" of G1. See my paper 
for more on this, or ask me.





> they can not be separated, you think secondary matter is the only sort of 
> matter that there is. And that would make your beliefs far more matter 
> orientated than mine because although I don't believe in the soul  I  do 
> believe in shape ,  although I prefer to say information .  I think 
> information and matter, although related, are 2 different things and I think 
> Leibniz was right, matter that has not been organized by information is just 
> a chaotic high entropy lump that can’t produce work or make calculations or 
> do anything else. 
> 
> 

No problem here.




> ​>> ​And for years you have been confused by the difference between the 2 
> different types of Turing Machines, the Turing Machines that can make a 
> calculation and the Turing Machines that can not. I like the type that can. 
> 
> ​> ​Read Turing and Church in Martin Davis “the undecidable”,
> 
> Don't​ tell me tell ​Apple ​, ​they would get much better battery life out of 
> their next generation iPhone if they just stuff the paper inside it instead 
> of a energy hungry microchip.  
> 
> ​> ​You repeat the same joke again and again
> 
> ​I'm not joking I'm dead serious!! Ever time I say nothing can be calculated 
> without matter that obeys the laws of physics and even then only if that 
> matter is in the form of a Turing Machine you point to some book or paper as 
> a counterexample,

Of course not. I point to some book and paper which provides a counter-example. 
The book or paper as such does not provide the counter-example. You fake to see 
so to make your joke “show me a book which do calculation”. But that is just a 
joke, given that we both know that a book is not a machine.




> well stop telling me and show me, show me how Apple used your idea in their 
> new iPhone. Put up or shut up.​ 
>  
> ​> ​Why do you invoke your God (Primary Matter) to block a metaphysical 
> argument? 
> 
> ​Not only are you ignorant what the term "primary matter" means you also 
> don't know what the word "God" means.

Nobody knows that, but that is why we (re)define the term. By “God” I made 
clear I mean a transcendant power at the origin of everything, consciousness 
included. So God refer to Primary Matter for a ma

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Fri, May 18, 2018 at 7:36 AM, Bruno Marchal  wrote:


> ​>​
>>  a Turing Machine knows nothing excepts what state it should go into, if
>> it should write a 1 or a 0, and if it should move left or right or halt.
>> That's it. And yet it can calculate anything that can be calculated
>> provided that it just follows the laws of physics when it moves and it uses
>> a minimum amount of energy (that can also be calculated) and produces
>> entropy whenever it changes one symbol to another.
>
>
> ​> ​
> *You change the definition.*
>

​
Huh?? I change the definition of what from what to what"


> ​> ​
> *And you seem to ignore that the notion of computation and implementation
> are definable in arithmetic*
>

​Definitions can't make calculations, only matter that obeys the laws of
physics can.

​> ​
> You assume a primary matter
> ​ ​
> for which there has never been evidence for
>
You keep saying that over and over and over again but I don't think you
even know what primary matter means.  Leibniz  invented the term and it
means matter in itself in bulk. Leibniz  said primary matter was not a
complete substance because it is missing some key things, soul and shape,
and therefore by itself primary matter is passive and can't do anything; if
you mix those things in with primary matter then you get what Leibniz
called secondary matter, and that is complete and that is active and can do
things. When you say you don't believe in primary matter you are saying you
don't think matter soul and shape are separate things, they can not be
separated, you think secondary matter is the only sort of matter that there
is. And that would make your beliefs far more matter orientated than mine
because although I don't believe in the soul  I  do believe in shape ,
 although I prefer to say information .  I think information and matter,
although related, are 2 different things and I think Leibniz was right,
matter that has not been organized by information is just a chaotic high
entropy lump that can’t produce work or make calculations or do anything
else.

> ​>> ​
>> And for years you have been confused by the difference between the 2
>> different types of Turing Machines, the Turing Machines that can make a
>> calculation and the Turing Machines that can not. I like the type that can.
>
>
> ​>* ​*
> *Read Turing and Church in Martin Davis “the undecidable”,*
>

Don't
​ tell me tell ​
Apple
​, ​
they would get much better battery life out of their next generation iPhone
if they just stuff the paper inside it instead of a energy hungry
microchip.

​> ​
> *You repeat the same joke again and again*


​I'm not joking I'm dead serious!! Ever time I say nothing can be
calculated without matter that obeys the laws of physics and even then only
if that matter is in the form of a Turing Machine you point to some book or
paper as a counterexample, well stop telling me and show me, show me how
Apple used your idea in their new iPhone. Put up or shut up.​



> *​> ​Why do you invoke your God (Primary Matter) to block a metaphysical
> argument? *
>

​Not only are you ignorant what the term "primary matter" means you also
don't know what the word "God" means.

is in a clear unambiguous way. A real Turing Machine is a Turing Machine
>> that can actually make a calculation.
>
>
> *​> ​A​​ll Turing machine can do a computation,*
>
Then a microchip is a real Turing Machine and a description of one in a
book is NOT a real Turing Machine, just as a description of Hogwarts castle
in a Harry Potter book is a real description but it is NOT a real castle.
You confuse fact and fantasy.

> ​> *​*
> *computer science invites us to reread Plato.*
>

​I politely decline the invitation because I prefer to read authors who
know where the sun goes at night. ​



> ​>* ​*
> *Here you confuse the content of a paper, where you could learn what is a
> computation, with a paper. *
>

I'm confuse?!! I think you're the one who is very VERY *VERY* confused, but
it would be easy to prove me wrong; just calculate 2+2, you are free to use
the contents of that paper you were talking about or any other paper or
anything else, the only restrictions I place is that you are not allowed to
use matter or energy or to increase entropy when you perform the
calculation, other than that anything goes. If you successfully accomplish
my little task I will publicly declare that I have been wrong all these
years and you have been totally right and is a genius. So what do you say,
do you accept my challenge?

> ​>
>>> ​>>​
>>> ​*What I said was only that if a computer find an even number not sum
>>> of two primes, I would believe the computer over a proof in ZF.*
>>
>>
>
>> ​>>​
>> I would trust the computer more than the axioms too, I would because I
>> think physics always tells the truth,
>
>
> ​> ​
> *Physics is neutral. Even metaphysics is neutral when done with the
> scientific method. Nobody knows the truth as such.*
>

Then why did you say "I would believe the computer over a proo

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 18 May 2018, at 01:37, John Clark  wrote:
> 
> On Wed, May 16, 2018 at 6:29 AM, Bruno Marchal  > wrote:
> 
> ​​>> ​A Turing Machine knows no theories
> 
> ​> ​I have no clues why you say so.
>  
> I say so because a Turing Machine knows nothing excepts what state it should 
> go into, if it should write a 1 or a 0, and if it should move left or right 
> or halt. That's it. And yet it can calculate anything that can be calculated 
> provided that it just follows the laws of physics when it moves and it uses a 
> minimum amount of energy (that can also be calculated) and produces entropy 
> whenever it changes one symbol to another. 

You change the definition. And you seem to ignore that the notion of 
computation and implementation are definable in arithmetic, where they operate.

You assume a primary matter, for which there has never been evidence for, and 
for which today we have evidence against, to only block an argument. That is 
bad science.



> 
> ​> >​and it operates under the laws of physics
> 
> ​>​That is a confusion between a Turing ​Machine and a physical 
> implementation of a Turing machine.
> 
> And for years you have been confused by the difference between the 2 
> different types of Turing Machines, the Turing Machines that can make a 
> calculation and the Turing Machines that can not. I like the type that can. 

Read Turing and Church in Martin Davis “the undecidable”, or read the fourth 
chapter of Martin Davis’ computability and unsolvability. You answer a remark 
by doing the same confusion which was under critics. I guess that what you say 
three times is true.



> 
> ​> ​I​​n which metaphysical theory would you define what is a *real* machine. 
> 
> I don't deal in metaphysical theories,

?

Then why this conversation. Why do you invoke your God (Primary Matter) to 
block a metaphysical argument? 



> that's your thing not mine, but I'll be happy to exactly define what a *real* 
> machine


In metaphysics, when done with the scientific attitude, you cannot use “real” 
in this way. That is like the pope. It is bad philosophy.



> is in a clear unambiguous way. A real Turing Machine is a Turing Machine that 
> can actually make a calculation.

All Turing machine can do a computation, and none can distinguish, from their 
first person view, if their computations is implemented through a physical 
incarnation of a universal machine/number, or by an arithmetical implementation 
of that same universal machine/number. Unless some non Turing emulable, and non 
FPI-recoverable, magic is in play, but then you have no *reason* to say “yes” 
to the doctor, nor even a reason to accept Church’s thesis.




>  
> ​> ​when we assume Aristotle’s metaphysics​ [...]
> 
> Bruno, I really want to know, why do you keep talking about those stupid 
> ignorant ancient Greeks who didn’t know where the sun went at night? You seem 
> incapable of writing an entire post without talking about them regardless of 
> the subject. 


Because in theology we have followed Aristotle, when computer science invites 
us to reread Plato.
Because we are brainwashed with Aristotle theology since 1500 years. Then, when 
we do that, we can see that Plato’s theology fits quite well with the theories 
and evidences that we have today. That is not astonishing given that theology 
is forbidden since. Why do you defend all the time Aristotle theology (the 
belief in Primary Matter)? 





> 
> ​> ​The laws of physics he nothing to do with the laws of computability and 
> computation. I suggest you read the original papers of the discoverers of the 
> universal machine (reprinted for example in Martin Davis 
> 
> If Martin Davis 's paper can make a calculation then send it to Apple,


You repeat the same joke again and again. Here you confuse the content of a 
paper, where you could learn what is a computation, with a paper. 



> they would get much better battery life out of their next generation iPhone 
> if they just stuff the paper inside it instead of a energy hungry microchip.  
> 
> ​> ​What I said was only that if a computer find an even number not sum of 
> two primes, I would believe the computer over a proof in ZF.
>  
> I would trust the computer more than the axioms too, I would because I think 
> physics always tells the truth,

Physics is neutral. Even metaphysics is neutral when done with the scientific 
method. Nobody knows the truth as such. You talk like an religious integrist. 
You claim to know the truth. 




> but that is not why you also trust the computer over the axioms;  you gave 
> your reason  for doing so but I couldn't make any sense out of it.​ ​
>  
> ​> ​The reason is that the negation of Goldbach conjecture is sigma_1, so​ 
> ​if a computer can refute Goldbach, so can ZF. You were assuming implicitly 
> that ZF is inconsistent.
> 
> Why don't you believe the ZFC axioms are still consistent , Goldbach is still 
> true, and all computers are always wrong when the

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Wed, May 16, 2018 at 6:29 AM, Bruno Marchal  wrote:

​
>> ​>> ​
>> A Turing Machine knows no theories
>
>
> ​> ​
> I have no clues why you say so.
>

I say so because a Turing Machine knows nothing excepts what state it
should go into, if it should write a 1 or a 0, and if it should move left
or right or halt. That's it. And yet it can calculate anything that can be
calculated provided that it just follows the laws of physics when it moves
and it uses a minimum amount of energy (that can also be calculated) and
produces entropy whenever it changes one symbol to another.

​> >​
>> and it operates under the laws of physics
>
>
> ​>​
> That is a confusion between a Turing
> ​Machine
>  and a physical implementation of a Turing machine.
>

And for years you have been confused by the difference between the 2
different types of Turing Machines, the Turing Machines that can make a
calculation and the Turing Machines that can not. I like the type that can.

*​> ​I​​n which metaphysical theory would you define what is a *real*
> machine. *


I don't deal in metaphysical theories, that's your thing not mine, but I'll
be happy to exactly define what a *real* machine is in a clear unambiguous
way. A real Turing Machine is a Turing Machine that can actually make a
calculation.


> ​*> ​*
> *when we assume Aristotle’s metaphysics​ [...]*
>

Bruno, I really want to know, why do you keep talking about those stupid
ignorant ancient Greeks who didn’t know where the sun went at night? You
seem incapable of writing an entire post without talking about them
regardless of the subject.

​> ​
> The laws of physics he nothing to do with the laws of computability and
> computation. I suggest you read the original papers of the discoverers of
> the universal machine (reprinted for example in Martin Davis
>

If Martin Davis 's paper can make a calculation then send it to Apple, they
would get much better battery life out of their next generation iPhone if
they just stuff the paper inside it instead of a energy hungry microchip.

​> ​
> *What I said was only that if a computer find an even number not sum of
> two primes, I would believe the computer over a proof in ZF.*
>

I would trust the computer more than the axioms too, I would because I
think physics always tells the truth, but that is not why you also trust
the computer over the axioms;  you gave your reason  for doing so but I
couldn't make any sense out of it.
​ ​


> *​> ​The reason is that the negation of Goldbach conjecture is sigma_1,
> so​ ​if a computer can refute Goldbach, so can ZF. You were assuming
> implicitly that ZF is inconsistent.*
>

Why don't you believe the ZFC axioms are still consistent , Goldbach is
still true, and all computers are always wrong when they say a particular
very large even number is not the sum of two primes?

​>>​
>> ​If two physical theories try to explain the same phenomena then they
>> are ALWAYS contradictory,  otherwise they'd be the same theory,
>
>
> ​> ​
> *Of course not. QM, for example, came up with different theories, proved
> to be equivalent, but they are still different (cf Heisenberg versus
> Schoredinger, versus Feynmann),*
>

​
None of these things contradicted the other, they are saying the same thing
with different words (or equations).

​> ​
> *you have to explain how that primary matter makes “more real” some
> computations, and "less real” others.*
>

No, it would be nice to know why but I am under no obligation to
explain why a real Turing Machine uses energy, produces entropy, and makes
calculations, but a description of a Turing Machine in a closed book can do
none of those things; I just have to observe that is the way things are.

 John K Clark

​


>
>
>

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 13 May 2018, at 21:53, John Clark  wrote:
> 
> 
> 
> On Sat, May 12, 2018 at 4:21 AM, Bruno Marchal  > wrote:
> 
> 
> ​> ​I use computer for “universal Turing machine”. That notion assumes (and 
> is Turing-equivalent with (very) elementary arithmetic).
> 
> ​A Turing Machine knows no theories

I have no clues why you say so. It is just false with the definition I have 
given of “knowing” (beweisbar and true).




> and it operates under the laws of physics

That is a confusion between a Turing machine and a physical implementation of a 
Turing machine.




> not because it assume them but because it has no choice in the matter.
> 
> ​>> ​Computers are made of matter that obeys the laws of physics,
> 
> Physical computer.
> 
> 
> A Turing Machine is a physical computer and a Turing Machine is the only type 
> of computer that there is; even a virtual computer needs a Turing machine 
> somewhere down the line​.​


Only when we assume Aristotle’s metaphysics. But that begs the question.



>  
> ​> ​But I do not assume​ [...]
> 
> ​A Turing Machine doesn't give a damn what you do or do not assume, it just 
> keeps on cranking away according to the laws of laws of physics.​ 


The laws of physics he nothing to do with the laws of computability and 
computation. I suggest you read the original papers of the discoverers of the 
universal machine (reprinted for example in Martin Davis (ed) “The undecidable” 
by Dover.



> 
> ​>>​when the voltage on one of the inputs of the microchip is positive 
> physics orders it will do one thing and when the voltage is negative it will 
> order it to do something different. By picking A you are in effect saying you 
> have looked at the pattern of voltages physics told the microchip to have and 
> you have interpreted that pattern to to be a even number that is not the sum 
> two prime numbers, and you believe what physics is telling you even if the 
> axioms of Number Theory says such a number can not exist.
> 
> ​> ​I have not assume physics anywhere,
>  
> That's OK, physics doesn't assume you either. But you have said if the ZFC 
> axioms say one thing and the computer says the opposite then you'd believe 
> the computer and not the axioms, and that is what any sane man would do 
> because theories come and go but physics always tells the truth,


Why would I believe a computer saying something? They can lie as much as the 
humans.

What I said was only that if a computer find an even number not sum of two 
primes, I would believe the computer over a proof in ZF. The reason is that the 
negation of Goldbach conjecture is sigma_1, so if a computer can refute 
Goldbach, so can ZF. You were assuming implicitly that ZF is inconsistent.




>  
> ​> ​so this does not make any sense.
> 
> Then how can you make sense out of ANY post from ANYBODY on this list? How 
> can you reply to any post when its just a pattern of voltages on the 
> microchip inside your computer?

Not at all. A post are ideas represented through a physical means, which is 
need n the physical reality.

That has nothing to do with the idea that a primary physical reality as to be 
assumed in computability theory.




> 
>  
> ​>>​By picking A you are saying physics is more trustworthy than any set of 
> axioms could be, if there is a contradiction between the two it is the axioms 
> that need to give way not physical law because although​ ​physics can be 
> weird it has no self contradictions, but man made axioms can.  
> 
> ​> ​Physical theories can be contradictory.
> 
> ​If two physical theories try to explain the same phenomena then they are 
> ALWAYS contradictory,  otherwise they'd be the same theory,

Of course not. QM, for example, came up with different theories, proved to be 
equivalent, but they are still different (cf Heisenberg versus Schoredinger, 
versus Feynmann), unless you identify a theory with all its theorem, in which 
case I can agree.




> but at least one of those theories must be wrong and that's where experiment 
> comes in. Physics (not to be confused with physical theories)

Physics is usually used for “physical theories”. It would help to use “the 
physical reality” instead of physics, which is the name of the science, not the 
reality.



> is never contradictory and will always tell you the truth, I would even say 
> its the very definition of truth.  

The physical reality is not a theory. It does not tell anything. Unless you 
1) assume that such a reality
2) identify that reality with the set of all propositions satisfied by that 
reality. But I prefer to avoid doing such identification, which in metaphysics 
can only be misleading. 
Then you identify “physics” with truth, which again is Aristotle main 
metaphysical assumption, andit has been shown not compatible with 
computationalism.




>  
> ​> ​And physical reality is not an assumption available at the start. 
> 
> ​To hell with assumptions! If I walk across a bridge it won't stay int

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Mon, May 14, 2018 at 8:38 PM, smitra  wrote:

​> ​
> But then, without a solid mathematical model that describes experimental
> outcomes, how can one draw any nontrivial conclusions from experiments at
> all?
> ​
>

By observation. We may be very surprised that the cannonball swerved to the
left and have absolutely no idea and no theories why it did so, but one
thing we do know, the cannonball swerved to the left.
​

John K Clark


​
>

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[smitra]

On 15-05-2018 02:06, John Clark wrote:

On Mon, May 14, 2018 at 7:01 PM, Russell Standish
 wrote:


​> ​How do you establish that the proof has no error? Why are we
supposing
that the ZFC axiom correctly describes the mathematical system? How
do
you establish that the computers haven't made an error?


It seems to me you're trying very hard to understand my question. In
arithmetic if  ZFC or any set of axioms says that a number with
certain mathematical traits can not exist but a computer finds a
number with exactly those mathematical traits then both of them can't
be correct, and in that situation I simply don't believe you'd take
the part of the axioms because you are not insane.


​> ​It really underscores Chaitin's point that at some level of
complexity, mathematics becomes an empirical subject, perhaps not
all
that different from physics.


Yes mathematics can be empirical, and that means regardless of how
beautiful your axioms are if the experimental evidence conflicts with
them then those axioms then they have to be junked because
experimental evidence outranks everything. The mathematical
counterpart to a test tube is a computer and the fundamental operating
system of any computer is the laws of physics. So physics can exercise
veto power even in pure mathematics.
​

John K Clark​



But then, without a solid mathematical model that describes experimental 
outcomes, how can one draw any nontrivial conclusions from experiments 
at all? Take e.g. experimental bounds on the photon mass:


https://arxiv.org/abs/hep-ph/0306245

which is shown to depend on the underlying model. In case of the photon 
charge, it turns out that the experimental results are totally junk:


https://arxiv.org/abs/hep-ph/0505250

Saibal




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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Mon, May 14, 2018 at 7:01 PM, Russell Standish 
wrote:


>
> * ​> ​How do you establish that the proof has no error? Why are we
> supposing that the ZFC axiom correctly describes the mathematical system?
> How do you establish that the computers haven't made an error?*


It seems to me you're trying very hard to understand my question. In
arithmetic if  ZFC or any set of axioms says that a number with certain
mathematical traits can not exist but a computer finds a number with
exactly those mathematical traits then both of them can't be correct, and
in that situation I simply don't believe you'd take the part of the axioms
because you are not insane.

​> ​
> It really underscores Chaitin's point that at some level of
> complexity, mathematics becomes an empirical subject, perhaps not all
> that different from physics.
>

Yes mathematics can be empirical, and that means regardless of how
beautiful your axioms are if the experimental evidence conflicts with them
then those axioms then they have to be junked because experimental evidence
outranks everything. The mathematical counterpart to a test tube is a
computer and the fundamental operating system of any computer is the laws
of physics. So physics can exercise veto power even in pure mathematics.
​


John K Clark​













>
>

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Russell Standish]

On Mon, May 14, 2018 at 11:41:34AM -0400, John Clark wrote:
> On Sun, May 13, 2018 at 9:06 PM, Russell Standish 
> wrote:
> 
> >
> > you already said, quite wisely, that if you had correctly used the ZFC
> >> > axioms to produce a proof the Goldbach Conjecture was true but then a
> >> > computer found a number that violated Goldbach you would place the
> >> blame on
> >> > the ZFC axioms and not on the laws of physics the computer operates
> >> under.
> >> > So like me you are saying it is physics and not axioms that is the
> >> ultimate
> >> > judge
> >> ​ t​
> >> hat​
> >> ​ ​
> >> decides what it true and what is not
> >
> >
> 
> ​> ​
> >
> > *That is probably putting a little too much faith in computers, and the
> > possibility of bug-free programs.*
> 
> 
> In the thought experiment I specifically said numerous computers had made
> the calculation and they all agree that there is a huge even number that is
> not the sum of 2 primes.

Hopefully you said independently implemented programs, on
independently implemented hardware. If all computers ran the same
buggy program, it wouldn't tell you much...

> pages long. To read and understand this thing you still need to have a
> boiling water IQ and you have to be prepared to devote the better part of a

At 100 degrees? That's a pretty average IQ! Maybe water boils at a
different temperature in your country... Perhaps you're from
Atlantis. Or perhaps you were referring to 373 Kelvin, in which case
I'd be quite happy with an icy IQ.

> mathematical proof than it is to follow a step by step argument. But it
> seems that that last thing may not be true, if I have a valid proof of
> the Riemann Hypothesis but it would take you as much brainpower to
> understand it as it would for you to find a proof on your own then there
> would be no point in you reading it.

I love it!

> 
> > ​>* ​*
> >
> >
> > *If the computer came up with a counter example to the Goldbach
> > conjecture, and lots of mathematicians independently verified the result by
> > hand,*
> 
> 
> ​By hand? The even number in question probably has about a hundred digits,
> so first of all you're going to have to find every prime number less than
> that super colossal ​
> number by long division and paper and pencil, and then show that no two of
> them add up to that number, and then you're going to have to do the same
> thing again and again to make sure you haven't made a mistake. And nobody
> is EVER going to do that by hand.​
>

That was actually my point :).

> 
> > ​> ​
> >
> > *what you say would be correct, and people would look to find the error in
> > th​e​ ZFC proof*
> 
> 
> In the thought experiment I specifically said there was no error in the
> proof and the ZFC axioms do indeed imply that Goldbach is true, but the
> computers disagree.
>

How do you establish that the proof has no error? Why are we supposing
that the ZFC axiom correctly describes the mathematical system? How do
you establish that the computers haven't made an error? (independent
implementations do help, of course).

It really underscores Chaitin's point that at some level of
complexity, mathematics becomes an empirical subject, perhaps not all
that different from physics.


-- 


Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Sun, May 13, 2018 at 9:06 PM, Russell Standish 
wrote:

>
> you already said, quite wisely, that if you had correctly used the ZFC
>> > axioms to produce a proof the Goldbach Conjecture was true but then a
>> > computer found a number that violated Goldbach you would place the
>> blame on
>> > the ZFC axioms and not on the laws of physics the computer operates
>> under.
>> > So like me you are saying it is physics and not axioms that is the
>> ultimate
>> > judge
>> ​ t​
>> hat​
>> ​ ​
>> decides what it true and what is not
>
>

​> ​
>
> *That is probably putting a little too much faith in computers, and the
> possibility of bug-free programs.*


In the thought experiment I specifically said numerous computers had made
the calculation and they all agree that there is a huge even number that is
not the sum of 2 primes.


> ​> *​*
>
> *There is a certain amount of​ ​scepticism of the proof of the 4 colour
> theorem, which is only available as an enormous computer generated proof.*


That proof was first demonstrated in 1976 and today I don't think there is
anybody who thinks it is untrue, they just grumble that it doesn't advance
human understanding of why it is true. As far as mathematical rigor is
concerned you have to be far more literal in a computer program than in a
mathematical proof because the computer will not fill in even the simplest
logical gaps and will not tolerate the slightest amount of hand waving.
And anyway, this sort of thing is not limited to computer proofs.

In 2012 Shinichi Mochizuki came up with a proof of the ABC conjecture, but
its 500 pages long and to this day about half of the world's mathematicians
think the proof is valid and the other half  think  it is not.  Recently
the fans of it held a workshop to streamline the proof, but its still 400
pages long. To read and understand this thing you still need to have a
boiling water IQ and you have to be prepared to devote the better part of a
decade studying it. Its a gamble, after devoting years of your life to it
when you could have been doing other things you may decide that Mochizuki's
proof is all bullshit, or maybe you'll decide its a work of genius. To a
lesser degree this happened with Andrew Wiles 's proof of Fermat's Last
Theorem , it took about a year for the mathematical community  to decide
that Wiles got it right. It's things like this that make me think that
maybe P really is equal to NP.

I think most people intuitively feel that P is not equal to NP because that
would sorta imply what we see in our everyday life, its harder to write a
book than to read a book, its harder to write a symphony than to listen to
one and appreciate its beauty, and it should be harder to discover a new
mathematical proof than it is to follow a step by step argument. But it
seems that that last thing may not be true, if I have a valid proof of
the Riemann Hypothesis but it would take you as much brainpower to
understand it as it would for you to find a proof on your own then there
would be no point in you reading it.

> ​>* ​*
>
>
> *If the computer came up with a counter example to the Goldbach
> conjecture, and lots of mathematicians independently verified the result by
> hand,*


​By hand? The even number in question probably has about a hundred digits,
so first of all you're going to have to find every prime number less than
that super colossal ​
number by long division and paper and pencil, and then show that no two of
them add up to that number, and then you're going to have to do the same
thing again and again to make sure you haven't made a mistake. And nobody
is EVER going to do that by hand.​


> ​> ​
>
> *what you say would be correct, and people would look to find the error in
> th​e​ ZFC proof*


In the thought experiment I specifically said there was no error in the
proof and the ZFC axioms do indeed imply that Goldbach is true, but the
computers disagree.


> ​>* ​*
> *or reject the ZFC axiom.*


So like me, and to my surprise like Bruno, if the ZFC axioms or ANY set of
axioms say one thing but a computer whose ultimate operating system is the
very laws of physics say the opposite then you reject the axioms and
believe the physics.

​John K Clark​

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Russell Standish]

On Sun, May 13, 2018 at 03:53:43PM -0400, John Clark wrote:
> 
> And you already said, quite wisely, that if you had correctly used the ZFC
> axioms to produce a proof the Goldbach Conjecture was true but then a
> computer found a number that violated Goldbach you would place the blame on
> the ZFC axioms and not on the laws of physics the computer operates under.
> So like me you are saying it is physics and not axioms that is the ultimate
> judge
> ​that​
>  decides what it true and what is not
> 
>  John K Clark

That is probably putting a little too much faith in computers, and the
possibility of bug-free programs. There is a certain amount of
scepticism of the proof of the 4 colour theorem, which is only
available as an enormous computer generated proof.

If the computer came up with a counter example to the Goldbach
conjecture, and lots of mathematicians independently verified the
result by hand, what you say would be correct, and people would look
to find the error in th ZFC proof, or reject the ZFC axiom. On the
other hand, since we probably require a computer to verify that a
large even number is not the sum of two primes, suspicion might well
settle on the computer program first.


-- 


Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Sat, May 12, 2018 at 4:21 AM, Bruno Marchal  wrote:


​> ​
> I use computer for “universal Turing machine”. That notion assumes (and is
> Turing-equivalent with (very) elementary arithmetic).
>

​
A Turing Machine knows no theories and it operates under the laws of
physics not because it assume them but because it has no choice in the
matter.

​>> ​
>> Computers are made of matter that obeys the laws of physics,
>
>
> Physical computer.
>


A Turing Machine is a physical computer and a Turing Machine is the only
type of computer that there is; even a virtual computer needs a Turing
machine somewhere down the line
​.​


> ​> ​
> But I do not assume
> ​ [...]
>

​A Turing Machine doesn't give a damn what you do or do not assume, it just
keeps on cranking away according to the laws of laws of physics.​


​>>​
>> when the voltage on one of the inputs of the microchip is positive
>> physics orders it will do one thing and when the voltage is negative it
>> will order it to do something different. By picking A you are in effect
>> saying you have looked at the pattern of voltages physics told the
>> microchip to have and you have interpreted that pattern to to be a even
>> number that is not the sum two prime numbers, and you believe what physics
>> is telling you even if the axioms of Number Theory says such a number can
>> not exist.
>
>
> *​> ​I have not assume physics anywhere,*
>

That's OK, physics doesn't assume you either. But you have said if the ZFC
axioms say one thing and the computer says the opposite then you'd believe
the computer and not the axioms, and that is what any sane man would do
because theories come and go but physics always tells the truth,


> *​> ​so this does not make any sense.*
>

Then how can you make sense out of ANY post from ANYBODY on this list? How
can you reply to any post when its just a pattern of voltages on the
microchip inside your computer?



> ​>>​
>> By picking A you are saying physics is more trustworthy than any set of
>> axioms could be, if there is a contradiction between the two it is the
>> axioms that need to give way not physical law because although
>> ​ ​
>> physics can be weird it has no self contradictions, but man made axioms
>> can.
>
>
> ​> ​
> Physical theories can be contradictory.
>

​I
f two physical theories try to explain the same phenomena then they are
ALWAYS contradictory,  otherwise they'd be the same theory, but at least
one of those theories must be wrong and that's where experiment comes in.
Physics (not to be confused with physical theories) is never contradictory
and will always tell you the truth, I would even say its the very
definition of truth.


> ​> ​
> And physical reality is not an assumption available at the start.
>

​To hell with assumptions! If I walk across a bridge it won't stay intact
if I make one assumption and collapse if I make another assumption. The
bridge will either collapse or it won't. The bridge doesn't care what I
assume and neither do the laws of physics.


​>> ​
>> A real machine will NEVER operate contrary to the laws of physics,
>
>
> *​> ​In which theory.*
>

What in the world that mean?? In which theory what?


> ​> ​
> *You are using implicit metaphysical assumption.*
>

​
A collapsed or intact bridge is not metaphysical nor is it a
​n​
assumption, it is matter operating according to the laws of physics.

​>> ​
>> but a set of axioms will ALWAYS be inconsistent or incomplete or both.
>
>
> ​> *​*
> *If a theory is inconsistent, it is obviously complete. *
>

Yes, you're right, my error. If I'm working with inconsistent axioms then I
can prove all true mathematical statements therefore its complete, the only
trouble is I can prove all false mathematical statements are true too. In a
lecture on logic Bertrand Russell said a false proposition implies any
proposition. A student challenged him on that and said ”In that case, given
that 1 = 0 prove that you are the Pope.” Without hesitation Russell said
”Add 1 to both sides of the equation: then we have 2 = 1. The set
containing just me and the Pope has 2 members. But 2 = 1, so it has only 1
member; therefore, I am the Pope.”


> *​> ​If a physical computer (assumed to have no bugs in it) can find an
> even number not being the sum of two prime, then that number can be find by
> very elementary arithmetic,*
>

And you already said, quite wisely, that if you had correctly used the ZFC
axioms to produce a proof the Goldbach Conjecture was true but then a
computer found a number that violated Goldbach you would place the blame on
the ZFC axioms and not on the laws of physics the computer operates under.
So like me you are saying it is physics and not axioms that is the ultimate
judge
​that​
 decides what it true and what is not

 John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 11 May 2018, at 23:32, John Clark  wrote:
> 
> On Fri, May 11, 2018 at 12:18 PM, Bruno Marchal  > wrote:
> 
> ​> ​If you started with the basic axioms of number theory and proved the 
> Goldbach Conjecture is true, and you were convinced you had not made an error 
> in the proof, and then the next day a computer found a huge even number that 
> was NOT the sum of 2 primes, would you:
> A) Conclude that there must be something wrong with the basic axioms of set 
> theory.
> Or
> B) Conclude that computers can’t be trusted because for some unknown reason 
> all computers always make an error when making that particular calculation.
> If its A then you are tacitly giving the laws of physics the right to 
> determine truth from falsehood because those laws determine how the machine 
> operates. If you choose B then madness awaits because your brain also 
> operates according to those very same laws. 
>  
> How so?
> 
> ​I'm surprised I have to spell this out.​
>  
> ​> ​In A, no physical assumption is used. Only the axioms of Number Theory.
> 
> A computer needs to know nothing about number theory and it assumes nothing. 

I use computer for “universal Turing machine”. That notion assumes (and is 
Turing-equivalent with (very) elementary arithmetic).



> Computers are made of matter that obeys the laws of physics,


Physical computer. But I do not assume a primary physical reality, given that I 
have shown that we have to justify it from arithmetic (or Turing equivalent).



> when the voltage on one of the inputs of the microchip is positive physics 
> orders it will do one thing and when the voltage is negative it will order it 
> to do something different. By picking A you are in effect saying you have 
> looked at the pattern of voltages physics told the microchip to have and you 
> have interpreted that pattern to to be a even number that is not the sum two 
> prime numbers, and you believe what physics is telling you even if the axioms 
> of Number Theory says such a number can not exist.

I have not assume physics anywhere, so this does not make any sense.




> By picking A you are saying physics is more trustworthy than any set of 
> axioms could be, if there is a contradiction between the two it is the axioms 
> that need to give way not physical law because althoughphysics can be weird 
> it has no self contradictions, but man made axioms can.  

Physical theories can be contradictory. And physical reality is not an 
assumption available at the start. 




>  
> ​> ​I guess you know that Gödel’s second incompleteness theorem shows that if 
> a machine or a theory is consistent,
> 
> A real machine will NEVER operate contrary to the laws of physics,


In which theory. You are using implicit metaphysical assumption. You take fro 
granted physicalism, which beg the question I am addressing.


> but a set of axioms will ALWAYS be inconsistent or incomplete or both.

If a theory is inconsistent, it is obviously complete. You can’t have both 
inconsistency and incompleteness.



> It could be that the the current axioms of number theory are not strong 
> enough to prove or disprove Goldbach, so if the laws of physics ever tell us, 
> by way of a computer, that there is a even number that is not the sum of 2 
> primes then it would be wise to add the negation of Goldbach as a new axiom 
> because physics is the ultimate arbiter about what is true and what is not​.​


If a physical computer (assumed to have no bugs in it) can find an even number 
not being the sum of two prime, then that number can be find by very elementary 
arithmetic, and this happens in arithmetic by the embedding of metamathematics 
in arithmetic (Gödel).

Bruno



> 
>  John K Clark
> 
> 
> 
> 
> 
> 
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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Fri, May 11, 2018 at 12:18 PM, Bruno Marchal  wrote:

​> ​
>> If you started with the basic axioms of number theory and proved the
>> Goldbach Conjecture is true, and you were convinced you had not made an
>> error in the proof, and then the next day a computer found a huge even
>> number that was NOT the sum of 2 primes, would you:
>
> A) Conclude that there must be something wrong with the basic axioms of
>> set theory.
>>
>> Or
>>
>> B) Conclude that computers can’t be trusted because for some unknown
>> reason all computers always make an error when making that particular
>> calculation.
>> If its A then you are tacitly giving the laws of physics the right to
>> determine truth from falsehood because those laws determine how the machine
>> operates. If you choose B then madness awaits because your brain also
>> operates according to those very same laws.
>
>

*How so? *


​I'm surprised I have to spell this out.​


> *​> ​In A, no physical assumption is used. Only the axioms of Number
> Theory.*


A computer needs to know nothing about number theory and it assumes
nothing.  Computers are made of matter that obeys the laws of physics, when
the voltage on one of the inputs of the microchip is positive physics
orders it will do one thing and when the voltage is negative it will order
it to do something different. By picking A you are in effect saying you
have looked at the pattern of voltages physics told the microchip to have
and you have interpreted that pattern to to be a even number that is not
the sum two prime numbers, and you believe what physics is telling you even
if the axioms of Number Theory says such a number can not exist. By picking
A you are saying physics is more trustworthy than any set of axioms could
be, if there is a contradiction between the two it is the axioms that need
to give way not physical law because althoughphysics can be weird it has no
self contradictions, but man made axioms can.


> ​> ​
> *I guess you know that Gödel’s second incompleteness theorem shows that if
> a machine or a theory is consistent,*
>

A real machine will NEVER operate contrary to the laws of physics, but a
set of axioms will ALWAYS be inconsistent or incomplete or both. It could
be that the the current axioms of number theory are not strong enough to
prove or disprove Goldbach, so if the laws of physics ever tell us, by way
of a computer, that there is a even number that is not the sum of 2 primes
then it would be wise to add the negation of Goldbach as a new axiom
because physics is the ultimate arbiter about what is true and what is not
​.​

 John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 10 May 2018, at 19:11, John Clark  wrote:
> 
> On Thu, May 10, 2018 at 10:36 AM, Bruno Marchal  > wrote:
> 
> ​>> ​if you can not then the word "model" has no meaning.   Unlike the 
> Continuum Hypothesis the Goldbach Conjecture is subject to the potential of 
> experimental falsification, if logicians eventually proved that it is true,
> 
> ​> ​We don’t prove that something is true. We just prove it. That plays some 
> role. No sound machine can ever prove that whatever she proves is true.
>  
> If you started with the basic axioms of number theory and proved the Goldbach 
> Conjecture is true, and you were convinced you had not made an error in the 
> proof, and then the next day a computer found a huge even number that was NOT 
> the sum of 2 primes, would you:
> 
> A) Conclude that there must be something wrong with the basic axioms of set 
> theory.
> 
> 

A.  (Guessing that you mean axiom of number theory, not set theory, as you said 
above)



> Or
> 
> B) Conclude that computers can’t be trusted because for some unknown reason 
> all computers always make an error when making that particular calculation.
> 
> 

If all computers do get the same error, that would only provide more weight on 
A 



> If its A then you are tacitly giving the laws of physics the right to 
> determine truth from falsehood because those laws determine how the machine 
> operates.
> 

How so? 

In A, no physical assumption is used. Only the axioms of Number Theory. If a 
computer get a different conclusion, I will believe that there is some bug in 
its relative (to me) implementation. If all computer gives that different 
conclusion, I will suspect an error in my proof. 
I guess you know that the universal dovetetailer emulate also the programs with 
bugs.
I guess you know that Gödel’s second incompleteness theorem shows that if a 
machine or a theory is consistent, then the statement that the machine or the 
theory is inconsistent *is* consistent with the axiom of the theory:

~[]f -> <>[]f.  (Not-provable(false) implies the consistency of (false is 
provable)

Bruno


> If you choose B then madness awaits because your brain also operates 
> according to those very same laws. 
> 
> 
> 
> ​ ​John K Clark 
> 
> 
> 
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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Thu, May 10, 2018 at 10:36 AM, Bruno Marchal  wrote:

>
​>> ​
>> if you can not then the word "model" has no meaning.   Unlike the
>> Continuum Hypothesis the Goldbach Conjecture is subject to the potential of
>> experimental falsification, if logicians eventually proved that it is true,
>
>
> *​> ​We don’t prove that something is true. We just prove it. That plays
> some role. No sound machine can ever prove that whatever she proves is
> true.*



If you started with the basic axioms of number theory and proved the
Goldbach Conjecture is true, and you were convinced you had not made an
error in the proof, and then the next day a computer found a huge even
number that was NOT the sum of 2 primes, would you:

A) Conclude that there must be something wrong with the basic axioms of set
theory.

Or

B) Conclude that computers can’t be trusted because for some unknown reason
all computers always make an error when making that particular calculation.

If its A then you are tacitly giving the laws of physics the right to
determine truth from falsehood because those laws determine how the machine
operates. If you choose B then madness awaits because your brain also
operates according to those very same laws.

​ ​
John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 8 May 2018, at 18:01, John Clark  wrote:
> 
> On Mon, May 7, 2018 at 8:12 PM, Russell Standish  > wrote:
> 
> >​>​ I think you're confused about the difference between what a model says
> and what reality says. One model may say you can safely march across that
> bridge and another model might say the bridge will collapse, but it makes
> no difference which model you believe when you cross th​​e​ bridge, it will 
> either fall down or it won't.
> 
> ​> ​Unfortunately you are using "model" in a different sense to how Bruno(or 
> logicians generally) uses it. The real world bridge is a​ ​model.
> If the real world bridge is a model then give me a example of something that 
> is not a model,
> 

Logician use “model" like painter. Model = the real thing, like the naked woman 
waiting to be painted. In that analogy, the theory is the painting.

Physicist use “model” like children. Model = toy model, like a small car to 
play with.

Example in mathematics.

A theory is a interpretation set of formula. A model is a mathematical 
structure. So here is a theory:

(Classical logic) +

0 ≠ s(x)
s(x) = s(y) -> x = y
x = 0 v Ey(x = s(y))
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x

A model of that theory is the structure (N, 0, +, *), where  N is the set of 
natural numbers, 0 denotes 0, and + and * is the usual addition and 
multiplication.

Exercise: find a model of the theory above in which 0 + x is ≠ x, and where 
there is a biggest natural number.

The theorem are true in all model, and a theory is consistent (does not prove A 
and ~A, for any A) iff it has a model.





> if you can not then the word "model" has no meaning.   Unlike the Continuum 
> Hypothesis the Goldbach Conjecture is subject to the potential of 
> experimental falsification, if logicians eventually proved that it is true,
> 

We don’t prove that something is true. We just prove it. That plays some role. 
No sound machine can ever prove that whatever she proves is true.




> that is to say they started with nothing but their axioms and derived it, but 
> then the next day a computer found a huge even number that was NOT the sum of 
> two prime numbers I think logicians would be very upset, or at least the 
> competent ones would be. I think they would say that shows their present 
> axioms must not be "sound" in the technical sense and need to be modified. I 
> don't think they would say "the laws of physics that the computer runs on 
> must be wrong and our model is right and every even number is the sum of two 
> primes and thats that and I don't want to hear anymore about it"; but if I'm 
> wrong and they did say that then I would no longer be interested in anything 
> logicians said in the future because they would be jackasses. But I don’t 
> think they’re jackasses because good logicians know there is a difference 
> between proof and truth, physics will always tell you the truth but a proof 
> is only as good as the axioms it is based on.
> 
> 

Aristotelian faith, like St-Thomas. You believe in what you see. Platonism are 
skeptical on every cilamied truth, especially about what they see, because they 
know they could be dreaming, or deluded, or that there is a systematic 
experimental error, etc.




> ​> ​Your models would be called theories, and the real world bridge​ ​either 
> satisfies it or not.
> 
> You say the real world bridge is a theory,

I don’t think Russell says that. He said that what you call “model” is called 
“theories” by logicians, and that logicians tackle the notion of reality with 
the notion of model. Logicians studies the relation between theories (finite or 
enumerable set of beliefs) and truth (a notion relative to interpretation, and 
which is usually infinite-.



> so now we have theories about theories?

Yes of course. That is what mathematical logic is all about. A synonym of 
“mathematical logic” is Metamathematics (used by Gödel, Kleene, etc.). 

The whole point of Gödel’s discovery, is that a large part of the 
metamathematics can be made in the mathematics. G formalises the logic of the 
meta-arithmetic that Peano Arithmetic can prove. G* formalises the whole truth 
of the standard model of arithmetic (what we learn at school). G* \ G 
formalises what is true but cannot be prove in that meta-arithmetic (roughly 
speaking, avoiding technical details).



> Give me an example of something that is not a theory, if you can not then 
> like "model" the word "theory" has no meaning either. ​


Nothing are more distinct than theories and models. It is as much different 
than a far away galaxy and Hubble telescope, or, the finger and the moon.

The theory (in logic) is a finite set of axioms, or a (recursively) enumerable 
set of axioms.

The model of a theory is a reality which satisfy (in some precise sense which 
would be long to describe here) the axioms and the theorems of the theory.

Think of the theory of group and an example of a “concrete”, like the gro

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Mon, May 7, 2018 at 8:12 PM, Russell Standish 
wrote:

>
> >
>> ​>​
>> I think you're confused about the difference between what a model says
>> and what reality says. One model may say you can safely march across that
>> bridge and another model might say the bridge will collapse, but it makes
>> no difference which model you believe when you cross th​
>> ​e​
>> bridge, it will either fall down or it won't.
>
>
> *​> ​Unfortunately you are using "model" in a different sense to how
> Bruno(or logicians generally) uses it. The real world bridge is a​ ​model.*

If the real world bridge is a model then give me a example of something
that is not a model, if you can not then the word "model" has no meaning.
Unlike the Continuum Hypothesis the Goldbach Conjecture is subject to the
potential of experimental falsification, if logicians eventually proved
that it is true, that is to say they started with nothing but their axioms
and derived it, but then the next day a computer found a huge even number
that was NOT the sum of two prime numbers I think logicians would be very
upset, or at least the competent ones would be. I think they would say that
shows their present axioms must not be "sound" in the technical sense and
need to be modified. I don't think they would say "the laws of physics that
the computer runs on must be wrong and our model is right and every even
number is the sum of two primes and thats that and I don't want to hear
anymore about it"; but if I'm wrong and they did say that then I would no
longer be interested in anything logicians said in the future because they
would be jackasses. But I don’t think they’re jackasses because good
logicians know there is a difference between proof and truth, physics will
always tell you the truth but a proof is only as good as the axioms it is
based on.

> ​> ​
>
> *Your models would be called theories, and the real world bridge​ ​either
> satisfies it or not.*


You say the real world bridge is a theory, so now we have theories about
theories? Give me an example of something that is not a theory, if you can
not then like "model" the word "theory" has no meaning either.
​

 John K Clark​



​

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 8 May 2018, at 02:20, Lawrence Crowell  
> wrote:
> 
> On Monday, May 7, 2018 at 11:51:46 AM UTC-5, Bruno Marchal wrote:
> 
>> On 7 May 2018, at 03:19, Brent Meeker > 
>> wrote:
>> 
>> 
>> 
>> On 5/6/2018 6:40 AM, Bruno Marchal wrote:
>>> 
 On 2 May 2018, at 02:28, Lawrence Crowell >>> > wrote:
 
 On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote:
 An interesting proof by Hamkins and a lot of discussion of its 
 significance on John Baez's blog.  It agrees with my intuition that the 
 mathematical idea of "finite" is not so obvious. 
 
 Brent 
 
 
 This gets into the rarefied atmosphere of degrees of unprovability. I have 
 a book by Lerman on the subject, which I can read maybe 25 pages into 
 before I am largely confused and lost. I would really need to be far 
 better grounded in this. The idea is that one may ask if things are 
 diagonal up to ω ordinarlity, which is standard Gödel/Turing machine 
 stuff. Then we might however have Halting or provability out to ω + n, or 
 2ω to nω and then how about ω^n and then n^ω and now make is bigger with 
 ω^ω and so forth. Then this in principle may continue onwards beyond the 
 alephs into least accessible cardinals and so forth. One has this vast and 
 maybe endless tower of greater transfinite models. 
 
 Finite systems that are well defined are cyclic groups and related 
 structures. A mathematical system that has some artificial bound on it is 
 not going to satisfy any universal requirements. The most one can have is 
 finite but unbounded. So long as one does not have some series or 
 progression that grows endlessly this can work.
>>> 
>>> 
>>> With mechanism, we don’t really have to take care of the non-standard model 
>>> of arithmetic, because it can be proved that even addition and 
>>> multiplication are not (Church-Turing) computable.
>>> 
>>> The church-Turing thesis makes computability absolute in the sense that 
>>> what can be proved to be computable or non computable will be true in *all* 
>>> models of any arithmetical theories. If a machine (or number, to emphasise 
>>> their finiteness) is universal, it is universal in all models or 
>>> interpretation of the ontological theories.
>> 
>> But don't you take all arithmetic theories to include the axioms that say 
>> every number has a successor?
> 
> Yes. Where is the problem? I could do without, and use the Gaussian integers, 
> where numbers can have an up and right successors, if you prefer.
> 
> I could do this point on all inductive system having some,operations making 
> them Turing universal. But elementary arithmetic, and its primary school 
> interpretation (assuming students and teachers are not zombie!) is enough.
> 
> Like I just said to John, I assume less, far less, than most scientists, 
> despite feeling close to Moderatus, the advaita veda, Lao-Ze, etc. The 
> universal machine which knows that she is universal is quite close, when you 
> look at its G/G* theology.
> 
> Bruno
> 
> Peano number theory is incomplete, for there is no way the system can prove 
> it will define every possible real number. 


All theories of arithmetic are incomplete. More generally all theories in which 
we can define a Universal machine is incomplete.

Then Peano arithmetic is just not talking about real numbers.

BTW, the first order theory of the real is complete, but that is why it is too 
weak to define a universal machine.

Then real numbers + trigonometry is Turing complete, but that is because 
trigonometry can bu used to define the natural numbers in the real numbers.

Logicians have understood that the real numbers is only a big simplification of 
the natural numbers. It is a simple exercise to solve Fremat in the real, and a 
very difficult subject research to solve the same problem for the natural 
numbers (cf Wiles).




> A form of this could be seen as a form of Berry paradox where most numbers 
> between 10^{10^{10^{10}}} and 10^{10^{10^{10^{10 have no possible way of 
> being "named.”

? (You can name each of them). If we give you enough time. It is different from 
the thing we can really not name or define in arithmetic, or in any theory 
having arithmetic as a sub theory. 




> From a practical perspective there are not enough quantum bits or particles 
> within our causal domain one might use to name most of these numbers.


Assuming such domain exists, but with mechanism, it can’t.



> What ever limits you place on the size of the name that bound is inevitably 
> violated, which leads in the infinite sense to a Cantor-like diagonalization 
> because it is non-enumerable. It does mean we can't prove there are not 
> oddball situation way out there on the number line. This does not though mean 
> things are really that quirky.


With mechanism, I prefer (and is probably forced) to not install sets or real 
numbers in the ontology. They are only a way the na

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 8 May 2018, at 01:32, John Clark  wrote:
> 
> On Mon, May 7, 2018 at 12:58 PM, Bruno Marchal  > wrote:
>  
> ​> ​in some model CH is true (Gödel) and in some model CH is false (Cohen).
>  
> That is incorrect. Godel showed that if the CH is false it would not produce 
> any contradictions in Zermelo–Fraenkel set theory plus the Axiom Of Choice 
> (ZFC), but that does not prove that the CH is false.


OK, but that is prove by building a model where CH is false, like we can prove 
the independence of Euclid postulate by building a model satisfying all axioms 
+ the negation of the parallel postulate. 
The notion of truth is always relativised to a model, in logic.

Bruno 



> And Cohen proved that if the CH is true it would not produce any 
> contradiction in ZFC, but that doesn't prove its true either. What the two of 
> them did prove is that ZFC has nothing to say about Continuum Hypothesis, it 
> just doesn't know if its true or not. 
>  
> And I think you're confused about the difference between what a model says 
> and what reality says. One model may say you can safely march across that 
> bridge and another model might say the bridge will collapse, but it makes no 
> difference which model you believe when you cross t​h​at bridge, it will 
> either fall down or it won't.
> 
> ​John K Clark​
> 
> 
>  
> 
> 
> 
> 
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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Lawrence Crowell]

On Monday, May 7, 2018 at 11:51:46 AM UTC-5, Bruno Marchal wrote:
>
>
> On 7 May 2018, at 03:19, Brent Meeker > 
> wrote:
>
>
>
> On 5/6/2018 6:40 AM, Bruno Marchal wrote:
>
>
> On 2 May 2018, at 02:28, Lawrence Crowell  > wrote:
>
> On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote: 
>>
>> An interesting proof by Hamkins and a lot of discussion of its 
>> significance on John Baez's blog.  It agrees with my intuition that the 
>> mathematical idea of "finite" is not so obvious. 
>>
>> Brent 
>>
>>
> This gets into the rarefied atmosphere of degrees of unprovability. I have 
> a book by Lerman on the subject, which I can read maybe 25 pages into 
> before I am largely confused and lost. I would really need to be far better 
> grounded in this. The idea is that one may ask if things are diagonal up 
> to ω ordinarlity, which is standard Gödel/Turing machine stuff. Then we 
> might however have Halting or provability out to ω + n, or 2ω to nω and 
> then how about ω^n and then n^ω and now make is bigger with ω^ω and so 
> forth. Then this in principle may continue onwards beyond the alephs into 
> least accessible cardinals and so forth. One has this vast and maybe 
> endless tower of greater transfinite models. 
>
> Finite systems that are well defined are cyclic groups and related 
> structures. A mathematical system that has some artificial bound on it is 
> not going to satisfy any universal requirements. The most one can have is 
> finite but unbounded. So long as one does not have some series or 
> progression that grows endlessly this can work.
>
>
>
> With mechanism, we don’t really have to take care of the non-standard 
> model of arithmetic, because it can be proved that even addition and 
> multiplication are not (Church-Turing) computable.
>
> The church-Turing thesis makes computability absolute in the sense that 
> what can be proved to be computable or non computable will be true in *all* 
> models of any arithmetical theories. If a machine (or number, to emphasise 
> their finiteness) is universal, it is universal in all models or 
> interpretation of the ontological theories.
>
>
> But don't you take all arithmetic theories to include the axioms that say 
> every number has a successor?
>
>
> Yes. Where is the problem? I could do without, and use the Gaussian 
> integers, where numbers can have an up and right successors, if you prefer.
>
> I could do this point on all inductive system having some,operations 
> making them Turing universal. But elementary arithmetic, and its primary 
> school interpretation (assuming students and teachers are not zombie!) is 
> enough.
>
> Like I just said to John, I assume less, far less, than most scientists, 
> despite feeling close to Moderatus, the advaita veda, Lao-Ze, etc. The 
> universal machine which knows that she is universal is quite close, when 
> you look at its G/G* theology.
>
> Bruno
>

Peano number theory is incomplete, for there is no way the system can prove 
it will define every possible real number. A form of this could be seen as 
a form of Berry paradox where most numbers between 10^{10^{10^{10}}} and 
10^{10^{10^{10^{10 have no possible way of being "named." From a 
practical perspective there are not enough quantum bits or particles within 
our causal domain one might use to name most of these numbers. What ever 
limits you place on the size of the name that bound is inevitably violated, 
which leads in the infinite sense to a Cantor-like diagonalization because 
it is non-enumerable. It does mean we can't prove there are not oddball 
situation way out there on the number line. This does not though mean 
things are really that quirky.

LC

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Russell Standish]

On Mon, May 07, 2018 at 07:32:21PM -0400, John Clark wrote:
> 
> And I think you're confused about the difference between what a model says
> and what reality says. One model may say you can safely march across that
> bridge and another model might say the bridge will collapse, but it makes
> no difference which model you believe when you cross t
> ​h​
> at bridge, it will either fall down or it won't.
> 

Unfortunately you are using "model" in a different sense to how Bruno
(or logicians generally) uses it. The real world bridge is a
model. Your models would be called theories, and the real world bridge
either satisfies it or not.

Confusing? You bet. But it is how things are, not something Bruno
arbitrarily introduced. See 
https://mathoverflow.net/questions/42298/the-use-of-the-word-model-in-mathematical-logic-vs-the-same-word-in-natural-sc


-- 


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Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

On Mon, May 7, 2018 at 12:58 PM, Bruno Marchal  wrote:


> ​> ​
> in some model CH is true (Gödel) and in some model CH is false (Cohen).
>

That is incorrect. Godel showed that if the CH is false it would not
produce any contradictions in Zermelo–Fraenkel set theory plus the Axiom Of
Choice (ZFC), but that does not prove that the CH is false. And Cohen
proved that if the CH is true it would not produce any contradiction in
ZFC, but that doesn't prove its true either. What the two of them did prove
is that ZFC has nothing to say about Continuum Hypothesis, it just doesn't
know if its true or not.

And I think you're confused about the difference between what a model says
and what reality says. One model may say you can safely march across that
bridge and another model might say the bridge will collapse, but it makes
no difference which model you believe when you cross t
​h​
at bridge, it will either fall down or it won't.

​John K Clark​

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 7 May 2018, at 16:38, John Clark  wrote:
> 
> ​If the Real numbers exist then the Continuum Hypothesis is either true or it 
> is not. 


That does not follow. Cunter-exemple: Intuitionist analysis admit Real Numbers, 
but certainly not with the CH being true or false.

You assume classical logic, on some first order axiomatisation of set theory.

Other counterexample. All models of ZF have real numbers; but in some model CH 
is true (Gödel) and in some model CH is false (Cohen).

Bruno


> But are the Real numbers really real? No less a mathematician than Gregory 
> Chaitin (of Chaitin's Omega fame) is on record as saying the real numbers do 
> not exist. If he's right and they don't exist then the Continuum Hypothesis 
> is neither true nor false, its gibberish. Perhaps a better example would be 
> "is the Goldbach Conjecture either true or not true?" because we know 
> integers exist and unlike the Continuum Hypothesis we can at least conceive 
> of experimental evidence proving that it is wrong; tomorrow a computer 
> grinding through ever larger integers could find some huge even number that 
> is not the sum of two prime numbers.  
>  John K Clark
> 
> 
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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 7 May 2018, at 12:52, Lawrence Crowell  
> wrote:
> 
> On Sunday, May 6, 2018 at 9:16:13 PM UTC-5, Russell Standish wrote:
> On Sun, May 06, 2018 at 06:19:01PM -0700, Brent Meeker wrote: 
> > But don't you take all arithmetic theories to include the axioms that say 
> > every number has a successor? 
> 
> Just because every number has a successor does not entail the 
> existence of ω. 
> 
> This is otherwise known as "potential infinity" versus "actual 
> infinity". 
> 
> I've come across a similar sort of issue in studying what I call 
> "open dimensional systems". An open dimensional system is 
> still a finite dimensional system, but quite a distinct beast from the 
> usual fixed dimensional systems studied in dynamical systems 
> theory. Just doing a quick Google search indicates that I have been 
> unsuccessful in getting the term "open dimensional" adopted - it looks 
> like "unbounded dimensional" might have won the day :P. 
> 
> I will try to respond to Bruno more completely, but this is a bit of the 
> conundrum. One can work up various models with different ideas about 
> transfinite numbers. ZF set theory embraces infinity or transfinite numbers 
> with all the issues that come with it. Other ideas are more restrictive. From 
> the perspective of physics these concerns in a sense flap in the breeze with 
> little direct concern.

With mechanism, what can be proved, is that ZF and ZFC have the same opinion, 
about number’s theology (the G/G* logics, with quantifiers).

Bruno



> 
> LC
>  
> 
> Cheers 
> -- 
> 
>  
> Dr Russell StandishPhone 0425 253119 (mobile) 
> Principal, High Performance Coders 
> Visiting Senior Research Fellowhpc...@hpcoders.com.au  
> Economics, Kingston University http://www.hpcoders.com.au 
>  
>  
> 
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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 7 May 2018, at 03:19, Brent Meeker  wrote:
> 
> 
> 
> On 5/6/2018 6:40 AM, Bruno Marchal wrote:
>> 
>>> On 2 May 2018, at 02:28, Lawrence Crowell >> > wrote:
>>> 
>>> On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote:
>>> An interesting proof by Hamkins and a lot of discussion of its 
>>> significance on John Baez's blog.  It agrees with my intuition that the 
>>> mathematical idea of "finite" is not so obvious. 
>>> 
>>> Brent 
>>> 
>>> 
>>> This gets into the rarefied atmosphere of degrees of unprovability. I have 
>>> a book by Lerman on the subject, which I can read maybe 25 pages into 
>>> before I am largely confused and lost. I would really need to be far better 
>>> grounded in this. The idea is that one may ask if things are diagonal up to 
>>> ω ordinarlity, which is standard Gödel/Turing machine stuff. Then we might 
>>> however have Halting or provability out to ω + n, or 2ω to nω and then how 
>>> about ω^n and then n^ω and now make is bigger with ω^ω and so forth. Then 
>>> this in principle may continue onwards beyond the alephs into least 
>>> accessible cardinals and so forth. One has this vast and maybe endless 
>>> tower of greater transfinite models. 
>>> 
>>> Finite systems that are well defined are cyclic groups and related 
>>> structures. A mathematical system that has some artificial bound on it is 
>>> not going to satisfy any universal requirements. The most one can have is 
>>> finite but unbounded. So long as one does not have some series or 
>>> progression that grows endlessly this can work.
>> 
>> 
>> With mechanism, we don’t really have to take care of the non-standard model 
>> of arithmetic, because it can be proved that even addition and 
>> multiplication are not (Church-Turing) computable.
>> 
>> The church-Turing thesis makes computability absolute in the sense that what 
>> can be proved to be computable or non computable will be true in *all* 
>> models of any arithmetical theories. If a machine (or number, to emphasise 
>> their finiteness) is universal, it is universal in all models or 
>> interpretation of the ontological theories.
> 
> But don't you take all arithmetic theories to include the axioms that say 
> every number has a successor?

Yes. Where is the problem? I could do without, and use the Gaussian integers, 
where numbers can have an up and right successors, if you prefer.

I could do this point on all inductive system having some,operations making 
them Turing universal. But elementary arithmetic, and its primary school 
interpretation (assuming students and teachers are not zombie!) is enough.

Like I just said to John, I assume less, far less, than most scientists, 
despite feeling close to Moderatus, the advaita veda, Lao-Ze, etc. The 
universal machine which knows that she is universal is quite close, when you 
look at its G/G* theology.

Bruno



> 
> Brent
> 
>> 
>> But this remark would become obsolete in case we add an infinity axioms in 
>> the ontology, like in set theories. To take no risk, I “forbid” even the 
>> induction axioms at the ontological level. So, induction, infinities, 
>> second-order logic, real numbers, analysis and physics will belong to the 
>> phenomenology of numbers, and this makes mechanism into a finitism. 0, 1, 2, 
>> 3 …. exist, but N or ω do not, except as number/machine’s mind’s tools.
>> 
>> Bruno
>> 
>> 
>> 
>> 
>>> 
>>> LC
>>> 
>>>  
>>> 
>>>  Forwarded Message  
>>> 
>>> On Tue, May 1, 2018 at 1:13 PM, James  wrote: 
>>> > On Tue, May 1, 2018 at 7:19 AM, Cris  wrote: 
>>> >> 
>>> >> ... For any set of axioms, there is a Turing machine which 1) never 
>>> >> halts and 2) that set of axioms cannot prove that it never halts. ... 
>>> > 
>>> >> But don’t you agree that the Halting Problem has a definite truth value? 
>>> >> In other words, that a given Turing machine (with a given input) either 
>>> >> runs forever or doesn’t, regardless of our ability to prove it? ... 
>>> > 
>>> > To answer the question posed, shouldn't we ask if, given any 
>>> > *particular* TM, there exists *some* consistent system/set of axioms 
>>> > that can prove whether it halts or not?  I was under the impression 
>>> > that the answer here was "yes", regardless of any individual 
>>> > consistent system being unable to tackle the general problem. 
>>> 
>>> The problem is when you have nonstandard natural numbers.  It's 
>>> perfectly valid, for instance, to have a Turing machine halt after ω + 
>>> 3 steps.  You can say, "oh, but we use the unique standard model 
>>> defined by the second-order theory", but then the second order theory 
>>> has to live in some universe, and there are universes in which what's 
>>> uncomputable in your universe can be computable in mine: 
>>> 
>>> http://jdh.hamkins.org/every-function-can-be-computable/ 
>>>  
>>> https://johncarlosbaez.wordpress.com/2016/04/02/computing-the-

Re: Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[John Clark]

​If the Real numbers exist then the Continuum Hypothesis is either true or
it is not.  But are the Real numbers really real? No less a mathematician
than Gregory Chaitin (of Chaitin's Omega fame) is on record as saying the
real numbers do not exist. If he's right and they don't exist then the
Continuum Hypothesis is neither true nor false, its gibberish. Perhaps a
better example would be "is the Goldbach Conjecture either true or not
true?" because we know integers exist and unlike the Continuum Hypothesis
we can at least conceive of experimental evidence proving that it is wrong;
tomorrow a computer grinding through ever larger integers could find some
huge even number that is not the sum of two prime numbers.

 John K Clark

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Lawrence Crowell]

On Sunday, May 6, 2018 at 9:16:13 PM UTC-5, Russell Standish wrote:
>
> On Sun, May 06, 2018 at 06:19:01PM -0700, Brent Meeker wrote: 
> > But don't you take all arithmetic theories to include the axioms that 
> say 
> > every number has a successor? 
>
> Just because every number has a successor does not entail the 
> existence of ω. 
>
> This is otherwise known as "potential infinity" versus "actual 
> infinity". 
>
> I've come across a similar sort of issue in studying what I call 
> "open dimensional systems". An open dimensional system is 
> still a finite dimensional system, but quite a distinct beast from the 
> usual fixed dimensional systems studied in dynamical systems 
> theory. Just doing a quick Google search indicates that I have been 
> unsuccessful in getting the term "open dimensional" adopted - it looks 
> like "unbounded dimensional" might have won the day :P. 
>

I will try to respond to Bruno more completely, but this is a bit of the 
conundrum. One can work up various models with different ideas about 
transfinite numbers. ZF set theory embraces infinity or transfinite numbers 
with all the issues that come with it. Other ideas are more restrictive. 
>From the perspective of physics these concerns in a sense flap in the 
breeze with little direct concern.

LC
 

>
> Cheers 
> -- 
>
>  
>
> Dr Russell StandishPhone 0425 253119 (mobile) 
> Principal, High Performance Coders 
> Visiting Senior Research Fellowhpc...@hpcoders.com.au 
>  
> Economics, Kingston University http://www.hpcoders.com.au 
>  
>
>

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Russell Standish]

On Sun, May 06, 2018 at 06:19:01PM -0700, Brent Meeker wrote:
> But don't you take all arithmetic theories to include the axioms that say
> every number has a successor?

Just because every number has a successor does not entail the
existence of ω.

This is otherwise known as "potential infinity" versus "actual
infinity".

I've come across a similar sort of issue in studying what I call
"open dimensional systems". An open dimensional system is
still a finite dimensional system, but quite a distinct beast from the
usual fixed dimensional systems studied in dynamical systems
theory. Just doing a quick Google search indicates that I have been
unsuccessful in getting the term "open dimensional" adopted - it looks
like "unbounded dimensional" might have won the day :P.

Cheers
-- 


Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Brent Meeker]

On 5/6/2018 6:40 AM, Bruno Marchal wrote:


On 2 May 2018, at 02:28, Lawrence Crowell 
> wrote:


On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote:

An interesting proof by Hamkins and a lot of discussion of its
significance on John Baez's blog.  It agrees with my intuition
that the
mathematical idea of "finite" is not so obvious.

Brent


This gets into the rarefied atmosphere of degrees of unprovability. I 
have a book by Lerman on the subject, which I can read maybe 25 pages 
into before I am largely confused and lost. I would really need to be 
far better grounded in this. The idea is that one may ask if things 
are diagonal up to ω ordinarlity, which is standard Gödel/Turing 
machine stuff. Then we might however have Halting or provability out 
to ω + n, or 2ω to nω and then how about ω^n and then n^ω and now 
make is bigger with ω^ω and so forth. Then this in principle may 
continue onwards beyond the alephs into least accessible cardinals 
and so forth. One has this vast and maybe endless tower of greater 
transfinite models.


Finite systems that are well defined are cyclic groups and related 
structures. A mathematical system that has some artificial bound on 
it is not going to satisfy any universal requirements. The most one 
can have is finite but unbounded. So long as one does not have some 
series or progression that grows endlessly this can work.



With mechanism, we don’t really have to take care of the non-standard 
model of arithmetic, because it can be proved that even addition and 
multiplication are not (Church-Turing) computable.


The church-Turing thesis makes computability absolute in the sense 
that what can be proved to be computable or non computable will be 
true in *all* models of any arithmetical theories. If a machine (or 
number, to emphasise their finiteness) is universal, it is universal 
in all models or interpretation of the ontological theories.


But don't you take all arithmetic theories to include the axioms that 
say every number has a successor?


Brent



But this remark would become obsolete in case we add an infinity 
axioms in the ontology, like in set theories. To take no risk, I 
“forbid” even the induction axioms at the ontological level. So, 
induction, infinities, second-order logic, real numbers, analysis and 
physics will belong to the phenomenology of numbers, and this makes 
mechanism into a finitism. 0, 1, 2, 3 …. exist, but N or ω do not, 
except as number/machine’s mind’s tools.


Bruno






LC


 Forwarded Message 

On Tue, May 1, 2018 at 1:13 PM, James  wrote:
> On Tue, May 1, 2018 at 7:19 AM, Cris  wrote:
>>
>> ... For any set of axioms, there is a Turing machine which 1)
never halts and 2) that set of axioms cannot prove that it never
halts. ...
>
>> But don’t you agree that the Halting Problem has a definite
truth value? In other words, that a given Turing machine (with a
given input) either runs forever or doesn’t, regardless of our
ability to prove it? ...
>
> To answer the question posed, shouldn't we ask if, given any
> *particular* TM, there exists *some* consistent system/set of
axioms
> that can prove whether it halts or not?  I was under the
impression
> that the answer here was "yes", regardless of any individual
> consistent system being unable to tackle the general problem.

The problem is when you have nonstandard natural numbers.  It's
perfectly valid, for instance, to have a Turing machine halt
after ω +
3 steps.  You can say, "oh, but we use the unique standard model
defined by the second-order theory", but then the second order
theory
has to live in some universe, and there are universes in which
what's
uncomputable in your universe can be computable in mine:

http://jdh.hamkins.org/every-function-can-be-computable/

https://johncarlosbaez.wordpress.com/2016/04/02/computing-the-uncomputable/




So as soon as you move away from "only physically implementable math
is real", then you have do deal with all these other models.
-- 
Mike

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Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Bruno Marchal]

> On 2 May 2018, at 02:28, Lawrence Crowell  
> wrote:
> 
> On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote:
> An interesting proof by Hamkins and a lot of discussion of its 
> significance on John Baez's blog.  It agrees with my intuition that the 
> mathematical idea of "finite" is not so obvious. 
> 
> Brent 
> 
> 
> This gets into the rarefied atmosphere of degrees of unprovability. I have a 
> book by Lerman on the subject, which I can read maybe 25 pages into before I 
> am largely confused and lost. I would really need to be far better grounded 
> in this. The idea is that one may ask if things are diagonal up to ω 
> ordinarlity, which is standard Gödel/Turing machine stuff. Then we might 
> however have Halting or provability out to ω + n, or 2ω to nω and then how 
> about ω^n and then n^ω and now make is bigger with ω^ω and so forth. Then 
> this in principle may continue onwards beyond the alephs into least 
> accessible cardinals and so forth. One has this vast and maybe endless tower 
> of greater transfinite models. 
> 
> Finite systems that are well defined are cyclic groups and related 
> structures. A mathematical system that has some artificial bound on it is not 
> going to satisfy any universal requirements. The most one can have is finite 
> but unbounded. So long as one does not have some series or progression that 
> grows endlessly this can work.


With mechanism, we don’t really have to take care of the non-standard model of 
arithmetic, because it can be proved that even addition and multiplication are 
not (Church-Turing) computable.

The church-Turing thesis makes computability absolute in the sense that what 
can be proved to be computable or non computable will be true in *all* models 
of any arithmetical theories. If a machine (or number, to emphasise their 
finiteness) is universal, it is universal in all models or interpretation of 
the ontological theories.

But this remark would become obsolete in case we add an infinity axioms in the 
ontology, like in set theories. To take no risk, I “forbid” even the induction 
axioms at the ontological level. So, induction, infinities, second-order logic, 
real numbers, analysis and physics will belong to the phenomenology of numbers, 
and this makes mechanism into a finitism. 0, 1, 2, 3 …. exist, but N or ω do 
not, except as number/machine’s mind’s tools.

Bruno




> 
> LC
> 
>  
> 
>  Forwarded Message  
> 
> On Tue, May 1, 2018 at 1:13 PM, James  wrote: 
> > On Tue, May 1, 2018 at 7:19 AM, Cris  wrote: 
> >> 
> >> ... For any set of axioms, there is a Turing machine which 1) never halts 
> >> and 2) that set of axioms cannot prove that it never halts. ... 
> > 
> >> But don’t you agree that the Halting Problem has a definite truth value? 
> >> In other words, that a given Turing machine (with a given input) either 
> >> runs forever or doesn’t, regardless of our ability to prove it? ... 
> > 
> > To answer the question posed, shouldn't we ask if, given any 
> > *particular* TM, there exists *some* consistent system/set of axioms 
> > that can prove whether it halts or not?  I was under the impression 
> > that the answer here was "yes", regardless of any individual 
> > consistent system being unable to tackle the general problem. 
> 
> The problem is when you have nonstandard natural numbers.  It's 
> perfectly valid, for instance, to have a Turing machine halt after ω + 
> 3 steps.  You can say, "oh, but we use the unique standard model 
> defined by the second-order theory", but then the second order theory 
> has to live in some universe, and there are universes in which what's 
> uncomputable in your universe can be computable in mine: 
> 
> http://jdh.hamkins.org/every-function-can-be-computable/ 
>  
> https://johncarlosbaez.wordpress.com/2016/04/02/computing-the-uncomputable/ 
>  
> 
> So as soon as you move away from "only physically implementable math 
> is real", then you have do deal with all these other models. 
> -- 
> Mike 
> ___ 
> math-fun mailing list 
> math...@mailman.xmission.com  
> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun 
>  
> 
> 
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Re: Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Lawrence Crowell]

On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote:
>
> An interesting proof by Hamkins and a lot of discussion of its 
> significance on John Baez's blog.  It agrees with my intuition that the 
> mathematical idea of "finite" is not so obvious. 
>
> Brent 
>
>
This gets into the rarefied atmosphere of degrees of unprovability. I have 
a book by Lerman on the subject, which I can read maybe 25 pages into 
before I am largely confused and lost. I would really need to be far better 
grounded in this. The idea is that one may ask if things are diagonal up 
to ω ordinarlity, which is standard Gödel/Turing machine stuff. Then we 
might however have Halting or provability out to ω + n, or 2ω to nω and 
then how about ω^n and then n^ω and now make is bigger with ω^ω and so 
forth. Then this in principle may continue onwards beyond the alephs into 
least accessible cardinals and so forth. One has this vast and maybe 
endless tower of greater transfinite models. 

Finite systems that are well defined are cyclic groups and related 
structures. A mathematical system that has some artificial bound on it is 
not going to satisfy any universal requirements. The most one can have is 
finite but unbounded. So long as one does not have some series or 
progression that grows endlessly this can work.

LC
 

>
>  Forwarded Message  
>
> On Tue, May 1, 2018 at 1:13 PM, James  wrote: 
> > On Tue, May 1, 2018 at 7:19 AM, Cris  wrote: 
> >> 
> >> ... For any set of axioms, there is a Turing machine which 1) never 
> halts and 2) that set of axioms cannot prove that it never halts. ... 
> > 
> >> But don’t you agree that the Halting Problem has a definite truth 
> value? In other words, that a given Turing machine (with a given input) 
> either runs forever or doesn’t, regardless of our ability to prove it? ... 
> > 
> > To answer the question posed, shouldn't we ask if, given any 
> > *particular* TM, there exists *some* consistent system/set of axioms 
> > that can prove whether it halts or not?  I was under the impression 
> > that the answer here was "yes", regardless of any individual 
> > consistent system being unable to tackle the general problem. 
>
> The problem is when you have nonstandard natural numbers.  It's 
> perfectly valid, for instance, to have a Turing machine halt after ω + 
> 3 steps.  You can say, "oh, but we use the unique standard model 
> defined by the second-order theory", but then the second order theory 
> has to live in some universe, and there are universes in which what's 
> uncomputable in your universe can be computable in mine: 
>
> http://jdh.hamkins.org/every-function-can-be-computable/ 
> https://johncarlosbaez.wordpress.com/2016/04/02/computing-the-uncomputable/ 
>
> So as soon as you move away from "only physically implementable math 
> is real", then you have do deal with all these other models. 
> -- 
> Mike 
> ___ 
> math-fun mailing list 
> math...@mailman.xmission.com  
> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun 
>
>

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Fwd: Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

[Brent Meeker]

An interesting proof by Hamkins and a lot of discussion of its 
significance on John Baez's blog.  It agrees with my intuition that the 
mathematical idea of "finite" is not so obvious.


Brent


 Forwarded Message 

On Tue, May 1, 2018 at 1:13 PM, James  wrote:

On Tue, May 1, 2018 at 7:19 AM, Cris  wrote:


... For any set of axioms, there is a Turing machine which 1) never halts and 
2) that set of axioms cannot prove that it never halts. ...



But don’t you agree that the Halting Problem has a definite truth value? In 
other words, that a given Turing machine (with a given input) either runs 
forever or doesn’t, regardless of our ability to prove it? ...


To answer the question posed, shouldn't we ask if, given any
*particular* TM, there exists *some* consistent system/set of axioms
that can prove whether it halts or not?  I was under the impression
that the answer here was "yes", regardless of any individual
consistent system being unable to tackle the general problem.


The problem is when you have nonstandard natural numbers.  It's
perfectly valid, for instance, to have a Turing machine halt after ω +
3 steps.  You can say, "oh, but we use the unique standard model
defined by the second-order theory", but then the second order theory
has to live in some universe, and there are universes in which what's
uncomputable in your universe can be computable in mine:

http://jdh.hamkins.org/every-function-can-be-computable/
https://johncarlosbaez.wordpress.com/2016/04/02/computing-the-uncomputable/

So as soon as you move away from "only physically implementable math
is real", then you have do deal with all these other models.
--
Mike
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