Re: 1P/3P CONFUSION again and again

[Bruno Marchal]

On 28 Sep 2015, at 18:21, John Clark wrote:


On Sun, Sep 27, 2015  Bruno Marchal  wrote:
​>​>>​ ​If you prove the existence of something in something  
else, you have that something,


​​>> ​Euclid proved 2500 years ago that there are infinitely  
many primes, so if what you say above is true you must have the  
423rd prime greater than 10^100^100.


​> ​Now you equate existence with constructive existence,

​What the hell?  You're the one that is equating those two things  
not me! I don't want you to answer the question "does the 423rd  
prime number greater than 10^100^100 exist?", I want you to tell me  
the answer to a completely different question, "what is the 423rd  
prime number greater than 10^100^100?".


So you are asking me a constructive existence of such a number, and  
even a consturctive in a not well defined physical sense.


But Computationalism, is at the start classical, not intutionist nor  
constructive. Some brnch of computer science are necessarily non  
constructive, and eventually we rediscover this in the epistemology of  
the machine.


The question was: does computation (in the original standard sense of  
Turing's or Church's definition of computability, using the  
intensional Church thesis (which says that not only all universal  
machines compute the same class of functions, but all universal  
machines can emulate all universal machine, that is, all universal  
machine can imitate exactly all digital processes starting from finite  
conditions (relatively or not to some oracle).


And the answer I gave was: I can prove (in RA, or let a theorem prover  
of RA prove ...) the existence of the  terminating computations, and  
of all the segments of the infinite computations.


This entails in particular that the computations are all emulated, or  
realized, in or by the usual "standard model" or arithmetic (N, 0, +,  
x) taught in high school.


So the relative computations, the sigma_1 arithmetical relations,  
exist in the usual 3p sense of asserting, for example, that the prime  
numbers, including those greater 100^(100^100).


Such existence should not be confuse with a stronger feasible  
existence (in which case we ask for an algorithm generating the  
existing object + the constraint to present it in some reasonable  
delay).
Nor, should that existence be confused with some notion of physical  
existence, especially in a context where we want explain the physical  
by something non-physical.




And to figure out what that number is and answer my question you are  
going to have perform a calculation. And to do that you are going to  
have to use matter that obeys the laws of physics. And there may not  
be enough matter in existence to do it. And if there isn't then the  
question "what is the 423rd prime number greater than 10^100^100?"  
is unanswerable.



I use computation is the mathematical sense of Alonzo Church, Emil  
Post, Stephen Kleene, Alan Turing, Matiyazevic, etc.






​>​>> ​ ​indeed a universal machine cannot distinguihs a  
physical computation from a non physical one,


​​>> ​I know, and that lack of ability is yet another example  
of something a non-physical machine can't do that a physical  
machine can.​ A physical machine, such as myself, has no  
difficulty whatsoever in making that distinction.


​> ​Then you have magical abilities not shared by any Turing  
machine, physical or non physical.


​Bullshit.​

 ​> ​Please don't confuse the computation with anything we use to  
represent and communicate about that computation.


​Gibberish. ​

​>> ​so just use ​immaterial computation to find ​the 423rd  
prime greater than 10^100^100​ and tell me what it is and you have  
won this argument. How hard can that be?​


​> ​Just define what *you* mean by "physical computation"

​It means computation using physics.


Computation in which sense? If it is the Turing sense, then that exist  
in arithmetic.


If by using physics you mean that there exist something which select  
one computation to make it more real, then that is using a god-of-the- 
gap to prevent the searching of a solution of the mind-body problem in  
the computationalist frame.






  Bruno, couldn't you have figured that out by yourself? ​Did you  
really need my help?



I figure that out since long, I mean ... that you restrict the  
standard sense of computation to their possible realization in the  
physical reality.


The problem is that you give the impression that you believe that  
computation does not exist in, or be emulated by, arithmetic. That has  
nothing to do with the question of the feasibility or of the physical  
realisability, especially in the context of the computational or  
digital thesis in philosophy of mind-matter.


Then I exploit the fact that sigma_1 complete provability is  
equivalent with universal computability.
And I interview machines having enough introspection power (in the  
standard Gödel sense) to know (in a technical 

Re: 1P/3P CONFUSION again and again

[John Clark]

On Tue, Sep 29, 2015  Bruno Marchal  wrote:

> ​>
>> ​>> ​
>> ​
>> Now you equate existence with constructive existence,
>>
>
> ​>> ​
> ​What the hell?  You're the one that is equating those two things not me!
> I don't want you to answer the question "does the 423rd prime number
> greater than 10^100^100 exist?", I want you to tell me the answer to
> ​a
> completely different question, "what is the 423rd prime number greater
> than 10^100^100?".
>
> ​> ​
> So you are asking me a constructive existence of such a number,
>

​The question I am asking is precise, easy to understand, and impossible
for you to answer;  what is the 423rd prime number greater than 10^100^100?
​
 I know why I can't answer that question but you have no explanation why
you can't answer that question.



> ​> ​
> and even a consturctive in a not well defined physical sense.
>

​Oh for Christ's sake! I don't give a damn if it's in the Bozo the Clown
sense, just tell me what the 423rd prime number greater than 10^100^100 is
or tell me why you can't figure it out. I can't figure it out because there
are not enough atoms in my brain that can be put into unique states that
can individually correspond with 10^100^100 numbers; but your mind doesn't
need matter that obeys the laws of physics to operate so I want to know why
you can't figure it out.


> ​> ​
> But Computationalism, is
> ​ [blah blah blah blah]
>

​Quit staling c
ut the
​bafflegab
and just tell me
​ ​
what the 423rd prime number greater than 10^100^100 is or tell me why you
can't figure it out. You say computation doesn't need physics just numbers,
well you have access to numbers, so why can't you tell me what the
​ ​
the 423rd prime number greater than 10^100^100 is
​ ​
?
​ What are you lacking?​


​> ​
> The question was: does computation (in the original standard sense of
> Turing's or Church's definition of computability, using the intensional
> Church thesis (which says that not only all universal machines compute the
> same class of functions, but all universal machines can emulate all
> universal machine, that is, all universal machine can imitate exactly all
> digital processes starting from finite conditions (relatively or not to
> some oracle).
>

​*NO*, that wasn't the question at all! In fact the above doesn't even look
like a question​. The question was "what the
​ ​
the 423rd prime number greater than 10^100^100 ?".

​> ​
> So the relative computations, the sigma_1 arithmetical relations, exist in
> the usual 3p sense of asserting, for example, that the prime numbers,
> including those greater 100^(100^100).
>

​Well good for "​
the relative computations, the sigma_1 arithmetical relations
​", I'm very happy for them. And now let's get back to the topic at hand,
what
​is ​
the
​ ​
the 423rd prime number greater than 10^100^100 ?


> I use computation is the mathematical sense of Alonzo Church, Emil Post,
> Stephen Kleene, Alan Turing, Matiyazevic, etc.
>

​That's nice good for you, then use use computation is the mathematical
sense of Alonzo Church, Emil Post, Stephen Kleene, Alan Turing and
Matiyazevic and tell me what what the 423rd prime number greater than
10^100^100 is.

> ​>
>>> ​>> ​
>>> Just define what *you* mean by "physical computation"
>>
>>
> ​
>> ​>> ​
>> It means computation using physics.
>
> ​> ​
> Computation in which sense?
>

​Sense in which sense? And I can't answer your question until you define
"in". And then define "which".

And that my friends is exactly why examples are so superior to definitions,
it avoids the absurd "define that word" endless loop that people always use
when they're losing a debate.


​> ​
> The problem is that you give the impression that you believe that
> computation does not exist in, or be emulated by, arithmetic.
>

​I'm sorry if I only gave a vague impression of that so let me say as
flatly and directly as I can that as of today there is ZERO evidence that
arithmetic can calculate anything without the help of physics; that
situation could change tomorrow but that's how things are right now. ​


> ​> ​
> I exploit the fact that sigma_1 complete provability is equivalent with
> universal computability.


​Mathematical objects may or may not exist independently of physics, but
mathematics proofs certainly do not; proofs are just a way humans have of
discovering (or maybe inventing) those mathematical objects.  ​


​> ​
> Saying that there is a physical universe doing that is no better than
> saying God made it.
>

Saying that there is a
​mathematical universe ​is no better than saying there is a
physical universe
​. And the physical universe at the time of the Big Bang was far simpler
that the universe is today, and was infinitely simpler than a omnipotent
omniscient
God. Bruno you're a logician so you tell me, if two logical systems produce
the exact same conclusions but one starts out with fewer and simpler axioms
than the other which one is superior?  I think
William of Ockham
​ made a pretty