Re: Answer to David 3

[David Nyman]

On 30 May 2017 at 12:10, Bruno Marchal  wrote:

>
> On 29 May 2017, at 20:30, David Nyman wrote:
>
> On 29 May 2017 at 17:40, Bruno Marchal  wrote:
>
>>
>> On 28 May 2017, at 19:32, David Nyman wrote:
>>
>> On 28 May 2017 at 18:02, Bruno Marchal  wrote:
>>
>>>
>>> On 28 May 2017, at 16:53, David Nyman wrote:
>>>
>>>
>>> On 28 May 2017 at 14:38, Bruno Marchal  wrote:
>>>
>>> ​Yes, that's what I meant.
>>> ​
>>>
 It is there that many confuse:

  the number s(0),
 the Gödel number of s(0),
 the Gödel number of the Gödel number of s(0), which plays very
 different role, all important, when we translate UDA in arithmetic.

 Of course, this needs a good familiarity with the understanding of the
 difference between language, theories, and truth (models).

>>>
>>> ​Indeed :(
>>> ​
>>>
>>> ​Well no, I still don't quite understand. I didn't mean that we couldn't
>>> accept a physical universe as 'true' in the sense of a brute fact. What I
>>> meant was in that case how would a notion ​of truth be related to the
>>> perception of that world? Would it merely be an identity relation between
>>> it being true that such a world was primitive and consequently true that
>>> this also entailed a perception of it on behalf of a subject? If so, I
>>> wouldn't find that either coherent or intelligible.
>>>
>>>
>>> It would make the identity-thesis consistent. I agree it is not really
>>> intelligible, but the actual infinities would could consistently be used to
>>> justify the magic. That crazy (I think we share the intuition here) move is
>>> no more available when we assume mechanism, as we inherit from arithmetic
>>> infinitely many copies, and we have to take them into account.
>>>
>>
>> ​Yes, and then in that case Brent really would be correct that an
>> 'engineering solution' would be about as close as we could get.
>>
>>
>> Yes. It is akin to the usual use of mechanism by atheists, to dismiss all
>> "religious" notions, from God to ... consciousness, and which lead to a
>> sort of eliminativism.
>>
>
> ​Yes, it even seems to lead to a kind of reactive or defensive dogmatism.
> I appreciate very much Feynman's suggestion that science is a method of
> checking that we aren't fooling ourselves. But of course we must remember
> that this method should also be applied to itself.
>
>
>> Somehow, mysteriously the mind and the brain becomes identifiable, by
>> being both actual non duplicable infinite entities. Typically, you can no
>> more say yes to the doctors, or if someone say yes, they can invoke that
>> infinities, as there are mysterious anyway. Everything becomes magic here:
>> the physical universe, consciousness, etc. It looks like a fairy tale
>> identifying all the mysteries, but logically, it can make sense by pushing
>> the substitution level in the infinitely low, if that can make sense.
>>
>
> ​Yes, it can make sense. In another, perhaps related sense the
> 'substitution' level is almost infinitely low, if indeed the 'tuning' were
> fine enough such that​ only a unique physics can be associated with our own
> existence. But nevertheless the assumption of CTM implies that the
> substitution level of our minds isn't necessarily that low, but could be
> approximated classically by a digital prosthesis. The doctor will have a
> lot to answer for.
>
>
> That moves seems to me premature to say the least, but we have to find a
>> difference between quantum logic, and the quantum logic associated to Z1*
>> to get a clue on the necessity of such moves.
>>
>
> ​I won't hold my breath.​
>
>
>
>> Usually, the scientists tries to discard the commitment into actual,
>> physical and psychological entities.
>>
>
> ​Understandably perhaps.​
>
>
>
> I would say that this is the only right attitude. The whole point of doing
> "scientific metaphysics or theology" is to be agnostic all the times, and
> not to assume any answers, at any time. Only hypothesis and deductions, and
> interpretation means, if possible with experimental verification means.
>
>
>
>
>
>
>
>> I'm not sure I fully understand you here. My intention recently has been
>>> to clarify
>>> ​in a certain way ​
>>> an explanatory distinction between ontology and epistemology in terms of
>>> theory in general. In this way of parsing the thing any 'observable', even
>>> if viewed from the imaginary Wittgenstein's ladder perspective of 3p, is
>>> part of the epistemological component of the theory. To simplify a bit,
>>> anything that requires interpretation and hence explanation is an inference
>>> from, not a part of, the assumptive ontology, which is by definition *not*
>>> itself in need of
>>> ​such ​
>>> explanation. Consequently it was that ontology that I referred to as 0p.
>>>
>>>
>>> OK. But when making the mechanist assumption explicit, that 0p becomes
>>> 3p, or that 3p becomes 0p, (unlike the apparent "3p physics", which becomes
>>> 1p 

Re: Answer to David 3

[Bruno Marchal]

On 29 May 2017, at 20:30, David Nyman wrote:


On 29 May 2017 at 17:40, Bruno Marchal  wrote:

On 28 May 2017, at 19:32, David Nyman wrote:


On 28 May 2017 at 18:02, Bruno Marchal  wrote:

On 28 May 2017, at 16:53, David Nyman wrote:



On 28 May 2017 at 14:38, Bruno Marchal  wrote:

​Yes, that's what I meant.
​
It is there that many confuse:

 the number s(0),
the Gödel number of s(0),
the Gödel number of the Gödel number of s(0), which plays very  
different role, all important, when we translate UDA in arithmetic.


Of course, this needs a good familiarity with the understanding of  
the difference between language, theories, and truth (models).


​Indeed :(
​

​Well no, I still don't quite understand. I didn't mean that we  
couldn't accept a physical universe as 'true' in the sense of a  
brute fact. What I meant was in that case how would a notion ​of  
truth be related to the perception of that world? Would it merely  
be an identity relation between it being true that such a world  
was primitive and consequently true that this also entailed a  
perception of it on behalf of a subject? If so, I wouldn't find  
that either coherent or intelligible.


It would make the identity-thesis consistent. I agree it is not  
really intelligible, but the actual infinities would could  
consistently be used to justify the magic. That crazy (I think we  
share the intuition here) move is no more available when we assume  
mechanism, as we inherit from arithmetic infinitely many copies,  
and we have to take them into account.


​Yes, and then in that case Brent really would be correct that an  
'engineering solution' would be about as close as we could get.


Yes. It is akin to the usual use of mechanism by atheists, to  
dismiss all "religious" notions, from God to ... consciousness, and  
which lead to a sort of eliminativism.


​Yes, it even seems to lead to a kind of reactive or defensive  
dogmatism. I appreciate very much Feynman's suggestion that science  
is a method of checking that we aren't fooling ourselves. But of  
course we must remember that this method should also be applied to  
itself.


Somehow, mysteriously the mind and the brain becomes identifiable,  
by being both actual non duplicable infinite entities. Typically,  
you can no more say yes to the doctors, or if someone say yes, they  
can invoke that infinities, as there are mysterious anyway.  
Everything becomes magic here: the physical universe, consciousness,  
etc. It looks like a fairy tale identifying all the mysteries, but  
logically, it can make sense by pushing the substitution level in  
the infinitely low, if that can make sense.


​Yes, it can make sense. In another, perhaps related sense the  
'substitution' level is almost infinitely low, if indeed the  
'tuning' were fine enough such that​ only a unique physics can be  
associated with our own existence. But nevertheless the assumption  
of CTM implies that the substitution level of our minds isn't  
necessarily that low, but could be approximated classically by a  
digital prosthesis. The doctor will have a lot to answer for.



That moves seems to me premature to say the least, but we have to  
find a difference between quantum logic, and the quantum logic  
associated to Z1* to get a clue on the necessity of such moves.


​I won't hold my breath.​


Usually, the scientists tries to discard the commitment into actual,  
physical and psychological entities.


​Understandably perhaps.​



I would say that this is the only right attitude. The whole point of  
doing "scientific metaphysics or theology" is to be agnostic all the  
times, and not to assume any answers, at any time. Only hypothesis and  
deductions, and interpretation means, if possible with experimental  
verification means.









I'm not sure I fully understand you here. My intention recently  
has been to clarify ​in a certain way ​an explanatory  
distinction between ontology and epistemology in terms of theory  
in general. In this way of parsing the thing any 'observable',  
even if viewed from the imaginary Wittgenstein's ladder  
perspective of 3p, is part of the epistemological component of the  
theory. To simplify a bit, anything that requires interpretation  
and hence explanation is an inference from, not a part of, the  
assumptive ontology, which is by definition *not* itself in need  
of ​such ​explanation. Consequently it was that ontology that I  
referred to as 0p.


OK. But when making the mechanist assumption explicit, that 0p  
becomes 3p, or that 3p becomes 0p, (unlike the apparent "3p  
physics", which becomes 1p plural).


​I'm OK with this. I think that people sometimes forget the  
crucial distinction between 3p and 1p-plural, by referring to  
epistemological constructs as 3p​. That's why I thought of the  
Wittgenstein ladder as a reminder of the implicit adoption of a  
privileged interpretation in this case. It 

Re: Answer to David 3

[David Nyman]

On 29 May 2017 at 17:40, Bruno Marchal  wrote:

>
> On 28 May 2017, at 19:32, David Nyman wrote:
>
> On 28 May 2017 at 18:02, Bruno Marchal  wrote:
>
>>
>> On 28 May 2017, at 16:53, David Nyman wrote:
>>
>>
>> On 28 May 2017 at 14:38, Bruno Marchal  wrote:
>>
>> ​Yes, that's what I meant.
>> ​
>>
>>> It is there that many confuse:
>>>
>>>  the number s(0),
>>> the Gödel number of s(0),
>>> the Gödel number of the Gödel number of s(0), which plays very different
>>> role, all important, when we translate UDA in arithmetic.
>>>
>>> Of course, this needs a good familiarity with the understanding of the
>>> difference between language, theories, and truth (models).
>>>
>>
>> ​Indeed :(
>> ​
>>
>> ​Well no, I still don't quite understand. I didn't mean that we couldn't
>> accept a physical universe as 'true' in the sense of a brute fact. What I
>> meant was in that case how would a notion ​of truth be related to the
>> perception of that world? Would it merely be an identity relation between
>> it being true that such a world was primitive and consequently true that
>> this also entailed a perception of it on behalf of a subject? If so, I
>> wouldn't find that either coherent or intelligible.
>>
>>
>> It would make the identity-thesis consistent. I agree it is not really
>> intelligible, but the actual infinities would could consistently be used to
>> justify the magic. That crazy (I think we share the intuition here) move is
>> no more available when we assume mechanism, as we inherit from arithmetic
>> infinitely many copies, and we have to take them into account.
>>
>
> ​Yes, and then in that case Brent really would be correct that an
> 'engineering solution' would be about as close as we could get.
>
>
> Yes. It is akin to the usual use of mechanism by atheists, to dismiss all
> "religious" notions, from God to ... consciousness, and which lead to a
> sort of eliminativism.
>

​Yes, it even seems to lead to a kind of reactive or defensive dogmatism. I
appreciate very much Feynman's suggestion that science is a method of
checking that we aren't fooling ourselves. But of course we must remember
that this method should also be applied to itself.


> Somehow, mysteriously the mind and the brain becomes identifiable, by
> being both actual non duplicable infinite entities. Typically, you can no
> more say yes to the doctors, or if someone say yes, they can invoke that
> infinities, as there are mysterious anyway. Everything becomes magic here:
> the physical universe, consciousness, etc. It looks like a fairy tale
> identifying all the mysteries, but logically, it can make sense by pushing
> the substitution level in the infinitely low, if that can make sense.
>

​Yes, it can make sense. In another, perhaps related sense the
'substitution' level is almost infinitely low, if indeed the 'tuning' were
fine enough such that​ only a unique physics can be associated with our own
existence. But nevertheless the assumption of CTM implies that the
substitution level of our minds isn't necessarily that low, but could be
approximated classically by a digital prosthesis. The doctor will have a
lot to answer for.


That moves seems to me premature to say the least, but we have to find a
> difference between quantum logic, and the quantum logic associated to Z1*
> to get a clue on the necessity of such moves.
>

​I won't hold my breath.​



> Usually, the scientists tries to discard the commitment into actual,
> physical and psychological entities.
>

​Understandably perhaps.​


> I'm not sure I fully understand you here. My intention recently has been
>> to clarify
>> ​in a certain way ​
>> an explanatory distinction between ontology and epistemology in terms of
>> theory in general. In this way of parsing the thing any 'observable', even
>> if viewed from the imaginary Wittgenstein's ladder perspective of 3p, is
>> part of the epistemological component of the theory. To simplify a bit,
>> anything that requires interpretation and hence explanation is an inference
>> from, not a part of, the assumptive ontology, which is by definition *not*
>> itself in need of
>> ​such ​
>> explanation. Consequently it was that ontology that I referred to as 0p.
>>
>>
>> OK. But when making the mechanist assumption explicit, that 0p becomes
>> 3p, or that 3p becomes 0p, (unlike the apparent "3p physics", which becomes
>> 1p plural).
>>
>
> ​I'm OK with this. I think that people sometimes forget the crucial
> distinction between 3p and 1p-plural, by referring to epistemological
> constructs as 3p​. That's why I thought of the Wittgenstein ladder as a
> reminder of the implicit adoption of a privileged interpretation in this
> case. It seems to be quite difficult sometimes for people to intuit that
> they are doing this.
>
>
> I continue to thing that we have a "level" problem here.
>

I don't think so. Probably I wasn't clear enough. ​By 'epistemological
construct' I meant a 1p-plural 

Re: Answer to David 3

[Bruno Marchal]

On 28 May 2017, at 19:32, David Nyman wrote:


On 28 May 2017 at 18:02, Bruno Marchal  wrote:

On 28 May 2017, at 16:53, David Nyman wrote:



On 28 May 2017 at 14:38, Bruno Marchal  wrote:

​Yes, that's what I meant.
​
It is there that many confuse:

 the number s(0),
the Gödel number of s(0),
the Gödel number of the Gödel number of s(0), which plays very  
different role, all important, when we translate UDA in arithmetic.


Of course, this needs a good familiarity with the understanding of  
the difference between language, theories, and truth (models).


​Indeed :(
​

​Well no, I still don't quite understand. I didn't mean that we  
couldn't accept a physical universe as 'true' in the sense of a  
brute fact. What I meant was in that case how would a notion ​of  
truth be related to the perception of that world? Would it merely  
be an identity relation between it being true that such a world was  
primitive and consequently true that this also entailed a  
perception of it on behalf of a subject? If so, I wouldn't find  
that either coherent or intelligible.


It would make the identity-thesis consistent. I agree it is not  
really intelligible, but the actual infinities would could  
consistently be used to justify the magic. That crazy (I think we  
share the intuition here) move is no more available when we assume  
mechanism, as we inherit from arithmetic infinitely many copies, and  
we have to take them into account.


​Yes, and then in that case Brent really would be correct that an  
'engineering solution' would be about as close as we could get.



Yes. It is akin to the usual use of mechanism by atheists, to dismiss  
all "religious" notions, from God to ... consciousness, and which lead  
to a sort of eliminativism. Somehow, mysteriously the mind and the  
brain becomes identifiable, by being both actual non duplicable  
infinite entities. Typically, you can no more say yes to the doctors,  
or if someone say yes, they can invoke that infinities, as there are  
mysterious anyway. Everything becomes magic here: the physical  
universe, consciousness, etc. It looks like a fairy tale identifying  
all the mysteries, but logically, it can make sense by pushing the  
substitution level in the infinitely low, if that can make sense. That  
moves seems to me premature to say the least, but we have to find a  
difference between quantum logic, and the quantum logic associated to  
Z1* to get a clue on the necessity of such moves. Usually, the  
scientists tries to discard the commitment into actual, physical and  
psychological entities.






​







I'm not sure I fully understand you here. My intention recently has  
been to clarify ​in a certain way ​an explanatory distinction  
between ontology and epistemology in terms of theory in general. In  
this way of parsing the thing any 'observable', even if viewed from  
the imaginary Wittgenstein's ladder perspective of 3p, is part of  
the epistemological component of the theory. To simplify a bit,  
anything that requires interpretation and hence explanation is an  
inference from, not a part of, the assumptive ontology, which is by  
definition *not* itself in need of ​such ​explanation.  
Consequently it was that ontology that I referred to as 0p.


OK. But when making the mechanist assumption explicit, that 0p  
becomes 3p, or that 3p becomes 0p, (unlike the apparent "3p  
physics", which becomes 1p plural).


​I'm OK with this. I think that people sometimes forget the crucial  
distinction between 3p and 1p-plural, by referring to  
epistemological constructs as 3p​. That's why I thought of the  
Wittgenstein ladder as a reminder of the implicit adoption of a  
privileged interpretation in this case. It seems to be quite  
difficult sometimes for people to intuit that they are doing this.


I continue to thing that we have a "level" problem here. Once we bet  
on mechanism, we accept the idea that "2+2=4" is pure 3p, and we  
asbrtact from the fact that we need the 1p to assert this, but that  
need is no more in the theoretical assumption, like blackboard's and  
chalk existences are not part of General relativity (despite we need  
them to discuss GR in between humans).


Any public theory is 3p, almost by definition. With mechanism, we can  
use, as ultimate 3p truth, all the arithmetical truth, or even just  
the sigma one (keeping the whole arithmetical truth at the meta- 
level). The 1p is retrieved by linking strongly the indexical 3p-self  
(the believer) with truth (which we cannot define, but can intuit,  
especially about the numbers' arithmetical relations). That gives the  
modality [1]p = (Bp & p). Consciousness, which is the essence of the  
1p, is explained in a first approximation by the facts that:


---  [1]p obeys a logic of S4 (which answers the desiderata of the  
analytical philosophers), it is the knowing aspect of consciousness.
--- [1]p is not definable in any third person 

Re: Answer to David 3

[David Nyman]

On 28 May 2017 at 18:02, Bruno Marchal  wrote:

>
> On 28 May 2017, at 16:53, David Nyman wrote:
>
>
> On 28 May 2017 at 14:38, Bruno Marchal  wrote:
>
>>
>> On 26 May 2017, at 21:51, David Nyman wrote:
>>
>> On 26 May 2017 at 18:32, Bruno Marchal  wrote:
>>
>>>
>>> On 26 May 2017, at 14:04, David Nyman wrote:
>>>
>>>



 where that elusive internal space (which we seek in vain in
 extrinsically-completed models such as physics tout court)


 Here we might differ, and you might be more mechanist than me (!). We
 could have used a notion of physical truth, instead of arithmetical truth.
 What the UDA shows is that this requires to abandon mechanism. But if we
 get evidence that consciousness reduces the wave, or that QM is false, then
 we might reasonably consider that a physical reality exists ontologically,
 and well, in that case we must find a non computationalist theory of mind,
 which of course, in that case, will rely on the physical notion of truth.
 It is an open problem if we can use or not the same hypostases with
 non-arithmetical modal boxes. G and G* remains correct for a vast class of
 non mechanical entities.

>>>
>>> ​Well, I think, with your help, that I've reached an elementary
>>> understanding (or at least a better intuition) of what you mean by
>>> arithmetical truth and its possible application in the resolution of the
>>> mind-body problem.​
>>>
>>>
>>> Arithmetical truth is easy, although its use is more delicate. It is
>>> easy, and it is taught in primary school (here = 6 to 12 years old).
>>>
>>> The complexity is only in metamathematics (mathematical logic). It comes
>>> from the fact that we cannot define a predicate of truth, V, such that a
>>> machine could prove
>>>
>>>p  <->  V("p")  (which is the least we can ask for a truth predicate).
>>>
>>> If that existed, by Gödel diagonal lemma, we could find a proposition k
>>> such that the machine will prove k <-> ~V(k), and so the machine would
>>> prove both k <-> V(k), and k <-> ~V(k), and eventually conclude k <-> ~k,
>>> and be inconsistent. That is of course the Epimenides paradox.
>>>
>>
>> ​Yes, so on pain of inconsistency, not everything the machine can say can
>> definitely be provably true (or false).
>>
>>
>> In a way ascertainable by the machine, or the entity under consideration.
>> OK.
>>
>> If you and me believe that PA is arithmetically sound (like all
>> mathematicians believe), and if PA proves X, then you and me can say that
>> it is provably true, but PA cannot. PA can say X, but cannot say true('X').
>> PA can express "I know X" in the sense of proving 'Beweisbar('X') & X, but
>> not in the sense "beweisbar('X') & true('X').
>>
>>
>>
>>
>>
>> ​
>>
>>>
>>> (The predicate ~V would also exist, and the diagonal lemma says that for
>>> all predicate P the machine can find a solution to the formula x <-> P(x),
>>> that is, can find a sentence k such that the machine will prove k <-> P(k).
>>>
>>> But we can define truth predicate on restricted set of sentences.
>>>
>>
>> ​Necessarily so, it would seem.
>>
>>
>> Yes, but it is not completely obvious.
>>
>>
>>
>>
>> ​
>>
>>> And we can use richer theories. In set theory, it is easy to define the
>>> arithmetical truth. Of course, in the background we use the notion of
>>> set-theoretical truth, which, if we would define it would requires strong
>>> infinity axiom (ZF + kappa exists) for example.
>>>
>>> Arithmetical truth is the simplest notion of all definition of truth.
>>> "AxP(x)" is true simply means that P(n) is true whatever n is. It is the
>>> infinite or:
>>>
>>> P(0) v P(1) v P(2), v P(3), etc.
>>>
>>> The amazing thing, alreadu apparent in Post 1922 and Gödel 1931, but
>>> quite clarified since, is that
>>>
>>> 1) we can describe the complete functioning of any universal (and non
>>> universal) system in the arithmetical language, but, and that is the key,
>>> in virtue of the true-ness of the relation between the numbers, the
>>> computations are not just describe in arithmetic, but they are emulated.
>>>
>>
>> ​In effect, they are actioned.
>>
>>
>> OK. In the out-of-time manner of the block-mindscape, in virtue of the
>> true realtion existing in the number relation.
>>
>
> ​Yes, that's what I meant.
> ​
>
>> It is there that many confuse:
>>
>>  the number s(0),
>> the Gödel number of s(0),
>> the Gödel number of the Gödel number of s(0), which plays very different
>> role, all important, when we translate UDA in arithmetic.
>>
>> Of course, this needs a good familiarity with the understanding of the
>> difference between language, theories, and truth (models).
>>
>
> ​Indeed :(
> ​
>
>>
>>
>>
>>
>> ​
>>
>>>
>>> I know you and some other have well understood this, but not all here
>>> seems to have grasped that quite important distinction, between truth,
>>> theories and languages. Also, I am sure you forget to apply 

Re: Answer to David 3

[Bruno Marchal]

On 28 May 2017, at 16:53, David Nyman wrote:



On 28 May 2017 at 14:38, Bruno Marchal  wrote:

On 26 May 2017, at 21:51, David Nyman wrote:


On 26 May 2017 at 18:32, Bruno Marchal  wrote:

On 26 May 2017, at 14:04, David Nyman wrote:





where that elusive internal space (which we seek in vain in  
extrinsically-completed models such as physics tout court)


Here we might differ, and you might be more mechanist than me (!).  
We could have used a notion of physical truth, instead of  
arithmetical truth. What the UDA shows is that this requires to  
abandon mechanism. But if we get evidence that consciousness  
reduces the wave, or that QM is false, then we might reasonably  
consider that a physical reality exists ontologically, and well,  
in that case we must find a non computationalist theory of mind,  
which of course, in that case, will rely on the physical notion of  
truth. It is an open problem if we can use or not the same  
hypostases with non-arithmetical modal boxes. G and G* remains  
correct for a vast class of non mechanical entities.


​Well, I think, with your help, that I've reached an elementary  
understanding (or at least a better intuition) of what you mean by  
arithmetical truth and its possible application in the resolution  
of the mind-body problem.​


Arithmetical truth is easy, although its use is more delicate. It  
is easy, and it is taught in primary school (here = 6 to 12 years  
old).


The complexity is only in metamathematics (mathematical logic). It  
comes from the fact that we cannot define a predicate of truth, V,  
such that a machine could prove


   p  <->  V("p")  (which is the least we can ask for a truth  
predicate).


If that existed, by Gödel diagonal lemma, we could find a  
proposition k such that the machine will prove k <-> ~V(k), and so  
the machine would prove both k <-> V(k), and k <-> ~V(k), and  
eventually conclude k <-> ~k, and be inconsistent. That is of  
course the Epimenides paradox.


​Yes, so on pain of inconsistency, not everything the machine can  
say can definitely be provably true (or false).


In a way ascertainable by the machine, or the entity under  
consideration. OK.


If you and me believe that PA is arithmetically sound (like all  
mathematicians believe), and if PA proves X, then you and me can say  
that it is provably true, but PA cannot. PA can say X, but cannot  
say true('X'). PA can express "I know X" in the sense of proving  
'Beweisbar('X') & X, but not in the sense "beweisbar('X') & true('X').







​

(The predicate ~V would also exist, and the diagonal lemma says  
that for all predicate P the machine can find a solution to the  
formula x <-> P(x), that is, can find a sentence k such that the  
machine will prove k <-> P(k).


But we can define truth predicate on restricted set of sentences.

​Necessarily so, it would seem.


Yes, but it is not completely obvious.





​
And we can use richer theories. In set theory, it is easy to define  
the arithmetical truth. Of course, in the background we use the  
notion of set-theoretical truth, which, if we would define it would  
requires strong infinity axiom (ZF + kappa exists) for example.


Arithmetical truth is the simplest notion of all definition of  
truth. "AxP(x)" is true simply means that P(n) is true whatever n  
is. It is the infinite or:


P(0) v P(1) v P(2), v P(3), etc.

The amazing thing, alreadu apparent in Post 1922 and Gödel 1931,  
but quite clarified since, is that


1) we can describe the complete functioning of any universal (and  
non universal) system in the arithmetical language, but, and that  
is the key, in virtue of the true-ness of the relation between the  
numbers, the computations are not just describe in arithmetic, but  
they are emulated.


​In effect, they are actioned.


OK. In the out-of-time manner of the block-mindscape, in virtue of  
the true realtion existing in the number relation.


​Yes, that's what I meant.
​
It is there that many confuse:

 the number s(0),
the Gödel number of s(0),
the Gödel number of the Gödel number of s(0), which plays very  
different role, all important, when we translate UDA in arithmetic.


Of course, this needs a good familiarity with the understanding of  
the difference between language, theories, and truth (models).


​Indeed :(
​





​

I know you and some other have well understood this, but not all  
here seems to have grasped that quite important distinction,  
between truth, theories and languages. Also, I am sure you forget  
to apply this sometimes, see below. I think you don't take  
mechanism seriously enough. (as working hypothesis of course).


​Oh dear. But I've looked below and I'm not sure where I'm going  
wrong :(


May be I have just misunderstood some proposition you made.






​


But what might be a corresponding notion of physical truth? Is it  
just Brent's insistence on a completed instrumental account of  
neurocognition 

Re: Answer to David 3

[David Nyman]

On 28 May 2017 at 14:38, Bruno Marchal  wrote:

>
> On 26 May 2017, at 21:51, David Nyman wrote:
>
> On 26 May 2017 at 18:32, Bruno Marchal  wrote:
>
>>
>> On 26 May 2017, at 14:04, David Nyman wrote:
>>
>>
>>>
>>>
>>>
>>> where that elusive internal space (which we seek in vain in
>>> extrinsically-completed models such as physics tout court)
>>>
>>>
>>> Here we might differ, and you might be more mechanist than me (!). We
>>> could have used a notion of physical truth, instead of arithmetical truth.
>>> What the UDA shows is that this requires to abandon mechanism. But if we
>>> get evidence that consciousness reduces the wave, or that QM is false, then
>>> we might reasonably consider that a physical reality exists ontologically,
>>> and well, in that case we must find a non computationalist theory of mind,
>>> which of course, in that case, will rely on the physical notion of truth.
>>> It is an open problem if we can use or not the same hypostases with
>>> non-arithmetical modal boxes. G and G* remains correct for a vast class of
>>> non mechanical entities.
>>>
>>
>> ​Well, I think, with your help, that I've reached an elementary
>> understanding (or at least a better intuition) of what you mean by
>> arithmetical truth and its possible application in the resolution of the
>> mind-body problem.​
>>
>>
>> Arithmetical truth is easy, although its use is more delicate. It is
>> easy, and it is taught in primary school (here = 6 to 12 years old).
>>
>> The complexity is only in metamathematics (mathematical logic). It comes
>> from the fact that we cannot define a predicate of truth, V, such that a
>> machine could prove
>>
>>p  <->  V("p")  (which is the least we can ask for a truth predicate).
>>
>> If that existed, by Gödel diagonal lemma, we could find a proposition k
>> such that the machine will prove k <-> ~V(k), and so the machine would
>> prove both k <-> V(k), and k <-> ~V(k), and eventually conclude k <-> ~k,
>> and be inconsistent. That is of course the Epimenides paradox.
>>
>
> ​Yes, so on pain of inconsistency, not everything the machine can say can
> definitely be provably true (or false).
>
>
> In a way ascertainable by the machine, or the entity under consideration.
> OK.
>
> If you and me believe that PA is arithmetically sound (like all
> mathematicians believe), and if PA proves X, then you and me can say that
> it is provably true, but PA cannot. PA can say X, but cannot say true('X').
> PA can express "I know X" in the sense of proving 'Beweisbar('X') & X, but
> not in the sense "beweisbar('X') & true('X').
>
>
>
>
>
> ​
>
>>
>> (The predicate ~V would also exist, and the diagonal lemma says that for
>> all predicate P the machine can find a solution to the formula x <-> P(x),
>> that is, can find a sentence k such that the machine will prove k <-> P(k).
>>
>> But we can define truth predicate on restricted set of sentences.
>>
>
> ​Necessarily so, it would seem.
>
>
> Yes, but it is not completely obvious.
>
>
>
>
> ​
>
>> And we can use richer theories. In set theory, it is easy to define the
>> arithmetical truth. Of course, in the background we use the notion of
>> set-theoretical truth, which, if we would define it would requires strong
>> infinity axiom (ZF + kappa exists) for example.
>>
>> Arithmetical truth is the simplest notion of all definition of truth.
>> "AxP(x)" is true simply means that P(n) is true whatever n is. It is the
>> infinite or:
>>
>> P(0) v P(1) v P(2), v P(3), etc.
>>
>> The amazing thing, alreadu apparent in Post 1922 and Gödel 1931, but
>> quite clarified since, is that
>>
>> 1) we can describe the complete functioning of any universal (and non
>> universal) system in the arithmetical language, but, and that is the key,
>> in virtue of the true-ness of the relation between the numbers, the
>> computations are not just describe in arithmetic, but they are emulated.
>>
>
> ​In effect, they are actioned.
>
>
> OK. In the out-of-time manner of the block-mindscape, in virtue of the
> true realtion existing in the number relation.
>

​Yes, that's what I meant.
​

> It is there that many confuse:
>
>  the number s(0),
> the Gödel number of s(0),
> the Gödel number of the Gödel number of s(0), which plays very different
> role, all important, when we translate UDA in arithmetic.
>
> Of course, this needs a good familiarity with the understanding of the
> difference between language, theories, and truth (models).
>

​Indeed :(
​

>
>
>
>
> ​
>
>>
>> I know you and some other have well understood this, but not all here
>> seems to have grasped that quite important distinction, between truth,
>> theories and languages. Also, I am sure you forget to apply this sometimes,
>> see below. I think you don't take mechanism seriously enough. (as working
>> hypothesis of course).
>>
>
> ​Oh dear. But I've looked below and I'm not sure where I'm going wrong :(
>
>
> May be I have just misunderstood some proposition you made.
>
>

Re: Answer to David 3

[Bruno Marchal]

On 26 May 2017, at 21:51, David Nyman wrote:


On 26 May 2017 at 18:32, Bruno Marchal  wrote:

On 26 May 2017, at 14:04, David Nyman wrote:





where that elusive internal space (which we seek in vain in  
extrinsically-completed models such as physics tout court)


Here we might differ, and you might be more mechanist than me (!).  
We could have used a notion of physical truth, instead of  
arithmetical truth. What the UDA shows is that this requires to  
abandon mechanism. But if we get evidence that consciousness  
reduces the wave, or that QM is false, then we might reasonably  
consider that a physical reality exists ontologically, and well, in  
that case we must find a non computationalist theory of mind, which  
of course, in that case, will rely on the physical notion of truth.  
It is an open problem if we can use or not the same hypostases with  
non-arithmetical modal boxes. G and G* remains correct for a vast  
class of non mechanical entities.


​Well, I think, with your help, that I've reached an elementary  
understanding (or at least a better intuition) of what you mean by  
arithmetical truth and its possible application in the resolution  
of the mind-body problem.​


Arithmetical truth is easy, although its use is more delicate. It is  
easy, and it is taught in primary school (here = 6 to 12 years old).


The complexity is only in metamathematics (mathematical logic). It  
comes from the fact that we cannot define a predicate of truth, V,  
such that a machine could prove


   p  <->  V("p")  (which is the least we can ask for a truth  
predicate).


If that existed, by Gödel diagonal lemma, we could find a  
proposition k such that the machine will prove k <-> ~V(k), and so  
the machine would prove both k <-> V(k), and k <-> ~V(k), and  
eventually conclude k <-> ~k, and be inconsistent. That is of course  
the Epimenides paradox.


​Yes, so on pain of inconsistency, not everything the machine can  
say can definitely be provably true (or false).


In a way ascertainable by the machine, or the entity under  
consideration. OK.


If you and me believe that PA is arithmetically sound (like all  
mathematicians believe), and if PA proves X, then you and me can say  
that it is provably true, but PA cannot. PA can say X, but cannot say  
true('X'). PA can express "I know X" in the sense of proving  
'Beweisbar('X') & X, but not in the sense "beweisbar('X') & true('X').







​

(The predicate ~V would also exist, and the diagonal lemma says that  
for all predicate P the machine can find a solution to the formula x  
<-> P(x), that is, can find a sentence k such that the machine will  
prove k <-> P(k).


But we can define truth predicate on restricted set of sentences.

​Necessarily so, it would seem.


Yes, but it is not completely obvious.





​
And we can use richer theories. In set theory, it is easy to define  
the arithmetical truth. Of course, in the background we use the  
notion of set-theoretical truth, which, if we would define it would  
requires strong infinity axiom (ZF + kappa exists) for example.


Arithmetical truth is the simplest notion of all definition of  
truth. "AxP(x)" is true simply means that P(n) is true whatever n  
is. It is the infinite or:


P(0) v P(1) v P(2), v P(3), etc.

The amazing thing, alreadu apparent in Post 1922 and Gödel 1931, but  
quite clarified since, is that


1) we can describe the complete functioning of any universal (and  
non universal) system in the arithmetical language, but, and that is  
the key, in virtue of the true-ness of the relation between the  
numbers, the computations are not just describe in arithmetic, but  
they are emulated.


​In effect, they are actioned.


OK. In the out-of-time manner of the block-mindscape, in virtue of the  
true realtion existing in the number relation. It is there that many  
confuse:


 the number s(0),
the Gödel number of s(0),
the Gödel number of the Gödel number of s(0), which plays very  
different role, all important, when we translate UDA in arithmetic.


Of course, this needs a good familiarity with the understanding of the  
difference between language, theories, and truth (models).






​

I know you and some other have well understood this, but not all  
here seems to have grasped that quite important distinction, between  
truth, theories and languages. Also, I am sure you forget to apply  
this sometimes, see below. I think you don't take mechanism  
seriously enough. (as working hypothesis of course).


​Oh dear. But I've looked below and I'm not sure where I'm going  
wrong :(


May be I have just misunderstood some proposition you made.






​


But what might be a corresponding notion of physical truth? Is it  
just Brent's insistence on a completed instrumental account of  
neurocognition in terms of physical action?


Brent defines truth by physical truth. It is OK, but cannot work  
with mechanism (uda, etc.)


​But then you say below there is 

Re: Answer to David 3

[David Nyman]

On 26 May 2017 at 18:32, Bruno Marchal  wrote:

>
> On 26 May 2017, at 14:04, David Nyman wrote:
>
> On 25 May 2017 at 16:23, Bruno Marchal  wrote:
>
>> On 24 May 2017, at 13:56, David Nyman wrote:
>>
>> Let me know if anything is still unclear.
>>
>> -- Forwarded message --
>> From: David Nyman 
>> Date: 20 May 2017 at 01:30
>> Subject: Re: ​Movie argument
>> To: everything-list 
>>
>>
>> On 19 May 2017 at 21:00, Brent Meeker  wrote:
>>
>>>
>>>
>>> On 5/19/2017 8:45 AM, John Clark wrote:
>>>
>>> On Thu, May 18, 2017 spudboy100 via Everything List <
>>> everything-list@googlegroups.com> wrote:
>>>
>>> ​> ​
  So which is the Boss, John, Mathematics, somehow at the 'base; of the
 universe, or is physics the top dog from the 1st split second?
>>>
>>>
>>> ​
>>>  One of
>>> ​ ​
>>>  René
>>> ​Magritte's​
>>>   most famous paintings is called "Ceci n'est pas une pipe", in English
>>> that means "
>>> ​this is not a pipe".
>>>
>>> http://i3.kym-cdn.com/entries/icons/facebook/000/022/133/the
>>> -treachery-of-images-this-is-not-a-pipe-1948(2).jpg
>>>
>>> ​This is how Magritte explained ​his painting:
>>>
>>> *​"​ The famous pipe. How people reproached me for it! And yet, could
>>> you stuff my pipe? No, it's just a representation, is it not? So if I had
>>> written on my picture 'This is a pipe', I'd have been lying! ​"​*
>>>
>>> ​Mathematics is a representation of something it is not the thing
>>> itself. Physics is the thing itself.
>>>
>>>
>>> Bruno's a Platonist.
>>>
>>
>> I am open that Plato is right, in theology. In mathematics, I am not that
>> "platonist", I just keep calm when I see that we tell the kids that 2+2=4.
>>
>> The point is that "Mathematics is a representation of something it is
>> not the thing itself. Physics is the thing itself" is the Aristotelian
>> theological credo. It makes no sense with Mechanism.
>>
>> (I comment Brent, I think here, and you, David, below)
>>
>> That means that conscious thoughts are what we have immediate access to
>>> and the physical world is an inference from perceptions (which are
>>> thoughts).  We take the physical world to bereal insofar as our
>>> inference has point-of-view-invariance so that others agree with us about
>>> perceptions.   Bruno observes that consciousness is associated with and
>>> dependent on brains, which are part of the inferred physical world.  He
>>> supposes this is because brains realize certain computations and he
>>> hypothesizes that conscious thoughts correspond to certain computations.
>>> But computation is an abstraction; given Church-Turing it exists in the
>>> sense that arithmetic exists.  So among all possible computations, there
>>> must be the computations that constitute our conscious thoughts and the
>>> inferences of a physical world to which those thoughts seem to refer... but
>>> not really.   It's the "not really" where I part company with his
>>> speculations.
>>>
>>
>> I prefer t say that I assume. I don't speculate that Mechanism is true. I
>> assume Mechanism is true, for the sake of showing it testable.
>>
>>
>>
>> That inferred physical world is just as computed as Max Tegmark's
>>>
>>
>> If that was the case, there would be no white rabbit problem. The problem
>> of mechanism, is that our first person conscious thought are associate to a
>> statistics on infinitely many computations, and that is NOT computable per
>> se, and it is part of the job to explain why the physical laws seem so much
>> computable. To invoke one computation, like in "digital physics", is still
>> a manner of doing physics, and putting the mind-body problem (the mechanist
>> one, now) under the rug.
>> Brent forget the first person indeterminacy problem here.
>>
>>
>>
>> and is just as necessary for consciousness as brains and skulls and
>>> planets are.  So, for me, the question is whether something is gained by
>>> this reification of computation.  Bruno says it provides the relation
>>> between mind and body.  But that's more a promise than a fact.
>>>
>>
>> Not at all. I show that there is a problem. First, there is no
>> reification of computation. They are unavoidably executed by the
>> arithmetical reality. We can't brush that away, because Mechanism requires
>> that arithmetical reality to just define what a computation is. Then, below
>> our substitution level, we have infinities of computation at play, and we
>> *have to* justifies the laws of physics from that statistics (structured by
>> the points of view).
>>
>>
>>
>>
>> It provides some classification of thoughts of an ideal thinker who
>>> doesn't even think about anything except arithmetic.
>>>
>>
>> Assuming mechanism, he thinks "Gosh, if mechanism is true, where does
>> this appeararance of material reality comes from?".
>>
>>
>>
>>
>>
>>
>> ​I really think you continue to miss something crucial here.
>>
>>
>> Brent miss 

Re: Answer to David 3

[Bruno Marchal]

On 26 May 2017, at 14:04, David Nyman wrote:


On 25 May 2017 at 16:23, Bruno Marchal  wrote:
On 24 May 2017, at 13:56, David Nyman wrote:


Let me know if anything is still unclear.

-- Forwarded message --
From: David Nyman 
Date: 20 May 2017 at 01:30
Subject: Re: ​Movie argument
To: everything-list 


On 19 May 2017 at 21:00, Brent Meeker  wrote:


On 5/19/2017 8:45 AM, John Clark wrote:
On Thu, May 18, 2017 spudboy100 via Everything List  wrote:


​> ​ So which is the Boss, John, Mathematics, somehow at the  
'base; of the universe, or is physics the top dog from the 1st  
split second?


​ One of ​ ​ René ​Magritte's​  most famous paintings is  
called "Ceci n'est pas une pipe", in English that means " ​this  
is not a pipe".


http://i3.kym-cdn.com/entries/icons/facebook/000/022/133/the-treachery-of-images-this-is-not-a-pipe-1948(2).jpg

​This is how Magritte explained ​his painting:

​"​ The famous pipe. How people reproached me for it! And yet,  
could you stuff my pipe? No, it's just a representation, is it  
not? So if I had written on my picture 'This is a pipe', I'd have  
been lying! ​"​


​Mathematics is a representation of something it is not the thing  
itself. Physics is the thing itself.




Bruno's a Platonist.


I am open that Plato is right, in theology. In mathematics, I am not  
that "platonist", I just keep calm when I see that we tell the kids  
that 2+2=4.


The point is that "Mathematics is a representation of something it  
is not the thing itself. Physics is the thing itself" is the  
Aristotelian theological credo. It makes no sense with Mechanism.


(I comment Brent, I think here, and you, David, below)

That means that conscious thoughts are what we have immediate  
access to and the physical world is an inference from perceptions  
(which are thoughts).  We take the physical world to bereal  
insofar as our inference has point-of-view-invariance so that  
others agree with us about perceptions.   Bruno observes that  
consciousness is associated with and dependent on brains, which are  
part of the inferred physical world.  He supposes this is because  
brains realize certain computations and he hypothesizes that  
conscious thoughts correspond to certain computations.  But  
computation is an abstraction; given Church-Turing it exists in the  
sense that arithmetic exists.  So among all possible computations,  
there must be the computations that constitute our conscious  
thoughts and the inferences of a physical world to which those  
thoughts seem to refer... but not really.   It's the "not really"  
where I part company with his speculations.


I prefer t say that I assume. I don't speculate that Mechanism is  
true. I assume Mechanism is true, for the sake of showing it testable.





That inferred physical world is just as computed as Max Tegmark's


If that was the case, there would be no white rabbit problem. The  
problem of mechanism, is that our first person conscious thought are  
associate to a statistics on infinitely many computations, and that  
is NOT computable per se, and it is part of the job to explain why  
the physical laws seem so much computable. To invoke one  
computation, like in "digital physics", is still a manner of doing  
physics, and putting the mind-body problem (the mechanist one, now)  
under the rug.

Brent forget the first person indeterminacy problem here.



and is just as necessary for consciousness as brains and skulls and  
planets are.  So, for me, the question is whether something is  
gained by this reification of computation.  Bruno says it provides  
the relation between mind and body.  But that's more a promise than  
a fact.


Not at all. I show that there is a problem. First, there is no  
reification of computation. They are unavoidably executed by the  
arithmetical reality. We can't brush that away, because Mechanism  
requires that arithmetical reality to just define what a computation  
is. Then, below our substitution level, we have infinities of  
computation at play, and we *have to* justifies the laws of physics  
from that statistics (structured by the points of view).





It provides some classification of thoughts of an ideal thinker who  
doesn't even think about anything except arithmetic.


Assuming mechanism, he thinks "Gosh, if mechanism is true, where  
does this appeararance of material reality comes from?".








​I really think you continue to miss something crucial here.


Brent miss the problem. he thinks I come up with some bizarre new  
theory, when I just show that an antic honorable theory, Mechanism,  
in the digital version, leads to a big problem: we *have to* explain  
the physical appearances from a statistics on first person (plural)  
views emulated infinitely often in arithmetic.


I show a problem, then I illustrate the beginning 

Re: Answer to David 3

[David Nyman]

On 25 May 2017 at 16:23, Bruno Marchal  wrote:

> On 24 May 2017, at 13:56, David Nyman wrote:
>
> Let me know if anything is still unclear.
>
> -- Forwarded message --
> From: David Nyman 
> Date: 20 May 2017 at 01:30
> Subject: Re: ​Movie argument
> To: everything-list 
>
>
> On 19 May 2017 at 21:00, Brent Meeker  wrote:
>
>>
>>
>> On 5/19/2017 8:45 AM, John Clark wrote:
>>
>> On Thu, May 18, 2017 spudboy100 via Everything List <
>> everything-list@googlegroups.com> wrote:
>>
>> ​> ​
>>>  So which is the Boss, John, Mathematics, somehow at the 'base; of the
>>> universe, or is physics the top dog from the 1st split second?
>>
>>
>> ​
>>  One of
>> ​ ​
>>  René
>> ​Magritte's​
>>   most famous paintings is called "Ceci n'est pas une pipe", in English
>> that means "
>> ​this is not a pipe".
>>
>> http://i3.kym-cdn.com/entries/icons/facebook/000/022/133/the
>> -treachery-of-images-this-is-not-a-pipe-1948(2).jpg
>>
>> ​This is how Magritte explained ​his painting:
>>
>> *​"​ The famous pipe. How people reproached me for it! And yet, could you
>> stuff my pipe? No, it's just a representation, is it not? So if I had
>> written on my picture 'This is a pipe', I'd have been lying! ​"​*
>>
>> ​Mathematics is a representation of something it is not the thing itself.
>> Physics is the thing itself.
>>
>>
>> Bruno's a Platonist.
>>
>
> I am open that Plato is right, in theology. In mathematics, I am not that
> "platonist", I just keep calm when I see that we tell the kids that 2+2=4.
>
> The point is that "Mathematics is a representation of something it is not
> the thing itself. Physics is the thing itself" is the Aristotelian
> theological credo. It makes no sense with Mechanism.
>
> (I comment Brent, I think here, and you, David, below)
>
> That means that conscious thoughts are what we have immediate access to
>> and the physical world is an inference from perceptions (which are
>> thoughts).  We take the physical world to bereal insofar as our
>> inference has point-of-view-invariance so that others agree with us about
>> perceptions.   Bruno observes that consciousness is associated with and
>> dependent on brains, which are part of the inferred physical world.  He
>> supposes this is because brains realize certain computations and he
>> hypothesizes that conscious thoughts correspond to certain computations.
>> But computation is an abstraction; given Church-Turing it exists in the
>> sense that arithmetic exists.  So among all possible computations, there
>> must be the computations that constitute our conscious thoughts and the
>> inferences of a physical world to which those thoughts seem to refer... but
>> not really.   It's the "not really" where I part company with his
>> speculations.
>>
>
> I prefer t say that I assume. I don't speculate that Mechanism is true. I
> assume Mechanism is true, for the sake of showing it testable.
>
>
>
> That inferred physical world is just as computed as Max Tegmark's
>>
>
> If that was the case, there would be no white rabbit problem. The problem
> of mechanism, is that our first person conscious thought are associate to a
> statistics on infinitely many computations, and that is NOT computable per
> se, and it is part of the job to explain why the physical laws seem so much
> computable. To invoke one computation, like in "digital physics", is still
> a manner of doing physics, and putting the mind-body problem (the mechanist
> one, now) under the rug.
> Brent forget the first person indeterminacy problem here.
>
>
>
> and is just as necessary for consciousness as brains and skulls and
>> planets are.  So, for me, the question is whether something is gained by
>> this reification of computation.  Bruno says it provides the relation
>> between mind and body.  But that's more a promise than a fact.
>>
>
> Not at all. I show that there is a problem. First, there is no reification
> of computation. They are unavoidably executed by the arithmetical reality.
> We can't brush that away, because Mechanism requires that arithmetical
> reality to just define what a computation is. Then, below our substitution
> level, we have infinities of computation at play, and we *have to*
> justifies the laws of physics from that statistics (structured by the
> points of view).
>
>
>
>
> It provides some classification of thoughts of an ideal thinker who
>> doesn't even think about anything except arithmetic.
>>
>
> Assuming mechanism, he thinks "Gosh, if mechanism is true, where does this
> appeararance of material reality comes from?".
>
>
>
>
>
>
> ​I really think you continue to miss something crucial here.
>
>
> Brent miss the problem. he thinks I come up with some bizarre new theory,
> when I just show that an antic honorable theory, Mechanism, in the digital
> version, leads to a big problem: we *have to* explain the physical
> appearances from a statistics on first