Re: Mathematical Universe Hypothesis

[John Clark]

On Fri, Oct 26, 2018 at 5:40 PM  wrote:

*> the concept of a plane wave, one of the solutions of Maxwell's
> equations. It certainly doesn't exist in THIS universe*


I agree with the general point you're trying to make, just because
something can be consistently described mathematically doesn't prove it
must exist physically. However if you're interested in the waves that enter
your radio telescope and consider them to be plane waves the error in doing
so can be made arbitrarily small by increasing the distance from the point
source or by decreasing the size of the antenna. As a practical matter
because the things astronomers study are so distant and their antennas are
so small they can treat the waves they're interested in as plane waves and
produce no measurable error by doing so. But a designer of optical
microscopes would not have that luxury because the lens of a microscope is
large compared to the distance from the sample, so he could not treat them
as plane waves.

John K Clark

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Saturday, October 27, 2018 at 2:55:57 AM UTC+2, Brent wrote:
>
>
> Logical consistency is a relation between sentences.  It's not about 
> existence.  The sentences might be about the existence of something, but 
> that's different.  Or the sentences may have variables quantified by 
> existential quantifiers, but that's different too.  To say logical 
> consistency is needed for existence would be a category error.
>

An inconsistent object is an inconsistently defined object. Sentences 
define objects by attributing properties to them. If a sentence is 
inconsistent, it says that an object has and does not have the same 
property, and thus that the object is not what it is. An inconsistent 
object cannot exist. 

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Friday, October 26, 2018 at 7:55:57 PM UTC-5, Brent wrote:
>
>
>
> On 10/26/2018 1:03 PM, Philip Thrift wrote:
>
>
>
> On Friday, October 26, 2018 at 2:33:13 PM UTC-5, Tomas Pales wrote: 
>>
>>
>>
>> On Friday, October 26, 2018 at 8:06:03 PM UTC+2, Bruno Marchal wrote: 
>>>
>>>
>>> OK. But it seemed to me you said that is better not to make unnecessary 
>>> assumption.
>>>
>>
>> My only ontological assumption is that existence is logical consistency. 
>> This assumption gives rise to the set-theoretic multiverse, and I don't 
>> mean just ZF or ZFC but all consistent versions of pure set theory. You add 
>> assumptions that restrict this set-theoretic multiverse to arithmetic.
>>
>
>
>
> "Logical consistency" is likely not needed for existence.
>
>  https://plato.stanford.edu/entries/dialetheism/
>
>
> Logical consistency is a relation between sentences.  It's not about 
> existence.  The sentences might be about the existence of something, but 
> that's different.  Or the sentences may have variables quantified by 
> existential quantifiers, but that's different too.  To say logical 
> consistency is needed for existence would be a category error.
>
> Brent
>

In other words:

https://www.lrb.co.uk/v08/n07/richard-rorty/the-contingency-of-language :


*As long as we think that there is some relation called ‘fitting the world’ 
or ‘expressing the real nature of the human self’ which can be possessed or 
lacked by vocabularies-as-wholes, we shall continue the traditional 
philosophical search for a criterion which will tell us which vocabularies 
have this desirable feature. But if we could ever become reconciled to the 
idea that reality is indifferent to our descriptions of it, and that the 
human self is created by the use of a vocabulary rather than being 
adequately or inadequately expressed in a vocabulary, then we should at 
last have assimilated what was true in the romantic idea that truth is made 
rather than found. What is true about this claim is just that languages are 
made rather than found, and that truth is a property of linguistic 
entities, of sentences.*

 - pt

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/26/2018 1:14 PM, Tomas Pales wrote:



On Friday, October 26, 2018 at 10:03:07 PM UTC+2, Philip Thrift wrote:



On Friday, October 26, 2018 at 2:33:13 PM UTC-5, Tomas Pales wrote:



On Friday, October 26, 2018 at 8:06:03 PM UTC+2, Bruno Marchal
wrote:


OK. But it seemed to me you said that is better not to
make unnecessary assumption.


My only ontological assumption is that existence is logical
consistency. This assumption gives rise to the set-theoretic
multiverse, and I don't mean just ZF or ZFC but all consistent
versions of pure set theory. You add assumptions that restrict
this set-theoretic multiverse to arithmetic.




"Logical consistency" is likely not needed for existence.

https://plato.stanford.edu/entries/dialetheism/



I disagree. I already mentioned dialetheism and I think it's 
nonsensical because it accepts the existence of objects that are not 
what they are.


You're confusing objects and sentences.

Brent

Such "objects" are nothing. And unless you arbitrarily block logical 
explosion, one inconsistency will make all ontology meaningless, even 
the property of existence will not be different from non-existence.


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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/26/2018 1:03 PM, Philip Thrift wrote:



On Friday, October 26, 2018 at 2:33:13 PM UTC-5, Tomas Pales wrote:



On Friday, October 26, 2018 at 8:06:03 PM UTC+2, Bruno Marchal wrote:


OK. But it seemed to me you said that is better not to make
unnecessary assumption.


My only ontological assumption is that existence is logical
consistency. This assumption gives rise to the set-theoretic
multiverse, and I don't mean just ZF or ZFC but all consistent
versions of pure set theory. You add assumptions that restrict
this set-theoretic multiverse to arithmetic.




"Logical consistency" is likely not needed for existence.

     https://plato.stanford.edu/entries/dialetheism/


Logical consistency is a relation between sentences.  It's not about 
existence.  The sentences might be about the existence of something, but 
that's different.  Or the sentences may have variables quantified by 
existential quantifiers, but that's different too.  To say logical 
consistency is needed for existence would be a category error.


Brent

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Friday, October 26, 2018 at 11:59:28 PM UTC+2, Philip Thrift wrote:
>
>
> As a practical matter though, AI and agent programmers have to deal with 
> inconsistent information in the world:
>
> https://www.hindawi.com/journals/isrn/2013/632319/
> https://arxiv.org/abs/1708.02851
> https://www.sciencedirect.com/science/article/abs/pii/S0004370216300108
> https://link.springer.com/chapter/10.1007/978-3-642-25664-6_46
> ...
>

Yes, a sentence (or a belief formulated in sentences) can contain words 
that contradict each other but that doesn't mean that the sentence is true. 
Maybe parts of the sentence can contain useful information but the sentence 
is not true. 

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Friday, October 26, 2018 at 3:14:05 PM UTC-5, Tomas Pales wrote:
>
>
>
> On Friday, October 26, 2018 at 10:03:07 PM UTC+2, Philip Thrift wrote:
>>
>>
>>
>> On Friday, October 26, 2018 at 2:33:13 PM UTC-5, Tomas Pales wrote:
>>>
>>>
>>>
>>> On Friday, October 26, 2018 at 8:06:03 PM UTC+2, Bruno Marchal wrote:


 OK. But it seemed to me you said that is better not to make unnecessary 
 assumption.

>>>
>>> My only ontological assumption is that existence is logical consistency. 
>>> This assumption gives rise to the set-theoretic multiverse, and I don't 
>>> mean just ZF or ZFC but all consistent versions of pure set theory. You add 
>>> assumptions that restrict this set-theoretic multiverse to arithmetic.
>>>
>>
>>
>>
>> "Logical consistency" is likely not needed for existence.
>>
>>  https://plato.stanford.edu/entries/dialetheism/
>>
>
> I disagree. I already mentioned dialetheism and I think it's nonsensical 
> because it accepts the existence of objects that are not what they are. 
> Such "objects" are nothing. And unless you arbitrarily block logical 
> explosion, one inconsistency will make all ontology meaningless, even the 
> property of existence will not be different from non-existence.
>




As a practical matter though, AI and agent programmers have to deal with 
inconsistent information in the world:

https://www.hindawi.com/journals/isrn/2013/632319/
https://arxiv.org/abs/1708.02851
https://www.sciencedirect.com/science/article/abs/pii/S0004370216300108
https://link.springer.com/chapter/10.1007/978-3-642-25664-6_46
...

- pt 

>   
>

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Friday, October 26, 2018 at 7:36:15 PM UTC, Tomas Pales wrote:
>
>
>
> On Friday, October 26, 2018 at 8:25:30 PM UTC+2, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Friday, September 28, 2018 at 9:32:04 AM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com 
>>> wrote:
>>>>
>>>> Hello I think this good forum for this topic - what do you think about 
>>>> Mathematical Universe, there are very big arguments for that hypothesis:
>>>> f
>>>> - applicability of mathematic, to natural sciences
>>>> - all we discovere are structures and I didnt find explanation of the 
>>>> diference beetwen physical structures and mathematical structures.
>>>> - scientists and philosophers of science tend to affirm belive in 
>>>> diverse structure and homogeneous substance (neutral monism) or 
>>>> mathematicism vide Ladyman, Ross, French, Tegmark etc.
>>>>
>>>> What are your thoughts. 
>>>>
>>>
>>> If it's what I think it is, it's demonstrably wrong. One counter example 
>>> suffices; there are plane wave solutions to Maxwell's equations, but if you 
>>> know what plane waves are, they clearly do NOT exist in physical reality. 
>>> If this is correct, other models also fall by  wayside. AG 
>>>
>>
>> the
>> *What I don't get is why this is a topic which generates so much 
>> interest, when it is easily falsified. AG* 
>>
>
> I don't know what a plane wave is but according to Tegmark's mathematical 
> universe hypothesis if a plane wave is a consistently defined object, it 
> exists. If not in our universe then in a different one. 
>

*You ought to familiarize yourself with the concept of a plane wave, one of 
the solutions of Maxwell's equations. It certainly doesn't exist in THIS 
universe, or any other unless you accept instantaneous action at a 
distance, and with a vengeance. Why a vengeance? You'll know when you know 
the behavior of a plane wave. AG *

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Friday, October 26, 2018 at 10:03:07 PM UTC+2, Philip Thrift wrote:
>
>
>
> On Friday, October 26, 2018 at 2:33:13 PM UTC-5, Tomas Pales wrote:
>>
>>
>>
>> On Friday, October 26, 2018 at 8:06:03 PM UTC+2, Bruno Marchal wrote:
>>>
>>>
>>> OK. But it seemed to me you said that is better not to make unnecessary 
>>> assumption.
>>>
>>
>> My only ontological assumption is that existence is logical consistency. 
>> This assumption gives rise to the set-theoretic multiverse, and I don't 
>> mean just ZF or ZFC but all consistent versions of pure set theory. You add 
>> assumptions that restrict this set-theoretic multiverse to arithmetic.
>>
>
>
>
> "Logical consistency" is likely not needed for existence.
>
>  https://plato.stanford.edu/entries/dialetheism/
>

I disagree. I already mentioned dialetheism and I think it's nonsensical 
because it accepts the existence of objects that are not what they are. 
Such "objects" are nothing. And unless you arbitrarily block logical 
explosion, one inconsistency will make all ontology meaningless, even the 
property of existence will not be different from non-existence.
  

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Friday, October 26, 2018 at 2:33:13 PM UTC-5, Tomas Pales wrote:
>
>
>
> On Friday, October 26, 2018 at 8:06:03 PM UTC+2, Bruno Marchal wrote:
>>
>>
>> OK. But it seemed to me you said that is better not to make unnecessary 
>> assumption.
>>
>
> My only ontological assumption is that existence is logical consistency. 
> This assumption gives rise to the set-theoretic multiverse, and I don't 
> mean just ZF or ZFC but all consistent versions of pure set theory. You add 
> assumptions that restrict this set-theoretic multiverse to arithmetic.
>



"Logical consistency" is likely not needed for existence.

 https://plato.stanford.edu/entries/dialetheism/

- pt

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Friday, October 26, 2018 at 8:25:30 PM UTC+2, agrays...@gmail.com wrote:
>
>
>
> On Friday, September 28, 2018 at 9:32:04 AM UTC, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com 
>> wrote:
>>>
>>> Hello I think this good forum for this topic - what do you think about 
>>> Mathematical Universe, there are very big arguments for that hypothesis:
>>> f
>>> - applicability of mathematic, to natural sciences
>>> - all we discovere are structures and I didnt find explanation of the 
>>> diference beetwen physical structures and mathematical structures.
>>> - scientists and philosophers of science tend to affirm belive in 
>>> diverse structure and homogeneous substance (neutral monism) or 
>>> mathematicism vide Ladyman, Ross, French, Tegmark etc.
>>>
>>> What are your thoughts. 
>>>
>>
>> If it's what I think it is, it's demonstrably wrong. One counter example 
>> suffices; there are plane wave solutions to Maxwell's equations, but if you 
>> know what plane waves are, they clearly do NOT exist in physical reality. 
>> If this is correct, other models also fall by the wayside. AG 
>>
>
> *What I don't get is why this is a topic which generates so much interest, 
> when it is easily falsified. AG* 
>

I don't know what a plane wave is but according to Tegmark's mathematical 
universe hypothesis if a plane wave is a consistently defined object, it 
exists. If not in our universe then in a different one. 

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Friday, October 26, 2018 at 8:06:03 PM UTC+2, Bruno Marchal wrote:
>
>
> OK. But it seemed to me you said that is better not to make unnecessary 
> assumption.
>

My only ontological assumption is that existence is logical consistency. 
This assumption gives rise to the set-theoretic multiverse, and I don't 
mean just ZF or ZFC but all consistent versions of pure set theory. You add 
assumptions that restrict this set-theoretic multiverse to arithmetic.

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Friday, September 28, 2018 at 9:32:04 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com 
> wrote:
>>
>> Hello I think this good forum for this topic - what do you think about 
>> Mathematical Universe, there are very big arguments for that hypothesis:
>> f
>> - applicability of mathematic, to natural sciences
>> - all we discovere are structures and I didnt find explanation of the 
>> diference beetwen physical structures and mathematical structures.
>> - scientists and philosophers of science tend to affirm belive in diverse 
>> structure and homogeneous substance (neutral monism) or mathematicism vide 
>> Ladyman, Ross, French, Tegmark etc.
>>
>> What are your thoughts. 
>>
>
> If it's what I think it is, it's demonstrably wrong. One counter example 
> suffices; there are plane wave solutions to Maxwell's equations, but if you 
> know what plane waves are, they clearly do NOT exist in physical reality. 
> If this is correct, other models also fall by the wayside. AG 
>

*What I don't get is why this is a topic which generates so much interest, 
when it is easily falsified. AG* 

>
>>
>> Regards
>>
>

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

Hi Tomas,


> as I see it, my ontology, whose relational aspect is defined by the relation 
> of similarity (and its special kinds - instantiation and composition), 
> includes your ontology, because pure set theory includes arithmetic.


OK. But it seemed to me you said that is better not to make unnecessary 
assumption. Indexical Digital Mechanism (the idea that we would personally 
survive in the usual clinical sense with a digitalis-able body) can be shown to 
make one simple inductive set enough, and actually needing the simplest model 
of arithmetic. Infinite computations do play an important role, but in the 
ontology, we can use only their finite portions. If we allow inductions and/or 
axiom of the infinite, things get awry with the first person indeterminacy, as 
you will need to take into account transfinite histories. I have not yet prove 
this, but I suspect the axiom of infinity making unnecessary mess.




> You may be right that arithmetic is sufficient to define physics

The arithmetical reality is sufficient, and eventually, even just the partial 
computable part (the Sigma_1 reality). But that is only true for the ontology. 
The phenomenology will not be bounded in any way. Even ZF + KAPPA (the 
existence of a inaccessible cardinal) can still only scratch on the 
arithmetical reality.



> but reality may also contain more than arithmetic.

If you are a digitalis able machine, arithmetic seen from inside *is* more than 
arithmetic. 

That is the reason why we would be foolish to commit oneself in any ontological 
commitment bigger than one universal 
machine/number/word/combinator/game-of-life-pattern, etc.




> On the other hand, if I understand Godel's second incompleteness theorem 
> correctly, as far as the relational/mathematical aspect of reality is 
> concerned, we will never be able to prove that there exists more than 
> arithmetic

No, but it is consistent to assume more. And the ontological arithmetical 
reality explains already, by incompleteness indeed, that the numbers will have 
to assume much more than the numbers to be able to understand themselves.

Like complex analysis is useful in Number Theory, incompleteness justify the 
helpfulness of some strong axioms. Löbian machine, like PA or ZF, or ZF+KAPPA 
can prove their own incompleteness and contemplate the geometry of their 
ignorance. The fact that all that is phenomenological does not make it less 
real.

There is a Skolem phenomenon. From outside the ontology is recursively 
enumerable, from inside it is above anything expressible.Somehow, the whole of 
possible math can only scratch it a little bit.



> (because we will never be able to prove that it is consistent). And if we are 
> not able to interact with infinite objects, we will never be able to observe 
> them either.

Yes, indeed. Same with the non-computable. Ae^iH(omega)t, with omega = Caitin 
or Post number is a solution of the schroedinger equation, but is not 
computable, but we would never recognise it as such, and confuse it with (pure) 
noise.


> 
> But I don't see a reason to exclude infinite objects from existence.

They do exist, the machines met them all the time, and are keeping in touch 
with them. Phenomenological existence is not non existence.

But we don’t need them in the theory: they are explained by the entity living 
in that theory, without f-havng them to commit an ontological act. So why would 
we do that? Plus the fact that if we do that, the semantic, which is what make 
the “consciousness flux” differentiate on the computations/histories. 

The problem of the machine is that it has the foot on the finite ground, living 
in the neighbourhood of 0. Bt its soul, where it truly live belongs to the 
neighbourhood of infinity. 

Infinity is a key notion, it is just that we don’t need to assume it, it is a 
necessary “meme” of all universal machine introspecting itself, and it is a key 
help to them in most situation.




> Some say that an infinite collection can never be "completed", as if 
> mathematical objects are created by some kind of process that must reach 
> completion. They are not created by a process; they exist timelessly; there 
> is nothing to complete. Only inconsistency would prevent their existence.

Yes. OK.



> 
> You said you don't really believe in sets. But a set is just a combination of 
> objects, where the combination is another object, isn't it? Everything you 
> see around you is structurally a set.

Yes, but with mechanism, that is the result of the work of a finite number, in 
front of (infinitely many variants) of a finite number.




> 
> About category theory vs. set theory, this is how I understand it: more 
> general (more abstract) mathematical objects are instantiated in more 
> specific mathematical objects (e.g. "geometric object" is instantiated in 
> "triangle") and ultimately in concrete mathematical objects (e.g. in concrete 
> triangles), which are not instantiated in anything else.

Oh, 

Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Wednesday, October 24, 2018 at 3:47:39 PM UTC-5, Tomas Pales wrote:
>
> Bruno,
>
> as I see it, my ontology, whose relational aspect is defined by the 
> relation of similarity (and its special kinds - instantiation and 
> composition), includes your ontology, because pure set theory includes 
> arithmetic. You may be right that arithmetic is sufficient to define 
> physics but reality may also contain more than arithmetic. On the other 
> hand, if I understand Godel's second incompleteness theorem correctly, as 
> far as the relational/mathematical aspect of reality is concerned, we will 
> never be able to prove that there exists more than arithmetic (because we 
> will never be able to prove that it is consistent). And if we are not able 
> to interact with infinite objects, we will never be able to observe them 
> either.
>
> But I don't see a reason to exclude infinite objects from existence. Some 
> say that an infinite collection can never be "completed", as if 
> mathematical objects are created by some kind of *process *that must 
> reach completion*. *They are not created by a process; they exist 
> timelessly; there is nothing to complete. Only inconsistency would prevent 
> their existence.
>
> You said you don't really believe in sets. But a set is just a combination 
> of objects, where the combination is another object, isn't it? Everything 
> you see around you is structurally a set.
>
> About category theory vs. set theory, this is how I understand it: more 
> general (more abstract) mathematical objects are instantiated in more 
> specific mathematical objects (e.g. "geometric object" is instantiated in 
> "triangle") and ultimately in concrete mathematical objects (e.g. in 
> concrete triangles), which are not instantiated in anything else. (Those 
> objects that can be instantiated in other objects are also called 
> properties.) All concrete objects are concrete collections, that is, 
> collections of concrete objects, so all mathematical objects are ultimately 
> instantiated in concrete collections. This fact is used in set theory, 
> where every mathematical object is represented as a collection (set), and 
> that's how set theory can be a foundation of mathematics. The collections 
> referred to in set theory are not concrete collections though but abstract 
> collections (generalized collections), because differences between concrete 
> collections of the same kind are not relevant for mathematical purposes. So 
> for example, set theory does not refer to concrete empty sets but to one 
> abstract empty set (which is instantiated in all concrete empty sets). 
> (Although I have also heard of the extension of set theory to so-called 
> "multiset" theory, which admits copies (instances) of the same object as 
> distinct members of a set.)
>
> The approach of category theory is not to represent mathematical objects 
> as collections but to study similarities (morphisms) directly between 
> mathematical objects themselves. Collections, there, are treated just as 
> one of many kinds of mathematical objects.
>
> About qualia, some time ago I imagined that maybe Godel sentences could 
> explain qualia, as Godel sentences depend on an axiomatic system and yet 
> cannot be proved from that system, similarly like qualia seem to depend on 
> a neural system and yet cannot be proved from it. But then I grew skeptical 
> of this idea because it seemed to me that numbers will always be just 
> numbers, even if they are infinitely big, and an infinitely big number may 
> be beyond our grasp in a sense but it will not somehow turn into red color, 
> for example. Gradually I started to lean to the idea that numbers and 
> mathematics in general are about the relation of similarity; that 
> mathematics basically says that something is similar to something else but 
> never says what that "something" is. So now it seems more plausible to me 
> that qualia are those "somethings" that stand in similarity relations. 
> Russellian monism is a similar explanation of qualia.
>
>
>


The future practice of mathematics is as an empirical science:

  https://www.youtube.com/watch?v=BkKBgA902Uk

Category theory is type theory "shorn of syntax":

  https://en.wikipedia.org/wiki/Type_theory#Relation_to_category_theory

(or: Category theory is a conspiracy to obfuscate type theory.)

Qualia from pure numbers (immaterial information) are like category theory 
relative to type: They are "bodiless". 

- pt

 

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

Bruno,

as I see it, my ontology, whose relational aspect is defined by the 
relation of similarity (and its special kinds - instantiation and 
composition), includes your ontology, because pure set theory includes 
arithmetic. You may be right that arithmetic is sufficient to define 
physics but reality may also contain more than arithmetic. On the other 
hand, if I understand Godel's second incompleteness theorem correctly, as 
far as the relational/mathematical aspect of reality is concerned, we will 
never be able to prove that there exists more than arithmetic (because we 
will never be able to prove that it is consistent). And if we are not able 
to interact with infinite objects, we will never be able to observe them 
either.

But I don't see a reason to exclude infinite objects from existence. Some 
say that an infinite collection can never be "completed", as if 
mathematical objects are created by some kind of *process *that must reach 
completion*. *They are not created by a process; they exist timelessly; 
there is nothing to complete. Only inconsistency would prevent their 
existence.

You said you don't really believe in sets. But a set is just a combination 
of objects, where the combination is another object, isn't it? Everything 
you see around you is structurally a set.

About category theory vs. set theory, this is how I understand it: more 
general (more abstract) mathematical objects are instantiated in more 
specific mathematical objects (e.g. "geometric object" is instantiated in 
"triangle") and ultimately in concrete mathematical objects (e.g. in 
concrete triangles), which are not instantiated in anything else. (Those 
objects that can be instantiated in other objects are also called 
properties.) All concrete objects are concrete collections, that is, 
collections of concrete objects, so all mathematical objects are ultimately 
instantiated in concrete collections. This fact is used in set theory, 
where every mathematical object is represented as a collection (set), and 
that's how set theory can be a foundation of mathematics. The collections 
referred to in set theory are not concrete collections though but abstract 
collections (generalized collections), because differences between concrete 
collections of the same kind are not relevant for mathematical purposes. So 
for example, set theory does not refer to concrete empty sets but to one 
abstract empty set (which is instantiated in all concrete empty sets). 
(Although I have also heard of the extension of set theory to so-called 
"multiset" theory, which admits copies (instances) of the same object as 
distinct members of a set.)

The approach of category theory is not to represent mathematical objects as 
collections but to study similarities (morphisms) directly between 
mathematical objects themselves. Collections, there, are treated just as 
one of many kinds of mathematical objects.

About qualia, some time ago I imagined that maybe Godel sentences could 
explain qualia, as Godel sentences depend on an axiomatic system and yet 
cannot be proved from that system, similarly like qualia seem to depend on 
a neural system and yet cannot be proved from it. But then I grew skeptical 
of this idea because it seemed to me that numbers will always be just 
numbers, even if they are infinitely big, and an infinitely big number may 
be beyond our grasp in a sense but it will not somehow turn into red color, 
for example. Gradually I started to lean to the idea that numbers and 
mathematics in general are about the relation of similarity; that 
mathematics basically says that something is similar to something else but 
never says what that "something" is. So now it seems more plausible to me 
that qualia are those "somethings" that stand in similarity relations. 
Russellian monism is a similar explanation of qualia.


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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

Hi Thomas,

Sorry for the delay, busy days, see the mail only now.


> On 22 Oct 2018, at 19:15, Tomas Pales  wrote:
> 
> 
> 
> On Monday, October 22, 2018 at 1:41:23 PM UTC+2, Bruno Marchal wrote:
> 
> The computable universe hypothesis cannot make sense. To define “computable” 
> you need to assume arithmetic. But arithmetic executes all computations, and 
> the measure problem will have to involve infinities. 
> So the correct passage from “mathematical universe” to computationalism 
> consists in 
> 
> 1) distinguish well the ontology and the phenomenology. Restrict the ontology 
> to the finite and computable finite objects,
> 
> In his paper, Tegmark included in CUH only mathematical structures defined by 
> halting computations. So I guess this would include only finite computable 
> objects?
>  
> 
> 2) allowing the infinite in the phenomenology, where indeed the physical 
> universe will appear.
> 
> The infinities ruins physics only if they are put in the ontology. This is 
> explained in details in basically all my papers (on this subject). I can give 
> the reference (again) if you are interested. Tegmark missed the mind-body 
> problem.
> 
> 
> How do you include the infinite in the phenomenology when you only have 
> finite objects in ontology? I imagine that we cannot really experience or 
> perceive the infinite, but we may infer it inductively from finite objects. 
> And this inductive inference may perhaps give us a kind of feeling or sense 
> of "the infinite", but it would be a feeling from the inferential process 
> rather than from the infinite itself.


If we are machine at some substitution level, we are duplicable at that level, 
and this leads to a first person duplication, which itself leads to a reduction 
of physics to a probability/credibility calculus on all computations going 
trough our actual relative state. There are infinitely many computations doing 
that, in arithmetic, so that the first person indeterminacy domain is infinite. 
Machine are “locally finite” as seen through their histories.







> 
> Anyway, I should tell you that I am no mathematician, so I am afraid I can't 
> digest the technicalities in your papers. I am not even a physicist or a 
> professional philosopher, I just dabble in philosophy.


My meta-goal consists in showing that with suitable hypothesis, we can proceed 
with the scientific attitude, in theology/metaphysics/philosophy. 
Unfortunately, this is not yet well seen in may places. 

There is no problem with musing and even with metaphysical poetry. Some poet 
can even be more rdigoruous than philosopher, like with Borges, Valery and 
Galouye.

What cannot be done is to use a personal conviction against a logical argument.

That cannot be done with all hypothesis, but with the ChurcTuring thesis, the 
notion of computation becomes a precise mathematical notion, and we can, by 
thought experiment and mathematical proof proceed and get results, some of 
which can lead to testable consequences.



> 
> In my ontological musings, I try to get to the bottom of what is necessary 
> and avoid arbitrary assumptions.


That is the best attitude.



> First, what is existence? All definitions of existence should follow the 
> principle of logical consistency, or in other words, the principle of 
> identity: an object (that which exists) should be identical to itself.


x = x

I agree.



> It should be what it is and not be what it is not. This also means that the 
> object should be defined consistently in relation to everything else, 
> otherwise its identity would be violated. I know there are people who believe 
> in the existence of inconsistently defined objects (dialetheists), but that 
> seems like craziness to me, sorry.

I rather follow you on this. Paraconsistent logic are interesting for the 
natural language, and the psychology of lies, but it would be insane to use it 
in metaphysics, unless a very good argument is provided.



> Moreover, unless you arbitrarily block logical explosion, such an 
> inconsistency would render all ontology meaningless, erasing even the 
> difference between existence and non-existence.

OK.



> 
> So, logical consistency is a necessary criterion of existence.

Hmm… I agree that theory of the fundamental things that we will assume has 
better to be consistent, but that is a meta-assumption. Logical consistency is 
an attribute of some being, it assumes already some ontology.

With the mechanist assumption, we will assume only the numbers, or the 
combinators, or any basic Turing complete/universal system. Then some machine 
will be consistent, but some machine can be inconsistent also. Arithmetic if 
full of inconsistent machines, which eventually get trivial.





> Is any other criterion necessary? I don't think so. Adding any other 
> criterion seems like an arbitrary restriction on what exists. If an object is 
> identical to itself, then it is something rather than nothing and so it is 
> there in 

Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Monday, October 22, 2018 at 1:41:23 PM UTC+2, Bruno Marchal wrote:

>
> The computable universe hypothesis cannot make sense. To define 
> “computable” you need to assume arithmetic. But arithmetic executes all 
> computations, and the measure problem will have to involve infinities. 
> So the correct passage from “mathematical universe” to computationalism 
> consists in 
>
> 1) distinguish well the ontology and the phenomenology. Restrict the 
> ontology to the finite and computable finite objects,
>

In his paper, Tegmark included in CUH only mathematical structures defined 
by halting computations. So I guess this would include only finite 
computable objects?
 

>
> 2) allowing the infinite in the phenomenology, where indeed the physical 
> universe will appear.
>
> The infinities ruins physics only if they are put in the ontology. This is 
> explained in details in basically all my papers (on this subject). I can 
> give the reference (again) if you are interested. Tegmark missed the 
> mind-body problem.
>
>
How do you include the infinite in the phenomenology when you only have 
finite objects in ontology? I imagine that we cannot really experience or 
perceive the infinite, but we may infer it inductively from finite objects. 
And this inductive inference may perhaps give us a kind of feeling or sense 
of "the infinite", but it would be a feeling from the inferential process 
rather than from the infinite itself.

Anyway, I should tell you that I am no mathematician, so I am afraid I 
can't digest the technicalities in your papers. I am not even a physicist 
or a professional philosopher, I just dabble in philosophy.

In my ontological musings, I try to get to the bottom of what is necessary 
and avoid arbitrary assumptions. First, what is existence? All definitions 
of existence should follow the principle of logical consistency, or in 
other words, the principle of identity: an object (that which exists) 
should be identical to itself. It should be what it is and not be what it 
is not. This also means that the object should be defined consistently in 
relation to everything else, otherwise its identity would be violated. I 
know there are people who believe in the existence of inconsistently 
defined objects (dialetheists), but that seems like craziness to me, sorry. 
Moreover, unless you arbitrarily block logical explosion, such an 
inconsistency would render all ontology meaningless, erasing even the 
difference between existence and non-existence.

So, logical consistency is a necessary criterion of existence. Is any other 
criterion necessary? I don't think so. Adding any other criterion seems 
like an arbitrary restriction on what exists. If an object is identical to 
itself, then it is something rather than nothing and so it is there in some 
sense. Instead of excluding some consistent object from existence, we can 
talk about the way in which it exists. And so, we can *identify* logical 
consistency with existence, as the property of all existing objects (there 
are actually no non-existing objects because such objects would have to be 
inconsistent and therefore they would not be objects but nothing).

Next, I find that if there are objects, then there must also be relations 
between them, as a special kind of objects that hold between other objects. 
Relations are just as necessary as the objects between which they hold. And 
while relations also hold between other relations, there must also be 
objects that are non-relations, as I explained in this thread earlier today.

Next, I find that the most general relation is "similarity", because it is 
a relation that holds between any two objects. It means that the two 
objects have some different properties and some same properties. Which 
gives rise to another general relation called "instantiation", which is the 
relation between a property and its instance. The instantiation relation is 
a special kind of the similarity relation but less general than similarity 
since it doesn't hold between arbitrary two objects. Finally, any objects 
can define a collection of them (for example based on their common 
property, as long as such a definition is consistent), which gives rise to 
another general relation called "composition", which is the relation 
between a collection and its part. The composition relation, too, is a 
special kind of the similarity relation but less general than similarity 
since it doesn't hold between arbitrary two objects.

So, the similarity relation, together with its special kinds - 
instantiation and composition, defines all possible relational structures. 
And all these three relations come together in set theory, the foundation 
of mathematics (instantiation is the satisfaction of a property/predicate 
by a set and composition is set membership or the derived relation of set 
inclusion). More accurately, by "set theory" I mean all consistent versions 
of pure set theory. What all versions of pure set theory 

Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 21 Oct 2018, at 21:59, Philip Thrift  wrote:
> 
> 
> 
> On Sunday, October 21, 2018 at 11:30:54 AM UTC-5, Tomas Pales wrote:
> 
> 
> On Sunday, October 21, 2018 at 5:22:20 PM UTC+2, Philip Thrift wrote:
> 
> BTW,  on "non-relations [which] are the non-mathematical objects and they (or 
> at least some of them) may be the qualities of consciousness (qualia)", that 
> is what I try to address in 
> 
> https://codicalist.wordpress.com/2018/10/14/experience-processing/ 
> 
> 
> where there is information processing (which is all mathematical processing) 
> and something else: experience processing.
> 
> - pt
> 
> I would say that any description is relational and therefore 
> mathematical/logical. When you describe an object you always define/present 
> it in relations to other objects - in relations to its parts or properties. 
> You can't describe the object itself, only give it a label. So you can't 
> describe qualities of consciousness themselves either. Not sure how you would 
> "process" them then.
> 
> Is there really a fundamental difference between hardware and software? I 
> mean, software can be seen as part of hardware: software is a particular 
> configuration of electron flows in hardware.
> 
> 
> Mathematics is genre of fiction [ 
> https://plato.stanford.edu/entries/fictionalism-mathematics/ ], so relations 
> are fictional. "Processing" relations/mathematics has no real meaning.
> 
> The difference between hardware and software today is somewhat blurred with 
> synthetic biology, programmable matter, reconfigurable hardware.

Assuming some form of non-mechanism, or non-digital-mechanism. OK. (Well, OK 
from a purely logical standpoint, but I find premature to invoke non-mechanism, 
when all available evidence favour mechanism, (consciousness, quantum 
mechanics, etc.).

Bruno




> 
> - pt
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 21 Oct 2018, at 18:30, Tomas Pales  wrote:
> 
> 
> 
> On Sunday, October 21, 2018 at 5:22:20 PM UTC+2, Philip Thrift wrote:
> 
> BTW,  on "non-relations [which] are the non-mathematical objects and they (or 
> at least some of them) may be the qualities of consciousness (qualia)", that 
> is what I try to address in 
> 
> https://codicalist.wordpress.com/2018/10/14/experience-processing/ 
> 
> 
> where there is information processing (which is all mathematical processing) 
> and something else: experience processing.
> 
> - pt
> 
> I would say that any description is relational and therefore 
> mathematical/logical. When you describe an object you always define/present 
> it in relations to other objects - in relations to its parts or properties. 
> You can't describe the object itself, only give it a label. So you can't 
> describe qualities of consciousness themselves either. Not sure how you would 
> "process" them then.
> 
> Is there really a fundamental difference between hardware and software? I 
> mean, software can be seen as part of hardware: software is a particular 
> configuration of electron flows in hardware.

Locally, that is right. Hardware is even an indexical (like “here” and “now”), 
but globally, the harwdware has to be recovered as a sum on all possible 
“software” generating my current state. That makes the hardware into a sort of 
absolute, and indeed all universal machine/number, “residing” in the 
arithmetical standard reality, will have the same physics, and differ only on 
histories and geographies.

There is no notion of mathematical universe, at least not in mathematics. We 
cannot define “arithmetical” in the arithmetical language, and it can only be 
worst for something as large as “mathematical”. A case can give given that 
“mathematical” might be defined in a richer theory, perhaps theology, but this 
can be shown to entail non-mechanism. All attempt to define mathematics 
mathematically leads to a new type of  structure, which embed itself naturally 
in something bigger. It is akin to the older problem of defining the set of all 
sets, which admits different formal solutions (it does not exist in ZF, it 
exists in NF, and it is a different sort of object in VBG. ZF = Zermelo 
Fraenkel set theory, NF = Quine’s New Foundations, and VBG = von Neuman Bernays 
Gödel set theory).

Bruno




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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 21 Oct 2018, at 18:12, Tomas Pales  wrote:
> 
> 
> 
> On Sunday, October 21, 2018 at 5:52:13 PM UTC+2, Philip Thrift wrote:
> 
> If our universe does not have infinitely-computing objects but there are 
> other universes that do, that would seem strange.
> 
> Why would our universe be left out? :)
> 
> 
> The mathematical multiverse would contain all possible (consistently defined) 
> mathematical structures, both finite and infinite. We would live in a finite 
> one. Why? I don't know. Maybe just by accident. Or maybe only finite 
> structures can contain conscious entities.  


By the first person indeterminacy; the finite structures are multiplied on 
infinitely many computations, which explains why there is a measure problem, 
already in arithmetic, when we do the mechanist assumption (in cognitive 
science, not in physics). 

Bruno


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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 21 Oct 2018, at 17:43, Tomas Pales  wrote:
> 
> 
> 
> On Sunday, October 21, 2018 at 4:28:21 PM UTC+2, Philip Thrift wrote:
> 
>   "reality contains all mathematical objects"
> 
> 
> Ironically, Tegmark doesn't believe that at all. He says infinite 
> mathematical entities are "ruining physics".
> - http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ 
> <http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/>
> 
> 
> The only thing to conclude is that Mad Max published his mathematical 
> universe hypothesis as a joke!
> - https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis 
> <https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis>
> 
> Already in his Mathematical Universe paper on arxiv, Tegmark discussed a 
> restricted version of MUH called CUH (computable universe hypothesis). He 
> mentioned that the attractive feature of CUH would be the disappearance of 
> the measure problem and also the exclusion of structures of which we may 
> never know whether they are consistent (due to Godel's second incompleteness 
> theorem) and thus whether they exist. On the other hand, the fact that we 
> cannot calculate probabilities (the measure problem) or find whether a 
> structure is consistent seems like an epistemic problem, not an ontological 
> one. The infinities may exist in reality, we just can't extract useful 
> statistics from them or confirm their existence. But reality doesn't depend 
> on whether we find it useful or whether we can confirm its existence.
> 
> The universe in which we live, or even the inflationary multiverse, may be a 
> finite/computable structure but there may also be infinite structures in the 
> larger mathematical multiverse.  

The computable universe hypothesis cannot make sense. To define “computable” 
you need to assume arithmetic. But arithmetic executes all computations, and 
the measure problem will have to involve infinities. 
So the correct passage from “mathematical universe” to computationalism 
consists in 

1) distinguish well the ontology and the phenomenology. Restrict the ontology 
to the finite and computable finite objects,

2) allowing the infinite in the phenomenology, where indeed the physical 
universe will appear.

The infinities ruins physics only if they are put in the ontology. This is 
explained in details in basically all my papers (on this subject). I can give 
the reference (again) if you are interested. Tegmark missed the mind-body 
problem.

Bruno






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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Sunday, October 21, 2018 at 11:16:29 PM UTC+2, Brent wrote:
>
>
>
> On 10/21/2018 7:11 AM, Tomas Pales wrote:
>
> I am generally sympathetic to Tegmark's mathematical multiverse idea, but 
> I have two comments/criticisms to it:
>
> 1) I am not sure whether Tegmark is aware of the so-called "instantiation" 
> relation. In philosophy, the instantiation relation is the relation between 
> a general and a particular object, where the particular object is an 
> instance of the general object. In other words, the general object is a 
> property of the particular object. Example: general triangle (or triangle 
> "in general") is the property of any particular triangle, and any 
> particular triangle is an instance of general triangle. Another example: 
> number 2 is a general relation that is instantiated in the particular 
> relation between any two objects. I am not sure whether Tegmark realizes 
> the difference between general objects and their instances, because he said 
> something like: when we probe matter we only find numbers (and hence 
> reality is just mathematics). But numbers cannot be found in our world; you 
> cannot find number 2 sitting on a tree or in the atomic nucleus. You can 
> only find instances of number 2, as relations between particular objects. 
> Mathematical objects are usually thought to be general objects, but in that 
> case there is more in reality than mathematical objects: there are general 
> objects *and* their instances. And in our physical world there are *no* 
> general objects, only their instances. If we want to say that there are 
> mathematical objects in our physical world, we should include among 
> mathematical objects also non-general objects, that is, objects that have 
> no instances. (By the way, there is a hierarchy of generality: more general 
> objects are instantiated in less general objects and those are ultimately 
> instantiated in non-general objects. Non-general objects are often called 
> "concrete", while general objects are also called "abstract".)
>
>
> This appears not to be a well-order hierarchy.  The thing I am sitting on 
> is an instance of a chair, and it's concrete.  But it's also an instance of 
> a matter, i.e. a collection of particles of the Standard Model (which may 
> or may not be the most general category).  It's also an instance of things 
> I own.
>

Yes, it is not always possible to say that one object is more general than 
another. Matter (the property of being a material object) is more general 
than chair (the property of being a chair) because the set of chairs is a 
subset of the set of material objects. But the property of being a chair is 
not necessarily more or less general than the property of being a thing you 
own.
 

>
>
> 2) While I agree with Tegmark that reality contains all mathematical 
> objects (both general and non-general), I think there is also a 
> non-mathematical aspect of reality. That's because mathematical objects are 
> relations or structures of relations, but relations cannot exist without 
> objects between which they hold. While it is true that relations can hold 
> between other relations, there should also be objects that are 
> non-relations, which ultimately make sense of all relations. These 
> non-relations are the non-mathematical objects and they (or at least some 
> of them) may be the qualities of consciousness (qualia) - because (1) they 
> have an unanalyzable/unstructured nature, and (2) they stand in relations 
> to other objects (relations or non-relations) that we call "correlates of 
> consciousness".
>
>
> Can  you clarify with some examples?
>

Relation is an object that holds between other objects. (By the way, all 
relations are instances of the similarity relation, which means that the 
objects between which a similarity relation holds have some same property 
and some different property.) But how could there only be relations between 
other relations that are relations between other relations etc., just 
relations? It seems that the definition of all those relations would be 
infinitely postponed; they would never be defined. And if you wanted to 
make a finite structure of relations that is ultimately cyclical, where 
relations are defined in relation to each other, every relation in that 
structure would end up being defined as a relation between *itself* and 
other relations. Which is another nonsense, because a relation holds 
between *other* objects than itself.

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/21/2018 7:11 AM, Tomas Pales wrote:
I am generally sympathetic to Tegmark's mathematical multiverse idea, 
but I have two comments/criticisms to it:


1) I am not sure whether Tegmark is aware of the so-called 
"instantiation" relation. In philosophy, the instantiation relation is 
the relation between a general and a particular object, where the 
particular object is an instance of the general object. In other 
words, the general object is a property of the particular object. 
Example: general triangle (or triangle "in general") is the property 
of any particular triangle, and any particular triangle is an instance 
of general triangle. Another example: number 2 is a general relation 
that is instantiated in the particular relation between any two 
objects. I am not sure whether Tegmark realizes the difference between 
general objects and their instances, because he said something like: 
when we probe matter we only find numbers (and hence reality is just 
mathematics). But numbers cannot be found in our world; you cannot 
find number 2 sitting on a tree or in the atomic nucleus. You can only 
find instances of number 2, as relations between particular objects. 
Mathematical objects are usually thought to be general objects, but in 
that case there is more in reality than mathematical objects: there 
are general objects /and/ their instances. And in our physical world 
there are /no/ general objects, only their instances. If we want to 
say that there are mathematical objects in our physical world, we 
should include among mathematical objects also non-general objects, 
that is, objects that have no instances. (By the way, there is a 
hierarchy of generality: more general objects are instantiated in less 
general objects and those are ultimately instantiated in non-general 
objects. Non-general objects are often called "concrete", while 
general objects are also called "abstract".)


This appears not to be a well-order hierarchy.  The thing I am sitting 
on is an instance of a chair, and it's concrete.  But it's also an 
instance of a matter, i.e. a collection of particles of the Standard 
Model (which may or may not be the most general category). It's also an 
instance of things I own.




2) While I agree with Tegmark that reality contains all mathematical 
objects (both general and non-general), I think there is also a 
non-mathematical aspect of reality. That's because mathematical 
objects are relations or structures of relations, but relations cannot 
exist without objects between which they hold. While it is true that 
relations can hold between other relations, there should also be 
objects that are non-relations, which ultimately make sense of all 
relations. These non-relations are the non-mathematical objects and 
they (or at least some of them) may be the qualities of consciousness 
(qualia) - because (1) they have an unanalyzable/unstructured nature, 
and (2) they stand in relations to other objects (relations or 
non-relations) that we call "correlates of consciousness".


Can  you clarify with some examples?

Brent

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, October 21, 2018 at 11:30:54 AM UTC-5, Tomas Pales wrote:
>
>
>
> On Sunday, October 21, 2018 at 5:22:20 PM UTC+2, Philip Thrift wrote:
>>
>>
>> BTW,  on "non-relations [which] are the non-mathematical objects and they 
>> (or at least some of them) may be the qualities of consciousness (qualia)", 
>> that is what I try to address in 
>>
>> 
>> https://codicalist.wordpress.com/2018/10/14/experience-processing/
>>
>> where there is information processing (which is all mathematical 
>> processing) and something else: experience processing.
>>
>> - pt
>>
>
> I would say that any description is relational and therefore 
> mathematical/logical. When you describe an object you always define/present 
> it in relations to other objects - in relations to its parts or properties. 
> You can't describe the object itself, only give it a label. So you can't 
> describe qualities of consciousness themselves either. Not sure how you 
> would "process" them then.
>
> Is there really a fundamental difference between hardware and software? I 
> mean, software can be seen as part of hardware: software is a particular 
> configuration of electron flows in hardware.
>


Mathematics is genre of fiction 
[ https://plato.stanford.edu/entries/fictionalism-mathematics/ ], so 
relations are fictional. "Processing" relations/mathematics has no real 
meaning.

The difference between hardware and software today is somewhat blurred with 
synthetic biology, programmable matter, reconfigurable hardware.

- pt

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Sunday, October 21, 2018 at 5:22:20 PM UTC+2, Philip Thrift wrote:
>
>
> BTW,  on "non-relations [which] are the non-mathematical objects and they 
> (or at least some of them) may be the qualities of consciousness (qualia)", 
> that is what I try to address in 
>
> https://codicalist.wordpress.com/2018/10/14/experience-processing/
>
> where there is information processing (which is all mathematical 
> processing) and something else: experience processing.
>
> - pt
>

I would say that any description is relational and therefore 
mathematical/logical. When you describe an object you always define/present 
it in relations to other objects - in relations to its parts or properties. 
You can't describe the object itself, only give it a label. So you can't 
describe qualities of consciousness themselves either. Not sure how you 
would "process" them then.

Is there really a fundamental difference between hardware and software? I 
mean, software can be seen as part of hardware: software is a particular 
configuration of electron flows in hardware.

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Sunday, October 21, 2018 at 5:52:13 PM UTC+2, Philip Thrift wrote:
>
>
> If our universe does not have infinitely-computing objects but there are 
> other universes that do, that would seem strange.
>
> Why would our universe be left out? :)
>
>
The mathematical multiverse would contain all possible (consistently 
defined) mathematical structures, both finite and infinite. We would live 
in a finite one. Why? I don't know. Maybe just by accident. Or maybe only 
finite structures can contain conscious entities.  

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, October 21, 2018 at 10:43:28 AM UTC-5, Tomas Pales wrote:
>
>
>
> On Sunday, October 21, 2018 at 4:28:21 PM UTC+2, Philip Thrift wrote:
>
>>
>>   "reality contains all mathematical objects"
>>
>>
>> Ironically, Tegmark doesn't believe that at all. He says infinite 
>> mathematical entities are "ruining physics".
>> - 
>> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/
>>
>>
>> The only thing to conclude is that Mad Max published his mathematical 
>> universe hypothesis as a joke!
>> - https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
>>
>
> Already in his Mathematical Universe paper on arxiv, Tegmark discussed a 
> restricted version of MUH called CUH (computable universe hypothesis). He 
> mentioned that the attractive feature of CUH would be the disappearance of 
> the measure problem and also the exclusion of structures of which we may 
> never know whether they are consistent (due to Godel's second 
> incompleteness theorem) and thus whether they exist. On the other hand, the 
> fact that we cannot calculate probabilities (the measure problem) or find 
> whether a structure is consistent seems like an epistemic problem, not an 
> ontological one. The infinities may exist in reality, we just can't extract 
> useful statistics from them or confirm their existence. But reality doesn't 
> depend on whether we find it useful or whether we can confirm its existence.
>
> The universe in which we live, or even the inflationary multiverse, may be 
> a finite/computable structure but there may also be infinite structures in 
> the larger mathematical multiverse.  
>




If our universe does not have infinitely-computing objects but there are 
other universes that do, that would seem strange.

Why would our universe be left out? :)

- pt 

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

On Sunday, October 21, 2018 at 4:28:21 PM UTC+2, Philip Thrift wrote:

>
>   "reality contains all mathematical objects"
>
>
> Ironically, Tegmark doesn't believe that at all. He says infinite 
> mathematical entities are "ruining physics".
> - 
> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/
>
>
> The only thing to conclude is that Mad Max published his mathematical 
> universe hypothesis as a joke!
> - https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
>

Already in his Mathematical Universe paper on arxiv, Tegmark discussed a 
restricted version of MUH called CUH (computable universe hypothesis). He 
mentioned that the attractive feature of CUH would be the disappearance of 
the measure problem and also the exclusion of structures of which we may 
never know whether they are consistent (due to Godel's second 
incompleteness theorem) and thus whether they exist. On the other hand, the 
fact that we cannot calculate probabilities (the measure problem) or find 
whether a structure is consistent seems like an epistemic problem, not an 
ontological one. The infinities may exist in reality, we just can't extract 
useful statistics from them or confirm their existence. But reality doesn't 
depend on whether we find it useful or whether we can confirm its existence.

The universe in which we live, or even the inflationary multiverse, may be 
a finite/computable structure but there may also be infinite structures in 
the larger mathematical multiverse.  

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, October 21, 2018 at 9:28:21 AM UTC-5, Philip Thrift wrote:
>
>
>
> On Sunday, October 21, 2018 at 9:11:03 AM UTC-5, Tomas Pales wrote:
>>
>> I am generally sympathetic to Tegmark's mathematical multiverse idea, but 
>> I have two comments/criticisms to it:
>>
>> 1) I am not sure whether Tegmark is aware of the so-called 
>> "instantiation" relation. In philosophy, the instantiation relation is the 
>> relation between a general and a particular object, where the particular 
>> object is an instance of the general object. In other words, the general 
>> object is a property of the particular object. Example: general triangle 
>> (or triangle "in general") is the property of any particular triangle, and 
>> any particular triangle is an instance of general triangle. Another 
>> example: number 2 is a general relation that is instantiated in the 
>> particular relation between any two objects. I am not sure whether Tegmark 
>> realizes the difference between general objects and their instances, 
>> because he said something like: when we probe matter we only find numbers 
>> (and hence reality is just mathematics). But numbers cannot be found in our 
>> world; you cannot find number 2 sitting on a tree or in the atomic nucleus. 
>> You can only find instances of number 2, as relations between particular 
>> objects. Mathematical objects are usually thought to be general objects, 
>> but in that case there is more in reality than mathematical objects: there 
>> are general objects *and* their instances. And in our physical world 
>> there are *no* general objects, only their instances. If we want to say 
>> that there are mathematical objects in our physical world, we should 
>> include among mathematical objects also non-general objects, that is, 
>> objects that have no instances. (By the way, there is a hierarchy of 
>> generality: more general objects are instantiated in less general objects 
>> and those are ultimately instantiated in non-general objects. Non-general 
>> objects are often called "concrete", while general objects are also called 
>> "abstract".)
>>
>> 2) While I agree with Tegmark that reality contains all mathematical 
>> objects (both general and non-general), I think there is also a 
>> non-mathematical aspect of reality. That's because mathematical objects are 
>> relations or structures of relations, but relations cannot exist without 
>> objects between which they hold. While it is true that relations can hold 
>> between other relations, there should also be objects that are 
>> non-relations, which ultimately make sense of all relations. These 
>> non-relations are the non-mathematical objects and they (or at least some 
>> of them) may be the qualities of consciousness (qualia) - because (1) they 
>> have an unanalyzable/unstructured nature, and (2) they stand in relations 
>> to other objects (relations or non-relations) that we call "correlates of 
>> consciousness".
>>
>> Tomas
>>
>
>
>
>
>   "reality contains all mathematical objects"
>
>
> Ironically, Tegmark doesn't believe that at all. He says infinite 
> mathematical entities are "ruining physics".
> - 
> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/
>
>
> The only thing to conclude is that Mad Max published his mathematical 
> universe hypothesis as a joke!
> - https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
>
>
> - pt 
>


BTW,  on "non-relations [which] are the non-mathematical objects and they 
(or at least some of them) may be the qualities of consciousness (qualia)", 
that is what I try to address in 

https://codicalist.wordpress.com/2018/10/14/experience-processing/

where there is information processing (which is all mathematical 
processing) and something else: experience processing.

- pt

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, October 21, 2018 at 9:11:03 AM UTC-5, Tomas Pales wrote:
>
> I am generally sympathetic to Tegmark's mathematical multiverse idea, but 
> I have two comments/criticisms to it:
>
> 1) I am not sure whether Tegmark is aware of the so-called "instantiation" 
> relation. In philosophy, the instantiation relation is the relation between 
> a general and a particular object, where the particular object is an 
> instance of the general object. In other words, the general object is a 
> property of the particular object. Example: general triangle (or triangle 
> "in general") is the property of any particular triangle, and any 
> particular triangle is an instance of general triangle. Another example: 
> number 2 is a general relation that is instantiated in the particular 
> relation between any two objects. I am not sure whether Tegmark realizes 
> the difference between general objects and their instances, because he said 
> something like: when we probe matter we only find numbers (and hence 
> reality is just mathematics). But numbers cannot be found in our world; you 
> cannot find number 2 sitting on a tree or in the atomic nucleus. You can 
> only find instances of number 2, as relations between particular objects. 
> Mathematical objects are usually thought to be general objects, but in that 
> case there is more in reality than mathematical objects: there are general 
> objects *and* their instances. And in our physical world there are *no* 
> general objects, only their instances. If we want to say that there are 
> mathematical objects in our physical world, we should include among 
> mathematical objects also non-general objects, that is, objects that have 
> no instances. (By the way, there is a hierarchy of generality: more general 
> objects are instantiated in less general objects and those are ultimately 
> instantiated in non-general objects. Non-general objects are often called 
> "concrete", while general objects are also called "abstract".)
>
> 2) While I agree with Tegmark that reality contains all mathematical 
> objects (both general and non-general), I think there is also a 
> non-mathematical aspect of reality. That's because mathematical objects are 
> relations or structures of relations, but relations cannot exist without 
> objects between which they hold. While it is true that relations can hold 
> between other relations, there should also be objects that are 
> non-relations, which ultimately make sense of all relations. These 
> non-relations are the non-mathematical objects and they (or at least some 
> of them) may be the qualities of consciousness (qualia) - because (1) they 
> have an unanalyzable/unstructured nature, and (2) they stand in relations 
> to other objects (relations or non-relations) that we call "correlates of 
> consciousness".
>
> Tomas
>




  "reality contains all mathematical objects"


Ironically, Tegmark doesn't believe that at all. He says infinite 
mathematical entities are "ruining physics".
- http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/


The only thing to conclude is that Mad Max published his mathematical 
universe hypothesis as a joke!
- https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis


- pt 

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Re: Mathematical Universe Hypothesis

[Tomas Pales]

I am generally sympathetic to Tegmark's mathematical multiverse idea, but I 
have two comments/criticisms to it:

1) I am not sure whether Tegmark is aware of the so-called "instantiation" 
relation. In philosophy, the instantiation relation is the relation between 
a general and a particular object, where the particular object is an 
instance of the general object. In other words, the general object is a 
property of the particular object. Example: general triangle (or triangle 
"in general") is the property of any particular triangle, and any 
particular triangle is an instance of general triangle. Another example: 
number 2 is a general relation that is instantiated in the particular 
relation between any two objects. I am not sure whether Tegmark realizes 
the difference between general objects and their instances, because he said 
something like: when we probe matter we only find numbers (and hence 
reality is just mathematics). But numbers cannot be found in our world; you 
cannot find number 2 sitting on a tree or in the atomic nucleus. You can 
only find instances of number 2, as relations between particular objects. 
Mathematical objects are usually thought to be general objects, but in that 
case there is more in reality than mathematical objects: there are general 
objects *and* their instances. And in our physical world there are *no* 
general objects, only their instances. If we want to say that there are 
mathematical objects in our physical world, we should include among 
mathematical objects also non-general objects, that is, objects that have 
no instances. (By the way, there is a hierarchy of generality: more general 
objects are instantiated in less general objects and those are ultimately 
instantiated in non-general objects. Non-general objects are often called 
"concrete", while general objects are also called "abstract".)

2) While I agree with Tegmark that reality contains all mathematical 
objects (both general and non-general), I think there is also a 
non-mathematical aspect of reality. That's because mathematical objects are 
relations or structures of relations, but relations cannot exist without 
objects between which they hold. While it is true that relations can hold 
between other relations, there should also be objects that are 
non-relations, which ultimately make sense of all relations. These 
non-relations are the non-mathematical objects and they (or at least some 
of them) may be the qualities of consciousness (qualia) - because (1) they 
have an unanalyzable/unstructured nature, and (2) they stand in relations 
to other objects (relations or non-relations) that we call "correlates of 
consciousness".

Tomas

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 4 Oct 2018, at 18:51, Brent Meeker  wrote:
> 
> 
> 
> On 10/4/2018 12:06 AM, Bruno Marchal wrote:
>> You need a universal machinery. Very elementary arithmetic (like Peano 
>> without induction) determines such a universal machinery (the phi_i), then, 
>> you get all the universal number u (such that phi_u(x,y) = phi_x(y), and 
>> each u defines its own universal machinerery: phi_u(0, _), phi_u(0, _), 
>> phi_u(1, _), phi_u(2, _), …
>> 
>> All universal “thing” mimic all universal “thing”, but they have special 
>> statistical relation, and different personal beliefs. They determine (in the 
>> arithmetical reality) the “consciousness flux”, which determine the 
>> (unique!) physical reality, which is a sort of multiverse/multi-dreams.
>> 
>> 
>> 
>> 
>>> 
>>> What would be the programs and languages (π,λ) that could be defined?
>>> 
>>> 
>> 
>> All of them, but with their different relative measure. They are 
>> mathematically determined by the G* logic (self-referential truth).
> 
> What is the measure on universal machines in arithmetic?

It is given by the “Gleason-like” unique measure on the proposition entailed by 
the variants of the logic of self-reference: mainly, with p 
sigma_1-arithmetical (or combinatorical) sentences, the variants are given by 
[]p & p, []p & <>t and []p & <>t & p. The facts that we obtain quantum logics 
there is a good sign, but much more work need to be done to get the 
mathematical form and uniqueness of it.If there is no such measure, which is 
still possible, Mechanism would be refuted. Up to now, the three quantum logic 
does not depart from the minimal quantum logic, part of all quantum logic 
inferred from the observation.

Bruno



> 
> Brent
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 4 Oct 2018, at 12:57, Philip Thrift  wrote:
> 
> 
> 
> On Thursday, October 4, 2018 at 2:06:30 AM UTC-5, Bruno Marchal wrote:
> 
>> On 3 Oct 2018, at 22:07, Philip Thrift > 
>> wrote:
>> 
>> 
>> Suppose one starts with the PLTOS template:
>> 
>> PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ that 
>> is transformed via a compiler/assembler τ into an output object ο that 
>> executes in a computing substrate Σ.
>> 
>> 
>> 
>> Suppose Σ = UniversalNumbers 
>> 
>> 
>> 
>> That is, the computing substrate is the actual Universal Numbers (arithmetic 
>> reality).
>> 
>> 
> 
> You need a universal machinery. Very elementary arithmetic (like Peano 
> without induction) determines such a universal machinery (the phi_i), then, 
> you get all the universal number u (such that phi_u(x,y) = phi_x(y), and each 
> u defines its own universal machinerery: phi_u(0, _), phi_u(0, _), phi_u(1, 
> _), phi_u(2, _), …
> 
> All universal “thing” mimic all universal “thing”, but they have special 
> statistical relation, and different personal beliefs. They determine (in the 
> arithmetical reality) the “consciousness flux”, which determine the (unique!) 
> physical reality, which is a sort of multiverse/multi-dreams.
> 
>> 
>> What would be the programs and languages (π,λ) that could be defined?
>> 
>> 
> 
> All of them, but with their different relative measure. They are 
> mathematically determined by the G* logic (self-referential truth).
> 
> Bruno
> 
> 
> 
> 
> 
> Approaching this with a PLTOS template identifies the parts  π,λ,τ,ο,Σ. What 
> is the compiler/assembler τ for example?
> 
> (PLTOS is a bit of a play-on-words: It looks like PLT Operating System.)
> 
> In PLT (programming language theory), one part of comprehending the whole 
> shebang is in terms of semantics, specifically its denotational vs 
> operational semantics [ 
> http://courses.cs.vt.edu/~cs3304/Spring04/notes/Chapter-3b ].
> 
> In the case of "real" hardware Σ (is there a CPU or a GPU or a TPU - Google's 
> NN chip?) then the operational semantics are significant.
> 
> In the case of Σ = UniversalNumbers/UniversalMachine it is a bit difficult to 
> see what the operational semantics would be.


It is the association i ==> phi_i, that is of a function (seen as infinite set 
of input/ouput) to its code, or anything recursively equivalent. Some caution 
is needed here, but they are not so important, because the main semantics will 
be brought by the machine/code themselves, by the numbers bring to figure out 
what happens, like we do now. The theology (including the physics) is 
independent of the choice of the initial universal system. I use elementary 
arithmetic (which has a simple familiar semantics), or the combinators (which 
are operationally easy, even if the usual extensional semantics is not obvious, 
but eventually clarified by the denotational work of Dana Scott). The hardware 
and software distinction is locally relative, but eventually, the hardware get 
absolute by being a first person statistics on all software possible below our 
substitution level. This follows simply from the first person/third person 
distinction.

Bruno



> 
> - pt
> 
> 
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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/4/2018 12:06 AM, Bruno Marchal wrote:
You need a universal machinery. Very elementary arithmetic (like Peano 
without induction) determines such a universal machinery (the phi_i), 
then, you get all the universal number u (such that phi_u(x,y) = 
phi_x(y), and each u defines its own universal machinerery: phi_u(0, 
_), phi_u(0, _), phi_u(1, _), phi_u(2, _), …


All universal “thing” mimic all universal “thing”, but they have 
special statistical relation, and different personal beliefs. They 
determine (in the arithmetical reality) the “consciousness flux”, 
which determine the (unique!) physical reality, which is a sort of 
multiverse/multi-dreams.







What would be the programs and languages (π,λ) that could be defined?




All of them, but with their different relative measure. They are 
mathematically determined by the G* logic (self-referential truth).


What is the measure on universal machines in arithmetic?

Brent

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, October 4, 2018 at 2:06:30 AM UTC-5, Bruno Marchal wrote:
>
>
> On 3 Oct 2018, at 22:07, Philip Thrift > 
> wrote:
>
>
> Suppose one starts with the PLTOS template:
>
> PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ 
> that is transformed via a compiler/assembler τ into an output object ο that 
> executes in a computing substrate Σ.
>
>
> Suppose Σ = *UniversalNumbers* 
>
>
> That is, the computing substrate is the actual Universal Numbers 
> (arithmetic reality).
>
>
> You need a universal machinery. Very elementary arithmetic (like Peano 
> without induction) determines such a universal machinery (the phi_i), then, 
> you get all the universal number u (such that phi_u(x,y) = phi_x(y), and 
> each u defines its own universal machinerery: phi_u(0, _), phi_u(0, _), 
> phi_u(1, _), phi_u(2, _), …
>
> All universal “thing” mimic all universal “thing”, but they have special 
> statistical relation, and different personal beliefs. They determine (in 
> the arithmetical reality) the “consciousness flux”, which determine the 
> (unique!) physical reality, which is a sort of multiverse/multi-dreams.
>
>
> What would be the programs and languages (π,λ) that could be defined?
>
>
> All of them, but with their different relative measure. They are 
> mathematically determined by the G* logic (self-referential truth).
>
> Bruno
>
>
>


Approaching this with a *PLTOS* template identifies the parts  π,λ,τ,ο,Σ. 
What is the compiler/assembler τ for example?

(PLTOS is a bit of a play-on-words: It looks like PLT Operating System.)

In PLT (programming language theory), one part of comprehending the whole 
shebang is in terms of semantics, specifically its denotational vs 
operational semantics 
[ http://courses.cs.vt.edu/~cs3304/Spring04/notes/Chapter-3b ].

In the case of "real" hardware Σ (is there a CPU or a GPU or a TPU - 
Google's NN chip?) then the operational semantics are significant.

In the case of Σ = UniversalNumbers/UniversalMachine it is a bit difficult 
to see what the operational semantics would be.

- pt



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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 3 Oct 2018, at 22:07, Philip Thrift  wrote:
> 
> 
> 
> On Wednesday, October 3, 2018 at 2:54:46 AM UTC-5, Bruno Marchal wrote:
> 
>> On 2 Oct 2018, at 17:11, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Tuesday, October 2, 2018 at 9:25:17 AM UTC-5, Bruno Marchal wrote:
>> 
>>> On 2 Oct 2018, at 09:53, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote:
>>> 
 On 1 Oct 2018, at 14:20, agrays...@gmail.com <> wrote:
 
 
 
 On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
 
> On 30 Sep 2018, at 16:30, Philip Thrift > wrote:
> 
> 
> 
> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
> [Re:] forcing theory in set theories with classes. 
> 
> 
> Bruno
> 
> 
> 
> Do you follow the work of Joel David Hamkins (forcing applied to 
> set-theoretic "multiverse", etc.)
> 
> (I have a basic idea of a type-theoretic parallel to this.)
> 
> The set-theoretic multiverse
> 
> https://arxiv.org/abs/1108.4223 
> 
> Joel David Hamkins
> @JDHamkins
> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow 
> in Philosophy, University College Oxford. Formerly of New York.
> http://jdh.hamkins.org 
> 
 
 The math is interesting, and could be of some use, but it is a priori far 
 too much Aristotelian to be coherent with the mechanist hypothesis. That 
 should follow “easily” from the result described in most of my papers on 
 this subject. The author does not seem aware of the mind-body problem, 
 which put extreme constraints on what the physical reality can come from. 
 Even Peano arithmetic, although integral part of the notion of observer, 
 is too much rich for the ontology, where not only the axiom of infinity is 
 too strong,
 
 Since you want to banish the concept of infinity from mathematics, how 
 would you define, say, the limit of an "infinite" series? How would you 
 even discuss this series in the context of finite mathematics? AG
>>> 
>>> 
>>> Good question.
>>> 
>>> The answer is not simple technically. The point is that using only the 
>>> theory Q (Robinson Arithmetic) or SK (the combinators), I can define the 
>>> universal (Turing, Church) machine, and the concept of infinity will be a 
>>> tool used by them in their mathematics.
>>> 
>>> I do not ban anything from mathematics, nor from physics. I ban only 
>>> infinity from the ontological terms. I ban only infinity in the 
>>> metaphysics/theology. (Even God is not ontological, like in Proclus or 
>>> Plotinus theology).
>>> 
>>> Have you understand the post on Church’s thesis. You might tell me as this 
>>> will help me to see how to proceed to make you grasp all this.
>>> 
>>> Bruno
>>> 
>>> 
>>> 
>>> 
>>> What do you think of bounded arithmetic and other "finitist" approaches?
>>> 
>>> https://en.wikipedia.org/wiki/Bounded_arithmetic 
>>> 
>>> see bibliography: 
>>> http://jeanpaulvanbendegem.be/home/papers/strict-finitism/ 
>>> 
>> 
>> I wrote a paper on this, in a book in honour to Jean-paul Vanbendegem. But 
>> its approach is more than finitist, and a bit less than ultra-finitism. It 
>> does not fit the study of the “theology” of the machine, and is thus useless 
>> for deriving physics. That does not mean it is not interesting 
>> pragmatically, on the contrary, it is well fitted with the goal to make 
>> usable programs. I do think that mathematically, it is also a restriction of 
>> Post creativity (Turing universality in set theoretical terms) to sub 
>> creativity. There is no possible universal machine there.
>> 
>> 
>> 
>> 
>>> 
>>> Computable real analysis (one can teach computable calculus instead of 
>>> "conventional" calculus) is essentially finitist:
>>> https://en.wikipedia.org/wiki/Computable_analysis 
>>> 
>>> 
>>> One can formulate the Axiom of Infinity [ 
>>> https://en.wikipedia.org/wiki/Axiom_of_infinity 
>>>  ] in a type of bounded 
>>> set theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski 
>>>  ], described in 
>>> https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC
>>>  
>>> 
>>>  ]. What results is an "ontology" of bigger and bigger finite sets of 
>>> numbers with gaps in them.
>> 
>> 
>> Yes, and that is interesting. But not so much for the mind-body problem, 
>> where we cannot bound anything, except by omega. 
>> 
>> The weaker theory known from which my approach can work, is the 

Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Wednesday, October 3, 2018 at 2:54:46 AM UTC-5, Bruno Marchal wrote:
>
>
> On 2 Oct 2018, at 17:11, Philip Thrift > 
> wrote:
>
>
>
> On Tuesday, October 2, 2018 at 9:25:17 AM UTC-5, Bruno Marchal wrote:
>>
>>
>> On 2 Oct 2018, at 09:53, Philip Thrift  wrote:
>>
>>
>>
>> On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote:
>>>
>>>
>>> On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:


 On 30 Sep 2018, at 16:30, Philip Thrift  wrote:



 On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
>
> [Re:] forcing theory in set theories with classes. 
>
>
> Bruno
>
>
>
 Do you follow the work of Joel David Hamkins (forcing applied to 
 set-theoretic "multiverse", etc.)

 (I have a basic idea of a type-theoretic parallel to this.)

 *The set-theoretic multiverse*
 https://arxiv.org/abs/1108.4223

 Joel David Hamkins
 @JDHamkins
 Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow 
 in Philosophy, University College Oxford. Formerly of New York.
 http://jdh.hamkins.org


 The math is interesting, and could be of some use, but it is a priori 
 far too much Aristotelian to be coherent with the mechanist hypothesis. 
 That should follow “easily” from the result described in most of my papers 
 on this subject. The author does not seem aware of the mind-body problem, 
 which put extreme constraints on what the physical reality can come from. 
 Even Peano arithmetic, although integral part of the notion of observer, 
 is 
 too much rich for the ontology, where not only the axiom of infinity is 
 too 
 strong, 

>>>
>>> *Since you want to banish the concept of infinity from mathematics, how 
>>> would you define, say, the limit of an "infinite" series? How would you 
>>> even discuss this series in the context of finite mathematics? AG*
>>>
>>>
>>>
>>> Good question.
>>>
>>> The answer is not simple technically. The point is that using only the 
>>> theory Q (Robinson Arithmetic) or SK (the combinators), I can define the 
>>> universal (Turing, Church) machine, and the concept of infinity will be a 
>>> tool used by them in their mathematics.
>>>
>>> I do not ban anything from mathematics, nor from physics. I ban only 
>>> infinity from the ontological terms. I ban only infinity in the 
>>> metaphysics/theology. (Even God is not ontological, like in Proclus or 
>>> Plotinus theology).
>>>
>>> Have you understand the post on Church’s thesis. You might tell me as 
>>> this will help me to see how to proceed to make you grasp all this.
>>>
>>> Bruno
>>>
>>>
>>>
>>
>> What do you think of bounded arithmetic and other "finitist" approaches?
>>
>> https://en.wikipedia.org/wiki/Bounded_arithmetic
>> see bibliography: 
>> http://jeanpaulvanbendegem.be/home/papers/strict-finitism/
>>
>>
>> I wrote a paper on this, in a book in honour to Jean-paul Vanbendegem. 
>> But its approach is more than finitist, and a bit less than ultra-finitism. 
>> It does not fit the study of the “theology” of the machine, and is thus 
>> useless for deriving physics. That does not mean it is not interesting 
>> pragmatically, on the contrary, it is well fitted with the goal to make 
>> usable programs. I do think that mathematically, it is also a restriction 
>> of Post creativity (Turing universality in set theoretical terms) to sub 
>> creativity. There is no possible universal machine there.
>>
>>
>>
>>
>>
>> Computable real analysis (one can teach computable calculus instead of 
>> "conventional" calculus) is essentially finitist:
>> https://en.wikipedia.org/wiki/Computable_analysis
>>
>> One can formulate the *Axiom of Infinity* [ 
>> https://en.wikipedia.org/wiki/Axiom_of_infinity ] in a type of bounded 
>> set theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski 
>> ], described in 
>> https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC
>>  
>> ]. What results is an "ontology" of bigger and bigger finite sets of 
>> numbers with gaps in them.
>>
>>
>>
>> Yes, and that is interesting. But not so much for the mind-body problem, 
>> where we cannot bound anything, except by omega. 
>>
>> The weaker theory known from which my approach can work, is the 
>> delta_0-induction based on Q + the axioms for the exponential, known as 
>> Delta_0Exp. That is Q:
>>
>> 1) 0 ≠ s(x)
>> 2) x ≠ y -> s(x) ≠ s(y)
>> 3) x ≠ 0 -> Ey(x = s(y)) 
>> 4) x+0 = x
>> 5) x+s(y) = s(x+y)
>> 6) x*0=0
>> 7) x*s(y)=(x*y)+x
>>
>> + 
>>
>> 8) x^0 = 1
>> 9) x^s(y) = x * (x^y)
>>
>> + the scheme of induction axioms:
>>
>> P(0) & [For all n (P(n) -> P(s(n)))] ->. For all n P(n),
>>
>> with P restricted to the delta_0 (= sigma_0 = pi_0 = recursive, 
>> decidable, …) formula.
>>
>>
>>
>> That is the weaker Löbian machine known 

Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 2 Oct 2018, at 17:11, Philip Thrift  wrote:
> 
> 
> 
> On Tuesday, October 2, 2018 at 9:25:17 AM UTC-5, Bruno Marchal wrote:
> 
>> On 2 Oct 2018, at 09:53, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote:
>> 
>>> On 1 Oct 2018, at 14:20, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
>>> 
 On 30 Sep 2018, at 16:30, Philip Thrift > wrote:
 
 
 
 On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
 [Re:] forcing theory in set theories with classes. 
 
 
 Bruno
 
 
 
 Do you follow the work of Joel David Hamkins (forcing applied to 
 set-theoretic "multiverse", etc.)
 
 (I have a basic idea of a type-theoretic parallel to this.)
 
 The set-theoretic multiverse
 
 https://arxiv.org/abs/1108.4223 
 
 Joel David Hamkins
 @JDHamkins
 Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in 
 Philosophy, University College Oxford. Formerly of New York.
 http://jdh.hamkins.org 
 
>>> 
>>> The math is interesting, and could be of some use, but it is a priori far 
>>> too much Aristotelian to be coherent with the mechanist hypothesis. That 
>>> should follow “easily” from the result described in most of my papers on 
>>> this subject. The author does not seem aware of the mind-body problem, 
>>> which put extreme constraints on what the physical reality can come from. 
>>> Even Peano arithmetic, although integral part of the notion of observer, is 
>>> too much rich for the ontology, where not only the axiom of infinity is too 
>>> strong,
>>> 
>>> Since you want to banish the concept of infinity from mathematics, how 
>>> would you define, say, the limit of an "infinite" series? How would you 
>>> even discuss this series in the context of finite mathematics? AG
>> 
>> 
>> Good question.
>> 
>> The answer is not simple technically. The point is that using only the 
>> theory Q (Robinson Arithmetic) or SK (the combinators), I can define the 
>> universal (Turing, Church) machine, and the concept of infinity will be a 
>> tool used by them in their mathematics.
>> 
>> I do not ban anything from mathematics, nor from physics. I ban only 
>> infinity from the ontological terms. I ban only infinity in the 
>> metaphysics/theology. (Even God is not ontological, like in Proclus or 
>> Plotinus theology).
>> 
>> Have you understand the post on Church’s thesis. You might tell me as this 
>> will help me to see how to proceed to make you grasp all this.
>> 
>> Bruno
>> 
>> 
>> 
>> 
>> What do you think of bounded arithmetic and other "finitist" approaches?
>> 
>> https://en.wikipedia.org/wiki/Bounded_arithmetic 
>> 
>> see bibliography: http://jeanpaulvanbendegem.be/home/papers/strict-finitism/ 
>> 
> 
> I wrote a paper on this, in a book in honour to Jean-paul Vanbendegem. But 
> its approach is more than finitist, and a bit less than ultra-finitism. It 
> does not fit the study of the “theology” of the machine, and is thus useless 
> for deriving physics. That does not mean it is not interesting pragmatically, 
> on the contrary, it is well fitted with the goal to make usable programs. I 
> do think that mathematically, it is also a restriction of Post creativity 
> (Turing universality in set theoretical terms) to sub creativity. There is no 
> possible universal machine there.
> 
> 
> 
> 
>> 
>> Computable real analysis (one can teach computable calculus instead of 
>> "conventional" calculus) is essentially finitist:
>> https://en.wikipedia.org/wiki/Computable_analysis 
>> 
>> 
>> One can formulate the Axiom of Infinity [ 
>> https://en.wikipedia.org/wiki/Axiom_of_infinity 
>>  ] in a type of bounded set 
>> theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski 
>>  ], described in 
>> https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC
>>  
>> 
>>  ]. What results is an "ontology" of bigger and bigger finite sets of 
>> numbers with gaps in them.
> 
> 
> Yes, and that is interesting. But not so much for the mind-body problem, 
> where we cannot bound anything, except by omega. 
> 
> The weaker theory known from which my approach can work, is the 
> delta_0-induction based on Q + the axioms for the exponential, known as 
> Delta_0Exp. That is Q:
> 
> 1) 0 ≠ s(x)
> 2) x ≠ y -> s(x) ≠ s(y)
> 3) x ≠ 0 -> Ey(x = s(y)) 
> 4) x+0 = x
> 5) x+s(y) = s(x+y)
> 6) x*0=0
> 7) x*s(y)=(x*y)+x
> 
> + 
> 
> 8) x^0 = 1

Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Tuesday, October 2, 2018 at 9:25:17 AM UTC-5, Bruno Marchal wrote:
>
>
> On 2 Oct 2018, at 09:53, Philip Thrift > 
> wrote:
>
>
>
> On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote:
>>
>>
>> On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 30 Sep 2018, at 16:30, Philip Thrift  wrote:
>>>
>>>
>>>
>>> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:

 [Re:] forcing theory in set theories with classes. 


 Bruno



>>> Do you follow the work of Joel David Hamkins (forcing applied to 
>>> set-theoretic "multiverse", etc.)
>>>
>>> (I have a basic idea of a type-theoretic parallel to this.)
>>>
>>> *The set-theoretic multiverse*
>>> https://arxiv.org/abs/1108.4223
>>>
>>> Joel David Hamkins
>>> @JDHamkins
>>> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow 
>>> in Philosophy, University College Oxford. Formerly of New York.
>>> http://jdh.hamkins.org
>>>
>>>
>>> The math is interesting, and could be of some use, but it is a priori 
>>> far too much Aristotelian to be coherent with the mechanist hypothesis. 
>>> That should follow “easily” from the result described in most of my papers 
>>> on this subject. The author does not seem aware of the mind-body problem, 
>>> which put extreme constraints on what the physical reality can come from. 
>>> Even Peano arithmetic, although integral part of the notion of observer, is 
>>> too much rich for the ontology, where not only the axiom of infinity is too 
>>> strong, 
>>>
>>
>> *Since you want to banish the concept of infinity from mathematics, how 
>> would you define, say, the limit of an "infinite" series? How would you 
>> even discuss this series in the context of finite mathematics? AG*
>>
>>
>>
>> Good question.
>>
>> The answer is not simple technically. The point is that using only the 
>> theory Q (Robinson Arithmetic) or SK (the combinators), I can define the 
>> universal (Turing, Church) machine, and the concept of infinity will be a 
>> tool used by them in their mathematics.
>>
>> I do not ban anything from mathematics, nor from physics. I ban only 
>> infinity from the ontological terms. I ban only infinity in the 
>> metaphysics/theology. (Even God is not ontological, like in Proclus or 
>> Plotinus theology).
>>
>> Have you understand the post on Church’s thesis. You might tell me as 
>> this will help me to see how to proceed to make you grasp all this.
>>
>> Bruno
>>
>>
>>
>
> What do you think of bounded arithmetic and other "finitist" approaches?
>
> https://en.wikipedia.org/wiki/Bounded_arithmetic
> see bibliography: 
> http://jeanpaulvanbendegem.be/home/papers/strict-finitism/
>
>
> I wrote a paper on this, in a book in honour to Jean-paul Vanbendegem. But 
> its approach is more than finitist, and a bit less than ultra-finitism. It 
> does not fit the study of the “theology” of the machine, and is thus 
> useless for deriving physics. That does not mean it is not interesting 
> pragmatically, on the contrary, it is well fitted with the goal to make 
> usable programs. I do think that mathematically, it is also a restriction 
> of Post creativity (Turing universality in set theoretical terms) to sub 
> creativity. There is no possible universal machine there.
>
>
>
>
>
> Computable real analysis (one can teach computable calculus instead of 
> "conventional" calculus) is essentially finitist:
> https://en.wikipedia.org/wiki/Computable_analysis
>
> One can formulate the *Axiom of Infinity* [ 
> https://en.wikipedia.org/wiki/Axiom_of_infinity ] in a type of bounded 
> set theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski 
> ], described in 
> https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC
>  
> ]. What results is an "ontology" of bigger and bigger finite sets of 
> numbers with gaps in them.
>
>
>
> Yes, and that is interesting. But not so much for the mind-body problem, 
> where we cannot bound anything, except by omega. 
>
> The weaker theory known from which my approach can work, is the 
> delta_0-induction based on Q + the axioms for the exponential, known as 
> Delta_0Exp. That is Q:
>
> 1) 0 ≠ s(x)
> 2) x ≠ y -> s(x) ≠ s(y)
> 3) x ≠ 0 -> Ey(x = s(y)) 
> 4) x+0 = x
> 5) x+s(y) = s(x+y)
> 6) x*0=0
> 7) x*s(y)=(x*y)+x
>
> + 
>
> 8) x^0 = 1
> 9) x^s(y) = x * (x^y)
>
> + the scheme of induction axioms:
>
> P(0) & [For all n (P(n) -> P(s(n)))] ->. For all n P(n),
>
> with P restricted to the delta_0 (= sigma_0 = pi_0 = recursive, decidable, 
> …) formula.
>
>
>
> That is the weaker Löbian machine known today.
>
> In between Q and Delta_0Exp, you have all the bounded arithmetics.
>
> An excellent book on this is (without the many accent for the names):
>
> Hajek, P. & Pudlak P., 1993, Metamathematics of First-Order Arithmetic, 
> Springer-Verlag.
>
> But no need of this for the mind body 

Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 2 Oct 2018, at 10:14, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Tuesday, October 2, 2018 at 7:20:10 AM UTC, Bruno Marchal wrote:
> 
>> On 1 Oct 2018, at 14:20, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
>> 
>>> On 30 Sep 2018, at 16:30, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
>>> [Re:] forcing theory in set theories with classes. 
>>> 
>>> 
>>> Bruno
>>> 
>>> 
>>> 
>>> Do you follow the work of Joel David Hamkins (forcing applied to 
>>> set-theoretic "multiverse", etc.)
>>> 
>>> (I have a basic idea of a type-theoretic parallel to this.)
>>> 
>>> The set-theoretic multiverse
>>> 
>>> https://arxiv.org/abs/1108.4223 
>>> 
>>> Joel David Hamkins
>>> @JDHamkins
>>> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in 
>>> Philosophy, University College Oxford. Formerly of New York.
>>> http://jdh.hamkins.org 
>>> 
>> 
>> The math is interesting, and could be of some use, but it is a priori far 
>> too much Aristotelian to be coherent with the mechanist hypothesis. That 
>> should follow “easily” from the result described in most of my papers on 
>> this subject. The author does not seem aware of the mind-body problem, which 
>> put extreme constraints on what the physical reality can come from. Even 
>> Peano arithmetic, although integral part of the notion of observer, is too 
>> much rich for the ontology, where not only the axiom of infinity is too 
>> strong,
>> 
>> Since you want to banish the concept of infinity from mathematics, how would 
>> you define, say, the limit of an "infinite" series? How would you even 
>> discuss this series in the context of finite mathematics? AG
> 
> 
> Good question.
> 
> The answer is not simple technically. The point is that using only the theory 
> Q (Robinson Arithmetic) or SK (the combinators), I can define the universal 
> (Turing, Church) machine, and the concept of infinity will be a tool used by 
> them in their mathematics.
> 
> I do not ban anything from mathematics, nor from physics. I ban only infinity 
> from the ontological terms. I ban only infinity in the metaphysics/theology. 
> (Even God is not ontological, like in Proclus or Plotinus theology).
> 
> Have you understand the post on Church’s thesis. You might tell me as this 
> will help me to see how to proceed to make you grasp all this.
> 
> Bruno
> 
> You only ban infinity from ontological terms? I have no idea what this means.


It means that 0 exist, 1, exists, 2 exists, etc.



> I do know you start with the natural numbers, presumably an infinite set and 
> existing in some Platonic realm.


Not really. Only 0, 1, 2, …

But not {0, 1, 2, 3 …}, which is not a natural number.

It means that my axioms, for the whole theory of everything including 
consciousness is literally just classical logic + the axioms of Q:

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

There is no infinity axiom, nor any infinite object in the intended model. What 
is proved from Q is true in all models (interpretations) of Q.

I don’t even allow the induction axioms, despite the phenomenology use them, as 
Q is rich enough to mimic the believer in the induction axioms, and indeed the 
believer in infinity (like the ZF machine).

To grasp this it is important to understand the difference between compute and 
proof.

Keep in mind that Q can mimic ZF proving the consistence of Q; but that cannot 
convince Q of its consistency (by the second incompleteness theorem of Gödel).






> So I have no idea about your aversion or denial of infinity.

No aversion at all. It is just part of the phenomenology, and if I put it in 
the ontology, the “white rabbits” becomes to numerous, and the physics predicts 
too many things.



> As for the Church's thesis, I have set aside a copy of Chrome with several 
> relevant topics which I see as prerequisites to that understanding including, 
> for example, Cantor's theorem, but have yet to get into it seriously due to 
> personal issues and computer problems in Russia and Ukraine (the latter now 
> solved). But when I do, I'll get back to you. AG


OK. Normally my post was self contained. (Except for the notion of function). 
Ask any question.

Bruno 


> 
> 
> 
> 
> 
>>  
>> but even the induction axioms are too strong. 
>> 
>> Pragmatically, sets and typed lambda terms or typed combinators can indeed 
>> be very useful. 
>> 
>> Bruno
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>>> 
>>> - pt
>>> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 2 Oct 2018, at 09:53, Philip Thrift  wrote:
> 
> 
> 
> On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote:
> 
>> On 1 Oct 2018, at 14:20, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
>> 
>>> On 30 Sep 2018, at 16:30, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
>>> [Re:] forcing theory in set theories with classes. 
>>> 
>>> 
>>> Bruno
>>> 
>>> 
>>> 
>>> Do you follow the work of Joel David Hamkins (forcing applied to 
>>> set-theoretic "multiverse", etc.)
>>> 
>>> (I have a basic idea of a type-theoretic parallel to this.)
>>> 
>>> The set-theoretic multiverse
>>> 
>>> https://arxiv.org/abs/1108.4223 
>>> 
>>> Joel David Hamkins
>>> @JDHamkins
>>> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in 
>>> Philosophy, University College Oxford. Formerly of New York.
>>> http://jdh.hamkins.org 
>>> 
>> 
>> The math is interesting, and could be of some use, but it is a priori far 
>> too much Aristotelian to be coherent with the mechanist hypothesis. That 
>> should follow “easily” from the result described in most of my papers on 
>> this subject. The author does not seem aware of the mind-body problem, which 
>> put extreme constraints on what the physical reality can come from. Even 
>> Peano arithmetic, although integral part of the notion of observer, is too 
>> much rich for the ontology, where not only the axiom of infinity is too 
>> strong,
>> 
>> Since you want to banish the concept of infinity from mathematics, how would 
>> you define, say, the limit of an "infinite" series? How would you even 
>> discuss this series in the context of finite mathematics? AG
> 
> 
> Good question.
> 
> The answer is not simple technically. The point is that using only the theory 
> Q (Robinson Arithmetic) or SK (the combinators), I can define the universal 
> (Turing, Church) machine, and the concept of infinity will be a tool used by 
> them in their mathematics.
> 
> I do not ban anything from mathematics, nor from physics. I ban only infinity 
> from the ontological terms. I ban only infinity in the metaphysics/theology. 
> (Even God is not ontological, like in Proclus or Plotinus theology).
> 
> Have you understand the post on Church’s thesis. You might tell me as this 
> will help me to see how to proceed to make you grasp all this.
> 
> Bruno
> 
> 
> 
> 
> What do you think of bounded arithmetic and other "finitist" approaches?
> 
> https://en.wikipedia.org/wiki/Bounded_arithmetic
> see bibliography: http://jeanpaulvanbendegem.be/home/papers/strict-finitism/

I wrote a paper on this, in a book in honour to Jean-paul Vanbendegem. But its 
approach is more than finitist, and a bit less than ultra-finitism. It does not 
fit the study of the “theology” of the machine, and is thus useless for 
deriving physics. That does not mean it is not interesting pragmatically, on 
the contrary, it is well fitted with the goal to make usable programs. I do 
think that mathematically, it is also a restriction of Post creativity (Turing 
universality in set theoretical terms) to sub creativity. There is no possible 
universal machine there.




> 
> Computable real analysis (one can teach computable calculus instead of 
> "conventional" calculus) is essentially finitist:
> https://en.wikipedia.org/wiki/Computable_analysis
> 
> One can formulate the Axiom of Infinity [ 
> https://en.wikipedia.org/wiki/Axiom_of_infinity ] in a type of bounded set 
> theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski ], 
> described in 
> https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC
>  ]. What results is an "ontology" of bigger and bigger finite sets of numbers 
> with gaps in them.


Yes, and that is interesting. But not so much for the mind-body problem, where 
we cannot bound anything, except by omega. 

The weaker theory known from which my approach can work, is the 
delta_0-induction based on Q + the axioms for the exponential, known as 
Delta_0Exp. That is Q:

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

+ 

8) x^0 = 1
9) x^s(y) = x * (x^y)

+ the scheme of induction axioms:

P(0) & [For all n (P(n) -> P(s(n)))] ->. For all n P(n),

with P restricted to the delta_0 (= sigma_0 = pi_0 = recursive, decidable, …) 
formula.



That is the weaker Löbian machine known today.

In between Q and Delta_0Exp, you have all the bounded arithmetics.

An excellent book on this is (without the many accent for the names):

Hajek, P. & Pudlak P., 1993, Metamathematics of First-Order Arithmetic, 
Springer-Verlag.

But no need of this for the mind body problem, which needs at least Delta_0Exp 
(Löbianity), for the observer. Of course I use the fact that Q can mimic 
Delta_0Exp. But Q does not 

Re: Mathematical Universe Hypothesis

[agrayson2000]

On Tuesday, October 2, 2018 at 7:20:10 AM UTC, Bruno Marchal wrote:
>
>
> On 1 Oct 2018, at 14:20, agrays...@gmail.com  wrote:
>
>
>
> On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 30 Sep 2018, at 16:30, Philip Thrift  wrote:
>>
>>
>>
>> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
>>>
>>> [Re:] forcing theory in set theories with classes. 
>>>
>>>
>>> Bruno
>>>
>>>
>>>
>> Do you follow the work of Joel David Hamkins (forcing applied to 
>> set-theoretic "multiverse", etc.)
>>
>> (I have a basic idea of a type-theoretic parallel to this.)
>>
>> *The set-theoretic multiverse*
>> https://arxiv.org/abs/1108.4223
>>
>> Joel David Hamkins
>> @JDHamkins
>> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow 
>> in Philosophy, University College Oxford. Formerly of New York.
>> http://jdh.hamkins.org
>>
>>
>> The math is interesting, and could be of some use, but it is a priori far 
>> too much Aristotelian to be coherent with the mechanist hypothesis. That 
>> should follow “easily” from the result described in most of my papers on 
>> this subject. The author does not seem aware of the mind-body problem, 
>> which put extreme constraints on what the physical reality can come from. 
>> Even Peano arithmetic, although integral part of the notion of observer, is 
>> too much rich for the ontology, where not only the axiom of infinity is too 
>> strong, 
>>
>
> *Since you want to banish the concept of infinity from mathematics, how 
> would you define, say, the limit of an "infinite" series? How would you 
> even discuss this series in the context of finite mathematics? AG*
>
>
>
> Good question.
>
> The answer is not simple technically. The point is that using only the 
> theory Q (Robinson Arithmetic) or SK (the combinators), I can define the 
> universal (Turing, Church) machine, and the concept of infinity will be a 
> tool used by them in their mathematics.
>
> I do not ban anything from mathematics, nor from physics. I ban only 
> infinity from the ontological terms. I ban only infinity in the 
> metaphysics/theology. (Even God is not ontological, like in Proclus or 
> Plotinus theology).
>
> Have you understand the post on Church’s thesis. You might tell me as this 
> will help me to see how to proceed to make you grasp all this.
>
> Bruno
>

You only ban infinity from ontological terms? I have no idea what this 
means. I do know you start with the natural numbers, presumably an infinite 
set and existing in some Platonic realm. So I have no idea about your 
aversion or denial of infinity. As for the Church's thesis, I have set 
aside a copy of Chrome with several relevant topics which I see as 
prerequisites to that understanding including, for example, Cantor's 
theorem, but have yet to get into it seriously due to personal issues and 
computer problems in Russia and Ukraine (the latter now solved). But when I 
do, I'll get back to you. AG

>
>
>
>
>
>  
>
>> but even the induction axioms are too strong. 
>>
>> Pragmatically, sets and typed lambda terms or typed combinators can 
>> indeed be very useful. 
>>
>> Bruno
>>
>>
>>
>>
>>
>>
>>
>>
>> - pt
>>
>> -- 
>> You received this message because you are subscribed to the Google Groups 
>> "Everything List" group.
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>> email to everything-li...@googlegroups.com.
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>>
>>
>>
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>
>

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote:
>
>
> On 1 Oct 2018, at 14:20, agrays...@gmail.com  wrote:
>
>
>
> On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 30 Sep 2018, at 16:30, Philip Thrift  wrote:
>>
>>
>>
>> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
>>>
>>> [Re:] forcing theory in set theories with classes. 
>>>
>>>
>>> Bruno
>>>
>>>
>>>
>> Do you follow the work of Joel David Hamkins (forcing applied to 
>> set-theoretic "multiverse", etc.)
>>
>> (I have a basic idea of a type-theoretic parallel to this.)
>>
>> *The set-theoretic multiverse*
>> https://arxiv.org/abs/1108.4223
>>
>> Joel David Hamkins
>> @JDHamkins
>> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow 
>> in Philosophy, University College Oxford. Formerly of New York.
>> http://jdh.hamkins.org
>>
>>
>> The math is interesting, and could be of some use, but it is a priori far 
>> too much Aristotelian to be coherent with the mechanist hypothesis. That 
>> should follow “easily” from the result described in most of my papers on 
>> this subject. The author does not seem aware of the mind-body problem, 
>> which put extreme constraints on what the physical reality can come from. 
>> Even Peano arithmetic, although integral part of the notion of observer, is 
>> too much rich for the ontology, where not only the axiom of infinity is too 
>> strong, 
>>
>
> *Since you want to banish the concept of infinity from mathematics, how 
> would you define, say, the limit of an "infinite" series? How would you 
> even discuss this series in the context of finite mathematics? AG*
>
>
>
> Good question.
>
> The answer is not simple technically. The point is that using only the 
> theory Q (Robinson Arithmetic) or SK (the combinators), I can define the 
> universal (Turing, Church) machine, and the concept of infinity will be a 
> tool used by them in their mathematics.
>
> I do not ban anything from mathematics, nor from physics. I ban only 
> infinity from the ontological terms. I ban only infinity in the 
> metaphysics/theology. (Even God is not ontological, like in Proclus or 
> Plotinus theology).
>
> Have you understand the post on Church’s thesis. You might tell me as this 
> will help me to see how to proceed to make you grasp all this.
>
> Bruno
>
>
>

What do you think of bounded arithmetic and other "finitist" approaches?

https://en.wikipedia.org/wiki/Bounded_arithmetic
see bibliography: http://jeanpaulvanbendegem.be/home/papers/strict-finitism/

Computable real analysis (one can teach computable calculus instead of 
"conventional" calculus) is essentially finitist:
https://en.wikipedia.org/wiki/Computable_analysis

One can formulate the *Axiom of Infinity* 
[ https://en.wikipedia.org/wiki/Axiom_of_infinity ] in a type of bounded 
set theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski ], 
described in 
https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC
 
]. What results is an "ontology" of bigger and bigger finite sets of 
numbers with gaps in them.


 - pt

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 1 Oct 2018, at 14:20, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
> 
>> On 30 Sep 2018, at 16:30, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
>> [Re:] forcing theory in set theories with classes. 
>> 
>> 
>> Bruno
>> 
>> 
>> 
>> Do you follow the work of Joel David Hamkins (forcing applied to 
>> set-theoretic "multiverse", etc.)
>> 
>> (I have a basic idea of a type-theoretic parallel to this.)
>> 
>> The set-theoretic multiverse
>> 
>> https://arxiv.org/abs/1108.4223 
>> 
>> Joel David Hamkins
>> @JDHamkins
>> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in 
>> Philosophy, University College Oxford. Formerly of New York.
>> http://jdh.hamkins.org 
>> 
> 
> The math is interesting, and could be of some use, but it is a priori far too 
> much Aristotelian to be coherent with the mechanist hypothesis. That should 
> follow “easily” from the result described in most of my papers on this 
> subject. The author does not seem aware of the mind-body problem, which put 
> extreme constraints on what the physical reality can come from. Even Peano 
> arithmetic, although integral part of the notion of observer, is too much 
> rich for the ontology, where not only the axiom of infinity is too strong,
> 
> Since you want to banish the concept of infinity from mathematics, how would 
> you define, say, the limit of an "infinite" series? How would you even 
> discuss this series in the context of finite mathematics? AG


Good question.

The answer is not simple technically. The point is that using only the theory Q 
(Robinson Arithmetic) or SK (the combinators), I can define the universal 
(Turing, Church) machine, and the concept of infinity will be a tool used by 
them in their mathematics.

I do not ban anything from mathematics, nor from physics. I ban only infinity 
from the ontological terms. I ban only infinity in the metaphysics/theology. 
(Even God is not ontological, like in Proclus or Plotinus theology).

Have you understand the post on Church’s thesis. You might tell me as this will 
help me to see how to proceed to make you grasp all this.

Bruno





>  
> but even the induction axioms are too strong. 
> 
> Pragmatically, sets and typed lambda terms or typed combinators can indeed be 
> very useful. 
> 
> Bruno
> 
> 
> 
> 
> 
> 
> 
>> 
>> - pt
>> 
>> -- 
>> You received this message because you are subscribed to the Google Groups 
>> "Everything List" group.
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>> email to everything-li...@googlegroups.com .
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>> .
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>> .
>> For more options, visit https://groups.google.com/d/optout 
>> .
> 
> 
> -- 
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Monday, October 1, 2018 at 8:33:10 PM UTC-5, Brent wrote:
>
>
>
> On 10/1/2018 12:32 AM, Philip Thrift wrote:
>
>
>
> On Sunday, September 30, 2018 at 6:14:22 PM UTC-5, Brent wrote: 
>>
>>
>>
>> On 9/30/2018 7:58 AM, Philip Thrift wrote:
>>
>>
>>
>> On Sunday, September 30, 2018 at 5:05:27 AM UTC-5, Bruno Marchal wrote: 
>>>
>>>
>>> On 30 Sep 2018, at 08:03, Philip Thrift  wrote:
>>>
>>>
>>> *What is a computer?*
>>>
>>> A computer is a device that executes programs.
>>>
>>> If we can synthesize bacteria that execute programs (which we can do), 
>>> then these bacteria are computers.
>>>
>>>
>>> OK. You might add “… that can execute all programs”. In any programming 
>>> language. All universal number (mathematical computer, universal Turing 
>>> machine, …) can imitate any other universal numbers. Either by Rogers 
>>> compilation theorem, or by the usual interpretation theorems.
>>>
>>> Bruno
>>>
>>>
>>> I now have a next version of 
>>
>> *Real computationalism*
>>
>>  https://codicalist.wordpress.com/2018/09/30/real-computationalism/
>>
>> =  my "pragmatic" definition of computing.
>>
>> 0.1. PTLOS configurations
>>
>>
>> A configuration PTLOS(π,λ,τ,ο,Σ) — lower case Greek letters π, λ, τ, ο, 
>> and capital Greek letter Σ are variables that take on concrete (particular) 
>> values — is defined:
>>
>>
>> PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ 
>> that is transformed via a compiler/assembler τ into an output object ο that 
>> executes in a computing substrate Σ.
>>
>>
>> (Turing-completeness is included.)
>>
>>
>> But I want to meet therein the "consciousness challenge" of Philip Golff 
>> and Gaylen Strawson in the PLTOS framework (the output object would be a 
>> conscious agent):
>>
>> 6.5. A programming language including experiential modalities (experiential 
>> modal logic, experiential modal operators or qualifiers) is needed to 
>> extend the picture we have of matter [Goff] to include consciousness.
>>
>> (Modal logic historically covers modalities such as 
>> possibility/necessity, belief, time, morality, knowability [ML1 
>> ], but also self-reference [
>> SR1 
>> ],[SR2 ],[SR3 
>> ].)
>>
>>
>> Are you trying to define consciousness into existence by assuming modal 
>> operators for it?  Or are you just trying to provide a language for talking 
>> about it?  Where is the subconscious in this theory? 
>>
>> Brent
>>
>>
>
>
> The proposal is in terms of the the PLTOS(π,λ,τ,ο,Σ) framework:
>
>
> π would be a program in a λ with experiential modalities (modal operators).
>
> A compiler τ (presumably a biocompiler [ 
> https://en.wiktionary.org/wiki/biocompiler ]) would produce a conscious 
> agent ο executing in some substate Σ.
>
> The *sub*conscious of ο would be whatever else is going on in ο's runtime 
> not having to do with the conscious stuff, I guess. (What else would it be?)
>
>
> In human terms the subconscious is thinking that is not conscious but 
> controls action and becomes or produces conscious thoughts.  It doesn't 
> include bodily housekeeping and transduction of signals. 
>
> Brent
>

I guess then in the case of the output object ο above, the part not 
implementing the experiential modalities of λ minus its the part 
implementing its "bodily house keeping" would be its subconscious.

- pt




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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 10/1/2018 12:32 AM, Philip Thrift wrote:



On Sunday, September 30, 2018 at 6:14:22 PM UTC-5, Brent wrote:



On 9/30/2018 7:58 AM, Philip Thrift wrote:



On Sunday, September 30, 2018 at 5:05:27 AM UTC-5, Bruno Marchal
wrote:



On 30 Sep 2018, at 08:03, Philip Thrift 
wrote:


*What is a computer?*

A computer is a device that executes programs.

If we can synthesize bacteria that execute programs (which
we can do), then these bacteria are computers.


OK. You might add “… that can execute all programs”. In any
programming language. All universal number (mathematical
computer, universal Turing machine, …) can imitate any other
universal numbers. Either by Rogers compilation theorem, or
by the usual interpretation theorems.

Bruno


I now have a next version of

*Real computationalism*
*
*
https://codicalist.wordpress.com/2018/09/30/real-computationalism/


=  my "pragmatic" definition of computing.

0.1. PTLOS configurations


A configuration PTLOS(π,λ,τ,ο,Σ) — lower case Greek letters π, λ,
τ, ο, and capital Greek letter Σ are variables that take on
concrete (particular) values — is defined:


PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a
language λ that is transformed via a compiler/assembler τ into an
output object ο that executes in a computing substrate Σ.



(Turing-completeness is included.)


But I want to meet therein the "consciousness challenge" of
Philip Golff and Gaylen Strawson in the PLTOS framework (the
output object would be a conscious agent):

6.5. A programming language including experiential modalities
(experiential modal logic, experiential modal operators or
qualifiers) is needed to extend the picture we have of matter
[Goff] to include consciousness.

(Modal logic historically covers modalities such as
possibility/necessity, belief, time, morality, knowability [ML1
], but also
self-reference [SR1
],[SR2
],[SR3
].)



Are you trying to define consciousness into existence by assuming
modal operators for it?  Or are you just trying to provide a
language for talking about it?  Where is the subconscious in this
theory?

Brent




The proposal is in terms of the the PLTOS(π,λ,τ,ο,Σ) framework:


π would be a program in a λ with experiential modalities (modal 
operators).


A compiler τ (presumably a biocompiler [ 
https://en.wiktionary.org/wiki/biocompiler ]) would produce a 
conscious agent ο executing in some substate Σ.


The /sub/conscious of ο would be whatever else is going on in ο's 
runtime not having to do with the conscious stuff, I guess. (What else 
would it be?)


In human terms the subconscious is thinking that is not conscious but 
controls action and becomes or produces conscious thoughts.  It doesn't 
include bodily housekeeping and transduction of signals.


Brent

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Monday, October 1, 2018 at 5:26:18 PM UTC, kujawski...@gmail.com wrote:
>
>  Agrays:
>>
>> I don't see how Bruno answered your question when he misstated and 
>> doesn't understand the MUH. Yet you thank him and not me. AG 
>>
>
> No, I thanked everybody in this topic in my earlier message, and here I 
> thanked Bruno not for answer about MUH but about Gerald Edelman movie. 
>


*OK. *

*Now we can think about this; the idea that I've falsified in the MUH  is 
that every mathematical form is reified in what we observe, or imagine, as 
an external reality. For me this idea is awfully close to another idea I 
find to be false, but not easily demonstrated; namely, the seminal idea of 
the MWI, that every possible outcome of a quantum experiment must be 
realized or measured, if not in this universe, then in another, and 
simultaneously. AG* 

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Re: Mathematical Universe Hypothesis

[kujawskilucjan85]

 Agrays:
>
> I don't see how Bruno answered your question when he misstated and doesn't 
> understand the MUH. Yet you thank him and not me. AG 
>

No, I thanked everybody in this topic in my earlier message, and here I 
thanked Bruno not for answer about MUH but about Gerald Edelman movie. 




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Re: Mathematical Universe Hypothesis

[John Clark]

On Sat, Sep 29, 2018 at 2:59 PM Brent Meeker  wrote:

*>It has been estimated that simulating a single neuron requires a
> micro-controller like an AVR, which contains 80,000 transistors.*


And 4 years ago in 2014 the human race manufactured 2.5 * 10^20
transistors, that works out to 8 trillion transistors a second 24/7 for an
entire year. I don't know how many transistors are made in 2018 but I'm
sure it's several times as large.

John K Clark






>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Fri, Sep 28, 2018 at 2:26 PM Philip Thrift  wrote:

> I think (along with Philip Goff*) that physics is not complete in its
> study of matter.
>

That is very true, today physics has no idea what Dark Energy or Dark
Matter is and they make up 95% of the matter/energy in the universe. And
physics doesn't know what will happen when 2 incompatible theories, General
Relativity and Quantum Mechanics, collide head on at the center of a Black
Hole. Hell we don't even have a very good theory about why friction works
the way it does, and the same goes for high temperature superconductors.

 John K Clark

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:
>
>
> On 30 Sep 2018, at 16:30, Philip Thrift > 
> wrote:
>
>
>
> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
>>
>> [Re:] forcing theory in set theories with classes. 
>>
>>
>> Bruno
>>
>>
>>
> Do you follow the work of Joel David Hamkins (forcing applied to 
> set-theoretic "multiverse", etc.)
>
> (I have a basic idea of a type-theoretic parallel to this.)
>
> *The set-theoretic multiverse*
> https://arxiv.org/abs/1108.4223
>
> Joel David Hamkins
> @JDHamkins
> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in 
> Philosophy, University College Oxford. Formerly of New York.
> http://jdh.hamkins.org
>
>
> The math is interesting, and could be of some use, but it is a priori far 
> too much Aristotelian to be coherent with the mechanist hypothesis. That 
> should follow “easily” from the result described in most of my papers on 
> this subject. The author does not seem aware of the mind-body problem, 
> which put extreme constraints on what the physical reality can come from. 
> Even Peano arithmetic, although integral part of the notion of observer, is 
> too much rich for the ontology, where not only the axiom of infinity is too 
> strong, 
>

*Since you want to banish the concept of infinity from mathematics, how 
would you define, say, the limit of an "infinite" series? How would you 
even discuss this series in the context of finite mathematics? AG*
 

> but even the induction axioms are too strong. 
>
> Pragmatically, sets and typed lambda terms or typed combinators can indeed 
> be very useful. 
>
> Bruno
>
>
>
>
>
>
>
>
> - pt
>
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Sep 2018, at 16:30, Philip Thrift  wrote:
> 
> 
> 
> On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
> [Re:] forcing theory in set theories with classes. 
> 
> 
> Bruno
> 
> 
> 
> Do you follow the work of Joel David Hamkins (forcing applied to 
> set-theoretic "multiverse", etc.)
> 
> (I have a basic idea of a type-theoretic parallel to this.)
> 
> The set-theoretic multiverse
> 
> https://arxiv.org/abs/1108.4223
> 
> Joel David Hamkins
> @JDHamkins
> Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in 
> Philosophy, University College Oxford. Formerly of New York.
> http://jdh.hamkins.org
> 

The math is interesting, and could be of some use, but it is a priori far too 
much Aristotelian to be coherent with the mechanist hypothesis. That should 
follow “easily” from the result described in most of my papers on this subject. 
The author does not seem aware of the mind-body problem, which put extreme 
constraints on what the physical reality can come from. Even Peano arithmetic, 
although integral part of the notion of observer, is too much rich for the 
ontology, where not only the axiom of infinity is too strong, but even the 
induction axioms are too strong. 

Pragmatically, sets and typed lambda terms or typed combinators can indeed be 
very useful. 

Bruno







> 
> - pt
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Sep 2018, at 13:42, Lawrence Crowell  
> wrote:
> 
> On Thursday, September 27, 2018 at 8:02:36 PM UTC-5, kujawski...@gmail.com 
> wrote:
> Hello I think this good forum for this topic - what do you think about 
> Mathematical Universe, there are very big arguments for that hypothesis:
> 
> - applicability of mathematic, to natural sciences
> - all we discovere are structures and I didnt find explanation of the 
> diference beetwen physical structures and mathematical structures.
> - scientists and philosophers of science tend to affirm belive in diverse 
> structure and homogeneous substance (neutral monism) or mathematicism vide 
> Ladyman, Ross, French, Tegmark etc.
> 
> What are your thoughts. 
> 
> 
> Regards
> 
>  I think it is best to assume pragmatic stance with respect to this.


I am not sure of this. I would have said that only a theoretical view can be 
given, where we make clear the metaphysical theological or psychological 
hypotheses. 



> The idea the physical universe is ultimately mathematics is a huge category 
> mixing that suffers from problems.

I agree with this, and that is why it is important to state the hypothesis, 
notably in the cognitive science.



> Physics is an empirical subject that tests the workings of a theory by 
> performing observations and measurements. Mathematics is a subject concerned 
> with abstract structures and objects and their logical relationships. 
> Physical objects move through space or are an aspect of geometrodynamics in 
> relativity and they obey conservation rules. As such mathematics is used to 
> describe physical systems and to compute things. This is different than 
> saying the two subjects are equivalent. Mathematics is not an empirical 
> subject, though with computers some areas of math have started to take one a 
> sort of synthetic empiricism. Physics is also not something that is 
> determined entirely by logical relationships and just pure theory. We have 
> some issues of course with quantum gravitation and whether that can ever be 
> empirically brought to tests. 

As I explain in my papers, once we assume the “indexical digital mechanist 
hypothesis”,(hereafter called simply Mechanism) physicalism does not work, and 
physics do not explain why the physical prediction fit with the psychological 
(first person) predictions. It uses implicitly a very strong induction axioms 
which can be shown inconsistent.

With Mechanism, there is no more a “physical universe” at the ontological 
level, and physics is reduced to the theology, or psychology if you prefer, 
intrinsic to the numbers and their arithmetical relations.

This makes the physical reality into pure arithmetic, with respect to 
psychology/theology.

The propositional logic of the observable, for example, is given by the logic 
of some variants of the logic of provability. This works in the sense that we 
get a quantum logic where it should be expected. 




> 
> Quantum mechanics is close to being a sort of physical logic. Quantum 
> mechanics is close to being a case of MUH, though I would not go so far as to 
> actually make that pronouncement. For  those who take the trouble to learn 
> about the bosonic string, say by reading Polchinski's vol 1 String Theory 
> will see this is really pure quantum mechanics according to a more complete 
> understanding of the complex plane. This may go further with modular forms. 
> Vol 2 of Polchinski's book works with supersymmetry. This might be ultimately 
> a deeper description of quantum mechanics. Maybe quantum mechanics is just a 
> modular system of automorphisms over the Fischer-Griess Monster Group that 
> maintains a conservation of this as the fundamental vacuum state. So this all 
> sounds highly mathematical, but I would still hesitate to say physics is 
> mathematics.


Physics is not mathematics. That would be the category error you allude to 
above. 

With mechanism, all this is rather well clarified. The physical reality emerges 
from a very special mathematical phenomenon: the way the "dreams by numbers" 
(the computations seen in the self-referential modes) get structured by the 
incompleteness phenomenon.



> 
> The relationship between physics and mathematics is maybe unknowable.

It is indeed, as Mechanism is unknowable too, but we can hope, prey, fear … it 
could be true.

Bruno



> I think of Garrison Keillor with his Guy Noir skits that start with, "One man 
> on the tenth floor of the Acme Building searches for answers to life's 
> persistent questions; Guy Noir private eye."
> 
> LC
> 
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, September 30, 2018 at 6:14:22 PM UTC-5, Brent wrote:
>
>
>
> On 9/30/2018 7:58 AM, Philip Thrift wrote:
>
>
>
> On Sunday, September 30, 2018 at 5:05:27 AM UTC-5, Bruno Marchal wrote: 
>>
>>
>> On 30 Sep 2018, at 08:03, Philip Thrift  wrote:
>>
>>
>> *What is a computer?*
>>
>> A computer is a device that executes programs.
>>
>> If we can synthesize bacteria that execute programs (which we can do), 
>> then these bacteria are computers.
>>
>>
>> OK. You might add “… that can execute all programs”. In any programming 
>> language. All universal number (mathematical computer, universal Turing 
>> machine, …) can imitate any other universal numbers. Either by Rogers 
>> compilation theorem, or by the usual interpretation theorems.
>>
>> Bruno
>>
>>
>> I now have a next version of 
>
> *Real computationalism*
>
>  https://codicalist.wordpress.com/2018/09/30/real-computationalism/
>
> =  my "pragmatic" definition of computing.
>
> 0.1. PTLOS configurations
>
>
> A configuration PTLOS(π,λ,τ,ο,Σ) — lower case Greek letters π, λ, τ, ο, 
> and capital Greek letter Σ are variables that take on concrete (particular) 
> values — is defined:
>
>
> PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ 
> that is transformed via a compiler/assembler τ into an output object ο that 
> executes in a computing substrate Σ.
>
>
> (Turing-completeness is included.)
>
>
> But I want to meet therein the "consciousness challenge" of Philip Golff 
> and Gaylen Strawson in the PLTOS framework (the output object would be a 
> conscious agent):
>
> 6.5. A programming language including experiential modalities (experiential 
> modal logic, experiential modal operators or qualifiers) is needed to 
> extend the picture we have of matter [Goff] to include consciousness.
>
> (Modal logic historically covers modalities such as possibility/necessity, 
> belief, time, morality, knowability [ML1 
> ], but also self-reference [SR1 
> ],[
> SR2 ],[SR3 
> ].)
>
>
> Are you trying to define consciousness into existence by assuming modal 
> operators for it?  Or are you just trying to provide a language for talking 
> about it?  Where is the subconscious in this theory? 
>
> Brent
>
>


The proposal is in terms of the the PLTOS(π,λ,τ,ο,Σ) framework:


π would be a program in a λ with experiential modalities (modal operators).

A compiler τ (presumably a biocompiler [ 
https://en.wiktionary.org/wiki/biocompiler ]) would produce a conscious 
agent ο executing in some substate Σ.

The *sub*conscious of ο would be whatever else is going on in ο's runtime 
not having to do with the conscious stuff, I guess. (What else would it be?)

- pt


>

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 9/30/2018 7:58 AM, Philip Thrift wrote:



On Sunday, September 30, 2018 at 5:05:27 AM UTC-5, Bruno Marchal wrote:



On 30 Sep 2018, at 08:03, Philip Thrift > wrote:


*What is a computer?*

A computer is a device that executes programs.

If we can synthesize bacteria that execute programs (which we can
do), then these bacteria are computers.


OK. You might add “… that can execute all programs”. In any
programming language. All universal number (mathematical computer,
universal Turing machine, …) can imitate any other universal
numbers. Either by Rogers compilation theorem, or by the usual
interpretation theorems.

Bruno


I now have a next version of

*Real computationalism*
*
*
 https://codicalist.wordpress.com/2018/09/30/real-computationalism/

=  my "pragmatic" definition of computing.

0.1. PTLOS configurations


A configuration PTLOS(π,λ,τ,ο,Σ) — lower case Greek letters π, λ, τ, 
ο, and capital Greek letter Σ are variables that take on concrete 
(particular) values — is defined:



PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language 
λ that is transformed via a compiler/assembler τ into an output object 
ο that executes in a computing substrate Σ.




(Turing-completeness is included.)


But I want to meet therein the "consciousness challenge" of Philip 
Golff and Gaylen Strawson in the PLTOS framework (the output object 
would be a conscious agent):


6.5. A programming language including experiential modalities 
(experiential modal logic, experiential modal operators or qualifiers) 
is needed to extend the picture we have of matter [Goff] to include 
consciousness.


(Modal logic historically covers modalities such as 
possibility/necessity, belief, time, morality, knowability [ML1 
], but also self-reference 
[SR1 
],[SR2 
],[SR3 
].)




Are you trying to define consciousness into existence by assuming modal 
operators for it?  Or are you just trying to provide a language for 
talking about it?  Where is the subconscious in this theory?


Brent



Selves: An Essay in Revisionary Metaphysics
Galen Strawson
[Selves ]


The Subject of Experience
Galen Strawson
[SubjExp 
]




- pt
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, September 30, 2018 at 5:05:27 AM UTC-5, Bruno Marchal wrote:
>
>
> On 30 Sep 2018, at 08:03, Philip Thrift > 
> wrote:
>
>
> *What is a computer?*
>
> A computer is a device that executes programs.
>
> If we can synthesize bacteria that execute programs (which we can do), 
> then these bacteria are computers.
>
>
> OK. You might add “… that can execute all programs”. In any programming 
> language. All universal number (mathematical computer, universal Turing 
> machine, …) can imitate any other universal numbers. Either by Rogers 
> compilation theorem, or by the usual interpretation theorems.
>
> Bruno
>
>
> I now have a next version of 

*Real computationalism*

 https://codicalist.wordpress.com/2018/09/30/real-computationalism/

=  my "pragmatic" definition of computing.

0.1. PTLOS configurations


A configuration PTLOS(π,λ,τ,ο,Σ) — lower case Greek letters π, λ, τ, ο, and 
capital Greek letter Σ are variables that take on concrete (particular) 
values — is defined:


PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ 
that is transformed via a compiler/assembler τ into an output object ο that 
executes in a computing substrate Σ.


(Turing-completeness is included.)


But I want to meet therein the "consciousness challenge" of Philip Golff 
and Gaylen Strawson in the PLTOS framework (the output object would be a 
conscious agent):

6.5. A programming language including experiential modalities (experiential 
modal logic, experiential modal operators or qualifiers) is needed to 
extend the picture we have of matter [Goff] to include consciousness.

(Modal logic historically covers modalities such as possibility/necessity, 
belief, time, morality, knowability [ML1 
], but also self-reference [SR1 
],[SR2 
],[SR3 
].)


Selves: An Essay in Revisionary Metaphysics
Galen Strawson
[Selves ]


The Subject of Experience
Galen Strawson
[SubjExp 

]


- pt
 

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:
>
> [Re:] forcing theory in set theories with classes. 
>
>
> Bruno
>
>
>
Do you follow the work of Joel David Hamkins (forcing applied to 
set-theoretic "multiverse", etc.)

(I have a basic idea of a type-theoretic parallel to this.)

*The set-theoretic multiverse*
https://arxiv.org/abs/1108.4223

Joel David Hamkins
@JDHamkins
Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in 
Philosophy, University College Oxford. Formerly of New York.
http://jdh.hamkins.org


- pt

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Re: Mathematical Universe Hypothesis

[Lawrence Crowell]

On Thursday, September 27, 2018 at 8:02:36 PM UTC-5, kujawski...@gmail.com 
wrote:
>
> Hello I think this good forum for this topic - what do you think about 
> Mathematical Universe, there are very big arguments for that hypothesis:
>
> - applicability of mathematic, to natural sciences
> - all we discovere are structures and I didnt find explanation of the 
> diference beetwen physical structures and mathematical structures.
> - scientists and philosophers of science tend to affirm belive in diverse 
> structure and homogeneous substance (neutral monism) or mathematicism vide 
> Ladyman, Ross, French, Tegmark etc.
>
> What are your thoughts. 
>
>
> Regards
>

 I think it is best to assume pragmatic stance with respect to this. The 
idea the physical universe is ultimately mathematics is a huge category 
mixing that suffers from problems. Physics is an empirical subject that 
tests the workings of a theory by performing observations and measurements. 
Mathematics is a subject concerned with abstract structures and objects and 
their logical relationships. Physical objects move through space or are an 
aspect of geometrodynamics in relativity and they obey conservation rules. 
As such mathematics is used to describe physical systems and to compute 
things. This is different than saying the two subjects are equivalent. 
Mathematics is not an empirical subject, though with computers some areas 
of math have started to take one a sort of synthetic empiricism. Physics is 
also not something that is determined entirely by logical relationships and 
just pure theory. We have some issues of course with quantum gravitation 
and whether that can ever be empirically brought to tests. 

Quantum mechanics is close to being a sort of physical logic. Quantum 
mechanics is close to being a case of MUH, though I would not go so far as 
to actually make that pronouncement. For  those who take the trouble to 
learn about the bosonic string, say by reading Polchinski's vol 1 *String 
Theory* will see this is really pure quantum mechanics according to a more 
complete understanding of the complex plane. This may go further with 
modular forms. Vol 2 of Polchinski's book works with supersymmetry. This 
might be ultimately a deeper description of quantum mechanics. Maybe 
quantum mechanics is just a modular system of automorphisms over the 
Fischer-Griess Monster Group that maintains a conservation of this as the 
fundamental vacuum state. So this all sounds highly mathematical, but I 
would still hesitate to say physics is mathematics.

The relationship between physics and mathematics is maybe unknowable. I 
think of Garrison Keillor with his Guy Noir skits that start with, "One man 
on the tenth floor of the Acme Building searches for answers to life's 
persistent questions; Guy Noir private eye."

LC

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Sep 2018, at 11:58, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Sunday, September 30, 2018 at 9:40:07 AM UTC, Bruno Marchal wrote:
> 
>> On 29 Sep 2018, at 13:34, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:
>> 
>>> On 28 Sep 2018, at 21:00, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com 
>>>  wrote:
>>>  
>>> Thank you everybody for your responses. 
>>> 
>>> Bruno Marchal I looked at your statement, they are very interesting but 
>>> some very good neruoscientists argue that brain is not like computer
>>> Here for example (4min video) Edelman:
>>> https://www.youtube.com/watch?v=qmyfQY4TaVc 
>>> 
>>> 
>>> The question can be turned around. Why would anyone think a brain is 
>>> strongly comparable or identical to a computer? It has some superficial 
>>> similarities such as being able to store memory and logical functions 
>>> (which are simulated by a computer), but its cells are not two state 
>>> systems like computer transistors. AG
>> 
>> 
>> A bacteria is already a computer (at least),
>> 
>> 
>> Really? Then you should be able to identify the entities that store binary 
>> information.
> 
> 
> By computer I mean a number u such that phi_u() = phi_x(y), for some 
> enumeration phi_i of the partial computable function. No need of binary 
> information. But it needs digitally coded information, and that is given by 
> the genome (the sequence of adenine, thymine, cytosine, guanine (French 
> spelling, sorry).
> 
> So now a computer isn't some device that executes programs, but a number? 
> Please elaborate on your mathematics. I have no idea what it is supposed to 
> mean. AG

I already did. See the thread “why is Church’s thesis a miracle”. I can explain 
again, but right now I have some work to finish. In a nutshell, choose your 
favorite Turing universal formalism, enumerate in that formalisme the code of 
the partial computable functions, and thus (with repetition) the partial 
computable functions themselves  phi_i, fix a bijection between NxN and N , then a number u is universal if phi_u() = phi_x(y). u is the computer, 
x the program, and y the data. We say that u emulates x on y.

Bruno




>> And where is the clock which pulses and advances the instruction pointer? 
>> And where is the instruction pointer located? AG
> 
> Dont confuse a computer (universal number, universal Turing machine, …)  and 
> a von Neumann physical computer. Reread my explanation in the thread “why is 
> Church’s thesis a miracle). Ask me question from there.
> 
> Bruno
> 
> 
> 
> 
>>  
>> and a neurone is already a rather sophisticated society of bacteria and 
>> viruses, plausibly enough. So, a society of billions of neurons should not 
>> be compared to transistors. The substitution level is plausibly much lower 
>> than the level of neurons.
>> 
>> But we don’t know in Nature anything which at some level is not emulable by 
>> a computer, except for controversial notion like
>> 
>> A) primary matter (if that exists, it is not emulable by a computer)
>> B) the reduction of the wave packet (if that exists, it is provably not 
>> emulable by a computer).
>> 
>> But there are no evidence neither for A) nor for B).
>> 
>> Bruno
>> 
>> 
>> 
>> 
>> 
>> 
>>> 
>>> Please give me your thought on that. 
>>> 
>>> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Sep 2018, at 11:53, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Sunday, September 30, 2018 at 9:35:18 AM UTC, Bruno Marchal wrote:
> 
>> On 29 Sep 2018, at 13:16, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:
>> 
>> 
>> On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com <> 
>> wrote:
>>  It claims that all mathematical objects exist in "physical" reality, which 
>> is sort-of isomorphic or in some sense identical to these objects. That is, 
>> no dichotomy between "physical" and mathematical objects, and all the latter 
>> including plane waves exist in this reality. But you will never observe a 
>> plane wave, so the MUH is falsified. AG 
>> 
>> 1. Tegmark claims everything in the universe is mathematical - that is, the 
>> universe consists of mathematical objects.
>> 2. Tegmark also says that infinities should be eliminated from physics - in 
>> fact, infinities are ruining physics.
>> [ 
>> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ 
>> 
>>  ]ac
>> 
>> Bruno wrote 1 & 2.  AG
>> 
>> So then via Tegmark there can be no real continuous (infinitely divisible) 
>> objects like (mathematical) waves, putting 1 and 2 together. Only particular 
>> mathematical objects exist.
>> 
>> According to Wiki, and what I've heard from its adherents, the MUH posits 
>> that ALL mathematical object or entities exist in nature. But plane waves do 
>> not exist in nature.
> 
> There is no nature that you can invoke. Once mechanism is assumed, a term 
> like nature needs to be (re-defined, or explained, without physicalist 
> assumption, implicit or explicit.
> 
> 
> 
> 
>> (Do you know what they are?) So the MUH as claimed by Wiki and its adherents 
>> is falsified. AG 
> 
> I agree with your conclusion, but you assume some nature or matter, which 
> cannot work in the mechanist context.
> 
> I didn't assume anything, except that plane waves will never be observed 
> (regardless of your model of external reality)

That is a too general statement. I can agree with some definition of 
observation. But then we never observe anything mathematical, still less 
infinite.

Anyway, you seem to use “observation” as a criteria of reality. Then I just did 
an observation of a plane wave, in my waking dream ...




> unless you agree to instantaneous action at a distance, and on steroids (!), 
> since as time evolves, the amplitude of a plane wave changes instantaneously 
> in all infinite directions. So I am just asserting that Tegmark's MUH has 
> been falsified since plane waves mathematically exist,

In which theory. With mechanism what exist is only the numbers (or only the 
combinators, …).



> but are never reified by whatever is out there -- matter, or nothing but 
> restrictions on motion giving rise the illusion of matter or something solid 
> existing.

OK. That is where we will be led, in the computationalist frame.



> Incidentally, I don't think the Wiki article refutes Tegmark as you claim; 
> rather it just describes it.


Read more carefully. I have refuted Tegmark in this list. Then I say that that 
wiki entry is very bad. Those are independent statements.

Bruno



> AG
> 
> Bruno
> 
> 
> 
> 
>> 
>>  - pt
>> 
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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Sunday, September 30, 2018 at 9:53:06 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Sunday, September 30, 2018 at 9:35:18 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 29 Sep 2018, at 13:16, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com 
>>> wrote:

 * It claims that all mathematical objects exist in "physical" reality, 
 which is sort-of isomorphic or in some sense identical to these objects. 
 That is, no dichotomy between "physical" and mathematical objects, and all 
 the latter including plane waves exist in this reality. But you will never 
 observe a plane wave, so the MUH is falsified. AG *

>>>
>>> 1. Tegmark claims everything in the universe is mathematical - that is, 
>>> the universe consists of mathematical objects.
>>> 2. Tegmark also says that infinities should be eliminated from physics - 
>>> in fact, *infinities are ruining physics*.
>>> [ 
>>> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ 
>>> ]ac
>>>
>>
>> Bruno wrote 1 & 2.  AG
>>
>>>
>>> So then via Tegmark there can be no real continuous (infinitely 
>>> divisible) objects like (mathematical) waves, putting 1 and 2 together. 
>>> Only particular mathematical objects exist.
>>>
>>
>> According to Wiki, and what I've heard from its adherents, the MUH posits 
>> that ALL mathematical object or entities exist in nature. But plane waves 
>> do not exist in nature. 
>>
>>
>> There is no nature that you can invoke. Once mechanism is assumed, a term 
>> like nature needs to be (re-defined, or explained, without physicalist 
>> assumption, implicit or explicit.
>>
>>
>>
>>
>> (Do you know what they are?) So the MUH as claimed by Wiki and its 
>> adherents is falsified. AG 
>>
>>
>> I agree with your conclusion, but you assume some nature or matter, which 
>> cannot work in the mechanist context.
>>
>
> *I didn't assume anything, except that plane waves will never be observed 
> (regardless of your model of external reality) unless you agree to 
> instantaneous action at a distance, and on steroids (!), since as time 
> evolves, the amplitude of a plane wave changes instantaneously in all 
> infinite directions. So I am just asserting that Tegmark's MUH has been 
> falsified since plane waves mathematically exist, but are never reified by 
> whatever is out there -- matter, or nothing but restrictions on motion 
> giving rise the illusion of matter or something solid existing. 
> Incidentally, I don't think the Wiki article refutes Tegmark as you claim; 
> rather it just describes it. AG*
>

*Last sentence above is factually wrong. The Wiki article does contain some 
interesting criticisms of Tegmark's MUH. AG* 

>
>
>> Bruno
>>
>>
>>
>>
>>
>>>  - pt
>>>
>>
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>>

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Sep 2018, at 08:41, kujawskilucja...@gmail.com wrote:
> 
> Bruno Marchal thank you for your anwser.
> 
> Physicist Paul Benioff make interesting idea 
> https://arxiv.org/abs/quant-ph/0201093
> that mathematics and laws of physics coemerged somehow randomly.  

I will take a look, but probably this is old stuff, still missing the 
“mind-body” issue, which I illustrate has a deep impact on this, and where 
incompleteness plays the key role in deducing physics from arithmetic.

Bruno


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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Sep 2018, at 08:03, Philip Thrift  wrote:
> 
> 
> 
> On Sunday, September 30, 2018 at 12:30:33 AM UTC-5, agrays...@gmail.com wrote:
> 
> 
> On Saturday, September 29, 2018 at 9:28:34 PM UTC, Philip Thrift wrote:
> 
> 
> On Saturday, September 29, 2018 at 3:53:04 PM UTC-5, Brent wrote:
> 
> 
> On 9/29/2018 1:45 PM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:
>> 
>> 
>> On 9/29/2018 4:34 AM, agrays...@gmail.com <> wrote:
>>> A bacteria is already a computer (at least),
>>> 
>>> 
>>> Really? Then you should be able to identify the entities that store binary 
>>> information. And where is the clock which pulses and advances the 
>>> instruction pointer? And where is the instruction pointer located? AG
>> 
>> Not all computers are von Neumann computers.
>> 
>> Brent
>> 
>> Maybe he means a parallel processor, but whatever he means should be spelled 
>> out explicitly. One can't just assert, as if it's obvious, that a bacteria 
>> is already a computer.
> 
> Of course it is obvious that a bacterium computes things...like swimming 
> toward nutrients and how to make another bacterium.
> 
> Brent
> 
>  
> Bacterial computing: a form of natural computing and its applications
> - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3971165/ 
> 
> 
> Bacteria make computers look like pocket calculators
> - https://www.theguardian.com/science/blog/2009/jul/24/bacteria-computer 
> 
> 
> Bacteria Can Now Be Programmed Like a Computer
> - 
> https://tonic.vice.com/en_us/article/43d9en/bacteria-can-now-be-programmed-like-a-computer
>  
> 
> 
>  
> - pt
> 
> What is a computer -- what is it -- that bacteria can be seen as being like? 
> Why bother to define it. Nothing obvious here except sloppy use of analogies. 
> AG
> 
>  
> 
> 
> 
> What is a computer?
> 
> A computer is a device that executes programs.
> 
> If we can synthesize bacteria that execute programs (which we can do), then 
> these bacteria are computers.

OK. You might add “… that can execute all programs”. In any programming 
language. All universal number (mathematical computer, universal Turing 
machine, …) can imitate any other universal numbers. Either by Rogers 
compilation theorem, or by the usual interpretation theorems.

Bruno



> 
> - pt
>  
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 30 Sep 2018, at 07:30, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Saturday, September 29, 2018 at 9:28:34 PM UTC, Philip Thrift wrote:
> 
> 
> On Saturday, September 29, 2018 at 3:53:04 PM UTC-5, Brent wrote:
> 
> 
> On 9/29/2018 1:45 PM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:
>> 
>> 
>> On 9/29/2018 4:34 AM, agrays...@gmail.com <> wrote:
>>> A bacteria is already a computer (at least),
>>> 
>>> 
>>> Really? Then you should be able to identify the entities that store binary 
>>> information. And where is the clock which pulses and advances the 
>>> instruction pointer? And where is the instruction pointer located? AG
>> 
>> Not all computers are von Neumann computers.
>> 
>> Brent
>> 
>> Maybe he means a parallel processor, but whatever he means should be spelled 
>> out explicitly. One can't just assert, as if it's obvious, that a bacteria 
>> is already a computer.
> 
> Of course it is obvious that a bacterium computes things...like swimming 
> toward nutrients and how to make another bacterium.
> 
> Brent
> 
>  
> Bacterial computing: a form of natural computing and its applications
> - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3971165/ 
> 
> 
> Bacteria make computers look like pocket calculators
> - https://www.theguardian.com/science/blog/2009/jul/24/bacteria-computer 
> 
> 
> Bacteria Can Now Be Programmed Like a Computer
> - 
> https://tonic.vice.com/en_us/article/43d9en/bacteria-can-now-be-programmed-like-a-computer
>  
> 
> 
>  
> - ptIs 
> 
> What is a computer -- what is it -- that bacteria can be seen as being like? 
> Why bother to define it. Nothing obvious here except sloppy use of analogies. 
> AG


If phi_i is an enumeration of the partial computable function, the one closed 
to diagonalisation as I explained in the thread “why Church thesis is a 
miracle”.  Reread that post, I wrote it for you.

Bruno




> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Sep 2018, at 22:52, Brent Meeker  wrote:
> 
> 
> 
> On 9/29/2018 1:45 PM, agrayson2...@gmail.com  
> wrote:
>> 
>> 
>> On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:
>> 
>> 
>> On 9/29/2018 4:34 AM, agrays...@gmail.com  wrote:
>>> A bacteria is already a computer (at least),
>>> 
>>> 
>>> Really? Then you should be able to identify the entities that store binary 
>>> information. And where is the clock which pulses and advances the 
>>> instruction pointer? And where is the instruction pointer located? AG
>> 
>> Not all computers are von Neumann computers.
>> 
>> Brent
>> 
>> Maybe he means a parallel processor, but whatever he means should be spelled 
>> out explicitly. One can't just assert, as if it's obvious, that a bacteria 
>> is already a computer.
> 
> Of course it is obvious that a bacterium computes things...like swimming 
> toward nutrients and how to make another bacterium.

Sure. But that would not be enough to be a “creative set” (a universal number). 
Typically, self-reproduction is not Turing universal (Royer wrote a nice book 
on when a control structure is Turing universal, and very powerful recursion 
are shown to be not Turing universal, this leads to interesting subset of the 
partial computable functions, known as the sub creative hierarchies). They 
verify the SMN theorem, but not the enumeration (universality) theorem.

But a bacteria can emulate a full universal machine. The hard part is the read 
and write interface, which requires handling well some phages (virus). Might 
say that it is only bacteria + phage which are operationally Turing universal. 

Bruno


> 
> Brent
> 
>> One thing for sure; he doesn't know what the MUH is, and therefore cannot 
>> understand my simple falsification of the hypothesis. AG 
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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Sunday, September 30, 2018 at 9:40:07 AM UTC, Bruno Marchal wrote:
>
>
> On 29 Sep 2018, at 13:34, agrays...@gmail.com  wrote:
>
>
>
> On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com 
>> wrote:
>>>
>>>  
>>> Thank you everybody for your responses. 
>>>
>>> Bruno Marchal I looked at your statement, they are very interesting but 
>>> some very good neruoscientists argue that brain is not like computer
>>> Here for example (4min video) Edelman:
>>> https://www.youtube.com/watch?v=qmyfQY4TaVc
>>>
>>
>> The question can be turned around. Why would anyone think a brain is 
>> strongly comparable or identical to a computer? It has some superficial 
>> similarities such as being able to store memory and logical functions 
>> (which are simulated by a computer), but its cells are not two state 
>> systems like computer transistors. AG
>>
>>
>>
>> A bacteria is already a computer (at least), 
>>
>
>
> *Really? Then you should be able to identify the entities that store 
> binary information. *
>
>
>
> By computer I mean a number u such that phi_u() = phi_x(y), for some 
> enumeration phi_i of the partial computable function. No need of binary 
> information. But it needs digitally coded information, and that is given by 
> the genome (the sequence of adenine, thymine, cytosine, guanine (French 
> spelling, sorry).
>

*So now a computer isn't some device that executes programs, but a number? 
Please elaborate on your mathematics. I have no idea what it is supposed to 
mean. AG*

> *And where is the clock which pulses and advances the instruction pointer? 
> And where is the instruction pointer located? AG*
>
>
> Dont confuse a computer (universal number, universal Turing machine, …) 
>  and a von Neumann physical computer. Reread my explanation in the thread 
> “why is Church’s thesis a miracle). Ask me question from there.
>
> Bruno
>
>
>
>
>  
>
>> and a neurone is already a rather sophisticated society of bacteria and 
>> viruses, plausibly enough. So, a society of billions of neurons should not 
>> be compared to transistors. The substitution level is plausibly much lower 
>> than the level of neurons.
>>
>> But we don’t know in Nature anything which at some level is not emulable 
>> by a computer, except for controversial notion like
>>
>> A) primary matter (if that exists, it is not emulable by a computer)
>> B) the reduction of the wave packet (if that exists, it is provably not 
>> emulable by a computer).
>>
>> But there are no evidence neither for A) nor for B).
>>
>> Bruno
>>
>>
>>
>>
>>
>>
>>
>> Please give me your thought on that. 
>>>
>>>
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Sep 2018, at 20:59, Brent Meeker  wrote:
> 
> 
> 
> On 9/29/2018 12:16 AM, Bruno Marchal wrote:
>> 
>>> On 28 Sep 2018, at 21:00, agrayson2...@gmail.com 
>>>  wrote:
>>> 
>>> 
>>> 
>>> On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com 
>>>  wrote:
>>>  
>>> Thank you everybody for your responses. 
>>> 
>>> Bruno Marchal I looked at your statement, they are very interesting but 
>>> some very good neruoscientists argue that brain is not like computer
>>> Here for example (4min video) Edelman:
>>> https://www.youtube.com/watch?v=qmyfQY4TaVc 
>>> 
>>> 
>>> The question can be turned around. Why would anyone think a brain is 
>>> strongly comparable or identical to a computer? It has some superficial 
>>> similarities such as being able to store memory and logical functions 
>>> (which are simulated by a computer), but its cells are not two state 
>>> systems like computer transistors. AG
>> 
>> 
>> A bacteria is already a computer (at least), and a neurone is already a 
>> rather sophisticated society of bacteria and viruses, plausibly enough. So, 
>> a society of billions of neurons should not be compared to transistors. The 
>> substitution level is plausibly much lower than the level of neurons.
> 
> It has been estimated that simulating a single neuron requires a 
> micro-controller like an AVR, which contains 80,000 transistors.
> 
> 


Nice illustration. Yes, a neurone is already an incredibly complex machinery. I 
bet that it would need even much more than 80.000 transistors.  Today we know 
that the glial cells do participate in the information treatment. They don’t 
use axons, but communicate through chemical wave. Our substitution level, 
assuming mechanism, might be the atomic level, in fact the electronically 
level, near the Heisenberg uncertainty position treshold. At least if we want 
to survive integrally, with our precise memory and character.

Bruno



> 
> Brent
> 
>> 
>> But we don’t know in Nature anything which at some level is not emulable by 
>> a computer, except for controversial notion like
>> 
>> A) primary matter (if that exists, it is not emulable by a computer)
>> B) the reduction of the wave packet (if that exists, it is provably not 
>> emulable by a computer).
>> 
>> But there are no evidence neither for A) nor for B).
>> 
>> Bruno
>> 
>> 
>> 
>> 
>> 
>> 
>>> 
>>> Please give me your thought on that. 
>>> 
>>> 
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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Sunday, September 30, 2018 at 9:35:18 AM UTC, Bruno Marchal wrote:
>
>
> On 29 Sep 2018, at 13:16, agrays...@gmail.com  wrote:
>
>
>
> On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:
>>
>>
>>
>> On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com 
>> wrote:
>>>
>>> * It claims that all mathematical objects exist in "physical" reality, 
>>> which is sort-of isomorphic or in some sense identical to these objects. 
>>> That is, no dichotomy between "physical" and mathematical objects, and all 
>>> the latter including plane waves exist in this reality. But you will never 
>>> observe a plane wave, so the MUH is falsified. AG *
>>>
>>
>> 1. Tegmark claims everything in the universe is mathematical - that is, 
>> the universe consists of mathematical objects.
>> 2. Tegmark also says that infinities should be eliminated from physics - 
>> in fact, *infinities are ruining physics*.
>> [ 
>> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ 
>> ]ac
>>
>
> Bruno wrote 1 & 2.  AG
>
>>
>> So then via Tegmark there can be no real continuous (infinitely 
>> divisible) objects like (mathematical) waves, putting 1 and 2 together. 
>> Only particular mathematical objects exist.
>>
>
> According to Wiki, and what I've heard from its adherents, the MUH posits 
> that ALL mathematical object or entities exist in nature. But plane waves 
> do not exist in nature. 
>
>
> There is no nature that you can invoke. Once mechanism is assumed, a term 
> like nature needs to be (re-defined, or explained, without physicalist 
> assumption, implicit or explicit.
>
>
>
>
> (Do you know what they are?) So the MUH as claimed by Wiki and its 
> adherents is falsified. AG 
>
>
> I agree with your conclusion, but you assume some nature or matter, which 
> cannot work in the mechanist context.
>

*I didn't assume anything, except that plane waves will never be observed 
(regardless of your model of external reality) unless you agree to 
instantaneous action at a distance, and on steroids (!), since as time 
evolves, the amplitude of a plane wave changes instantaneously in all 
infinite directions. So I am just asserting that Tegmark's MUH has been 
falsified since plane waves mathematically exist, but are never reified by 
whatever is out there -- matter, or nothing but restrictions on motion 
giving rise the illusion of matter or something solid existing. 
Incidentally, I don't think the Wiki article refutes Tegmark as you claim; 
rather it just describes it. AG*

>
> Bruno
>
>
>
>
>
>>  - pt
>>
>
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Sep 2018, at 14:59, Philip Thrift  wrote:
> 
> 
> 
> On Saturday, September 29, 2018 at 6:34:15 AM UTC-5, agrays...@gmail.com 
> wrote:
> 
> 
> On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:
> 
> 
> A bacteria is already a computer (at least),
> 
> 
> Really? Then you should be able to identify the entities that store binary 
> information. And where is the clock which pulses and advances the instruction 
> pointer? And where is the instruction pointer located? AG
>  
> 
> 
> There is the famous tic-tac-toe playing enzymes [ 
> https://en.wikipedia.org/wiki/DNA_computing#Tic-tac-toe_game ] created in 
> 2002. Maybe the first synbio life forms to compute things. (More recent 
> little biocomputers are in the news all the time.)


Intersting. I have myself work with the geneticist René Thomas on how far we 
can program a bacteria to do some typical elementary calculation. He succeeded 
in implementing the if then else, and some infinite loop, like adding a plasmid 
(a little circular DNA strand) back in and out the main bacterial “chromosome”. 

Unfortunately, the mathematicians refuse that I continue this cooperation 
(which was my master thesis) and ask me to work on forcing theory in set 
theories with classes. 

We did biocomputing 40 years ago. I planned a concentration of bacteria and 
bacteriophages allowing a vey huge parallel processing. I have kept contact 
with biologist and biochemist all my life. I really discovered the universal 
machine in biology book, before discovering that all this was already implement 
in the numbers, which makes me decide to study mathematical logic instead. My 
goal has always been philosophical or theological, but those field are sick 
since long (since 529, precisely albeit symbolically).

Bruno





> 
> - pt
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Sep 2018, at 13:34, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:
> 
>> On 28 Sep 2018, at 21:00, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com 
>>  wrote:
>>  
>> Thank you everybody for your responses. 
>> 
>> Bruno Marchal I looked at your statement, they are very interesting but some 
>> very good neruoscientists argue that brain is not like computer
>> Here for example (4min video) Edelman:
>> https://www.youtube.com/watch?v=qmyfQY4TaVc 
>> 
>> 
>> The question can be turned around. Why would anyone think a brain is 
>> strongly comparable or identical to a computer? It has some superficial 
>> similarities such as being able to store memory and logical functions (which 
>> are simulated by a computer), but its cells are not two state systems like 
>> computer transistors. AG
> 
> 
> A bacteria is already a computer (at least),
> 
> 
> Really? Then you should be able to identify the entities that store binary 
> information.


By computer I mean a number u such that phi_u() = phi_x(y), for some 
enumeration phi_i of the partial computable function. No need of binary 
information. But it needs digitally coded information, and that is given by the 
genome (the sequence of adenine, thymine, cytosine, guanine (French spelling, 
sorry).





> And where is the clock which pulses and advances the instruction pointer? And 
> where is the instruction pointer located? AG

Dont confuse a computer (universal number, universal Turing machine, …)  and a 
von Neumann physical computer. Reread my explanation in the thread “why is 
Church’s thesis a miracle). Ask me question from there.

Bruno




>  
> and a neurone is already a rather sophisticated society of bacteria and 
> viruses, plausibly enough. So, a society of billions of neurons should not be 
> compared to transistors. The substitution level is plausibly much lower than 
> the level of neurons.
> 
> But we don’t know in Nature anything which at some level is not emulable by a 
> computer, except for controversial notion like
> 
> A) primary matter (if that exists, it is not emulable by a computer)
> B) the reduction of the wave packet (if that exists, it is provably not 
> emulable by a computer).
> 
> But there are no evidence neither for A) nor for B).
> 
> Bruno
> 
> 
> 
> 
> 
> 
>> 
>> Please give me your thought on that. 
>> 
>> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Sep 2018, at 13:16, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:
> 
> 
> On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com <> 
> wrote:
>  It claims that all mathematical objects exist in "physical" reality, which 
> is sort-of isomorphic or in some sense identical to these objects. That is, 
> no dichotomy between "physical" and mathematical objects, and all the latter 
> including plane waves exist in this reality. But you will never observe a 
> plane wave, so the MUH is falsified. AG 
> 
> 1. Tegmark claims everything in the universe is mathematical - that is, the 
> universe consists of mathematical objects.
> 2. Tegmark also says that infinities should be eliminated from physics - in 
> fact, infinities are ruining physics.
> [ http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ 
>  
> ]ac
> 
> Bruno wrote 1 & 2.  AG
> 
> So then via Tegmark there can be no real continuous (infinitely divisible) 
> objects like (mathematical) waves, putting 1 and 2 together. Only particular 
> mathematical objects exist.
> 
> According to Wiki, and what I've heard from its adherents, the MUH posits 
> that ALL mathematical object or entities exist in nature. But plane waves do 
> not exist in nature.

There is no nature that you can invoke. Once mechanism is assumed, a term like 
nature needs to be (re-defined, or explained, without physicalist assumption, 
implicit or explicit.




> (Do you know what they are?) So the MUH as claimed by Wiki and its adherents 
> is falsified. AG 

I agree with your conclusion, but you assume some nature or matter, which 
cannot work in the mechanist context.

Bruno




> 
>  - pt
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Sep 2018, at 12:41, Philip Thrift  wrote:
> 
> 
> 
> On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com 
> wrote:
>  It claims that all mathematical objects exist in "physical" reality, which 
> is sort-of isomorphic or in some sense identical to these objects. That is, 
> no dichotomy between "physical" and mathematical objects, and all the latter 
> including plane waves exist in this reality. But you will never observe a 
> plane wave, so the MUH is falsified. AG 
> 
> 1. Tegmark claims everything in the universe is mathematical - that is, the 
> universe consists of mathematical objects.
> 2. Tegmark also says that infinities should be eliminated from physics - in 
> fact, infinities are ruining physics.
> [ http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ 
> ]

But that is correct, as I urge Tegmark to avoid the axiom of infinity, or to 
propose clearly a non-computationalist hypothesis. He agreed. 

Bruno



> 
> So then via Tegmark there can be no real continuous (infinitely divisible) 
> objects like (mathematical) waves, putting 1 and 2 together. Only particular 
> mathematical objects exist.
> 
>  - pt
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Sep 2018, at 11:48, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Saturday, September 29, 2018 at 9:22:30 AM UTC, agrays...@gmail.com wrote:
> 
> 
> On Saturday, September 29, 2018 at 8:57:54 AM UTC, Bruno Marchal wrote:
> 
>> On 29 Sep 2018, at 09:16, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:
>> 
>>> On 28 Sep 2018, at 18:37, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:
>>> 
 On 28 Sep 2018, at 11:32, agrays...@gmail.com <> wrote:
 
 
 
 On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com 
  wrote:
 Hello I think this good forum for this topic - what do you think about 
 Mathematical Universe, there are very big arguments for that hypothesis:
 f
 - applicability of mathematic, to natural sciences
 - all we discovere are structures and I didnt find explanation of the 
 diference beetwen physical structures and mathematical structures.
 - scientists and philosophers of science tend to affirm belive in diverse 
 structure and homogeneous substance (neutral monism) or mathematicism vide 
 Ladyman, Ross, French, Tegmark etc.
 
 What are your thoughts. 
 
 If it's what I think it is, it's demonstrably wrong. One counter example 
 suffices; there are plane wave solutions to Maxwell's equations, but if 
 you know what plane waves are, they clearly do NOT exist in physical 
 reality.
>>> 
>>> 
>>> With mathematicalism, we don’t assume that there is a 
>>> (primitive/irreducible) physical reality.
>>> 
>>> You are begging the question.
>>> 
>>> In what way?  The MUH says, for example, that for every mathematical 
>>> solution or equation, there is a (perceived) physical universe mapped 
>>> identically from, or into that solution or equation. I gave a simple 
>>> counter example. AG
>> 
>> If that is the MUH, then that it is plainly ridiculous, indeed. To have a 
>> perceived universe, you need a measure on the computation/sigma-sentences. 
>> The physical emerges from an arithmetical phenomenon (assuming mechanism in 
>> cognitive science). 
>> 
>> The version of mathematicalism implied by mechanism does not lead any choice 
>> for the “physical reality”, it has to be a statistic on computations 
>> structured by the “observable” mode of self-reference. That indeed predicts 
>> quantum logic, and the many “histories” interpretation of arithmetic. Oracle 
>> are not impossible, but there are no evidence for them, and should be 
>> invoked in last resort (a bit like the “Alien” in cosmology).
>> 
>> The empirical evidence is that there is no physical universe at all.
>> 
>> Bruno
>> 
>> This double-talk nonsense IMO. I clearly gave a counter-example to the MUH,
> 
> 
> You want make some mathematical object physical real. That assume some 
> physical reality, which cannot be done.
> 
> This is the MUH, not what I want or believe. AG 
> 
> https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis 
> 
> 
> Tegmark's MUH is: Our external physical reality is a mathematical 
> structure.[3] 
> 
>  That is, the physical universe is not merely described by mathematics, but 
> is mathematics (specifically, a mathematical structure 
> ). Mathematical 
> existence equals physical existence, and all structures that exist 
> mathematically exist physically as well. Observers, including humans, are 
> "self-aware substructures (SASs)". In any mathematical structure complex 
> enough to contain such substructures, they "will subjectively perceive 
> themselves as existing in a physically 'real' world".[4] 
> 
> 
> 
> To say that a mathematical object  exist physically, does not make sense. It 
> starts with a category error.
> 
> I don't think you know what the MUH is. I have falsified it. AG 
> 
> No mathematical object can be a physical object. But what remains possible is 
> that a physical object belongs to the dream of a person supported by 
> (infinity) of computation (which are arithmetical object a priori).
> 
> 
> 
> 
> 
>> falsifying it. Moreover, I explained clearly why I used "perceived". I just 
>> meant that plane waves can never be observed,
> 
> 
> You don’t need to go that far. The numbers 0, 1, 2, … cannot be observed. No 
> mathematical object can be observed. They do not belong to the category of 
> what can be observed.
> 
> Now, an observation might be explained by a sort of arithmetical 
> prestidigitation. Some numbers can make some numbers believing in a lot of 
> things.
> 
> 
> 
>> and since they are solutions to Maxwell's equations, the MUH is 

Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Sep 2018, at 11:22, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Saturday, September 29, 2018 at 8:57:54 AM UTC, Bruno Marchal wrote:
> 
>> On 29 Sep 2018, at 09:16, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:
>> 
>>> On 28 Sep 2018, at 18:37, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:
>>> 
>>>> On 28 Sep 2018, at 11:32, agrays...@gmail.com <> wrote:
>>>> 
>>>> 
>>>> 
>>>> On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com 
>>>> <http://gmail.com/> wrote:
>>>> Hello I think this good forum for this topic - what do you think about 
>>>> Mathematical Universe, there are very big arguments for that hypothesis:
>>>> f
>>>> - applicability of mathematic, to natural sciences
>>>> - all we discovere are structures and I didnt find explanation of the 
>>>> diference beetwen physical structures and mathematical structures.
>>>> - scientists and philosophers of science tend to affirm belive in diverse 
>>>> structure and homogeneous substance (neutral monism) or mathematicism vide 
>>>> Ladyman, Ross, French, Tegmark etc.
>>>> 
>>>> What are your thoughts. 
>>>> 
>>>> If it's what I think it is, it's demonstrably wrong. One counter example 
>>>> suffices; there are plane wave solutions to Maxwell's equations, but if 
>>>> you know what plane waves are, they clearly do NOT exist in physical 
>>>> reality.
>>> 
>>> 
>>> With mathematicalism, we don’t assume that there is a 
>>> (primitive/irreducible) physical reality.
>>> 
>>> You are begging the question.
>>> 
>>> In what way?  The MUH says, for example, that for every mathematical 
>>> solution or equation, there is a (perceived) physical universe mapped 
>>> identically from, or into that solution or equation. I gave a simple 
>>> counter example. AG
>> 
>> If that is the MUH, then that it is plainly ridiculous, indeed. To have a 
>> perceived universe, you need a measure on the computation/sigma-sentences. 
>> The physical emerges from an arithmetical phenomenon (assuming mechanism in 
>> cognitive science). 
>> 
>> The version of mathematicalism implied by mechanism does not lead any choice 
>> for the “physical reality”, it has to be a statistic on computations 
>> structured by the “observable” mode of self-reference. That indeed predicts 
>> quantum logic, and the many “histories” interpretation of arithmetic. Oracle 
>> are not impossible, but there are no evidence for them, and should be 
>> invoked in last resort (a bit like the “Alien” in cosmology).
>> 
>> The empirical evidence is that there is no physical universe at all.
>> 
>> Bruno
>> 
>> This double-talk nonsense IMO. I clearly gave a counter-example to the MUH,
> 
> 
> You want make some mathematical object physical real. That assume some 
> physical reality, which cannot be done.
> 
> This is the MUH, not what I want or believe. AG 
> 
> https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
> 
> Tegmark's MUH is: Our external physical reality is a mathematical 
> structure.[3] 
> <https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis#cite_note-Tegmark2008-3>
>  That is, the physical universe is not merely described by mathematics, but 
> is mathematics (specifically, a mathematical structure 
> <https://en.wikipedia.org/wiki/Mathematical_structure>). Mathematical 
> existence equals physical existence, and all structures that exist 
> mathematically exist physically as well. Observers, including humans, are 
> "self-aware substructures (SASs)". In any mathematical structure complex 
> enough to contain such substructures, they "will subjectively perceive 
> themselves as existing in a physically 'real' world".[4] 
> <https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis#cite_note-4>

That is refuted by the mechanist hypothesis and its consequence, although it is 
less wrong that materialism, it fails to see that the physical is 
phenomenological. I have developed this with more details a long time ago in 
this list. The shorter way to understand this is to study my papers. To equate 
mathematical existence with physical existence does not make any sense, and 
might be unfair to Tegmark (but his view have evolve

Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, September 30, 2018 at 1:41:43 AM UTC-5, kujawski...@gmail.com 
wrote:
>
> Bruno Marchal thank you for your anwser.
>
> Physicist Paul Benioff make interesting idea 
> https://arxiv.org/abs/quant-ph/0201093
> that mathematics and laws of physics coemerged somehow randomly.  
>


Thanks for this reference! Much of it jibes with my codicalist-materialist 
view.


*The essential point to make here is that language is physical.  *


*Gödel maps can also be used in physical theories. However, for these 
theories, they have some different properties. For a coherent theory of 
mathematics and physics, or for any physical theory that is universally 
applicable, a G¨odel map does not extend the domain of applicability of the 
theory. The reason is that, since language is physical, all expressions of 
any language are already in the theory domain as states of physical 
systems. *

*Finally it should be noted that it may be worthwhile to replace validity 
in the basic requirement with consistency.*

- pt

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Sunday, September 30, 2018 at 6:48:14 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Sunday, September 30, 2018 at 6:41:43 AM UTC, kujawski...@gmail.com 
> wrote:
>>
>> Bruno Marchal thank you for your anwser.
>>
>> Physicist Paul Benioff make interesting idea 
>> https://arxiv.org/abs/quant-ph/0201093
>> that mathematics and laws of physics coemerged somehow randomly.  
>>
>
> You wanted an answer to a question; whether the MUH is valid. I falsified 
> it. Did you understand and appreciate my answer? AG 
>

I don't see how Bruno answered your question when he misstated and doesn't 
understand the MUH. Yet you thank him and not me. AG 

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Sunday, September 30, 2018 at 6:41:43 AM UTC, kujawski...@gmail.com 
wrote:
>
> Bruno Marchal thank you for your anwser.
>
> Physicist Paul Benioff make interesting idea 
> https://arxiv.org/abs/quant-ph/0201093
> that mathematics and laws of physics coemerged somehow randomly.  
>

You wanted an answer to a question; whether the MUH is valid. I falsified 
it. Did you understand and appreciate my answer? AG 

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Re: Mathematical Universe Hypothesis

[kujawskilucjan85]

Bruno Marchal thank you for your anwser.

Physicist Paul Benioff make interesting idea 
https://arxiv.org/abs/quant-ph/0201093
that mathematics and laws of physics coemerged somehow randomly.  

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, September 30, 2018 at 1:03:12 AM UTC-5, Philip Thrift wrote:
>
>
>
> On Sunday, September 30, 2018 at 12:30:33 AM UTC-5, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Saturday, September 29, 2018 at 9:28:34 PM UTC, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Saturday, September 29, 2018 at 3:53:04 PM UTC-5, Brent wrote:



 On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:



 On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote: 
>
>
>
> On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:
>
> A bacteria is already a computer (at least), 
>>
>
>
> *Really? Then you should be able to identify the entities that store 
> binary information. And where is the clock which pulses and advances the 
> instruction pointer? And where is the instruction pointer located? AG*
>
>
> Not all computers are von Neumann computers.
>
> Brent
>

 *Maybe he means a parallel processor, but whatever he means should be 
 spelled out explicitly. One can't just assert, as if it's obvious, that a 
 bacteria is already a computer. *


 Of course it is obvious that a bacterium computes things...like 
 swimming toward nutrients and how to make another bacterium.

 Brent

  
>>> Bacterial computing: a form of natural computing and its applications
>>> - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3971165/
>>>
>>> Bacteria make computers look like pocket calculators
>>> - https://www.theguardian.com/science/blog/2009/jul/24/bacteria-computer
>>>
>>> Bacteria Can Now Be Programmed Like a Computer
>>> - 
>>> https://tonic.vice.com/en_us/article/43d9en/bacteria-can-now-be-programmed-like-a-computer
>>>
>>>  
>>> - pt
>>>
>>
>> What is a computer -- what is it -- that bacteria can be seen as being 
>> like? Why bother to define it. Nothing obvious here except sloppy use of 
>> analogies. AG
>>
>>  
>>>
>>
>
>
> *What is a computer?*
>
> A computer is a device that executes programs.
>
> If we can synthesize bacteria that execute programs (which we can do), 
> then these bacteria are computers.
>
> - pt
>  
>


*Scientists have built the most complex biomolecular computer yet and 
stored a movie*
https://spectrum.ieee.org/biomedical/devices/biocomputer-and-memory-built-inside-living-bacteria
 



- pt 

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Saturday, September 29, 2018 at 8:53:04 PM UTC, Brent wrote:
>
>
>
> On 9/29/2018 1:45 PM, agrays...@gmail.com  wrote:
>
>
>
> On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote: 
>>
>>
>>
>> On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:
>>
>> A bacteria is already a computer (at least), 
>>>
>>
>>
>> *Really? Then you should be able to identify the entities that store 
>> binary information. And where is the clock which pulses and advances the 
>> instruction pointer? And where is the instruction pointer located? AG*
>>
>>
>> Not all computers are von Neumann computers.
>>
>> Brent
>>
>
> *Maybe he means a parallel processor, but whatever he means should be 
> spelled out explicitly. One can't just assert, as if it's obvious, that a 
> bacteria is already a computer. *
>
>
> Of course it is obvious that a bacterium computes things...like swimming 
> toward nutrients and how to make another bacterium.
>
> Brent
>


*So anything that shows intentional behavior you're going to call a 
computer? A comet which misses the Sun, or one that doesn't, can be 
imagined as having intentional behavior. AG *

>
> *One thing for sure; he doesn't know what the MUH is, and therefore cannot 
> understand my simple falsification of the hypothesis. AG *
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>
>
>

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Sunday, September 30, 2018 at 12:30:33 AM UTC-5, agrays...@gmail.com 
wrote:
>
>
>
> On Saturday, September 29, 2018 at 9:28:34 PM UTC, Philip Thrift wrote:
>>
>>
>>
>> On Saturday, September 29, 2018 at 3:53:04 PM UTC-5, Brent wrote:
>>>
>>>
>>>
>>> On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote: 



 On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:

 A bacteria is already a computer (at least), 
>


 *Really? Then you should be able to identify the entities that store 
 binary information. And where is the clock which pulses and advances the 
 instruction pointer? And where is the instruction pointer located? AG*


 Not all computers are von Neumann computers.

 Brent

>>>
>>> *Maybe he means a parallel processor, but whatever he means should be 
>>> spelled out explicitly. One can't just assert, as if it's obvious, that a 
>>> bacteria is already a computer. *
>>>
>>>
>>> Of course it is obvious that a bacterium computes things...like swimming 
>>> toward nutrients and how to make another bacterium.
>>>
>>> Brent
>>>
>>>  
>> Bacterial computing: a form of natural computing and its applications
>> - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3971165/
>>
>> Bacteria make computers look like pocket calculators
>> - https://www.theguardian.com/science/blog/2009/jul/24/bacteria-computer
>>
>> Bacteria Can Now Be Programmed Like a Computer
>> - 
>> https://tonic.vice.com/en_us/article/43d9en/bacteria-can-now-be-programmed-like-a-computer
>>
>>  
>> - pt
>>
>
> What is a computer -- what is it -- that bacteria can be seen as being 
> like? Why bother to define it. Nothing obvious here except sloppy use of 
> analogies. AG
>
>  
>>
>


*What is a computer?*

A computer is a device that executes programs.

If we can synthesize bacteria that execute programs (which we can do), then 
these bacteria are computers.

- pt
 

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Saturday, September 29, 2018 at 9:28:34 PM UTC, Philip Thrift wrote:
>
>
>
> On Saturday, September 29, 2018 at 3:53:04 PM UTC-5, Brent wrote:
>>
>>
>>
>> On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:
>>>
>>> A bacteria is already a computer (at least), 

>>>
>>>
>>> *Really? Then you should be able to identify the entities that store 
>>> binary information. And where is the clock which pulses and advances the 
>>> instruction pointer? And where is the instruction pointer located? AG*
>>>
>>>
>>> Not all computers are von Neumann computers.
>>>
>>> Brent
>>>
>>
>> *Maybe he means a parallel processor, but whatever he means should be 
>> spelled out explicitly. One can't just assert, as if it's obvious, that a 
>> bacteria is already a computer. *
>>
>>
>> Of course it is obvious that a bacterium computes things...like swimming 
>> toward nutrients and how to make another bacterium.
>>
>> Brent
>>
>>  
> Bacterial computing: a form of natural computing and its applications
> - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3971165/
>
> Bacteria make computers look like pocket calculators
> - https://www.theguardian.com/science/blog/2009/jul/24/bacteria-computer
>
> Bacteria Can Now Be Programmed Like a Computer
> - 
> https://tonic.vice.com/en_us/article/43d9en/bacteria-can-now-be-programmed-like-a-computer
>
>  
> - ptIs 
>

What is a computer -- what is it -- that bacteria can be seen as being 
like? Why bother to define it. Nothing obvious here except sloppy use of 
analogies. AG

 
>

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Saturday, September 29, 2018 at 3:53:04 PM UTC-5, Brent wrote:
>
>
>
> On 9/29/2018 1:45 PM, agrays...@gmail.com  wrote:
>
>
>
> On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote: 
>>
>>
>>
>> On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:
>>
>> A bacteria is already a computer (at least), 
>>>
>>
>>
>> *Really? Then you should be able to identify the entities that store 
>> binary information. And where is the clock which pulses and advances the 
>> instruction pointer? And where is the instruction pointer located? AG*
>>
>>
>> Not all computers are von Neumann computers.
>>
>> Brent
>>
>
> *Maybe he means a parallel processor, but whatever he means should be 
> spelled out explicitly. One can't just assert, as if it's obvious, that a 
> bacteria is already a computer. *
>
>
> Of course it is obvious that a bacterium computes things...like swimming 
> toward nutrients and how to make another bacterium.
>
> Brent
>
>  
Bacterial computing: a form of natural computing and its applications
- https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3971165/

Bacteria make computers look like pocket calculators
- https://www.theguardian.com/science/blog/2009/jul/24/bacteria-computer

Bacteria Can Now Be Programmed Like a Computer
- 
https://tonic.vice.com/en_us/article/43d9en/bacteria-can-now-be-programmed-like-a-computer

 
- pt
 

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 9/29/2018 1:45 PM, agrayson2...@gmail.com wrote:



On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:



On 9/29/2018 4:34 AM, agrays...@gmail.com  wrote:


A bacteria is already a computer (at least),



*Really? Then you should be able to identify the entities that
store binary information. And where is the clock which pulses and
advances the instruction pointer? And where is the instruction
pointer located? AG*


Not all computers are von Neumann computers.

Brent

*
*
*Maybe he means a parallel processor, but whatever he means should be 
spelled out explicitly. One can't just assert, as if it's obvious, 
that a bacteria is already a computer. *


Of course it is obvious that a bacterium computes things...like swimming 
toward nutrients and how to make another bacterium.


Brent

*One thing for sure; he doesn't know what the MUH is, and therefore 
cannot understand my simple falsification of the hypothesis. AG *

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:
>
>
>
> On 9/29/2018 4:34 AM, agrays...@gmail.com  wrote:
>
> A bacteria is already a computer (at least), 
>>
>
>
> *Really? Then you should be able to identify the entities that store 
> binary information. And where is the clock which pulses and advances the 
> instruction pointer? And where is the instruction pointer located? AG*
>
>
> Not all computers are von Neumann computers.
>
> Brent
>

*Maybe he means a parallel processor, but whatever he means should be 
spelled out explicitly. One can't just assert, as if it's obvious, that a 
bacteria is already a computer. One thing for sure; he doesn't know what 
the MUH is, and therefore cannot understand my simple falsification of the 
hypothesis. AG *

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 9/29/2018 4:34 AM, agrayson2...@gmail.com wrote:


A bacteria is already a computer (at least),



*Really? Then you should be able to identify the entities that store 
binary information. And where is the clock which pulses and advances 
the instruction pointer? And where is the instruction pointer located? AG*


Not all computers are von Neumann computers.

Brent

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Re: Mathematical Universe Hypothesis

[Brent Meeker]

On 9/29/2018 12:16 AM, Bruno Marchal wrote:


On 28 Sep 2018, at 21:00, agrayson2...@gmail.com 
 wrote:




On Friday, September 28, 2018 at 6:49:37 PM UTC, 
kujawski...@gmail.com  wrote:


Thank you everybody for your responses.

Bruno Marchal I looked at your statement, they are very
interesting but some very good neruoscientists argue that brain
is not like computer
Here for example (4min video) Edelman:
https://www.youtube.com/watch?v=qmyfQY4TaVc



The question can be turned around. Why would anyone think a brain is 
strongly comparable or identical to a computer? It has some 
superficial similarities such as being able to store memory and 
logical functions (which are simulated by a computer), but its cells 
are not two state systems like computer transistors. AG



A bacteria is already a computer (at least), and a neurone is already 
a rather sophisticated society of bacteria and viruses, plausibly 
enough. So, a society of billions of neurons should not be compared to 
transistors. The substitution level is plausibly much lower than the 
level of neurons.


It has been estimated that simulating a single neuron requires a 
micro-controller like an AVR, which contains 80,000 transistors.




Brent



But we don’t know in Nature anything which at some level is not 
emulable by a computer, except for controversial notion like


A) primary matter (if that exists, it is not emulable by a computer)
B) the reduction of the wave packet (if that exists, it is provably 
not emulable by a computer).


But there are no evidence neither for A) nor for B).

Bruno








Please give me your thought on that.


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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Saturday, September 29, 2018 at 6:34:15 AM UTC-5, agrays...@gmail.com 
wrote:
>
>
>
> On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:
>>
>>
>>
>> A bacteria is already a computer (at least), 
>>
>
>
> *Really? Then you should be able to identify the entities that store 
> binary information. And where is the clock which pulses and advances the 
> instruction pointer? And where is the instruction pointer located? AG*
>  
>
>>
>>
There is the famous tic-tac-toe playing enzymes 
[ https://en.wikipedia.org/wiki/DNA_computing#Tic-tac-toe_game ] created in 
2002. Maybe the first synbio life forms to compute things. (More recent 
little biocomputers are in the news all the time.)

- pt

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Saturday, September 29, 2018 at 6:16:26 AM UTC-5, agrays...@gmail.com 
wrote:
>
>
>
> On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:
>>
>>
>>
>> On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com 
>> wrote:
>>>
>>> * It claims that all mathematical objects exist in "physical" reality, 
>>> which is sort-of isomorphic or in some sense identical to these objects. 
>>> That is, no dichotomy between "physical" and mathematical objects, and all 
>>> the latter including plane waves exist in this reality. But you will never 
>>> observe a plane wave, so the MUH is falsified. AG *
>>>
>>
>> 1. Tegmark claims everything in the universe is mathematical - that is, 
>> the universe consists of mathematical objects.
>> 2. Tegmark also says that infinities should be eliminated from physics - 
>> in fact, *infinities are ruining physics*.
>> [ 
>> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ 
>> ]ac
>>
>
> Bruno wrote 1 & 2.  AG
>
>>
>> So then via Tegmark there can be no real continuous (infinitely 
>> divisible) objects like (mathematical) waves, putting 1 and 2 together. 
>> Only particular mathematical objects exist.
>>
>
> According to Wiki, and what I've heard from its adherents, the MUH posits 
> that ALL mathematical object or entities exist in nature. But plane waves 
> do not exist in nature. (Do you know what they are?) So the MUH as claimed 
> by Wiki and its adherents is falsified. AG 
>
>>
>>
>>
In his original arXiv  [ https://arxiv.org/abs/0704.0646 ] and in other 
places he presents MUH as different "levels", so a level-one MUH would have 
different mathematics than a level-four MUH, etc.

To be honest, I find MUH to be both boring, adding nothing to science, and 
somewhat (or maybe a lot) confused.

- pt

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:
>
>
> On 28 Sep 2018, at 21:00, agrays...@gmail.com  wrote:
>
>
>
> On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com 
> wrote:
>>
>>  
>> Thank you everybody for your responses. 
>>
>> Bruno Marchal I looked at your statement, they are very interesting but 
>> some very good neruoscientists argue that brain is not like computer
>> Here for example (4min video) Edelman:
>> https://www.youtube.com/watch?v=qmyfQY4TaVc
>>
>
> The question can be turned around. Why would anyone think a brain is 
> strongly comparable or identical to a computer? It has some superficial 
> similarities such as being able to store memory and logical functions 
> (which are simulated by a computer), but its cells are not two state 
> systems like computer transistors. AG
>
>
>
> A bacteria is already a computer (at least), 
>


*Really? Then you should be able to identify the entities that store binary 
information. And where is the clock which pulses and advances the 
instruction pointer? And where is the instruction pointer located? AG*
 

> and a neurone is already a rather sophisticated society of bacteria and 
> viruses, plausibly enough. So, a society of billions of neurons should not 
> be compared to transistors. The substitution level is plausibly much lower 
> than the level of neurons.
>
> But we don’t know in Nature anything which at some level is not emulable 
> by a computer, except for controversial notion like
>
> A) primary matter (if that exists, it is not emulable by a computer)
> B) the reduction of the wave packet (if that exists, it is provably not 
> emulable by a computer).
>
> But there are no evidence neither for A) nor for B).
>
> Bruno
>
>
>
>
>
>
>
> Please give me your thought on that. 
>>
>>
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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:
>
>
>
> On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com 
> wrote:
>>
>> * It claims that all mathematical objects exist in "physical" reality, 
>> which is sort-of isomorphic or in some sense identical to these objects. 
>> That is, no dichotomy between "physical" and mathematical objects, and all 
>> the latter including plane waves exist in this reality. But you will never 
>> observe a plane wave, so the MUH is falsified. AG *
>>
>
> 1. Tegmark claims everything in the universe is mathematical - that is, 
> the universe consists of mathematical objects.
> 2. Tegmark also says that infinities should be eliminated from physics - 
> in fact, *infinities are ruining physics*.
> [ 
> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ 
> ]ac
>

Bruno wrote 1 & 2.  AG

>
> So then via Tegmark there can be no real continuous (infinitely divisible) 
> objects like (mathematical) waves, putting 1 and 2 together. Only 
> particular mathematical objects exist.
>

According to Wiki, and what I've heard from its adherents, the MUH posits 
that ALL mathematical object or entities exist in nature. But plane waves 
do not exist in nature. (Do you know what they are?) So the MUH as claimed 
by Wiki and its adherents is falsified. AG 

>
>  - pt
>

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com 
wrote:
>
> * It claims that all mathematical objects exist in "physical" reality, 
> which is sort-of isomorphic or in some sense identical to these objects. 
> That is, no dichotomy between "physical" and mathematical objects, and all 
> the latter including plane waves exist in this reality. But you will never 
> observe a plane wave, so the MUH is falsified. AG *
>

1. Tegmark claims everything in the universe is mathematical - that is, the 
universe consists of mathematical objects.
2. Tegmark also says that infinities should be eliminated from physics - in 
fact, *infinities are ruining physics*.
[ 
http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ 
]

So then via Tegmark there can be no real continuous (infinitely divisible) 
objects like (mathematical) waves, putting 1 and 2 together. Only 
particular mathematical objects exist.

 - pt

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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Saturday, September 29, 2018 at 9:22:30 AM UTC, agrays...@gmail.com 
wrote:
>
>
>
> On Saturday, September 29, 2018 at 8:57:54 AM UTC, Bruno Marchal wrote:
>>
>>
>> On 29 Sep 2018, at 09:16, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:
>>>
>>>
>>> On 28 Sep 2018, at 18:37, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:


 On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:



 On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com 
 wrote:
>
> Hello I think this good forum for this topic - what do you think about 
> Mathematical Universe, there are very big arguments for that hypothesis:
> f
> - applicability of mathematic, to natural sciences
> - all we discovere are structures and I didnt find explanation of the 
> diference beetwen physical structures and mathematical structures.
> - scientists and philosophers of science tend to affirm belive in 
> diverse structure and homogeneous substance (neutral monism) or 
> mathematicism vide Ladyman, Ross, French, Tegmark etc.
>
> What are your thoughts. 
>

 If it's what I think it is, it's demonstrably wrong. One counter 
 example suffices; there are plane wave solutions to Maxwell's equations, 
 but if you know what plane waves are, they clearly do NOT exist in 
 physical 
 reality. 



 With mathematicalism, we don’t assume that there is a 
 (primitive/irreducible) physical reality.

 You are begging the question.

>>>
>>> *In what way?  The MUH says, for example, that for every mathematical 
>>> solution or equation, there is a (perceived) physical universe mapped 
>>> identically from, or into that solution or equation. I gave a simple 
>>> counter example. AG*
>>>
>>>
>>> If that is the MUH, then that it is plainly ridiculous, indeed. To have 
>>> a perceived universe, you need a measure on the 
>>> computation/sigma-sentences. The physical emerges from an arithmetical 
>>> phenomenon (assuming mechanism in cognitive science). 
>>>
>>> The version of mathematicalism implied by mechanism does not lead any 
>>> choice for the “physical reality”, it has to be a statistic on computations 
>>> structured by the “observable” mode of self-reference. That indeed predicts 
>>> quantum logic, and the many “histories” interpretation of arithmetic. 
>>> Oracle are not impossible, but there are no evidence for them, and should 
>>> be invoked in last resort (a bit like the “Alien” in cosmology).
>>>
>>> The empirical evidence is that there is no physical universe at all.
>>>
>>> Bruno
>>>
>>
>> *This double-talk nonsense IMO. I clearly gave a counter-example to the 
>> MUH, *
>>
>>
>>
>> You want make some mathematical object physical real. That assume some 
>> physical reality, which cannot be done.
>>
>
>
> *This is the MUH, not what I want or believe. AG *
>
> *https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis 
> *
>
> Tegmark's MUH is: *Our external physical reality is a mathematical 
> structure*.[3] 
> 
>  
> That is, the physical universe is not merely *described by* mathematics, 
> but *is* mathematics (specifically, a mathematical structure 
> ). *Mathematical 
> existence equals physical existence, and all structures that exist 
> mathematically exist physically as well. *Observers, including humans, 
> are "self-aware substructures (SASs)". In any mathematical structure 
> complex enough to contain such substructures, they "will subjectively 
> perceive themselves as existing in a physically 'real' world".[4] 
> 
>
>
>> To say that a mathematical object  exist physically, does not make sense. 
>> It starts with a category error.
>>
>
> *I don't think you know what the MUH is. I have falsified it. AG* 
>
>>
>> No mathematical object can be a physical object. But what remains 
>> possible is that a physical object belongs to the dream of a person 
>> supported by (infinity) of computation (which are arithmetical object a 
>> priori).
>>
>>
>>
>>
>>
>> *falsifying it. Moreover, I explained clearly why I used "perceived". I 
>> just meant that plane waves can never be observed,*
>>
>>
>>
>> You don’t need to go that far. The numbers 0, 1, 2, … cannot be observed. 
>> No mathematical object can be observed. They do not belong to the category 
>> of what can be observed.
>>
>> Now, an observation might be explained by a sort of arithmetical 
>> prestidigitation. Some numbers can make some numbers believing in a lot of 
>> things.
>>
>>
>>
>> * and since they are solutions to 

Re: Mathematical Universe Hypothesis

[Philip Thrift]

The arithmeticalist thinks matter is fiction.
The materialist thinks arithmetic is fiction.

That's all I know. :)

- pt

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 29 Sep 2018, at 09:16, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:
> 
>> On 28 Sep 2018, at 18:37, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:
>> 
>>> On 28 Sep 2018, at 11:32, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com 
>>>  wrote:
>>> Hello I think this good forum for this topic - what do you think about 
>>> Mathematical Universe, there are very big arguments for that hypothesis:
>>> f
>>> - applicability of mathematic, to natural sciences
>>> - all we discovere are structures and I didnt find explanation of the 
>>> diference beetwen physical structures and mathematical structures.
>>> - scientists and philosophers of science tend to affirm belive in diverse 
>>> structure and homogeneous substance (neutral monism) or mathematicism vide 
>>> Ladyman, Ross, French, Tegmark etc.
>>> 
>>> What are your thoughts. 
>>> 
>>> If it's what I think it is, it's demonstrably wrong. One counter example 
>>> suffices; there are plane wave solutions to Maxwell's equations, but if you 
>>> know what plane waves are, they clearly do NOT exist in physical reality.
>> 
>> 
>> With mathematicalism, we don’t assume that there is a 
>> (primitive/irreducible) physical reality.
>> 
>> You are begging the question.
>> 
>> In what way?  The MUH says, for example, that for every mathematical 
>> solution or equation, there is a (perceived) physical universe mapped 
>> identically from, or into that solution or equation. I gave a simple counter 
>> example. AG
> 
> If that is the MUH, then that it is plainly ridiculous, indeed. To have a 
> perceived universe, you need a measure on the computation/sigma-sentences. 
> The physical emerges from an arithmetical phenomenon (assuming mechanism in 
> cognitive science). 
> 
> The version of mathematicalism implied by mechanism does not lead any choice 
> for the “physical reality”, it has to be a statistic on computations 
> structured by the “observable” mode of self-reference. That indeed predicts 
> quantum logic, and the many “histories” interpretation of arithmetic. Oracle 
> are not impossible, but there are no evidence for them, and should be invoked 
> in last resort (a bit like the “Alien” in cosmology).
> 
> The empirical evidence is that there is no physical universe at all.
> 
> Bruno
> 
> This double-talk nonsense IMO. I clearly gave a counter-example to the MUH,


You want make some mathematical object physical real. That assume some physical 
reality, which cannot be done.

To say that a mathematical object  exist physically, does not make sense. It 
starts with a category error.

No mathematical object can be a physical object. But what remains possible is 
that a physical object belongs to the dream of a person supported by (infinity) 
of computation (which are arithmetical object a priori).





> falsifying it. Moreover, I explained clearly why I used "perceived". I just 
> meant that plane waves can never be observed,


You don’t need to go that far. The numbers 0, 1, 2, … cannot be observed. No 
mathematical object can be observed. They do not belong to the category of what 
can be observed.

Now, an observation might be explained by a sort of arithmetical 
prestidigitation. Some numbers can make some numbers believing in a lot of 
things.



> and since they are solutions to Maxwell's equations, the MUH is false.


The MUH is only the idea that the physical might be a part of the mathematical. 
Not that mathematical things have to exist physically. 

Tp put it simply, mathematicalism is the idea that there is no physical 
universe at all.

There is no time, no space, no energy, those are just Löbian machine's 
elaborate fiction to figure out our indexical local geography.

Look at a experimental physicist. He measured numbers, and infer relation 
between numbers, and then avoid the qualia:consciousness question, which indeed 
is only “physical” in string version of materialism, which requires the brain 
and body to be infinite entities.

To refute mathematicalism, you need a theory of matter giving an observable 
role to some infinite entities, having secondary observable consequence. 
Mechanism is a bit like that: if the physics deducible from mechanism is 
different from what we observe, that might be used to infer such infinite 
entities, but the preliminary results, and QM, does not go in that direction.




> Deal with that directly and stop with the double talk about the non-existence 
> of the physical universe. That's not even an issue, since I am only dealing 
> with what can be observed. AG


If you take “observation” as a criteria of reality, you assume right at the 
start the theology of Aristotle.

I just say that this is incompatible with the idea that a brain is Turing 
emulable. 

Study the sane04 paper, which 

Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 28 Sep 2018, at 21:00, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:
>  
> Thank you everybody for your responses. 
> 
> Bruno Marchal I looked at your statement, they are very interesting but some 
> very good neruoscientists argue that brain is not like computer
> Here for example (4min video) Edelman:
> https://www.youtube.com/watch?v=qmyfQY4TaVc 
> 
> 
> The question can be turned around. Why would anyone think a brain is strongly 
> comparable or identical to a computer? It has some superficial similarities 
> such as being able to store memory and logical functions (which are simulated 
> by a computer), but its cells are not two state systems like computer 
> transistors. AG


A bacteria is already a computer (at least), and a neurone is already a rather 
sophisticated society of bacteria and viruses, plausibly enough. So, a society 
of billions of neurons should not be compared to transistors. The substitution 
level is plausibly much lower than the level of neurons.

But we don’t know in Nature anything which at some level is not emulable by a 
computer, except for controversial notion like

A) primary matter (if that exists, it is not emulable by a computer)
B) the reduction of the wave packet (if that exists, it is provably not 
emulable by a computer).

But there are no evidence neither for A) nor for B).

Bruno






> 
> Please give me your thought on that. 
> 
> 
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Re: Mathematical Universe Hypothesis

[agrayson2000]

On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:
>
>
> On 28 Sep 2018, at 18:37, agrays...@gmail.com  wrote:
>
>
>
> On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com 
>> wrote:
>>>
>>> Hello I think this good forum for this topic - what do you think about 
>>> Mathematical Universe, there are very big arguments for that hypothesis:
>>> f
>>> - applicability of mathematic, to natural sciences
>>> - all we discovere are structures and I didnt find explanation of the 
>>> diference beetwen physical structures and mathematical structures.
>>> - scientists and philosophers of science tend to affirm belive in 
>>> diverse structure and homogeneous substance (neutral monism) or 
>>> mathematicism vide Ladyman, Ross, French, Tegmark etc.
>>>
>>> What are your thoughts. 
>>>
>>
>> If it's what I think it is, it's demonstrably wrong. One counter example 
>> suffices; there are plane wave solutions to Maxwell's equations, but if you 
>> know what plane waves are, they clearly do NOT exist in physical reality. 
>>
>>
>>
>> With mathematicalism, we don’t assume that there is a 
>> (primitive/irreducible) physical reality.
>>
>> You are begging the question.
>>
>
> *In what way?  The MUH says, for example, that for every mathematical 
> solution or equation, there is a (perceived) physical universe mapped 
> identically from, or into that solution or equation. I gave a simple 
> counter example. AG*
>
>
> If that is the MUH, then that it is plainly ridiculous, indeed. To have a 
> perceived universe, you need a measure on the computation/sigma-sentences. 
> The physical emerges from an arithmetical phenomenon (assuming mechanism in 
> cognitive science). 
>
> The version of mathematicalism implied by mechanism does not lead any 
> choice for the “physical reality”, it has to be a statistic on computations 
> structured by the “observable” mode of self-reference. That indeed predicts 
> quantum logic, and the many “histories” interpretation of arithmetic. 
> Oracle are not impossible, but there are no evidence for them, and should 
> be invoked in last resort (a bit like the “Alien” in cosmology).
>
> The empirical evidence is that there is no physical universe at all.
>
> Bruno
>

*This double-talk nonsense IMO. I clearly gave a counter-example to the 
MUH, falsifying it. Moreover, I explained clearly why I used "perceived". I 
just meant that plane waves can never be observed, and since they are 
solutions to Maxwell's equations, the MUH is false. Deal with that directly 
and stop with the double talk about the non-existence of the physical 
universe. That's not even an issue, since I am only dealing with what can 
be observed. AG*

>
>
>
>> Since the antic dream argument, we know that observation cannot be used 
>> to prove that anything exist, but an observer.
>>
>> Bruno
>>
>>
>>
>> If this is correct, other models also fall by the wayside. AG 
>>
>>>
>>>
>>> Regards
>>>
>>
>> -- 
>> You received this message because you are subscribed to the Google Groups 
>> "Everything List" group.
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>> Visit this group at https://groups.google.com/group/everything-list.
>> For more options, visit https://groups.google.com/d/optout.
>>
>>
>>
> On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:
>>
>>
>> On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com 
>> wrote:
>>>
>>> Hello I think this good forum for this topic - what do you think about 
>>> Mathematical Universe, there are very big arguments for that hypothesis:
>>> f
>>> - applicability of mathematic, to natural sciences
>>> - all we discovere are structures and I didnt find explanation of the 
>>> diference beetwen physical structures and mathematical structures.
>>> - scientists and philosophers of science tend to affirm belive in 
>>> diverse structure and homogeneous substance (neutral monism) or 
>>> mathematicism vide Ladyman, Ross, French, Tegmark etc.
>>>
>>> What are your thoughts. 
>>>
>>
>> If it's what I think it is, it's demonstrably wrong. One counter example 
>> suffices; there are plane wave solutions to Maxwell's equations, but if you 
>> know what plane waves are, they clearly do NOT exist in physical reality. 
>>
>>
>>
>> With mathematicalism, we don’t assume that there is a 
>> (primitive/irreducible) physical reality.
>>
>> You are begging the question.
>>
>> Since the antic dream argument, we know that observation cannot be used 
>> to prove that anything exist, but an observer.
>>
>> Bruno
>>
>>
>>
>> If this is correct, other models also fall by the wayside. AG 
>>
>>>

Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 28 Sep 2018, at 20:49, kujawskilucja...@gmail.com wrote:
> 
>  
> Thank you everybody for your responses. 
> 
> Bruno Marchal I looked at your statement, they are very interesting but some 
> very good neruoscientists argue that brain is not like computer
> Here for example (4min video) Edelman:
> https://www.youtube.com/watch?v=qmyfQY4TaVc 
> 
> 
> Please give me your thought on that. 

I don’t like to be negative on people. Edelman makes a lot of good points, but 
he seems to have no idea what a computer is. He has, like many, a reductionist 
conception of machine, which is totally impossible to maintain after Gödel’s 
discovery of Incompleteness in 1930 (transformed by Turing, Kleene, and some 
others). 

Before Gödel, mathematicians hoped to reduced the mathematics of the infinite 
by the mathematics of finite system having discourse on the infinite. But Gödel 
found that this is not only impossible, but that even by using the mathematics 
of the infinite, we can control the mathematics of the *finite*. 
The responsible of incompleteness has been found, by Tarski (somehow), and is 
the (Turing) universal machine. We know today that we know nothing about them, 
and if the Church Turing thesis is true, we will never know them completely, we 
can only scratch the surface. Those negative result are constructive. Today we 
know that the universal machine, once “rich enough cognitively” (which does not 
ask for much) is aware that it has a soul that this soul is not a machine, and 
that this can be verified empirically, because the theory of matter becomes a 
sub-theory of that soul theory. Here soul is basically the representational 
body (the relative code) in conjunction with a notion of truth. 

Bruno






> 
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 28 Sep 2018, at 20:26, Philip Thrift  wrote:
> 
> 
> 
> On Friday, September 28, 2018 at 11:00:58 AM UTC-5, Bruno Marchal wrote:
> 
> Yet, I define matter by “the object of study of physics”, or the study of the 
> observable mode, making strong materialism implying physicalism.
> 
> 
> Bruno
> 
> I think (along with Philip Goff*) that physics is not complete in its study 
> of matter.

I agree. Physics can predict an eclipse, but is unable to predict why we feel 
to see an eclipse when we can predict it.
It uses to that effect an identity thesis linking “my mind” to “my brain”, but 
with mechanism, we all have an infinity of brain in arithmetic. 




> Either a new physics is needed, of there is a theoretical gap between physics 
> and brains.

With mechanism, it is easy to understand that there is a theoretical gap 
between brains, mind, and physics.

But Mechanism solves that problem, although probably not like the Aristotelians 
(weak materialist) would like.

Bruno



> 
> 
> * https://twitter.com/philipthrift/status/1045666843304890368
> 
> - pt
> 
> 
> 
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