> On 23 Sep 2019, at 06:12, Alan Grayson <agrayson2...@gmail.com> wrote:
> 
> 
> 
> On Sunday, September 22, 2019 at 9:16:38 AM UTC-6, Bruno Marchal wrote:
> 
>> On 19 Sep 2019, at 17:00, Alan Grayson <agrays...@gmail.com <javascript:>> 
>> wrote:
>> On Wednesday, September 18, 2019 at 12:14:14 PM UTC-6, Brent wrote:
>> 
>> 
>> On 9/18/2019 3:02 AM, Alan Grayson wrote: 
>> > I think he means one can replace a human brain and/or nervous system 
>> > with computer microchips and consciousness will be preserved, or 
>> > perfectly simulated so the person who says "Yes doctor", will awake 
>> > from the surgery thinking he/she's the same person, like awakening 
>> > from unremarkable surgery. From my pov, this belief is a huge, huge 
>> > stretch since we can even define what consciousness IS. 
>> 
>> Define in terms of what?  We define it ostensively.  How would it help 
>> to define it in words? 
>> 
>> Brent 
>> 
>> I think you've nailed the problem. We don't know how to define 
>> "consciousness”.
> 
> Not we don”t have a definition of consciousness, but for those who claim to 
> not know, I suggest to ask their dentist to not use anesthetiser, and they 
> will have a pretty good idea of what is it to be like having consciousness. 
> Consciousness is what gives sense to pain, pleasure, knowledge, etc.
> 
> I know I have consciousness. That's not the issue.

OK.




> What I don't know is how it can exist or the conditions for its existence.

Assuming that the brain works “digitally-mechanically” at some level of 
description will eventually answer this, but the price is that physics will 
have to be reduced to machine theology (which is itself reducible to 
arithmetic).





> I also know that some chemicals can dramatically alter consciousness,


Which is easy to explain in the mechanist theory, as the chemical will perturb 
the *functioning* of the brain.




> and in some cases destroy it absolutely.

This will never happens, but that is highly not obvious, so I will not try to 
explain here. It necessitates to understand that mechanism makes the physical 
universe having no ontological status at all (which contradicts 1500 years of 
enforced materialist theology, so people will take time to swallow this, no 
doubt).



> So its material basis seems pretty firm. 

Yes. But eventually, that material basis emerges from the statistic on all 
computations. Matter exists, and indeed the physical laws describe a reality, 
but it is no more fundamental or ontological.



> Also, more fundamentally, I find your Platonic theory of numbers on dubious 
> grounds.

I do not assume platonism. I assume only what I have to assume to define what 
is a machine, mathematically.

If you agree with proposition like “2+2=4”, and that we can deduce from it that 
the equation x + 2 = 4 has a solution, that is enough. That is assumed by most 
theory in physics. 

So Platonism and neoplatonism are not assumed, but derived from Mechanism.




> Numbers can easily be inferred from observations of the physical world,

That is correct. But that does not imply that the physical world is primary.

What you miss is perhaps, like some other, the fact (and here that *is* a fact) 
that the notion of computation have been shown being purely arithmetical. 
Turing’s original definition is purely mathematical already (set of quadruples 
verifying some conditions) and later it has been shown to be arithmetical 
(although the proof is already in Gödel 1931, but Gödel did not see this as he 
did not believe the Church-Turing thesis at that time, only later).



> whereas the reverse Platonic claim is hugely difficult if not impossible. I 
> see a single object, from which I conceive "1". I see another indentical 
> object and I conceive "2”.

The idea of defining “real” by what we see IS Aristotle theology. It is what 
Plato warns us to not taken for granted.

To be honest with you, I confess that I have less doubt that 2 divides 24, than 
any extrapolation in some reality or in any laws inferred from it. I doubt less 
“2 divide 24” than F = GmM/r^2. I can conceive waking up in the morning and 
discovering that F = GmM/r^2. Is false, but it is harder to conceive that I can 
wake up in the morning and believe that 2 does not divide 24. In fact, to 
accept F = GmM/r^2, I already needs the believe in elementary arithmetic. 




> And so forth. I also dispute your claim that the successor function or 
> principle is derivable independent of the physical world, which you see as 
> illusional.

I am a logician. I don’t know the truth. I just explain the consequence of 
Mechanism, and show that Nature confirms them up to now, at a place where the 
materialist ignores consciousness or dismiss it entirely.




> The successor principle as codified in Peano's postulates seems a simply 
> inference from observations,

Yes, the successor can be inferred from physical experience and life, like with 
birthday and the idea of death, but most results obtained have been got through 
logical reflection. Euclid might have got the intuition of natural number from 
observation and life, but he got the fundamental theorems of arithmetic through 
reflexion. Same for the infinity of primes, which is not something observable 
in any strict sense of observation.





> that is, an extension of them. It's not sometime inherently mysterious 
> dependent on what Godel proved. Can you say exactly, in a few words, why 
> Godel is relevant to any of this? AG


Gödel’s theorem is important, but there is something more important: the 
discovery of the universal machineries and of the universal machine, made by 
Emil Post, Alan Turing, Alonzo Church and  very well understood by Stephen 
Kleene, who with Emil Post, will create the field of theoretical computer 
science (aka Recursion Theory, or now, Computability theory).

Gödel’s first incompleteness theorem is an easy theorem when you accept the 
Church-turing thesis (stating that we get all computable functions through 
their respective formalism, and it is provable that they are equivalent, like 
all formalism found since, including the quantum computer.

So, Gödel’s first incompleteness theorem, found independently of Church thesis 
confirms it, and will add some important precision.

More important is Gödel’s second theorem, and the generalisation which will 
follow, like Löb’s theorem, and Solovay’s theorem. It shows that a class of 
machine are not only universal, but that they can know that they are universal 
(without knowing defined technically/mathematically), and such machine know 
their limitation and do postulate a reality which they are aware not being able 
to prove its existence (they mystical, somehow). Eventually they do understand 
that there is a physical reality which is observable, and that the physical 
reality emerges from the computation. The finding is basically what Plato and 
the neoplatonist already found. In a nutshell, the physical reality is an 
illusion by numbers. But with Turing, Gödel and Co, we have the math to derive 
that physics, and thus we can test if the physics that we infer from 
observation fit with the physics in the head of the machine (and deducible from 
“1+1=2 & Co.).

And, thanks to QM without collapse, it fits, up to now.

What is a universal machinery? It is an enumeration (with repetition) of all 
(partial and total) computable functions. Choose your favorite universal 
programming language, and order the one argument programs (by length and 
alphabetically for those having the same length), and you get a universal 
machinery: phi_0, phi_1, phi_2, … (noted phi_i).
Then we can define a universal “machine” or “number” by a number u such that 
phi_u(x, y) = phi_x(y). U is called a computer, x is called a programme, and y 
is called “data”.

I can explain why this entails a very strong form of incompleteness. Since 
Gödel, we know not only that elementary arithmetic is Turing universal (and 
thus explains the existence of all universal machineries), but we know that 
some universal knows that they are universal, and here the theorem of Löb and 
Solovay add much more precision. 
To be continue, if you are interested. Ask any question, but be patient ...

Bruno





>> In terms of what?
> With mechanism, we can define knowledge by the conjunction-onjction of belief 
> and truth. For belief, we can use Gödel’s definition in elementary arithmetic 
> (where you assume x + 0 = x, & Co.), fortieth you can study Tarski theory of 
> truth, it quite enough, and yes, tarski is the one showing that the 
> arithmetical truth cannot be defined by machines, or actually, even by most 
> non-mechanical entities too, with some exception.
>> Presumably it's properties, as we define other entities in physics, such as 
>> the electron.
> You cannot use 3p notions to define consciousness which is a pure 1p notion.
> (Eventually the physical will appear as a 1p-plural notion, but that’s for 
> later).
> 
> I am merely stating that an electron is defined by its measured properties 
> which anyone, with sufficient
> effort, can confirm. I don't see that 1p or 3p has anything to do with this, 
> other than to obfuscate. AG 
>> Who was the SC justice who said you know pornography when you see it, but 
>> you can't define it prior to the observation?  So far, the most we can say 
>> about consciousness, that is, its properties, is that it's self-referential. 
>> AG
> 
> Indeed, but it has two main level: the simple non reflexive consciousness, 
> which is implicitly self-referential, and the consciousness of the Löbian 
> machine (which are not just universal, they know that they are universal) 
> where the self-reference is made explicit by the machine. It has about the 
> difference between the consciousness of low animals compared to higher 
> vertebrate, although I suspect the cuttlefish and some others invertebrate to 
> have it too.
> 
> Bruno
> 
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