Dear John, Dear colleagues,

> On 25 Feb 2018, at 20:51, John Collier <> wrote:
> Daer Krassimir, List
> I basically support what you are saying. I understand the mathematics you 
> presented, I am good at mathematics and studied logic with some of the best. 
> However, and this is a big however, giving a mathematical or logical proof by 
> itself, in its formalism, does not show anything at all. One has to be able 
> to connect teh mathematics to experience in a comprehensible way. This was 
> partly the topic of my dissertation, and I take a basically Peircean 
> approach, though there are others that are pretty strong as well.
> I fgenerally skip over the mathematics and look for the empirical 
> connections. If I find them, then generally all becomes clear. Without this, 
> the formalism is nothing more than formalism. It does not help to give formal 
> names to things and assume that this identifies things, Often trying to 
> follow up approaches kine this is a profound waste of time. I try to, and 
> often am able to, express my ideas in a nonformal way. Some mathematically 
> oriented colleagues see this as automatically defective, since they think 
> that formal representation is all that really rigorously explains things. 
> This sort of thinking (in Logical Positivism) eventually led to its own 
> destruction as people started to ask the meaning of theoretical terms and 
> their relation to observations. It is a defunct and self destructive 
> metaphysics. Irt leads nowhere -- my PhD thesis was about this problem. It 
> hurts me to see people making the same mistake, especially when it leads them 
> to bizarre conclusions that are compatible with the formalism (actually, it 
> is provable that almost anything is compatible with a specific formalism, up 
> to numerosity).

Since Gödel, in mathematics we have to distinguish between truth and proof, and 
even when we restrict ourself to arithmetic, we know that the truth escape 
*all* formalism. Logical positivism is dead since long for logicians and 

Then, when we assume mechanism (the brain is a digitalizable natural 
machinery), and as elementary arithmetic emulates all Turing universal 
machinery and all computations (we assume the Church-Turing thesis, and a small 
amount of passive understanding of Gödel’s method or proofs), it becomes an 
open problem in (scientific) metaphysics if there could be a physical primary 

The evidence we get so far is that there are none. Mechanism and materialism 
can be shown incompatible logically. Mechanism forces a reduction of the 
physical appearance to computer science, which embeds itself in number theory. 
Mechanism becomes empirically testable: extract physics from arithmetic, and 
compare to the observation. This has been done, and the result sustain 
mechanism, and not materialism.

So, we in that frame, we have to come back to Plato, where the shadow on the 
wall, mentioned by Krassimir,  is given by the empirical reality, which appears 
to be the logical border of the mind of the universal machine. To get this, it 
is imperative to well understand that the notion of computation and of 
universal machine have been discovered in pure mathematics (and quickly after 
even in elementary arithmetic).

The God/non-God debate hides since long the original debate among the antic 
greeks, which was about the existence or inexistence of a primary physical 
universe. Is physics or mathematics the fundamental science/realm? Now with 
Mechanism, we do have a testable explanation of consciousness. It is testable 
because physics *is* reduced to the statistics on the first person view that we 
can associate to the machine.

How to define such first person notions? Gödel’s incompleteness shows that 
proof and truth are different, but also that the machine will makes a 
difference between all the modal variants of provability, and this leads to 
eight different logic of self-reference. Most of them were foreseen by the 
Neoplatonist inquirers.

p (truth)
[]p (provability, Gödel’s beweisbar)
[]p & p (theatetus’ notion of knower, the first person: that notion is not 
definable in the language of the machine: it is non nameable self)
[]p & <>t. (Observability, measure one on the computable consistent extension) 
——————> this gives a quantum logic
[]p & <>t & p. (Perception, sensibility)

Those are 8, not fives, because not only incompleteness does makes those 
vertical distinction, but it separates three of those modes in two, along the 
separation of truth and what the machine can prove Abi-out itself. We get six 
quantum logics, making us able to distinguish the sharable quanta and the 
private non sharable qualia which actually extends the quanta. So even the 
quanta are not “objective” but belongs to the “shadow” which hides the deeper 
and simpler reality of the numbers (or of anything Turing equivalent).

So, yes, the shadow are real, and include the whole of physics. But the shadows 
are only phenomenologically real, and the whole physics is reduced, in 
principle, to the biology-psychology, and theology (in Plato’s sense) of the 
universal machine.

The physical reality is real, and its basic quantum formalism is explained by 
the logic of self-reference. But we can’t invoke a primary physical universe to 
select a (conscious) computation in arithmetic. Below our substitution level, 
physics is a statistics on infinitely many computations, as seen from some of 
the self-referential modes described above.

I insist all this makes sense only because incompleteness shows that most the 
mathematical reality is beyond all formalism/machine. But, as Gödel understood 
already, those limitations are reflected by the machine, and in the Theaetetus’ 
sense of knowing, the universal “enough rich” machine is aware of those 
limitations, and infer easily that there is something which transcend it.

With the mechanist assumption, it becomes up to the materialist to explain what 
would be matter, and how it can select a computation among all the one in 
arithmetic, and that seems impossible without re-introducing some magical 
ability in the mind (a universal machine cannot distinguish a physical reality 
from an arithmetical reality by conscious introspection, but it can do it by 
observation, and that is what we have done, and nature confirms mechanism 
against materialism.

Of course, mechanism can still be false, but up to now, the empirical evidence 
(thanks to quantum mechanics) favours strongly the digital mechanist thesis, 
and its reduction of all sciences and their relation to the neoplatonic or 
neopythagorean machine theoretical theology.

Of course, all details on this should be consulted in my papers (available on, or Research Gate).


> I don't like to waste my time with such emptiness,
> John
> On 2018/02/25 6:22 PM, Krassimir Markov wrote:
>> Dear Sung,
>> I like your approach but I think it is only a part of the whole.
>> 1. The shadows are real but only a part of the whole. What is needed is a 
>> systematic research from what they are part.
>> 2. About the whole now I will use the category theory I have seen you like:
>> CATA => F => CATB => G => CATC
>> CATA => H => CATC
>> F ○ G = H
>> where
>> F, G, and H are functors;
>> CATII Î CAT is the category of information interaction categories;
>> CATA Î CATII and CATC Î CATII  are the categories of mental models’ 
>> categories;
>> CATB Î CATII  is the category of models’ categories.
>> Of course, I will explain this in natural language (English) in further 
>> posts. 
>> <wlEmoticon-smile[1].png>
>> ;
>> Dear  Karl,
>> Thank you for your post – it is very useful and I will discus it in further 
>> posts.
>> ;
>> Dear Pedro,
>> Thank you for your nice words. 
>> Mathematics is very good to be used when all know the mathematical languages.
>> Unfortunately, only a few scientists are involved in the mathematical 
>> reasoning, in one hand, and, as the Bourbaki experiment had shown, not 
>> everything is ready to be formalized. 
>> How much of FIS members understood what I had written above?
>> The way starts from philosophical reasoning  and only some times ends in 
>> mathematical formal explanations.
>> Friendly greetings
>> Krassimir
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>> <>
> -- 
> John Collier
> Emeritus Professor and Senior Research Associate
> Philosophy, University of KwaZulu-Natal, Durban
> Collier web page  <>
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