Re: Existence and Properties

[Bruno Marchal]

On 01 Oct 2011, at 17:42, David Nyman wrote:
On 1 October 2011 14:50, Bruno Marchal <marc...@ulb.ac.be> wrote:

But UDA shows (I think) that matter and consciousness are first
person collective constructs of all the numbers.

Yes, I agree.  But my general point was that even in terms of
physicalism, the way matter ordinarily "appears" to the (unexplained)
first person is very obviously not in terms of its supposed material
primitives.

I agree. That can be related to the weakness of the physicalist  
approach.
I will try to answer in my other comment why this does not apply to  
digital mechanism (DM).
In a sense, you remark does apply to DM, and I refer to it sometimes  
by the 0,0001% of consciousness that DM cannot explain. Then point  
will be that we (and machines) can explain why IF mechanism is true,  
there must remain something which just cannot be explained, and this  
without postulating any new first person primitive experience.
You put your finger on the crux of the difficulty of the mind-body  
problem.


When we seek an explanation for such non-primitive
experiential constructs, we look for appropriate compound concepts
that in turn are expected to cash out, ultimately, in terms of these
selfsame primitives.

Not necessarily. Consciousness does not need to be a compound things.  
It is here that consciousness, as a notion, differ from the nameable  
constructs; like prime numbers, universal numbers, etc. With  
mechanism, we can relate consciousness with modal qualitative, and non  
compounded notion, like arithmetical truth, which can already be said  
not compounded for any machine approaching it closely. Machines just  
lacks the vocabulary here: there are none.


 But, because of this very process of
explanation, such constructs, considered at the level of the
primitives that exhaustively comprise them, are exposed as unnecessary
supplementary hypotheses.

I see what you mean. But they are implicit in the belief that our  
axioms makes sense. This is the implicit (and often unconscious)  
religious belief of any scientist. We still have to bet that our  
theories make sense, despite we know that no public theories can  
provide by itself such a sense. We are using implicitly, at the very  
moment we suggest (any) theory, an assumption of self-consistency, or  
an assumption that there is something real. That reality is not  
compounded, and cannot be reduced into its components, *by us*. Some  
alien might be able to do this for us, like we can do it for simpler  
machine than us, but those aliens will not been able to do this for  
themselves. Colin McGuin is right: consciousness need some amount of  
mysterianism.



They are needed to justify appearances, not
to provide unlooked-for additional influence over what, ex hypothesi,
are already "primitive", self-sufficient mechanisms.  Their demand for
attention stems exclusively from the manifest fact that such things
*appear to us*.

That is the heart of the qualia problem. You single out the 0,0001% of  
consciousness that mechanism cannot explain by the conscious entities  
themselves, *for themselves*. But machine can understand why it has to  
be like that, once they bet that they are machines. And this implies  
that we cannot explain completely how mechanism work, and why  
mechanism does need some act of faith in the case we use it (in  
practice, or in theory). That's the key reason why mechanism *is* a  
theology.




Consequently, unless one (unintelligibly) attempts to deny such
appearances, despite relying on them for the very explanations in
question, such "conceptual realities" must be accepted as having some
distinct existence (even if only "for us") over and above the
primitives of which they are "composed".

They will be distinct in the sense that they need, from the part of  
the machine, an (instinctive) bet in  a reality. With mechanism, the  
bet in arithmetical truth (or more weakly self-consistency) is enough,  
despite or thanks to the fact that this cannot be an entirely  
intelligible act. But the machine can describe it at some metalevel,  
and that is what is done with the internal modal logics.




So matter seems this
(strong) sense to be "a first person collective construct" even under
the primitive assumptions of physicalism.

Yes. But this shows physicalism being contradictory or eliminativist.  
Nice point.



One may call this construct
epistemological reality, or consciousness, or the first-person.  But
whatever one calls it, subtracting it leaves nothing but a barren
primitive arena; one which, notwithstanding this, continues, at its
"own level", to do exactly what it always did.  This is the zombie
argument writ large, except that here the "zombie" stands revealed as
merely an undifferentiated and uninterpreted primitive background.
Consequently, in my view, denial of a distinct first person ontology
ought to be seen as having the consequence of radical reduction of the
remainder to some such arena of primitives and their relations,
independent of any metaphysical postulate of their fundamental nature.
Hence, such denial is unintelligible.

Not really, even for a physicalist. Because my point above explain why  
for machine, their consciousness will appear to be both "ontologically  
real" yet quite distinct from anything postulated as primitive in the  
theory. The fact that it is not will seem, rightly, to be  
unexplainable by the machine, but the non-explainability, betting on  
mechanism (and not on physicalism), can be explained by the machine.  
It is necessarily mysterious, and it is necessary related to the  
global picture which has to be simple (not compounded, like Plotinus'  
one actually) and which has to be transcendental, and quite distinct  
from any intelligible object the machine can meet or imagine.
I think that this is the big discovery made by Plotinus: reality as a  
whole has to be distinct that anything which is real or being. That is  
why Plotinus explain that we need the ONE, and it has to be above the  
realm of the intelligible (even of the divine intelligible). he dares  
to say that God is not a being, or even that it does not exist  
(meaning he does not belong to th realm of the intelligible).
Put it more simply, that is why we need a notion of god, and why  
mechanism make theology the fundamental science.
 You can *almost* define it by what makes possible the distinction  
between the first and third person, but again, with mechanism this is  
"only" an epistemological distinction, indeed it is the distinction  
between believing p, and believing p when p is true. Now, the machine  
cannot even define such a notion of "truth" in a way encompassing  
herself completely. But a rich LUMs can do this for a less rich LUMs,  
and extrapolating it on herself, but this is necessarily at her own  
risk and peril. The fact that it might seems to work (like surviving  
with an artificial brain) will remain like an unintelligible mystery  
for the machine.

Mechanism is very like Plotinian theology. To be short, only  
intelligible ideas exist [only numbers and definable relations exist].  
God and matter does NOT exist, but they do exist epistemologically.  
And they are quite distinct for what really exist. This does not work  
for a physicalist, because he want to avoid that GOD, and make the  
global picture a compound of the elementary things: he want a universe  
composed of material stuff, but that cannot work if we want maintain  
the existence (even if epistemological) of first person, and that is  
why honest and rational materialist are bounded to eliminate the very  
existence of the persons.

Feel free to ask for further precisions, it is a rather subtle (and  
fundamental) point. Remember that arithmetic, viewed from inside is  
FAR bigger than arithmetic as conceived from pure (extensional) number  
theory. A physicalist universe has not that property a priori, and  
cannot do those internal epistemological distinctions (except in some  
ad hoc ways). This might explain why materialist are often dualist, or  
believer in some God (but that is usually an ad hoc completion of the  
gap).


Bruno



David


On 01 Oct 2011, at 02:18, David Nyman wrote:

On 30 September 2011 16:55, Bruno Marchal <marc...@ulb.ac.be> wrote:

They are ontologically primitive, in the sense that ontologically  
they are

the only things which exist. even computations don't exist in that  
primitive

sense. Computations already exists only relationally. I will keep  
saying

that computations exists, for pedagogical reasons. For professional

logicians, I make a nuance, which would look like total jargon in  
this list.

I've been following this discussion, though not commenting (I don't
understand all of it).  However, your remark above caught my eye,
because it reminded me of something that came up a while back, about
whether reductive explanations logically entail elimination of
non-primitive entities.  I argued that this is their whole point;
Peter Jones disputed it.  Your comment (supporting my view, I think)
was that reductionism was necessarily ontologically eliminative,
though of course not epistemologically so.

Yes. This makes sense. Certainly a wise attitude, given that UDA  
shows that
if Mechanism is correct then both consciousness and matter are  
reduced to
number relations. If reduction was elimination, we should conclude  
that
consciousness does not exist (that would be nonsensical for any  
conscious
creature) and that the physical reality does not exist, which does  
not make
much sense either.
A physicalist would also be obliged to say  that molecules, living  
organism,
etc. don't exist. Note that James Watson seemed to have defended  
such a
strong reductive eliminativism.
But I don't see any problem with reduction, once we agree that some  
form of
existence can be reduced to other, without implying elimination.
Mechanism makes it clear that machine are *correct* when they  
believe in
material form. Indeed all LUMs can see by themselves the rise of  
matter, or
the correct laws of matter by introspection, and they will all see  
the same
laws.



 Indeed this seemed to me
uncontroversial, in that the whole point of a reductionist program is
to show how all references to compound entities can be replaced by
more primitive ones.

Your remark above seems now to be making a similar point about
arithmetical "reductionism" in the sense that, presumably,
computations can analogously (if loosely) be considered compounds of
arithmetical primitives, a point that had indeed occurred to me at  
the
time. If so, what interests me is the question that inspired the  
older
controversy.  If the primitives of a given ontology are postulated to
be all that "really" exist, how are we supposed to account for the
apparent "existence" of compound entities?

We need two things. The primitive objects, and the basic laws to  
which the
primitive objects obeys, and which will be responsible of making  
possible
the higher level of organization of those primitive objects, or  
some higher
level appearances of structures.
In the case of mechanism, we can take as primitive objects the  
natural
numbers: 0, s(0), s(s(0), etc.
And, we need only the basic laws of addition and multiplication,  
together
with succession laws:
0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
There is some amount of latitude here. We could consider that there  
is only
one primitive object, 0. Given that we can define 1, 2, 3, by Ex(x=
s(0)), Ex(x= s(s(0))), etc.
[Or we could take the combinators (K, S, SK, KS, KKK, K(KK), etc.) as
primitive, and the combinators laws:
Kxy = x
Sxyz = xz(yz)  ]
It might seems amazing but those axioms are enough to prove the  
existence of
UMs and LUMs, and the whole "Indra Matrix" from which consciousness  
and
physical laws appears at some (different) epistemological levels.
It is the same as the brick in the house example. You need the  
primitive
elements (brick) and some laws which makes them holding together  
(ciment,
gravitation, for example).
The same occur with physicalism. You need elementary particles, and
elementary forces which makes them interact. What I show is that IF
mechanism is correct, elementary particles and elementary forces  
are not
primitive but arise as the "border of some universal mind" (to be  
short),
which lives, at some epistemological level, in arithmetic.


If the supposedly
fundamental underlying mechanism is describable (in principle)
entirely at the level of primitives, there would appear to be no need
of any such further entities, and indeed Occam would imply that they
should not be hypothesised.

Yes. And that is indeed why we can say that we explain them. We can  
explain
the DNA structure entirely from the atoms quantum physical laws. So  
DNA does
not need to be taken as a new "elementary" particle. With digital  
mechanism,
atoms and particles are themselves reducible to the non trivial  
intrinsic
unavoidable consequences of addition and multiplication laws.



Yet the bald fact remains that this is
not how things appear to us.

Why? DNA seems clearly to be explainable by the atoms and their  
laws, like
house seems clearly to be explainable in term of bricks and cement.
For the reduction of physics to numbers, it might seems less obvious,
because we are programmed to take seriously our "epistemological  
beliefs". A
cat would have less chance of surviving in case he doubts the  
existence of
the mouth. So brain have emerged by simplifying the possible world  
view, but
this is due to habitude, and is comparable with many illusion we  
have had in
the past: the sun looks like moving around the earth, but on close
inspection, it is the earth rotating on itself, and the move of the  
sun is a
local "illusion". Matter seems to exist in some ontological  
primitive way,
but on closer inspection, it emerges from group symmetries, which  
themselves
emerges from the provable symmetries of the sigma_1 arithmetical  
sentences
when observed by machine.


So should such compound appearances be
considered entirely a matter of epistemology?

Yes, but there are many layers of realities available inside  
arithmetic, and
nuances can be introduced. Take the example of prime number, or  
even of
universal numbers. Those can be said, if we want to, as existing as  
much as
the primitive 0, 1, 2, 3, ... After all they are only special  
numbers.
But consciousness and matter are more properly epistemological  
(first person
singular and first person plural respectively). Those are not  
numbers, but
are number experiences, and those, mainly due to our self- 
multiplication in
arithmetic, are related to infinities of arithmetical relations.
A notion like a computation, or a computable functions is  
intermediate, they
can have description, which will be numbers, and extension which  
will be,
usually, sequences of numbers.



IOW, is the
first-person - the "inside" view - in some sense the necessary  
arena -
and the sole explanation - for the emergence of anything at all  
beyond
the primitive ontological level?

You don't need a notion of first person to say that prime numbers  
exist, or
that universal numbers exist. Those are just numbers having special  
property
due to the richness of the laws of addition and multiplication when  
taken
together. But UDA shows (I think) that matter and consciousness are  
first
person collective constructs of all the numbers.
Usually, and conventionally I consider that numbers exist  
primitively even
if they have special properties. So I gave the same type of  
existence to
prime numbers, even numbers, or universal numbers. They are  
captured by
sentences with the shape:
 Ex ( ... x ...), where (... x ...) represent some arithmetical  
proposition
(which contains only the symbols 0, x, y, ..., +, *, s, and the  
logical
symbols).
(The proper epistemological existence will be defined by the modal  
logics
like BEx(B(.... x ...), or []<>Ex([]<>(... x ...). The last one are  
still
pure arithmetical formula (thanks to Gödel translation of B in  
arithmetic),
but they have a special "meta-role", and describe what machines can  
believe,
feel, observe, etc.
OK?
Bruno



David


On 30 Sep 2011, at 13:44, Stephen P. King wrote:

On 9/30/2011 5:45 AM, Bruno Marchal wrote:

If comp +Theaetus is correct, you have to distinguish physical  
existence,

which is of the type []<>#, and existence, which is of the type  
"Ex ...

x...". I will use the modal box [] and diamond <> fro the  
intelligible

hypostases ([]X = BX & DX).

[SPK]

    It seems that we have very different ideas of the meaning of  
the word

Existence. "Ex ... x..." seems to be a denotative definition and  
thus is not

neutral with respect to properties. I may not comprehend  you  
thoughts on

this.

It seems that you introduce meta-difficulties to elude simple  
question.


Do you have a concept for "the totality of all that exists"?

A priori and personally: no.

Assuming comp: yes. N is the totality of what exists, but, assuming  
comp, I

have to add this is a G* minus G proposition. It is not really

communicable/provable. You have to grasp it by your own  
understanding (of

UDA, for example).


Would such be unnamable for you? It is for me.

Yes. Arithmetical truth, which relies on the ontic N whole, is  
unnamable for

me, that is why I can only refer to it indirectly, by making the comp

assumption explicit.

As I see it, existence itself is the neutral primitive ground of  
all things,

abstract and concrete. Perhaps my philosophy is more like dual- 
aspect monism

than neutral monism.

Can you elaborate shortly on the difference between dual-aspect and  
neutral

monism? Comp is octal-aspect monism, when Theaetetus enters into  
play.



[SPK]

    Once I have constructed a mental representation of the subject  
of a

reasoning or concept I can use the symbolic representations in a  
denotative

capacity. This is how we dyslexics overcome our disability. :-)

Why don't you do that for "Ex ... x ...."? in the numbers domain?






My result is: mechanism entails immateralism (matter can exist but  
as no

more any relation with consciousness, and so is eliminated with the  
usual

weak occam principle). This should be a problem for you if you want  
to keep

both mechanism and weak materialism, but why do you want to do  
that. On the

contrary, mechanism makes the laws of physics much more solid and  
stable, by

providing an explanation relying only on diophantine addition and

multiplication.

[SPK]

    I reject all form of monism except neutral monism. Existence  
itself is

the only primitive.

In what sense would mechanism, after UDA, not be a neutral monism.

When you use the word "existence" without saying what you assume to  
exist,

it look like the joke "what is the difference between a raven?".

[SPK]

    The totality of all that exists, it merely exists.

In non founded set theories, perhaps. But this is assuming far too  
much,

again in the comp frame. The totality of all that exists does not  
make much

sense to me. I can imagine model of Quine New Foundation playing  
that role,

but that is too much literal, and seems to me contradictory, or

quasi-contradictory. But with comp this would be a reification of the

epistemological. We just cannot do that.


Prior to the specification of properties, even distinctions  
themselves,

there is only existence. Existence is not a property such as Red,  
two or

heavy. It has no extension or form in itself but is the possibility  
to be

and have all properties.


This seems to me quite speculative, and useless in the comp theory.  
If you

were betting that comp is false, I could understand the motivation  
for such

postulation, but are you really betting that comp is false?



[SPK]

    Numbers and arithmetic presuppose a specific meaning, valuation  
and

relation.

This is fuzzy. In the TOE allowed by comp, we can presuppose only  
0, s, *,

and + and the usual first order axioms.


This implies, in my reasoning, that they are not primitive.

They are ontologically primitive, in the sense that ontologically  
they are

the only things which exist. even computations don't exist in that  
primitive

sense. Computations already exists only relationally. I will keep  
saying

that computations exists, for pedagogical reasons. For professional

logicians, I make a nuance, which would look like total jargon in  
this list.



You seem to assume that they are objects in the mind of God, making  
God =

Existence. I disagree with this thinking.

But with comp, God = arithmetical truth, although we have to be  
careful,

because no machines, including perhaps me, can really assert that.  
It is a

just non rationally communicable, but "betable", once we bet on comp.



Could you define to me what you mean by topological dual of a  
number, or a

program?

[SPK]

    I do not recognize the idea that a number or a program has a  
meaning

isolate from all else. I do not understand your theory of  
meaningfulness.

How does meaningfulness arise in your thinking? I use a non-well  
founded set

type Dictionary model and have discussed it before.

Meaning arise in the mind of number, and the mind of numbers arise  
by the

computational relations they have with other numbers, probably so  
in the

comp theory.

I have never stop to give references on this, beyond my own work.  
See the

name Boolos, Smorynski, Smullyan in my papers and books, or in my  
URL.

What is it that you don't understand in the second part of the sane  
paper.

[SPK]

    I do not understand how you ignore the fact that one must have  
a means

to implement a set of distinguishable symbols, configuration of  
chalk mark

on slate, etc. to denote and connote an abstraction. It is as if you

presuppose physicality without giving it credit for what it does. I  
do not

know what else to say now to make this idea more clear.

You keep confusing the number 17, with physical representation of it.

I do have symbols, but why should they be physical. I use the mark  
"0", but

I can use anything else, physical or not. Arithmetic does not  
presuppose

physicalness? Book on numbers say nothing about any possible  
relations with

physics.




Physicist seems not to have the notion of models, and use that term  
where

logician use the term "theory". Roughly speaking, for a logician  
"model" is

for "a reality". I remind you also that Deutch advocates  
physicalism, and

so, if you get the UDA as you said, you know that Deustch  
physicalism is

incoherent with digital mechanism (which he advocates in FOR).

[SPK]

    I wish that you would write more addressing this critique of  
Deutsch's

argument.

Recently on the FOR list Deustch admitted not having a reply to my

objection. I think he wants still searching one.



Arithmetical truth is the territory. Machines and numbers are what  
build

maps of the territory. When you say "yes" to a doctor, you are just  
changing

a map for another. Nowhere is a confusion between map and  
territory, except

for the fixed points, like the here and now indexical  
consciousness. But we

can be thankful that this is possible (in computer science) because  
it makes

the map/brain useful when relating with a probable part of the  
territory.

[SPK]

    But are when maps and territories are made of the "same stuff"  
we have

problems.

Not necessarily. Or you take the word stuff too literally perhaps.

[SPK]

    I used the word 'stuff" in quotes so that it would not be taken  
as

literal.

OK, but then there is no problem with maps and territories having  
the same

"stuff". You can use Kleene second recursion theorem, of your  
unfounded set

theories to provide sense to such fixed points.



You can use Scott topology to modelize computations. Stopping  
programs will

correspond to fixed point transformations.

But my question was more easy, and can be recasted in physical  
terms: does a

machine stop or not stop (accepting a robust physical universe, and  
no

accidental asteroid destructing the machine)?

[SPK]

    OK, I still do not comprehend how you can say this and still be  
a ideal

monist. I am tired.

Take a nap, and then you might answer the simple question: accept  
you the

truth that [phi_i(j) converge V phi_i(j) does not converge].

I remind you also that you can classify me as an ideal monist only  
if you

accept that numbers are ideas (in God's mind, perhaps), but I  
prefer to

classify the comp's consequence as being neutral monism, or octal- 
monism.

But this might only be a vocabulary problem.

I am not arguing for or against any philosophical truth. My point is

technical. It is that IF we can survive with a material digital  
body/brain,

THEN the physical laws emerge, in a precise way, from already only  
addition

and multiplication of (non negative) integers.

Another way to put it: IF we can survive in a digital "matrix",  
then we are

already in a digital matrix.

I am not pretending that the proof is without flaw, but up to now,  
I can

find flaws in the way people describe flaws in the reasoning: they  
almost

introduce systematically a supplementary philosophical hypothesis  
implicitly

somewhere.  No philosophical hypothesis can refute a deductive  
argument per

se (it might certainly help to find a flaw, but then they have to  
find it).

Bruno

http://iridia.ulb.ac.be/~marchal/


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