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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