On 10/1/2011 9:50 AM, Bruno Marchal wrote:

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

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

Let me try to be sure that I understand this comment. When you write: "they will all see the same laws" are you referring to those invariant quantities and relations/functions with respect to transformations of reference frames/coordinate systems (which has become the de facto definition of physical laws) or are you referring to our collective human idea of physical laws? Why does it seem to me that you assume that the physical laws that we observe are the only possible ones? To badly echo Leibniz: How these and not some others? It seems to me that we observe exactly the physical laws that are consistent with our existence as observers within this universe, a universe where we can communicate representations of the contents of our 1p to each other. Communication requires a plurality of possible 1p for each and every separate observer in one universe to act as the template from which signal is distinguished from noise, plurality is insufficient to communications between observers. One needs something like the Hennessy-Milner property <http://scholar.google.com/scholar?q=hennessy-milner+property&hl=en&as_sdt=0&as_vis=1&oi=scholart> for a coherent notion of communication. There seems to be no a priori reason why we do not experience a universe that contains only a single conscious entity or a universe with completely different laws along with completely different physicality for the observers wherein. IMHO, There is something to the self-selection that Nick Bostrom tedand others have writen about that needs to be included in this discussion in addition to the contraints that communications between many separate entities generates.

 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.
But why some particular type of primitive rather than some other? It seems to me, for symmetry reasons, that a truly ultimate primitive would have no particular properties associated with it at all! I think that there is a flaw in this reductionist idea, the idea that there exists a fundamental primitive that both is irreducible (by definition!) and has some properties rather than some others. We have been considering some form of Number as our primitive and I have been raising objections to this because while numbers definitely do seem to be irreducible primitives, the very notion that they are numbers vanishes when we consider them at this primitive level because the structure of Arithmetic, which gives meaning and haecceity to them, was dissolved away by the Aqua Regia of Reduction. One cannot have properties and not the means that generates them, to claim otherwise is a contradiction

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)

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.
But that definitive arithmetic structure does not even exist at the level of our one Primitive, 0, therefore we are wrong to claim that our primitive is a number! It is no more a number than a purple and pink polka-dotted Pony! It is the (0, +, *, =) that gives our primitive "number-ness", and it by definition cannot be an ontological primitive because it lacks the necessary multiplicity of extrinsic possible positions that a physical space generates. Just because it is possible to fully express Arithmetic via Goedelian sentences coded as numbers does not require us to believe that the primitive is a number and that that quality of being a number is itself irreducible. Unless there is some form of manifold or non-singular set unto which valuations can be compared and contrasted, each and every number collapses into 0. There is simply no *space* for multiple copies of numbers. "No cloning" follows from "no room to put the clones".

[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.

The Indra Matrix (aka Net of Indra) is a *non-well founded* set, it has no true primitives and reductionism goes very wrong in it. Every jewel in the Matrix reflects and is defined by relations to all others. It has no *One* primitive in the well founded sense of a minimal element.

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.


I agree, physicalist, as a form of material monism is incomplete; but so is any for of idea monism! Only a neutral monism escapes this but at the price of dissolving Everything into Nothing at all. This is why I am motivated to rehabilitate dualism, it solves the incompleteness problems of both material and idea monism and becomes neutral monism in the limit of all possible reductions, thus my proposal is more like dual-aspect monism but not exactly.

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.

What needs to be understood about reductionism is that is is showing us that *meaningfulness* itself vanishes at some point in the dissolving. Reduction leads, eventually, to Neutral and Unnameable Monism, not to Number or Arithmetic Realism.

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.

At the level of atoms there in no such thing as Van Der Walls forces, for instance, just as there is no such thing as temperature at the level of atoms. So I am skeptical of this claim of explainability. 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. Brick and cement can be used to construct a blue print of the house, but the process of using concrete and bricks to build blueprints is a tiny bit different from building a house of those same brick. There is nothing inherent in a brink that demands that it build a house...

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.

That very same emergence from symmetries is true for numbers!!!!! THis is shown by how we can identify numbers as the equivalence over a class of arithmetic operations. There is not thing *special* about numbers that allows us to violate the neutrality principle that I mentioned above. You seem to ignore the fact that to be "observed by a machine" is not a purely arithmetic act. Numbers, in themselves, do not act at all. They are static relations. A static relation cannot implement an observation or any other kind of action.

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.

Layers which reduction dissolves into nothingness. Eventually the very property of being distinguishable dissolves away too and no properties at all are left with which to distinguish 0 from anything else.

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.
*special properties*? How so? Where does the difference between being a number and not being a number remain at the most primitive level?

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.



Idealism is an epic fail, not matter how sophisticated it is, just as materialism fails and for exactly the same reason.



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