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 <[email protected]
<mailto:[email protected]>> 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.
[SPK]
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.
[SPK]
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)
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.
[SPK]
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.
[SPK]
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.
[SPK]
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.
[SPK]
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.
[SPK]
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.
[SPK]
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.
[SPK]
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.
[SPK]
*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.
OK?
Bruno
[SPK]
Idealism is an epic fail, not matter how sophisticated it is, just
as materialism fails and for exactly the same reason.
Onward!
Stephen
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