On 2/26/2012 12:27 PM, Bruno Marchal wrote:
On 25 Feb 2012, at 20:01, Stephen P. King wrote:
On 2/25/2012 4:31 AM, Bruno Marchal wrote:
On 24 Feb 2012, at 22:59, acw wrote:
On 2/24/2012 12:59, David Nyman wrote:
On 24 February 2012 11:52, acw<[email protected]> wrote:
I look at it like this, there's 3 notions: Mind (consciousness,
experience),
(Primitive) Matter, Mechanism.
Those 3 notions are incompatible, but we have experience of all
3, mind is
the sum of our experience and thus is the most direct thing
possible, even
if non-communicable, matter is what is directly inferred from our
experience
(but we don't know if it's the base of everything) and mechanism
which means
our experience is lawful (following rules). By induction we build
mechanistic (mathematical) models of matter. We can't really
avoid any of
the 3: one is primary, the other is directly sensible, the other
can be
directly inferred.
However, there are many thought experiments that illustrate that
these
notions are incompatible - you can have any 2 of them, but never
all 3.
Take away mind and you have eliminative materialism - denying the
existence
of mind to save primary matter and its mechanistic appearence.
(This tends
to be seen as a behavioral COMP). Too bad this is hard to stomach
because
all our theories are learned through our experiences, thus it's a
bit
self-defeating.
Take away primitive matter and you have COMP and other platonic
versions
where matter is a mathematical shadow. Mind becomes how some
piece of
abstract math feels from the inside. This is disliked by those
that wish
matter was more fundamental or that it allows too many fantasies
into
reality (even if low-measure).
Take away mechanism and you get some magical form of matter which
cannot
obey any rules - not even all possible rules
Nice summary. You say "Mind becomes how some piece of abstract math
feels from the inside", which is essentially how Bruno puts it.
However, this must still fall short of an identity claim - i.e. it
seems obvious that mind is no more "identical" to math or computation
than it is to matter, unless that relation is to be re-defined as
"categorically different". Math and mind are still distinct, though
correlated. Do you think that such a duality can still be
subsumed in
some sort of neutral monism?
Obviously not all computations have minds like ours associated with
them. I'm not sure if identity is the right claim, but I'm not sure
there's much to gain by adding extra "indirection layers" - it's
not that consciousness is associated with some scribbles on a piece
of paper, it's associated with some abstract truths and we could
say that 3p-wise those truths look like some specific structure we
can talk about (using pen and paper or computers), but at the same
time, that that abstract structure does have some sensory
experience associated with it. Other structure might represent some
machines implementing some partial local physics. In that way it's
neutral monist. We could try to keep experience separate and
supervening on arithmetical truth, but I'm not sure if there's
anything to gain by introducing such a dualism - it might make
epistemological sense, but I'm not sure it makes sense
ontologically. I'm rather unsure of such a move myself, I wonder
what Bruno's opinion is on this.
I think that we don't have to introduce an ontological dualism,
because the dualism is unavoidable from the machine points of view,
if you agree to
1) model belief (by ideally arithmetically and self-referentially
correct machine) by Gödel's provability. I can provide many reason
to do that, even if it oversimplifies the problem. The interesting
things is that it leads to an already very complex "machine's
theology". We might take it as a toy theology, but then all theories
are sort of toys.
2) to accept that S4 (or T, = S4 without Bp -> BBp) provides the
best axiomatic theories for knowledge.
Then it can be shown that the modality (Bp & p) gives a notion of
knowledge, i.e. (Bp & p) obeys S4, even a stronger S4Grz theory.
The relevant results here are that G* proves that Bp is equivalent
with Bp & p, but G does not prove that, and so, this is a point
where the "divine intellect" (G*), the believer (G) and the kower
(soul) Bp & p, will completely differ, and this will account for a
variety of dualism, unavoidable for the machine.
So yes, this is neutral monism. The TOE is just arithmetic, and the
definition above explains why, at the least, the machine will
behaves as if dualism was true for her ... until she bet on comp and
understand the talk of her own G*, without making the error of
taking that talk for granted (because she cannot know, nor believe,
nor even explictly express that she is correct).
Hope this might help, but if you want I can explain more on G, G*,
S4Grz, and the Z and X logics. Those are not logic invented to solve
problems, like in analytical philosophy, but unavoidable nuances
brought by the provably correct self-reference logic of machines in
theoretical computer science.
Dear Bruno,
I think that it would help all of us if you wrote up more about G,
G*, S4Grz, Z and X logics.
It needs familiarity with mathematical logic. I can try, but the real
understanding can only come from some work.
G and G* axiomatizes completely the propositional laws of Gödel's
arithmetical provability provable(x), and its dual consistency notion
consistent(x).
To explain this we need to explain how we can program a theory about
numbers in a language containing only the symbol 0, s, + and *. (and
the logical symbol).
This is done in the paper of Gödel, except he used a typed set theory
instead of arithmetic, like it is done in all textbook.
Technically it is long and tedious, with lot of subtle traps, to do
that task. It is like programming a high level programming language in
a low level assembly language, you can expect bugs. So you need to
prove each steps, among many, and you need to ensure that the proofs
you do can be done by the system itself.
For example G proves Dt -> ~BDt means that the Löbian entity (=
self-referentially correct "rich" machine or non-machine different
from "god") can prove their own incompleteness theorem:
consistent('1=1') implies non-provable(consistent('1=1').
S4Grz, will be the logic of an intensional variant of provable(x),
which is provable('p') & p. We cannot use provable(x) & true(x), as
"true" cannot be defined in the language of the entity, so we model it
for each arithmetical sentences p by provable('p') & p. (That's the
essence of what is clever in the Theaetetus' definition of knowledge,
which fits well with the step 6 of UDA, and more generally with the
dream argument in metaphysics.
Likewize Bp & Dt, and Bp & Dt & p, are other important variants. I
will say more when I get more time, but by searching 'S4Grz' or
'hypostase' in the archive you might find the many explanations I
already give. See my papers and the reference therein. Ask precise
question when you don't understand, so I can help.
Dear Bruno,
Thank you for this brief set of remarks. I would like to see an
elaboration of the Löbian entity such that we can see the means by which
the 1p content is encoded. Can, for example, we include a free or atomic
boolean algebra in a Löbian entity?
I would also appreciate your comments on this paper by Barry Cooper:
http://www1.maths.leeds.ac.uk/~pmt6sbc/preprints/rome.paper.pdf
Here is its Abstract:
"Amongst the huge literature concerning emergence, reductionism and
mech-
anism, there is a role for analysis of the underlying mathematical
constraints.
Much of the speculation, confusion, controversy and descriptive
verbiage might
be clari fied via suitable modelling and theory. The key ingredients
we bring
to this project are the mathematical notions of defi nability and
invariance, a
computability theoretic framework in a real-world context, and within
that,
the modelling of basic causal environments via Turing's 1939 notion
of interac-
tive computation over a structure described in terms of reals. Useful
outcomes
are: a re finement of what one understands to be a causal
relationship, includ-
ing non-mechanistic, irreversible causal relationships; an
appreciation of how
the mathematically simple origins of incomputability in defi nable
hierarchies
are materialized in the real world; and an understanding of the
powerful ex-
planatory role of current computability theoretic developments."
Interesting, but still not taking into account the comp mind-body
problem, or the comp first person indeterminacy.
Might say more on this later. It would have been nice I (re)discovered
that paper soon, but many thanks :)
Please also see
http://homepages.inf.ed.ac.uk/jrl/Research/laplace1.pdf which contains
many of the same questions that I have been asking but expressed in a
more formal and erudite manner.
I am still not seeing how you define the philosophical terms that
you are using, as the way that you are using words, such as "dualism"
and "monism" are inconsistent with their usage by others in philosophy.
I use them in the sense of the wiki you did provide to me.
Neutral monism, in the "philosophy of mind" consists in explaining
mind and matter, and the relation between, in term of something else.
Yes, but I see numbers as belonging to the category of mental
content and thus not capable of forming a neutral "something else".
OTOH, if we stick to your consideration that minds are only the 1p then
your argument that COMP is a neutral monism is consistent modulo finite
considerations. I think that considerations of 3p spoils this neutrality
(the Laplace draft paper above touches on this), but let us see what
happens in our discussions.
If your theory is scientific, the something else must be clearly
specifiable, that is itself described by a reasonable theory, so that
the explanation of mind and body from it makes (sharable) sense.
With comp, in short, a TOE is given by RA (ontological), and its
epistemological laws is given by the variants of relative
self-reference of all the (Löbian) numbers. Physics consists in some
of those variants (hypostases).
Some believe that the numbers belongs to the mind, but with comp it is
more natural to define the mind, in a large sense, by the universal
numbers imagination.
This is my prejudice and I am working hard to overcome it. My
resent comment that we have computations (as abstract logical machines)
and physical processes as orthogonal intersections on 1p is an attempt
in this direction. I am trying to remain consistent with Pratt's idea of
state transitions via chained residuation.
The mind is, notably, what computer can explore, quasi by definition
with comp.
Local computers, like the one you are using right now, are universal
number written in physical universal sublanguage of physics. And
normally UDA should help you to convince yourself that physics becomes
necessarily a sort of projective limit of the mind, with comp.
I see physics, in the sense of groups and other relations, as the
mutually consistent sharable content of 1p, but this does not alone
cover us to solve the problem of time. The only solution that I have
seen that is semi-congruent with COMP is Hitoshi Kitada's proposal
(http://arxiv.org/abs/physics/0212092 ).
With comp, the only way to singularize you or your neighborhood
consists in layering down the substitution level in the transfinite.
Why not? The study of comp can help to build rigorous non comp theory.
Sets and hypersets can be helpful for this, indeed. For comp too,
probably.
Ben Goertzel has a very nice paper discussing the use of hypersets
and consciousness here
<goertzel.org/consciousness/consciousness_paper.pdf>. Craig's discussion
of it is here <http://s33light.org/post/17993511503>.
Onward!
Stephen
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