On 11 Feb 2012, at 07:32, Stephen P. King wrote:
Hi ACW,
Thank you for the time and effort to write this up!!!
On 2/9/2012 3:40 PM, acw wrote:
Bruno has always said that COMP is a matter of theology (or
religion), that is, the provably unprovable, and I agree with this.
However, let's try and see why that is and why someone would take
COMP as an assumption:
- The main assumption of COMP is that you admit, at some level, a
digital substitution, and the stronger assumption that if you were
to implement/run such a Turing-emulable program, it would be
conscious and you would have a continuation in it. Isn't that a
strong theological assumption?
[SPK]
Yes, but it is the "substitution" of one configuration of
"stuff" with another such that the functionality (that allows for
the implementation/running of the Turing-emulable (Turing
equivalence!)) program to remain invariant. One thing interesting to
point out about this is that this substitution can be the
replacement of completely different kinds of stuff, like carbon
based stuff with silicon based stuff and does not require a
continuous physical process of transformation in the sense of
smoothly morphism the carbon stuff into silicon stuff at some
primitive level. B/c of this it may seem to bypass the usual
restrictions of physical laws, but does it really?
What exactly is this "physical stuff" anyway? If we take a hint
from the latest ideas in theoretical physics it seems that the
"stuff" of the material world is more about properties that remain
invariant under sets of symmetry transformations and less and less
about anything like "primitive" substances. So in a sense, the
physical world might be considered to be a wide assortment of
bundles of invariants therefore it seems to me that to test COMP we
need to see if those symmetry groups and invariants can be derived
from some proposed underlying logical structure. This is what I am
trying to do. I am really not arguing against COMP, I am arguing
that COMP is incomplete as a theory as it does not yet show how the
appearance of space, time and conservation laws emerges in a way
that is invariant and not primitive.
So you miss the UDA point. The UDA point is that if COMP is true, it
has to be complete as a theory, independently of the fact that the
shorter time to derive physics might be 10^1000 millenia. Comp
explains, by the UDA, that whatever you add to comp, or to RA, or to
the UD, cannot play any role in consciousness, including the feeling
that the worlds obeys some role. So if comp is correct the las of
physics have to be derived from arithmetic alone. Then AUDA makes a
non trivial part of the derivation. We have already the symmetry of
the core bottom physics, the quantum indeterminacy, non locality, non
cloning. But this is just for illustrating the consistency: the UDA
conclusion is that no matter what, the appearance of matter cannot use
any supplementary assumption to comp and/or arithmetic. You can sum up
the UD by "comp is not completable". It is the Bell-von Neuman answer
to Einstein, in your analogy below. Arithmetic is made conceptually
complete. Whatever you add to it will prevent the comp solution of the
mind-body problem, a bit like evruthing you add to the SWE will
reintroduce the measurement problem in quantum physics. Comp and
arithmetic are conceptually complete, but of epistemologically highly
incomplete and uncompletable.
Also, once you agree that stuff is not primitive, you have to define
it from your primitive terms, which I don't see possible given that
your primitive is the word "existence" which is not defined, nor even
a theory.
I guess I have the temerity to play Einstein against Bruno's Bohr. :-)
See just above.
OTOH, I am not arguing for any kind of return to naive realism or
that the physical world is the totality of existence. I do know that
I am just a curious amateur, so I welcome any critique that might
help me learn.
Comp like QM does not admit supplementary axioms, or variables, to
reinstall a physical realism.
I think it is, but at the same time, it has solid consequences and
a belief in it can be justified for a number of reasons:
a) Fading qualia thought experiment, which shows that
consciousness is utterly fickle if it doesn't follow a principle of
functional / organizational invariance. Most of our sense data
tends to point that such a principle makes sense. Avoiding it means
consciousness does not correspond to brain states and p. zombies.
Certainly! We need a precise explanation for psycho-physical
parallelism.
But there is no psycho-physical parallelism. The metaphysical physical
*is* an illusion, naïve or not. The physical itself is arithmetical
truth see from the observable point of view (suggested to be handled
by the logics of observation Bp & Dt (& p), at the G and G* levels).
My tentative explanation is that at our level a form of dualism
holds. A dualism quite unlike that of Descartes, since instead of
"separate substances", it is proposed that the logical and the
physical are two distinct aspect of reality that follow on equal yet
anti-parallel tracks. As Vaughan Pratt explains in his papers, the
logical processes and the physical processes have dynamics that have
arrows that point in opposite directions. Schematically and crudely
we can show a quasi-category theory diagram of this duality:
---- > X -----> Y ----->
| |
<----- A <------B <-----
I am OK with this. This is already derivable from the many dualisms
contained in the octalist machines points of view, notably between
"intelligible" (Bp) and (matter intelligible Bp & Dt). It does reverse
the arrow in a way akin to Pratt. It is not a parallelism, or anti-
parallelism, though, for the 1p and 3p are not symmetrical. Then the
qualia, and the first person plural quanta, are given by the machine's
semantics for the logic obeyed by Bp & Dt & p.
I have no idea what your neutral monism refer too, except a sort of
vague God-like notion of Existence, but that's not a (scientific)
theory, yet. And, by UDA, whatever it adds to comp and arithmetic has
to refute the comp physics, or comp itself. Craig is, at least,
coherent on this: he abandon comp, to save an unintelligible notion of
matter and mind (alas).
Bruno
The vertical lines represent the Stone duality relation and the
horizontal arrow represent logical entailment and physical
causation. The chaining (or "residuation") rule is "X causes Y iff
B necessitates A", where X and A and duals and Y and B and duals.
This duality prohibits zombies and disembodied spirits. There is
much more to this diagram as it does not include the endomorphisms,
homeomorphisms and other mappings and objects that are involved in
the full implementation of the residuation rule.
I just found a paper by Martin Wehr www.dcs.ed.ac.uk/home/wehr/newpage/Papers/qc.ps.gz
that elaborates on Pratt's idea and explains residuation better!
Here is the abstract:
Quantum Computing: A new Paradigm and it's Type Theory
Martin Wehr
Quantum Computing Seminar, Lehrstuhl Prof. Beth,
Universit"at Karlsruhe, July 1996
To use quantum mechanical behavior for computing has
been proposed by Feynman. Shor gave an algorithm for
the quantum computer which raised a big stream of research.
This was because Shor's algorithm did reduce the yet assumed
exponential
complexity of the security relevant factorization problem, to
a quadratic complexity if quantum computed.
In the paper a short introduction to quantum mechanics can be
found in the appendix. With this material the operation of the
quantum computer, and the ideas of quantum logic will be explained.
The focus will be the argument that a connection
of quantum logic and linear logic is the right type theory for
quantum computing. These ideas are inspired by Vaughan Pratt's
view that the intuitionistic formulas argue about states
(i.e physical quantum states) and linear formulas argue
about state transformations (i.e computation steps).
***
b) Neuroscience and physics suggests that we do indeed admit such
a substitution level, or that the functions of the brain are Turing-
emulable (although obviously the architecture is massively parallel
and running it on a TM is not optimal, but then, neither is running
physics, either way, this is unimportant due to specific(provable)
instances of the CTT(Church Turing Thesis)).
I agree but we do need more detail of the 1p and 3p aspects of
this idea.
c) a and b do not directly suggest the continuity part, although
we can't really guarantee continuity that much ourselves. Given
that we can never experience a moment past our death, we would
always experience being alive, that is, the Anthropic Principle
where the laws of physics happen to be that which support or is
compatible with us (trivial statement, maybe even too general). The
continuity bet is a matter of past observations, although it's
utterly unprovable, on the other hand, we usually expect a next OM
and that we will wake up in the morning, that the sun will "rise"
and so on (by induction, regardless if consciously realized or
not). That one could continue their existence in a different
machine body which is functionally equivalent is not utterly
preposterous to me, at least not much more than when one
considers how strange it must be that their consciousness
follows their body/senses even when the body moves through space
and time, sometimes even with discontinuities (sleep, etc).
This assumption is almost magical, but not really: it's a
consequence of some strong "no magic" assumptions in the nature of
reality, but as we can see, sufficiently advanced technology is
indistinguishable from magic and sufficiently strong "no magic"
assumptions can also be quite indistinguishable from magic (more on
this later).
Pratt's duality explains all of this without any magic at all!
Well there is some magical mathematics... ;-)
d) The UDA paints a picture which seems to include an explanation
for QM/MWI, thus confirming some current physical theories. Your
objection to COMP immortality applies to MWI as well - there is MWI
immortality as well, just a bit more limited in fancifulness. Yet,
MWI is one of the simplest possible realist interpretations of QM
(by various Occam's Razor formalizations). COMP itself scores high
on the simplicity
score - easy to describe ontology (after reasoning is done),
although very rich, it also gives reasonably satisfactory (partial
or full) answers/hints to some ancient questions (such as "why
something instead of nothing", "what is matter", "what is mind"
along with some more concrete questions...)
Yes, MWI still suffers from a basis problem even though
decoherence arguments can seem to make the problem go away
temporarily in calculations, but it returns every time a new basis
is introduced to consider a different set of observables. I
conjecture that "there is something rather than nothing because
something is just a piece of nothing distinguished from another
piece of nothing by a third piece of nothing." As Russell Standish
argued in his book, Nothing and Everything are indistinguishable.
- Another assumption of COMP is the Church Turing Thesis. Very
strong mathematical evidence is for it being true, and we can show
it for just about any finite (but unbounded) machine following
finite rules. It's a hypothesis/assumption because in the general
form it's not provable because it's too general, but we can prove
any individual case we care to try, there's also many strong
intuitions for why it has to be true. I don't think there are many
computer scientists who don't believe in it, but usually those that
don't just try to define CTT in wider scope than it is (such as
hypercomputation, which it obviously doesn't include), such issues
are a matter of definition and shouldn't be considered to be
included in this assumption.
I have no problem at all with CTT, i just have a serious problem
with the idea that CTT is completely divorced from the physical.
- Consistency of arithmetic (existence of the standard model of
arithmetic), existence of truth value of arithmetical sentences.
The existence of truth values does not, in itself, define them.
Additional structure is required to define not only what domain the
truth value lies in but how it is mapped to our propositions and
sentences.
The consistency belief is both intuitive as well as one about a
certain Turing Machine never halting (which can be made in stronger
theories, but cannot be believed any more than you can believe that
arithmetic is consistent). A belief in a sentence being either true
or false independent of anything is not much different from the
belief that a machine either halts or doesn't halt (and no other
choice exists).
This is again a matter of theology - of the provably unprovable
stuff.
Although, again, it's a strong "no magic" assumption, that given a
finite self-contained set of rules (addition, multiplication)
applied on finite self-contained objects (numbers), it will always
yield the same result and nothing whatsoever can change that.
I agree that "given a finite self-contained set of rules
(addition, multiplication) applied on finite self-contained objects
(numbers), it will always yield the same result" but this does not
address my problem. Unless there is something physical that is
somehow different but equal in ontological level to show results
side by side, there is no proof of equivalence, all there is is
modulo isomorphism and barely even that.
- A hidden assumption: we have minds/are conscious/experience
qualia. This is a bit magical, but it's hidden in the first
assumption that I listed.
It is not magical, it is quite ordinary. It is the most ordinary
of facts that I am conscious of what my hands are doing at this
moment, for example... But what is this "my"? If it is just an
illusion generated by some kind of feedback loop, how does the delay
that allows the loop come to be? It is interesting that there is a
mapping in category theory that shows this exact kind of mapping:
the Idempotent Endomap
<endomapIdempotent.png>
It is interesting to note the properties of this mapping. See,
for example: ls.poly.edu/~jbain/Cat/lectures/13.MoreCats.pdf
The thing is - the only thing we can be certain of, but cannot
communicate is having a mind. From our observations we can infer
the existence of the external world and that our bodies are part of
it, we can also observe that the states of our brain correlate very
well with our conscious experience. A different computationalist
theory (eliminative materialism) takes this hidden assumption and
posts its negation as an axiom. The problem with that is that the
external world is only inferred by using observation, thus it
cannot really be accepted by most conscious observers (who are
delusional in such a theory), however such a theory is not
inconsistent if consciousness is ignored. If you ignore the mind
assumption, you can completely ignore almost all of COMP's strange
conclusions because none of them would matter, but the existence of
primitive matter would be saved in such a theory.
I agree. I just do not require matter nor mind to be primitive,
I argue that both are aspects of a single neutral primitive.
All of these are assumptions which are not uncommon for most
secular-minded people: the first is widely considered by the "no
magic" camp, it also is required if you don't want consciousness to
be utterly strange and magic current evidence, the second is widely
considered true by anyone who studied computability/math/comp sci,
the third is usually considered true, if it's false, pretty much
all math we know is false, and there are many intuitions why it's
likely true. Given these assumptions, COMP is a fairly rational
theory with a few unprovable, but widely accepted "no magic"
assumptions. However, even with these assumptions, you can't really
avoid some really unusual magic (given only the first assumption).
The strange conclusion is hidden in the assumptions, just most
people don't see it (strangely it's not uncommon for people to hold
those assumptions and still not see that primitive matter is
utterly incompatible with a non-eliminative form of
computationalism).
I agree.
Onward!
Stephen
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