On 2/5/2012 2:09 AM, Russell Standish wrote:
On Sat, Feb 04, 2012 at 01:22:10PM +0100, Bruno Marchal wrote:
On 03 Feb 2012, at 23:24, Stephen P. King wrote:
I am not missing a thing, Bruno. You are missing something
that is obvious to the rest of us.
If someone else can confirm this, and put some light on what Stephen
is saying, I would be pleased.
Having had some skype discussions with Stephen, I believe Stephen is
referring to "that which breathes fire into the equations", as Hawking
puts it.
Hi Russell,
Thank you for these remarks!
We all agree that COMP does not posit any particular "fire breather" -
any entity capable of universal computation will do. Bruno selects
Peano arithmetic as a sufficient system (PA supports universal
computation), for pedagogical reasons, although he'd really rather use
combinators, which would also suit the purpose, but are less known.
Yes, "no particular "fire breather"". My claim is that while that
claim is true, we simply cannot remove the need for the in principle
existence of a "fire breather", to use the analogy. Universality removes
the restriction of computation as an abstract process but it does not
eliminate the need for some form of physical implementation albeit not
limited to an "actual physical thing". Any form of physical
implementation will do. So we can talk about a pair of logical theories
"interviewing" each other in a coherent fashion but only when those
logical theories are implemented on a common concrete substrate.
Entities in Platonia cannot have conversations. There is no "fermionic"
aspect in Platonia.
Stephen is objecting that such abstract systems are, well, too
abstract. He'd prefer something more concrete - whatever "concrete"
might actually be.
Not quite so, I claim that however abstract an entity is, it will
always have a concrete dual however ephemeral that level of abstraction.
I prefer to not fall into the trap of reducing that which cannot be
captured by our abstract representations intoepiphenomena
<http://en.wikipedia.org/wiki/Epiphenomenalism> and thereby undermine
the entire edifice of mathematical integrity. What good is it to claim
that our mental life is a causally ineffective "illusion" and yet has
the power to discover all of the wonders of mathematical properties, for
instance. To do so is to only sweep the hard parts of the mind-body
problem into a far distant corner. We can push the hard problem out to
infinity but it is still there.
My point is that some form of dualism is inevitable. Platonism is
ultimately dualistic because it has to include the ability of entities
to percieve the properties of mathematical object, aka The Forms. Unless
we posit our existence to be at the same level as the Forms, how can we
explain the effect that the Forms have on our individual and finite
minds? To do this would be to obviate the entire point of the Forms
being "perfect". To be consistent with the requirements of Ideal Monism,
we cannot even consider any notion of implementation of it, this
includes the ability to make sounds about it or make marks on our papers
about it or type out email postings, etc. Ideal Monism is a theory of
free floating casually ineffective ideas that, like pure photons, can
never touch each other.
It is true, I understand, that the UDA (and AUDA) does
not eliminate the possibility of a "concrete physical
underpinning".
And that is the ground upon which I am making my claim. All I am
asking for is the mere "possibility of a "concrete physical
underpinning"". That is sufficient for the duality to flow. The duality
that I am considering is just an extension of the Stone duality, where
instead of fixed and static "snap shots" of Boolean Algebras dual to
fields of sets (such as topological profinite spaces), we are
considering the "movie" version of this. That way we can include notions
of evolution and, possibly, novelty as Vaughan Pratt pointed out in his
ground breaking paper <http://boole.stanford.edu/pub/ratmech.pdf>.
It is just that such a concrete physical underpinning has
no measurable, or detectable effect on our phenomonology other than
that due to its capability of universal computation.
I disagree. The concrete physical underpinning *does* have a local
(not global) effect on how one computation can interface with another,
which is important in discussions of "interviews". By considering only
the global aspects we are completely neglecting problems such as
concurrency <http://en.wikipedia.org/wiki/Dining_philosophers_problem>.
The problem that I have with the Platonic interpretation is that it
tacitly assumes a single absolute space (ala Newton) in and on which
computations, as in the UD and UD*, and since there is an implied
infinite speed of connections on such a space, the notion of time
vanishes. The problem is that we cannot handle questions about multiple
finite non-anthropomorphic observers in such a scenario. "Time exists
because not everything can happen simultaneously."
Which is why I'd like to remind people of Witgenstein's comment: Whereof
one cannot speak, thereof one must be silent.
Most assuredly! But we should never just retreat from hard problems
into obscurantism <http://en.wikipedia.org/wiki/Obscurantism>.
Onward!
Stephen
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