On 17 Aug 2014, at 06:28, meekerdb wrote:
On 8/16/2014 4:57 PM, James Lindsay wrote:
Hi Brent,
Thanks for the note. I like the thought about mathematics as a
refinement of language. I also think of it as a specialization of
philosophy, or even a highly distilled variant upon it with limited
scope. Indeed, I frequently conceive of mathematics as a branch of
philosophy where we (mostly) agree upon the axioms and (mostly)
know we're talking about abstract ideas, to be distinguished from
what I feel like I get from many philosophers.
I am not familiar with Bruno Marchal,
Here's his paper that describes his TOE. It rests on two points for
which he gives arguments: (1) If consciousness is instantiated by
certain computational processes which could be realized in different
media (so there's nothing "magici" about them being done in brains)
then they can exist the way arithmetic exist (i.e. in "platonia").
And in platonia there is a universal dovetailer, UD, that computes
everything computable (and more), so it instantiates all possible
conscious thoughts including those that cause us to infer the
existence of an external physical world. The problem with his
theory, which he recognizes, is that this apparently instantiates
too much. But as physicist like Max Tegmark, Vilenkin, and Krause
talk about eternal inflation and infinitely many universes in which
all possible physics is realized, maybe the UD doesn't produce too
much. He thinks he can show that what it produces is like quantum
mechanics except for a measure zero. But I'm not convinced his
measure is more than wishful thinking.
Hmm ... You should say instead: "he claims having proved that if the
brain works like a digital computer, then physics is given by a
measure on all computations, making comp + some theory of knowledge
testable, but I think there is a flaw.
The existence of that measure is a consequence of "taking comp
seriously enough", without adding ad hoc selection principles. It
might be wishful thinking, but then the point would be that
computationalism would be itself wishful thinking.
He's a nice fellow though and not a crank. So if you'd like to
engage him on any of this you can join the discussion list everything-list@googlegroups.com
.
Thanks Brent.
and I am not expert in theories of anything, much less everything,
based upon computation or even computation theories. I remain a bit
skeptical of them, and overall, I would suggest that such things
are likely to be theories of everything, which is to say still on
the map side of the map/terrain divide.
I agree. But some people assume that there must be some ultimate
ontology of ur-stuff that exists necessarily - and mathematical
objects are their favorite candidates (if they're not religious).
But I disagree. There is no ur-stuff at all. There is an appearance of
ur-stuff. Numbers or combinators are not stuff. Nothing is made-of
numbers, but numbers relation can support hallucination, when we
suppose comp, and the hard part of the mind-body problem consists in
explaining the stability of some those hallucinations, as there is an
inflation of dreams in the arithmetical reality (with dreams in the
large sense of computation enough rich to support the activity in the
brain of a conscious person at the right level or below).
Despite with comp we can take (N, +, *) as the ultimate reality,
science like physics or theology remains quite distinct from number
theory per se. Arithmetic is the absolute reality, but only because we
are willing to commit the religious act of faith of believing in some
technological reincarnation.
I don't think this is a compelling argument since I regard numbers
as inventions (not necessarily human - likely evolution invented
them). I think of ontologies as the stuff that is in our theories.
Since theories are invented to explain things they may ultimately be
circular, sort of like: mathematics-> physics-> chemistry->biology->
intelligence-> mathematics. So you can start with whatever you
think you understand. If this circle of explanation is big enough
to include everything, then I claim it's "virtuously" circular.
But mathematics, even arithmetic are not theories, they are realities
or realms. The theory are PA, or, in a slightly larger sense, machine,
bodies, finite piece of thing.
With comp you can start from any Turing complete theory, without
adding any extra ontology, which will reappear as appearance from the
internal, first person view, of the enough rich self-observers whose
existence is a consequence of the axioms defining the Turing complete
theory we start with. That can lead to some virtuous circle, running
in a non circular way.
Bruno
Brent
"What is there? Everything! So what isn't there? Nothing!"
--- Norm Levitt, after Quine
Regarding your note about my Chapter 2, that's an interesting point
that he raises, and interestingly, I don't wholly
disagree with him that it is an integral feature of arithmetic that
it is axiomatically incomplete (though maybe I thought differently
when I wrote the book). Particularly, I don't think of it as a
"bug," but I don't necessarily think of it as a "feature" either.
I'm pretty neutral to it, and I feel like I was trying to express
the idea in my book that it reveals mostly how theoretical, as
opposed to real, mathematics is. I'm not sure about this "more than
a map" thing yet, as by "map" I just mean abstract way to work with
reality instead of reality itself and hadn't read more into my own
statement than that.
I would disagree with him, however, that it is related to the hard
problem of consciousness, I think, or perhaps it's better to say
that I'm very skeptical of such a claim. Brains are, however
"immensely" complex, finite things, and as such, I do not think
that the lack of a complete axiomatization of arithmetic is likely
to be integrally related to the hard problem of consciousness.
Maybe I just don't understand what he's getting at, though. Who
knows?
I also tend to agree with you--in some senses--about the
ultrafinitists probably being right. My distinction is that I'm
fine with infinity as a kind of fiction that we play with or use to
make calculus/analysis more accessible. I certainly agree with you
that infinity probably shouldn't be taken too seriously,
particularly once they start getting weird and (relatively) huge.
There's something interesting to think about, though, when it comes
to the ideas of some infinities being larger than others. I was
thinking a bit about it the other day, in fact. That seems to be a
necessary consequence of little more than certain definitions on
certain kinds of sets (with "infinite" perhaps not even necessary
here, using the finitists' "indefinite" instead) and one-to-one
correspondences.
Anyway, thanks again for the note.
Kindly,
James
On Sat, Aug 16, 2014 at 1:14 AM, meekerdb <meeke...@verizon.net>
wrote:
After seeing your posts on Vic's avoid-L list, I ordered your
book. I'm generally inclined to see mathematics as a refinement of
language - or in your terms a "map", not to be confused with the
thing mapped. However I often argue with Bruno Marchal, a logician
and neo-platonist, who has a TOE based on computation (Church-
Turing) or number theory. I thought you book might help me. But I
think Bruno would rightly object to your Chapter 2. He considers
it an important feature of arithmetic that it is
axiomatically incomplete, i.e. per Godel's theorem
it is bigger than what can be proven from the axioms. He takes
this as a feature, not a bug, to explain that if conscious thought
is a computation this is why it cannot fully explain itself; and
that is why "the hard problem" of consciousness is hard. I think
there are simpler, evolutionary explanations for why consciousness
does not include perception of brain functions, but I think Bruno
has a point that arithmetic is bigger than what follows from
Peano's axioms and so it is more than a map.
I'm inclined to say Peano's axioms already "prove too much" and the
ultrafinitists are right. Infinity is just a convenience to avoid
saying how big, and shouldn't be taken too seriously.
Brent Meeker
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