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.
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.
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). 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.
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
<mailto: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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