OOPS! I didn't intend to post this to the everything-list; although it may serve as an
introduction for James Lindsay if he decides to join the list. I wrote to him after
reading his book "dot dot do" which is about infinity in mathematics and philosophy.
Brent
On 8/16/2014 9:28 PM, 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.
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 [email protected].
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 <[email protected]
<mailto:[email protected]>> 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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