On 17 Aug 2014, at 07:23, LizR wrote:
PS You do know you can delete posts from the EL, don't you?
But not from the mail boxes. Besides, I am against all post deletions,
except on facebook when people use your wall for advertising, or when
they repeat insults.
What would be nice is an ability to edit mails, for the typo.
Bruno
On 17 August 2014 17:23, LizR <lizj...@gmail.com> wrote:
Never mind, you stated your position nice and clearly, perhaps more
clearly than you normally do on the EL.
(...or is that why you're saying "OOPS!" ? :-)
On 17 August 2014 16:54, meekerdb <meeke...@verizon.net> wrote:
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 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>
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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