Bruno Marchal wrote:
On 22 Jan 2010, at 20:52, Brent Meeker wrote:
Bruno Marchal wrote:
Hi John,
On 21 Jan 2010, at 22:19, John Mikes wrote:
Dear Bruno,
you took extra pain to describe (in your vocabulary) what I stand
for (using MY vocabulary).
-------------------------------------------------
On Thu, Jan 21, 2010 at 2:17 PM, Bruno Marchal <marc...@ulb.ac.be
<mailto:marc...@ulb.ac.be>> wrote:
John,
What makes you think that a brain is something material? I mean
/primitively/ material.
JM:
I refer to 'matter' as a historically developed */figment/* as used
in "physical worldview" (I think in parentheses _by both of us_).
Nothing (materially) PRIMITIVE, it is an 'explanation' of poorly
understood and received observations at the various levels of the
evolving human mindset (~actual enriching epistemic cognitive
inventory and the pertinent (at that level) application of
relational changing (=function??).
I think we agree on that.
You know (I hope) that I pretend (at least) to have shown that
*IF* we are machine, and thus if our (generalized) brain is a
machine, (for example: we say "yes" to the doctor) *THEN* "we"
are immaterial, and eventually matter itself emerges from the
statistical interference of computations. The term computation is
taken in its original mathematical (and unphysical, immaterial)
sense (of Church, Turing, Post, ...)
Remember that "comp" is the belief (axiom, theory, hypothesis,
faith) that we can survive with an artificial digital (a priori
primitively material for the aristotelian) brain. Then I show
that if we believe furthemore that matter is primitive, like
99,999%of the Aristotelians, we get a contradiction.
JM:
"you have shown..." - your *_DESCRIPTION_ of comp* and I do not
throw out my belief to accept yours;
"Mine" is just the usual one, make enough pecise to prove theorems
from it. But it is really just Descartes, update with the discovery
of the universal machine.
first of all I carry a close, but different term for 'machine'
because IMO numbers are not "god-made" primitives.
I can prove that no theory can prove the existence of the natural
numbers without postulating them (or equivalent things).
They are the inventions in human speculation (cf: D. Bohm)
Of course I differ here. It is the notion of "humans" which is a
speculation by the numbers/machines.
Yet above you note that numbers can only be postulated. Isn't this
an example of misplacing the concrete? You point out that arithmetic
is not only almost all unknown but is, ex hypothesi, unknowable.
What I said is related to the failure of logicism. Some people thought
that we could derive the existence of natural numbers from logic or
very weak theory. But this can be shown impossible. So any theory in
which we have terms denoting the natural numbers contains arithmetic
as a sub-theory. Anyone wanting the natural numbers in its reality,
like a wave physicist who would desire interferences processes, will
have to explicitly or implicitly assumes arithmetic.
Now, having postulated the natural numbers with addition and
multiplication, they organized themselves, independently of our
whishes, in a way which escapes *any* attempt of *complete*
unification. They defeat all our theories, in a sense. Once we
postulate them, they get a life of their own. To understand them, we
have literally no choice, in general, than to observe them and infer
laws.
We can prove that they have definite behaviors, but we can prove
(assuming mechanism) that we cannot predict them, in general.
ISTM that can be read as a reductio against the reality of arithmetic.
On the contrary. It shows that arithmetical reality kicks back. We may
also know greater and greater portion of it. We may discover new
interesting properties, and we progress indeed since a long time. From
Diophantus to Matiyasevitch, to mention a beautiful line.
Are you alluding to fictionalism? Do you defend the idea that "3 is
prime" is a false proposition?
No, I just don't think it's truth implies the existence of "3".
I have no real clue of what that could seriously mean.
Of course I would never expect that someone who doesn't believe that 3
is prime can say anything about the consequence of DIGITAL mechanism.
Such a move cut the uda (and the auda) at their roots, and everything
becomes infinitely mysterious. Frankly I would not ask him to compute
my taxes either.
So why not suppose that the natural numbers are just a model of
perceptual counting; and their potential infinity is a convenient
fiction whereby we avoid having to worry about where we might run out
of numbers to count with?
You can do that. But assuming you are not fictionalist, if you say
that the infinity of natural numbers is a fiction, you are lead, ITSM,
to ultrafinitism.
What's the difference between finitism and ultrafinitism? Doesn't
postulating the integers plus ZF also commit you to existence of the
whole hierarchy of infinite cardinals?
With fictionalism, I think that you can say "yes" to the doctor, and
reject the reversal consequences. This leads to a matter problem, a
mind problem, and the usual mind/matter problem. I would take this as
a defect of fictionalism.
Brent, I am not saying that ultrafinitism and fictionalism are false.
I am just saying that IF you say yes to your doctor's proposal to
substitute the brain for a computer, and this with a reasonable
understanding of what a computer is (and this asks for a minimal
amount of arithmetical realism) then the laws of physics are
necessarily a consequence of the (usual, recursive) definition of
addition and multiplication. Indeed it is the global coupling
consciousness/realities which emerges from + and * (and classical
logic). (or from K and S and the combinators rules, + equality rules
(this is much less)).
A sentence like "naturals numbers are just a model of perceptual
counting" already assumes (postulates) arithmetic. And with digital
mechanism you can explain why universal number can use natural numbers
as "model of their perceptual counting".
You should not confuse the numbers as thought by the philosophical
humans (what are they? does they exists?) with the numbers as used by
mathematicians, physicists or neurophysiologists, like in "this
flatworm has a brain constituted by 2 * 39 neurons" or "all positive
integers can be written as the sum of *four* integers squares.
(Then the number takes another dimension once you say "yes" to the
doctor, because in that case, relatively to the (quantum) environment,
you say "yes", not for a "model", but because you bet the doctor will
put in your skull the actual thing "you", yet through "other matter",
and all what counts is that he put the right number, relatively to the
current environment. That other dimension is somehow the object of all
our discussions).
May be I can ask you a question, which I asked to Peter Jones, and
which is this. Do you see that NON-COMP + arithmetical realism entails
the existence of a realm full of zombies?
No, I don't see that.
Yet, like in the empty wave of the Bohmians, those zombie acts and
talk like you and me, have thought processes, and asks themselves
about mechanism, consciousness, realities, and what constitute their
environment (matter), and all this in a genuine way, as defined by the
logics of (correct/consistent) (relative) self-references. With
NON-COMP, I would be tended toward fictionalism myself, because I
would wish those zombies could not exist.
Such zombies seem like an incoherent concept to me.
In a sense, there *exist* local zombies, because from their own first
person points of view, they belong to the projection of the set of all
computations. Their first person indeterminacy bears on the whole
computational space, and what is observable in any stable way can only
belong to the border of that space.
How do you define the border of computational space?
This is really just a consequence of the impossibility to be aware of
the UD delays, or of where "we" are in (Sigma_1)-reality, or
comp-reality. The comp supervenience thesis is hard to explain without
digging in the details, but consciousness, our consciousness, is
related to a big infinite cloud of intricate number relations. The
"identity thesis" is partially justified only in a very relative and
local way. It is a bit like the appearance of a collapse in the QM
without collapse.
I don't find the multiple-worlds interpretation of QM very convincing
either. In conventional QM it implies that a single radioactive atom
causes a continuous splitting of the world. I suspect that real numbers
should not be taken seriously.
Brent
Bruno
http://iridia.ulb.ac.be/~marchal/
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