On 28 Jan 2014, at 14:09, Craig Weinberg wrote:
On Tuesday, January 28, 2014 6:09:33 AM UTC-5, Bruno Marchal wrote:
On 28 Jan 2014, at 07:52, LizR wrote:
On 28 January 2014 17:35, Craig Weinberg <[email protected]> wrote:
On Monday, January 27, 2014 5:24:06 PM UTC-5, Liz R wrote:
On 28 January 2014 10:59, Craig Weinberg <[email protected]> wrote:
I think that 0+1=1 already requires consciousness. If we assume
that from the start, then all further argument is begging the
question. If something can 'equal' something else, then
consciousness is unnecessary.
Could you explain? (I don't understand what's being said in any of
the three sentences above, so would appreciate a "blow by blow"
explanation if that's OK).
By saying that 0+1=1 already requires consciousness, I mean that
all mathematical expressions are intentional communication of a
conscious appreciation of symbolic relations.
In itself, that looks like a confusion of the map with the
territory. Fortunately, however, you have a lot more to say on the
subject...
If we start with disembodied mathematical concepts as realities in
their own right, then we are automatically smuggling in all kinds
of assumptions about what the universe comes with out of the box.
Integers, operators, and equivalence are the end result of a kind
of manufacturing process which includes a lot of ontological raw
materials; sequence, representation, symmetry, universality, ideal
objects, participation in manipulating formulas...lots of things
which have no plausible origin within mathematics.
False. We know now that arithmetic is full of mathematicians. That
is the essence of Gödel discovery (not just in the light of
computationalism). This is brought from Gödel understanding that
arithmetic already do meta-arithmetic. More on this later, probably.
From what I have read, I suspect that Gödel would disagree.
You are right, but I was talking in the comp theory. I should have
said that if comp is true, then arithmetic is full of mathematicians.
By the way, arithmetic is also full of non-machine entities, and some
(most self-referentially correct one) are still Löbian and obeys the
same theology. Infinity by itself does not help to escape the
consequence of comp.
I do not think that incompleteness implicates consciousness within
arithmetic,
Indeed. But the self-consciousness or self-awareness will start, not
from incompleteness, but from the provable incompleteness. (Already
mirrored by Gödel second incompleteness theorem, or by Löb theorem).
Löbian machines are aware of their limitations.
and in fact suggests the opposite - that arithmetic is not complete
enough to contain consciousness.
You misunderstand Gödel. Arithmetic is the reality for which machines,
theories, and any finite beings, are only capable to scratch.
To say that arithmetic is full of mathematicians sounds
unfalsifiable and arbitrary to me.
It is a direct consequence of comp, and of a theorem showing the
representability of the partial recursive function in (Robinson
already) arithmetic (RA). (with comp = Church's thesis + it exists a
level n such ... yes doctor).
If you bet in comp, it exists an infinity of computations going
through you actual state "S". And Löbian machines can prove that. The
existence of all such computations are theorem in RA.
At the very least it is a discovery which is yours and not a popular
understanding within mathematics.
Since how long can woman vote?
It is the normal fear of the others. That kind of thing takes time.
How would you tell the difference between arithmetic being full of
mathematicians and arithmetic being full of impersonal reflections
of the mathematician?
No, no, it is full of mathematicians. With comp, Euler is there, and
Ramanujan too. It is a triviality. Astonishing, but trivial (and only
a tiny part of a difficult but interesting problem deriving physics
from the statistics on those computations).
I think it is a problem of your theory: it solves the problem. It is
more interesting when a theory lead to a problem. Especially to
attract the serious guy with competence, in this morbid and taboo
field. Comp leads to reducing physics to a dreamy arithmetical complex
structures.
They are all figures of experience which are valid because of
aesthetic familiarity - because of the sense that cognitive
awareness furnishes us with. If math can do all of that by itself,
then an additional type of 'consciousness' would be redundant.
That's a good point.
Yes. That is the mind-body problem (that some physicalist call "hard
problem of consciousness", but I prefer the more neutral standard
expression in philosophy of mind).
If we are talking about math though, then we don't need the body. It
is more like the mind-math problem. If you have the math, why do you
need an aesthetic mind?
After Gödel we have reason to expect arithmetic or computerland to be
a very vast country, not unifiable in any effective theory, and full
of infinitely many surprises, good and bad, for everybody or somebody.
But the main interest is that it provides an explanation of the origin
of the physical reality without assuming it, and it provides an
explanation of consciousness (quasi-complete, but with a remaining
mystery which is not hidden). And it is testable.
Comp allows the use of computer science to formulate the question in
math (arithmetic). Mathematical logic provides help to talk about what
the machine cannot talk, yet know.
Bruno
Craig
Bruno
At a slight tangent, it seems possible that the universe has some
of these concepts built in (in some sense). This isn't an objection
to what you're saying, but maybe it should be borne in mind, in
case these are somehow indicative of what can be considered
primitive...
Equivalence - all electrons (say) appear to be identical.
Counting - a BEC (for example) does a sort of simple arithmetic, in
that the universe keeps track of the number of objects involved
even when they aren't even in theory distinguishable.
Symmetry - as I'm sure you know there all lots of examples of this
in physics. All the conservation laws (energy, momentum, etc) can
be expressed in terms of symmetries.
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