On 06 Aug 2011, at 13:42, Craig Weinberg wrote:

On Aug 6, 6:16 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 05 Aug 2011, at 20:26, Craig Weinberg wrote:

That is my point exactly: inter-subjective agreement is as close to
objectivity that we can get.

Of course this is debatable. I would say that elementary arithmetic
is
objective per se. But physical realities can indeed be shown, or
argued to be,  a first person plural construct in the DM theory.

It's an interesting proposition, but gets semantic and murky around
what we really mean by arithmetic.

I don't think so. We just need to agree on elementary principles, like
"0 is not a successor, two different numbers have different
successors, the addition and multiplication laws.

If we 'need to agree on elementary principles' doesn't that mean it's
intersubjective?

If we agree on principles, it means it is intersubjective, but this does not mean it is necessarily not objective. Something can be both intersubjective and objective.


That being burned causes pain or that pain hurts
doesn't need to be agreed upon at all.

We are not on the same wave-length. If you do a theory of sensations, you might use the assertion that "pain hurts" as an axiom. You will have to ask them to agree on them. It is not because many will agree that there is no an agreement. Of course "pain hurts" is a rather objective statements on a subjective experience. I guess in many theory things like that might be derived from more primitive definitions.






We would personally have to access
arithmetic through subjective awareness,

I am not sure we can access anything out of our subjective awareness.

That's what I'm saying.

OK (with this).



so wouldn't that make it part
of our physical reality?

This does not follow from being accessible through our subjective
awareness, given that the physical is not, a priori.

"physical" is not something many people agree on, despite the
Aristotelian persisting brainwashing (and millions years of evolution).
But arithmetic is without doubt part of our reality, whatever it is.
It is certainly reflected in some way in our (emergent) physical
reality.

Physical to me is just an intellectual category of phenomena which can
be characterized by their adherence to physical law.

And what is a physical law?



Can they be
described primarily by terms like mass, local boundaries, temperature,
density,

That are measurable numbers. The one normally related to mathematical laws.



interactions with other phenomena that are considered
physical.

That is circular.




I think that I could have a dream where 2+2=5
and it could make perfect sense in the dream.

Dreams illustrates that sense can be put on anything.

Right. That's the point. If you turn it around, nothing can make sense
unless you make sense of it also

Not sure. The dinosaurs made sense before the humans made sense of them. I think that the primality of 17 makes sense independently of any observer or physical reality. I mean that the proposition that there is no numbers different from 1 and 17 capable to divide 17" is true in all circumstance. Even in absence of a physical reality. Indeed I begin to explain that such arithmetical truth implies the existence of consciousness and stable first person plural beliefs in local observable physical phenomena.




. Including arithmetic. It doesn't
make sense by itself.

Why would you need an observer for making true that only 1 and 17 divides 17?
That seems to me super-anthropocentric.

I think you are confusing the truth of "1 and 17 are the only numbers dividing 17" with the proposition "humans have discovered that 1 and 17 are the only numbers dividing 17"






It needs the physical abacus of a microchip or a
loom or a brain to do that.

Why?
Also, those object makes use of more complex arithmetical relations.



In a dream I
thought that some windows' curtain disproved "p -> p".
"2+2 = 5" can make sense in a lot of real contexts, like biological
one, but this just means you have to use something else, nit the
natural numbers, to describe the process. One proton + one proton can
give thousand of particles, if smashed with the relevant energy, but
one proton is not the number one, and smashing is not arithmetical
addition.

I would say that it's
still intersubjective, only the scope of phenomena which shares access
to it encompasses non-living matter as well as symbolic abstraction.

The day I wake up believing that comp is true, I don't believe in non
living matter, nor any stuffy matter at all. It is in our number mind.
Matter is a projection from inside coherent sharable piece of dream/
computations.

I agree that matter, as it is experienced subjectively, is a
projection of the PRIF, which is at heart mathematical relations, but
they are mathematical relations of what? Feeling. Sense. Experience.
These things can insist without even mathematical coherence. Pain
needs nothing except it's ability to inspire the motivation for it to
end. Any mathematics are superimposed as an afterthought.

In your opinion. If by math you mean analysis and physics, I can give sense to what you say in the comp theory. But I have to assume the numbers at the start. Most theories do it. On the mind-body issue, which is transdisciplinar, we have just to be entirely explicit.



Also, what if a system of arithmetic is derived from physical
isomorphism instead? If, like drops of water, 2+2 =1 big water drop.

Computers used all the time the boolean law 1+1= 0. But this does not
put any doubt that the natural 1 added to the natural number 1 gives
the natural number 2. It just means that there are different sort of
numbers, and/or different operation on them.

If there are different sorts of numbers and operation, then how can
they really be objectively primitive?

I don't see any problem. There are different sorts of dinosaurs too. They might be, in some theory, different sort of particles. This might be in each case independent of the objective nature, or relative objective nature of such objects.



Natural numbers are an invention
of an entity that thinks,

The existence of numbers, with the laws of addition and multiplication, entails the existence of universal numbers. They can introspect themselves and discover, for themselves, the numbers and their laws. They can even discover themselves in there, and this on a variety of levels.






and thought is an invention of an entity
that feels.

The question which interests me is: who invented the entity that feels?





I do agree that arithmetic may be as close to objective that we can
get,

OK, nice.

but I'm not convinced that it doesn't arise from proto-numerical
phenomena of an infra-quantitative, gestural nature.

It can't. Natural numbers can't be explained from something which does
not assume them, or equivalent. The very concept of formal system use
the notion of numbers at the meta-level.
Also, everyone can agree on simple axioms for the (natural) numbers. I
am not sure this might be sustained for concepts or words like proto-
numerical, phenomenon, infra-quantity, gestural, and nature.

It's only humans who are educated in mathematics that can agree on
natural number axioms.

Well, that's enough, if *you* agree with them.
But I think it is false. Aliens will agree with us, or without us, that 17 is prime (when asserted in their language). All Löbian entity agrees with this, and the class of Löbian entity can be said to enlarge a lot the class of humans. (I am no talking about *correct* Löbian machines). Even RA asserts that (x divides 17) implies that ((x = 1) or (x = 17)), with (x divides y) defined by (it exists z such that x*z = y).



Other species would not necessarily be able to
do so.

Why not?



Where were numbers 100MY ago? There were certainly gestural,
natural phenomena present on the biosphere, but I don't believe that a
single natural number was yet conceived.

By humans? Probably not. But 17 is prime in an out of time and out of space manner. Indeed, subjective time, and varieties of physical times emerge from "17 is prime" & Co (assuming comp). This makes comp testable.

(UDA explains why, assuming comp, and AUDA explains how, assuming just addition and multiplication (and definitions, of course, notably Theaetetus' classical definition of knowledge).

Bruno


http://iridia.ulb.ac.be/~marchal/



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