On 05 Aug 2011, at 20:26, Craig Weinberg wrote:

On Aug 5, 1:00 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 05 Aug 2011, at 01:37, 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.



We would personally have to access
arithmetic through subjective awareness,

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



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.




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. 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.



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.



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.

Bruno

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



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