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

> > 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.

> > 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. Can they be
described primarily by terms like mass, local boundaries, temperature,
density, interactions with other phenomena that are considered
physical.

> > 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. Including arithmetic. It doesn't
make sense by itself. It needs the physical abacus of a microchip or a
loom or a brain to do that.

> 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.

> > 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? Natural numbers are an invention
of an entity that thinks, and thought is an invention of an 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. Other species would not necessarily be able to
do so. 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.

Craig

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