On 7/1/2012 5:21 PM, Jason Resch wrote:


On Jul 1, 2012, at 6:27 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:

On 7/1/2012 2:46 PM, Jason Resch wrote:


On Jul 1, 2012, at 2:07 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:

On 7/1/2012 11:50 AM, Jason Resch wrote:


On Sun, Jul 1, 2012 at 1:20 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:

    On 7/1/2012 4:59 AM, Bruno Marchal wrote:


        On 01 Jul 2012, at 09:41, meekerdb wrote:

            On 7/1/2012 12:17 AM, Bruno Marchal wrote:


                On 30 Jun 2012, at 22:31, meekerdb wrote:

                    On 6/30/2012 12:20 PM, Bruno Marchal wrote:


                        On 30 Jun 2012, at 18:44, Evgenii Rudnyi wrote:


                            I think that you have mentioned that mechanism is
                            incompatible with materialism. How this follows 
then?


                        Because concerning computation and emulation (exact
                        simulation) all universal system are equivalent.

                        Turing machine and Fortran programs are completely
                        equivalent, you can emulate any Turing machine  by a 
fortran
                        program, and you can emulate any fortran program by a 
Turing
                        machine.

                        More, you can write a fortran program emulating a 
universal
                        Turing machine, and you can find a Turing machine 
running a
                        Fortran universal interpreter (or compiler). This means 
that
                        not only those system compute the same functions from N 
to
                        N, but also that they can compute those function in the 
same
                        manner of the other machine.


                    But the question is whether they 'compute' anything outside 
the
                    context of a physical realization?


                Which is addressed in the remaining of the post to Evgenii.  
Exactly
                like you can emulate fortran with Turing, a little part of
                arithmetic emulate already all program fortran, Turing, etc. 
(see
                the post for more).


            Except neither fortran nor Turing machines exist apart from physical
            realizations.


        Of course they do. Turing machine and fortran program are mathematical,
        arithmetical actually, object. They exist in the same sense that the 
number
        17 exists.


    Exactly, as ideas - patterns in brain processes.


Brent,

What is the ontological difference between 17 and the chair you are sitting in? Both admit objective analysis, so how is either any more real than the other?

You might argue 17 is less real because we can't access it with our senses, but neither can we access the insides of stars with our senses. Yet no one disputes the reality of the insides of stars.

We access them indirectly via instruments and theories of those instruments.


Are numbers not also inferred from theories of our instruments?

But not perceived.  They are part of the theory, i.e. the language.

Other branches of the wave function are not perceived either. They are part of the theory though, so can be considered real.

Or not. They are part of a theory that has great predictive power, which is why we think the theory is a good one - not necessarily *really real*. Being 'considered real' is just a sort of provisional assumption for purposes of calculation. The wave function that is written down is just a way of summarizing an experimental preparation. Whether there is also a *really real* wave function of the universe (or even of the laboratory) is moot.


Numbers and Turing machines are part of Bruno's theory. I don't see the difference. Why can't Turing machines exist?

Sure they can.  I can program this computer to be one - except it might run out 
of 'tape'.





For example, computers are instruments that let us observe and study the properties of various Turing machines, which themselves are mathematical objects.

You might argue the chair is more real because we can affect it, but then you would have to conclude the anything outside our light cone is not real, for we cannot affect anything outside our light cone.

You can kick it and it kicks back.

Math kicks back too. If you come up with a proposition, it kicks back with either true or false.

Only metaphorically.

The whole "it's real if it kicks back" idea is a metaphor. I think the point of the metaphor is that to be real something needs to have its own properties which we have limited or no control over. It is not malleable to our whims or will, but resists attempts to change it.

But we can interact with it and potentially change it.






Of course there are many events outside one's lightcones which one infers as part of a model of reality based on the events within one's lightcones, e.g. I suppose that the Sun continues to exist even though the photons I from which I infer it's existence are from it's past.

Explain then why one is mistaken in supposing mathematical objects exist, when they can be inferred according to some models of reality.

Explain why Sherlock Holmes doesn't exist according to Conan Doyle's model of 
reality.

Sherlock holmes does exist, but then what is Sherlock holmes? A character described in some books.

Conan could have changed anything he wanted about Sherlock holmes, and therefore he doesn't "kick back".

You forget how he was forced to revive Holmes by the public after he killed him 
off.


If you asked two people what properties Sherlock holmes has that were not answered in the book there would be no agreement, and no way to study Sherlock holmes as an objectively real object. Only the texts can be studied.

That's right. We can discover properties of real things that are not part of their defining description - unlike say the number 17.


This is not true of mathematical objects. Properties are not enumerated in some text. They are not subject to be defined or changed by some authority. Two mathematicians, whether on earth or on different planets can make the same discoveries about the same objects.

Further, mathematical realism is a useful scientific theory. It provides explanations for scientific questions. Why you don't see it as a legitimate theory is a mystery to me.

I see arithmetic as a legitimate theory of things you can count, i.e. it describes the results of some operations with them, provided you map the theory to the things in a valid way. But the same it true of say the theory of elastic bodies.


If you don't support the theory, that is fine, but it seems like you discount it's possibility altogether because only "real physical things" can be real.

I don't discount the possibility that Bruno's 'everything is arithmetic' might be a good model, I just haven't seen any predictive power yet. My metaphysical view is that only some things are real. When you start from premises like 'everything exists' you've just set yourself the task of saying why we have only the experiences we do, the ones for which we invented the word 'real'. If you can't satisfy that task, then you haven't gotten anywhere.








Also, how do you know the chair is anything more than a pattern in a brain 
process?

How do you know you're not a brain in a vat?  or a pattern in arithmetic?

This was my point. You say math exists only in our minds. But an immaterialist could say the same of the chair.

He could say it, but he would be redefining what 'exists' means.

What is your definition?

Of course we could all be deluded and living the Matrix, but that idea has no predictive power. I already gave a definition of exists, that which we can interact with; although it's more than that since we interact with things in our dreams. Have you ever read one of those adventure novels written for kids in which at various points you make a choice and it says go to page xx, so that the continuation of the story depends on your choice? That's the way math textbooks are. You start with axioms and you deduce things from them or a while, then you introduce a new axiom and see where it leads, then you consider a contrary axiom and consider what it implies.

Bruno says digital computation is unique because all the different models of computation seem equivalent. That makes his theory interesting, but it doesn't make it true. After all it was invented to model what people can do by rote using pencil and paper - and finite resources; the infinite tape is just a theoretical convenience, just like the assumption of infinitely many integers. If you're going to elevate mathematics to ontology then there's no reason it has to be constrained by human understanding. We could take geometry, or set theory, or hypercomputers to be fundamental.

Brent




To escape this we need some model of reality which postulates more exists "out there" than can be found in one's mind.

Materialism generally postulates more than what exists in your mind. That's how it explains the intersubjective agreement of perceptions.


Right.


Your model seems to assume an external world exists, but it stops exactly where our instruments and inferences from their observations end.

Not at all. That's whole point of having a model and not just an encyclopedia of data. A model makes predictions beyond the data on which it was based.

I agree.




Humanity's model of reality has over the centuries, been repeatedly extended. Therefore I think it is more conservative to believe there is more "out there" than we can see or imagine.

I'm not a conservative.

Good to know.

Jason



Brent
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