On 01 Jul 2012, at 20:20, meekerdb 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.

That would contradict the Arithmetical realism, and thus Church thesis, comp, etc.


We can implement them in physical system, but this does not make them physical.

They are abstractions.

If you want. This changes nothing.

There is no need of step 8, here. It is just a mathematical fact that arithmetic emulates all programs, in the mathematical sense of "emulate".

That's a metaphorical sense.

Not at all.

"Arithmetic" doesn't act or perform anything,

Acting and performing are the metaphor here. Computation is a purely mathematical notion discovered before the building of physical computer. Some could even argue that the physical reality can only approximate them.

Right.  They are idealizations.

And with comp we have to define eventually notion like acting and performing from the relation between numbers, and this is rather easy to do.

That doesn't follow. Comp only says that we could substitute some different physical structure for part (or all) of a brain, and so long as the input/output functions were always

At some level,

the same consciousness would be unchanged.


So comp allows that we may still need a physical realization of the functionality.

In which case physical inactive object, with respect to a particular computation, must be physically active. That is a contradiction. Cf step 8.

That this can be described by relations between numbers does not entail that it is replaceable by the abstraction.

Indeed, and that is why there is a step 8.

What is difficult is to get the right measure on the computations, not to define action and performance. I am explaining what is a computation on the FOAR list, but you can find it also in any textbook on theoretical computer science. No notion of physics are involved at all in the definition.

But those definitions are concerned with abstracting away the physical,

If you want.

since the physical realization can be different for (approximately) the same function.

You are confusing a computation with its implementation in a physical reality. Computations have been discovered in the mathematical reality, before we implemented them in the physical reality. They exist independently of us, once you agree that 17 is prime is true independently of us. And "17 is prime independently of us" is obligatory to explain what Church thesis is, so we assume that implicitly when saying "yes" to the doctor.

It is no different than abstracting apples and oranges as fruit so that we can add one apple to one orange and get two fruit. It doesn't make apples and oranges the same thing.

Sure. But it makes both of them being incarnation of fruit, showing that fruit can exist even without apple or without orange.



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