On 7/2/2012 4:10 AM, Bruno Marchal wrote:

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

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

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.


A big carve out of the preceding thread... We need an exact definition of Realism!


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,

But is this level reachable by finite means?

the same consciousness would be unchanged.


But how exactly would we measure this invariance of consciousness? How do we deal with the parochial nature of the encodings of the diaries that the various observers write such that we have something like a 3p account of the experience? What I write in my diary might be in a code that only I might understand, so how do we compensate for this variability of language?

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.

In the case of a Mach–Zehnder interferometer we see that what appears to be physically purely passive and inactive arms can and does play a real and causal part such that its removal makes a difference.

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.

But Step 8 makes a leap too far. It mistakes the relative independence of computations for complete separation from physical systems.

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.

We do!

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.

There simply is not such thing as a computation if we remove its implicated connection to the possibility of actual physical implementation. To remove the possibility is to disconnect it completely from the ability to be communicated. Purely abstract statements by your definition cannot cause any change in a physical system nor be correlated with any particular configuration of brain states, thus they are perpetually beyond our ability to apprehend them.

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.

Nope, sorry. That simply doesn't work. Categories cannot be defined from the inside that do not have non-labelable members. To claim otherwise is to refute your entire result. How can you communicate its significance if you cannot write it down?



"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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