On 30 Oct 2012, at 19:52, meekerdb wrote:

On 10/30/2012 10:43 AM, Quentin Anciaux wrote:

2012/10/30 Stephen P. King <stephe...@charter.net>
On 10/30/2012 12:51 PM, Bruno Marchal wrote:

On 30 Oct 2012, at 17:04, meekerdb wrote:

On 10/30/2012 4:30 AM, Bruno Marchal wrote:

My argument is that concepts of truth and provability of theorems apply only to the concepts of numbers and their constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them for some machine/numbers. If not, comp does not even makes sense.

So your are agreeing? "Two" has no truth value, but "Two equals one plus one." does.

Yes I agree. It seems I insisted on this a lot.
But in this context, it seems that Stephen was using this to assert that the truth of, say "Two equals one plus one." depend on some numbers or subject having to discover it, or prove it.



Dear Bruno,

My point is that a number is not a capable of being an ontological primitive *and* having some particular set of values and meanings. A statement, such as 2 = 1+1 or two equals one plus one, are said truthfully to have the same meaning because there are multiple and separable entities that can have the agreement on the truth value. In the absence of the ability to judge a statement independently of any particular entity capable of "understanding" the statement, there is no meaning to the concept that the statement is true or false. To insist that a statement has a meaning and is true (or false) in an ontological condition where no entities capable of judging the meaning, begs the question of meaningfulness! You are taking for granted some things that your arguments disallow.

Hmm... but that's what arithmetical realism is all about... If you deny meaning to '17 is prime' absent an entity which gives to it its meaning... then you're simply negating arithmetical realism and with it computationalism (ie: consciousness is emulable qua computatio).

I don't see why denying mathematical realism would entail saying no to the doctor.

It implies not saying "yes" qua computatio. It implies NOT understanding what Church thesis is about, as to show it consistent you need the diagonalization, which use the excluded middle principle.
You can still say "yes", but only by using some magic.

The doctor isn't proposing to replace part of you brain with a piece of Platonia, he has a real physical device to implant.

This is not related. That will follow step 8.

Here, you have to be arithmetical realist to get an idea of what a computer is, and how it functions, as the physical one will approximate it, well enough, it is hoped.

Of course you can say "yes" to the doctor, just because you trust him. But comp is not "saying yes" to the doctor. Comp is the doctrine that saying yes will indeed work, once the artificial brain is a *computer*. The definition of computer makes no sense with arithmetical realism.



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