From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
You seem to confuse arithmetical realism, used in all branches of science, and Platonism (which is part of the consequence). To define mathematically what a computation is, we need arithmetical realism. In SANE04, my definition is redundant because the Church-Turing thesis makes no sense at without arithmetical realism.
It is not at all clear what you mean by arithmetical realism -- there seem to be two distinct concepts that are confused. The difference is perhaps most easily captured in the use of the word "exists". If we say that there "exists" an integer between 2 and 4, then that could be called mathematical existence. And that is all that is necessary for mathematics to be used in the rest of science. It is only when you go beyond this concept of mathematical existence and use the word in the same way as we would say that the moon "exists", that you run into trouble. The Church-Turing thesis is nothing magical -- it states only that any function computable by a human using some algorithm is also computable by a Turing machine. One side of this -- the human computing via an algorithm -- requires physical existence of the human. The other side -- the Turing machine -- does not necessarily require a physical machine -- the definition of the machine and its operations would suffice. So the Church-=Turing thesis, in itself, contains a confusion of the two meanings of "exists".
If anyone would believe that arithmetical realism is false, we would have heard argument that Rieman hypothesis or the twin conjecture or Goldbach are senseless. But that does not exist.
That is only one meaning of the word "exists" -- arithmetical realism as I have defined it above. This is not a mode of existence that would allow any actual computation -- it allows only descriptions of computations.
But then, I don't expect that this will convince you that platonism is the confusion of the two meanings of the word "exists", or that the UD in platonia cannot compute anything.
If you could avoid ad hominem remark, that would be nice. Also.
I don't think you know the meaning of '/ad hominem/'. You seem to think that any personal remark is '/ad hominem/'. But strictly, '/argumentum ad hominem/' is something quite different. Look it up!
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