On 22 Apr 2017, at 21:58, John Clark wrote:
On Sat, Apr 22, 2017 Stathis Papaioannou <[email protected]> wrote:
>> Suppose just for the sake of argument that non-
physical computations did not exist, how would our physical world be
different? There would be no difference. Therefore either non-
physical computations do not exist or they do but are utterly
unimportant, rather like the luminiferous aether.
> This is equivalent to supposing that mathematical Platonism
is false.
Not exactly. Einstein didn't prove the luminiferous
aether didn't exist in the Platonic sense, he just proved it was
unimportant. I suppose you could say in the vague way that Greek
philosophers love that correct mathematical calculations exist
independently of matter, but the trouble is incorrect mathematical
calculations exist too, and the only way to differentiate the
correct from the incorrect is by using matter that obeys the laws of
physics. And separating the stuff we want from the stuff we don't is
important, that's why we say Michelangelo's huge statue of David is
500 years old and not far older even though in the platonic sense
David was inside a gigantic block of Carrara marble for 100
million years and all Michelangelo did was unpack it, he just
removed the parts of the block that weren't David.
Bruno likes to talk about Robinson Arithmetic but as far as I can
tell even Raphael Robinson never claimed he had proven the
existence of non-physical calculations,
Perhaps not explicitly. What Robinson showed was the essential
undecidability of his Arithmetic theory, (PA without induction + the
predecessor axiom), and it has been shown soon after that essential
undecidability is equivalent with being powerful enough to prove and
represents in arithmetic all computations.
instead he showed that if you do certain activities in a certain
sequence then you can produce correct mathematical calculations
without producing any incorrect mathematical calculations. But
without matter that obeys the laws of physics you can't "do" anything,
You beg the question and just make an ontological commitment.
that's why a book by itself can't perform a calculation or "do"
anything else either, not even a book on Robinson Arithmetic.
No one ever asked a book to compute anything, but a book on Robinson
Arithmetic, if you read it carefully, should help you to understand
that the notion of computation is not a physical notion at all.
Bruno
John K Clark
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