[FOM] Simple Turing machines, Universality, Encodings, etc.

joeshipman@aol.com joeshipman at aol.com
Mon Oct 29 17:40:30 EDT 2007

>-----Original Message-----
>From: Steven Ericsson-Zenith <steven at semeiosis.org>
>Speaking of fallacies and not wishing to push my luck either. But it
>seems to me that the very notion of a Principle of Computational
>Equivalence is unwarranted and fallacious, and fortunately falsifiable.

Do you mean falsifiable, or already falsified?

I think Wolfram's PCE is reasonably well-specified, though not 
mathematically precise, and as I said in a recent post,

PCE doesn't need to be precise to be refutable. All one needs to do to 
refute it is produce a process which

i) is simpler to define than Wolfram's "universal" examples
ii) does not obviously fail to be c.e.-complete
iii) is nonetheless provably not c.e.-complete

I am not aware that Wolfram's PCE has in fact been refuted; if you know 
of no refutation, do you at least have a good argument why it is 
probably false?

-- JS
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