On 3/23/2015 9:59 AM, Bruno Marchal wrote:
On 22 Mar 2015, at 22:57, meekerdb wrote:
On 3/22/2015 11:25 AM, Bruno Marchal wrote:
Who? (Jean-Paul Delahaye? Bill Taylor? Invite them to present themselves an argument,
because if it is a valid argument, you have not yet succeeded to present it here).
Peter Jones.
I am not sure. In my conversation with him, he admitted somehow is magical use of
matter, to avoid step 8.
I don't know that Bruno is wrong, but would say, in the legal phrase, he assumes things
not in evidence.
Which one?
That every number has a unique successor for one.
That 2+2=4 even without me or you to verify it?
Church's thesis?
"yes doctor" (that an artificial brain can work in principle at some
substitution level)?
I am OK with saying that the last one is a strong assumption, in metaphysics or
theology, but it is implicit and usually accepted in the natural science (even sometimes
for reason incompatible with comp).
Church thesis is also a quite string hypothesis, equivalent with the existence of
universal machine, but there are strong evidence that numbers, combinators, Fortran,
Lisp, etc. are universal systems. And the closure of the set of partial computable
functions computed for the diagonalization procedure, makes it explanatively close in
some deep sense, and that provides also a strong evidence for it.
Again, I am not entirely sure what you mean by assuming things not in evidence.
Well, may be you allude to your temptation of ultrafinitism in math. You allude that the
first three axiom of PA or RA are wrong?
That would be the extraordinary claim, and you give some evidence of why there is a
bigger number, without invoking a God or a Material Universe, as that would beg the
question. Most people believe that all natural numbers x have a unique successor s(x).
Most people believe God is a big guy in the sky too. Most believe a world must be
accessible from itself. Most people haven't thought about the infinity of the integers.
Brent
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