On 01 May 2014, at 20:42, Craig Weinberg wrote:
On Friday, April 18, 2014 3:23:13 AM UTC-4, Bruno Marchal wrote:
On 16 Apr 2014, at 20:10, Craig Weinberg wrote:
What generates Platonia?
Nothing generates Platonia, although addition and multiplication can
generate the comp-relevant part of platonia, that is the UD or
equivalent.
Elementary arithmetic cannot be justified by anything less complex
(in Turing or logical sense). It is the minimum that we have to
assume to start.
Saying that elementary arithmetic is the minimum that we have to
start doesn't make sense to me. Elementary arithmetic depends on
many less complex expectations of sequence, identity, position,
motivation, etc. I keep repeating this but I don't think that you
are willing to consider it scientifically.
To define, is a reasonable precise sense, "expectations", "sequence",
"identity", "position", or "motivation" (which I doubt is a simple
notion) you need arithmetic.
It is, I think, your unwillingness to study a bit of math and logic
which prevents you from seeing this. You get a lot about the numbers
with few axioms written in first order language. I doubt you can
define "expectation of sequence" in such a simple way. How will you
define "sequence" without mentioning some function from N (the set of
natural numbers) to some set?
Again, I remind you that "simple" means "simple in the 3p sharable
sense", not "simple" in the 1p personal experiential sense. All
scientists agree on the arithmetic axioms, and I have to almost lie to
myself to fake me into doubting them. Something like "expectation"
might already have a different meaning for spiders, for different
humans, etc.
Bruno
http://iridia.ulb.ac.be/~marchal/
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