On 2/28/2013 7:46 AM, Bruno Marchal wrote:
On 28 Feb 2013, at 05:04, meekerdb wrote:
You are assuming that justification comes from logic; and indeed it
is too much to expect from such a weak source. I look for such
"justification" as can be found from experience, which you demoted to
mere "motivation".
Hi Bruno and Brent,
Where did I say "motivation"? I use the term "intuition", and I demote
nothing, as it correspond to to the first person (the hero of comp,
the inner God, the third hypostase, Bp & p; S4Grz1, etc.).
ISTM that 'motivation' is a 3p view of 'intuition'!
But justification for me invokes "proof", formal or informal.
Justification requires a model and/or implementation,no?
[BM] I don't think that what you ask is possible, even if I am
pretty sure that x + 0 = x, x + s(y) = s(x + y), etc.
I'm not at all sure that there is successor for every x.
Then you adopt ultrafinitism, and indeed comp does not make sense with
such hypothesis, and UDA1-7 suggests that ultrafinitism might save
physicalism, but step 8 put a doubt on this.
The axiom that all natural numbers have a successor is used in
basically all scientific paper though. You need it, or equivalent, to
define "machine", "formal systems", "programs", "Church's thesis",
"string theory", "eigenvector", "trigonometry", etc.
I need to be sure that I understand this: Numbers are prior to
computations. Is that correct? If so, then ultrafinitism fails, but if
computations are prior to numbers, ultrafinitism (of some kind) seems
inevitable. I have always balked at step 8 in that is seems a bridge too
far... Why does the doubt have to be taken so far?
My intuition doesn't reach to infinity. It seems like an hypothesis
of convenience.
I propose a theory, that's all. You don't need to believe in infinity,
unlike in set theory (yet also used by many). You need just to believe
(assume) that 0 ≠ s(x), and that x ≠ y entails s(x) ≠ s(y). Notion
like provability and computability are based on this.
Bruno
I still don't understand how we cannot assume some implicit set
with even arithmetic realism. How are integers not a set?
--
Onward!
Stephen
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