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.


I still don't understand how we cannot assume some implicit set with even arithmetic realism. How are integers not a set?



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