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


--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.


Reply via email to