On 28 Feb 2013, at 05:04, meekerdb wrote:

On 2/27/2013 7:17 PM, Bruno Marchal wrote:On 27 Feb 2013, at 20:40, meekerdb wrote:On 2/27/2013 2:59 AM, Bruno Marchal wrote:On 26 Feb 2013, at 21:40, meekerdb wrote:On 2/26/2013 1:24 AM, Bruno Marchal wrote:How did number arise? We don't know that, but we can show thatif we don't assume them, or equivalent (basically anythingTuring Universal), then we cannot derive them.I'm not sure how you mean that?I meant that you cannot build a theory, simpler than arithmeticin appearance, from which you can derive the existence of thenumbers. All theories which want talk about the numbers have tobe turing universal.So I meant this in the concrete sense that if you write youraxioms, and want talk about numbers, you need to postulate them,or equivalent. You can derive the numbers from the equationaltheory:Kxy = x Sxyz = xz(yz) + few equality rules,But that theory is already Turing universal, and assume as muchthe number than elementary arithmetic.We know that we experience individual objects and so we cancount them by putting them in one-to-one relation with fingersor notches or marks. So what are you calling an "assumption" inthis?A theory is supposed to abstract from the experiences. Theexperiences motivates the theory, but does not justify itlogically.But "justify logically" seems like a bizarre concept to me. Wejust make up rules of logic so that inferences from some axioms,which we also make up, preserve 'true'.We have intuition and/or evidences for accepting the axiom. Herethe question is really: do you accept the axiom of Peano Arithmetic(for example). And with comp we don't need more. Then we provetheorems, which can be quite non trivial.To say that it is "justified logically" seems to mean no more than"we have avoided inconsistency insofar as we know."Yes. We can't hope for more. But in case of arithmetic, we do haveintuition. Well, in physics too.Sure it's important that our model of the world not haveinconsistencies (at least if our rules of inference include excontradictione sequitur quodlibet) but mere consistency doesn'tjustify anything.Consistency justifies our existence. I would say. We are ourselfhypothetical with comp. We are divine hypotheses, somehow. I thinkyou ask too much for a justification.You are assuming that justification comes from logic; and indeed itis too much to expect from such a weak source. I look for such"justification" as can be found from experience, which you demotedto mere "motivation".

`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.).`

But justification for me invokes "proof", formal or informal.

I don't think that what you ask is possible, even if I am prettysure 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.`

My intuition doesn't reach to infinity. It seems like an hypothesisof 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 http://iridia.ulb.ac.be/~marchal/ -- 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.