On 28 Feb 2013, at 14:58, Stephen P. King wrote:

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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 indeedit is 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".Hi Bruno and Brent,Where did I say "motivation"? I use the term "intuition", and Idemote nothing, as it correspond to to the first person (the heroof comp, the inner God, the third hypostase, Bp & p; S4Grz1, etc.).ISTM that 'motivation' is a 3p view of 'intuition'!

`I don't see this at all. Motivation is somehow even more a`

`psychological notion than 'intuition', which admit logical`

`specification.`

But justification for me invokes "proof", formal or informal.Justification requires a model and/or implementation,no?

`Not necessarily, in case of formal justification, or in first order`

`logic: we need only formulas and sequences of formulas, at the meta-`

`level.`

[BM] I don't think that what you ask is possible, even if I ampretty 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 sensewith such hypothesis, and UDA1-7 suggests that ultrafinitism mightsave physicalism, but step 8 put a doubt on this.The axiom that all natural numbers have a successor is used inbasically all scientific paper though. You need it, or equivalent,to define "machine", "formal systems", "programs", "Church'sthesis", "string theory", "eigenvector", "trigonometry", etc.I need to be sure that I understand this: Numbers are prior tocomputations. Is that correct?

`Once you agree on the axioms and rules of elementary arithmetic,`

`numbers and computations coexist, like even numbers and prime numbers.`

`You can' have one without the other.`

If so, then ultrafinitism fails, but if computations are prior tonumbers, ultrafinitism (of some kind) seems inevitable. I havealways balked at step 8 in that is seems a bridge too far... Whydoes the doubt have to be taken so far?

`It is a conclusion. We will come back on step 8 on the FOAR list,`

`soon. In your neutral monism, primary matter (and thus time and space)`

`also does not exist. I don't see why you have a problem with this non-`

`existence at the ontological level, given that those have to be`

`explained at some other level.`

My intuition doesn't reach to infinity. It seems like anhypothesis of convenience.I propose a theory, that's all. You don't need to believe ininfinity, unlike in set theory (yet also used by many). You needjust to believe (assume) that 0 ≠ s(x), and that x ≠ y entailss(x) ≠ s(y). Notion like provability and computability are basedon this.BrunoI still don't understand how we cannot assume some implicit setwith even arithmetic realism. How are integers not a set?

`You can assume the numbers, without assuming sets. That means that set`

`will not be "first order citizen" in the reality that you assume, a`

`bit like classes in ZF set theory.`

`Set appears at the metalevel, when you assume only numbers. They can`

`appear also as "mental" objects in the mind of the relative numbers,`

`but they are not existing objects, you can't prove ExP(x) with x`

`denoting them, unless you represent a set by a numbers, which can be`

`done for the RE sets, but not for any set. But yes, some set will`

`exist, even explicitly, through some possible representations. But`

`those sets are not assume, then, they are proven to exist.`

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.