On 5/29/2012 11:39 AM, Bruno Marchal wrote:

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On 29 May 2012, at 19:27, meekerdb wrote:On 5/29/2012 12:27 AM, Bruno Marchal wrote:I doubt infinities.I can doubt actual infinities. Not potential infinities, which gives sense to any nonstooping program notion.Comp is ontologically finitist. As long as you don't claim that there is a biggestprime number, there should be no problem with the comp hyp. Infinities can be put inthe epistemology, or at the meta-level: they are mind tool, souls attractor etc.BrunoBut diagonalization arguments assume realized infinities.Set theoretical diagonalizations, à-la Cantor, assume realized infinities (likeanalysis, by the way). I don't use them, if only to explain diagonalization.Computer science or "arithmetical" diagonalization does not assume realized infinities,only potential. Kleene second theorem is constructive. Gödel's diagonalization isconstructive: for each effective theory, it provides the undecidable sentences.

But they do depend on infinity (i.e. the axiom of succession).

The intensional diagonalization, leading to reproduction, self-generation andself-reference are all constructive concepts.

Can you explain "intensional diagonalization"? Brent

The theory of everything is really just logic and Ax ~(0 = s(x)) (For all number x the successor of x is different from zero). AxAy ~(x = y) -> ~(s(x) = s(y)) (different numbers have different successors) Ax x + 0 = x AxAy x + s(y) = s(x + y) ( meaning x + (y +1) = (x + y) +1) = laws of addition Ax x *0 = 0 AxAy x*s(y) = x*y + x laws of multiplicationThe observer is the same + the induction axioms. To define it in the theory above is ofcourse a very long subtle and tedious exercise.Bruno http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/> --You received this message because you are subscribed to the Google Groups "EverythingList" group.To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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