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, whichgives sense to any non stooping program notion.Comp is ontologically finitist. As long as you don't claim thatthere is a biggest prime number, there should be no problem withthe comp hyp. Infinities can be put in the epistemology, or at themeta-level: they are mind tool, souls attractor etc.BrunoBut diagonalization arguments assume realized infinities.

`Set theoretical diagonalizations, à-la Cantor, assume realized`

`infinities (like analysis, 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 is constructive: for each`

`effective theory, it provides the undecidable sentences.`

`The intensional diagonalization, leading to reproduction, self-`

`generation and self-reference are all constructive concepts.`

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 multiplication

`The observer is the same + the induction axioms. To define it in the`

`theory above is of course a very long subtle and tedious exercise.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" 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.