On 03 Sep 2012, at 14:50, Richard Ruquist wrote:

Bruno, In comp, what is the function of god.

`It is responsible for the existence of numbers and their relations,`

`notably in distinguishing what is true and false.`

My hope is that the function of a god might be to reduce 3p tp 1p.

It does exactly that. Both:

`- informally, as making true the statement "I am reconstituted in`

`Moscow" in the case I am reconstituted in Moscow, and perhaps else`

`where.`

`- and formally (or meta-formally) when, following Theaetetus, we`

`define knowledge as the conjunction of provability (ideal machine's`

`believability), and truth (like in Knowable('p') = provable('p') & p).`

`This gives God (Truth) a mean to, well, not exactly reducing, but`

`"awakening" the 1p, from the 3p. It makes the first person as`

`unnameable as God/Truth.`

Everything else seems to be capable of running according to algorithms.

`In the hierarchy of complexity, what is computable is at the Sigma_0`

`and sigma_1 arithmetical level, but the sigma_2 is no more computable,`

`nor is any Sigma_n level for n bigger than 1.`

`Arithmetical truth is maximally non computable as being a union of all`

`Sigma_i.`

`Just to say that the computable part of the arithmetical truth is very`

`tiny.`

`And the first person indeterminacy can be used to explain why the`

`average universal number is confronted to the whole hierarchy, and`

`actually even beyond, epistemologically.`

Is there anything in comp that is non-algorithmic?

`The search for the truth of arithmetical sentences which are more`

`complex than the sigma_1 one.`

`By a theorem of Kleene and Mostowski, the sigma_1 sentences can be`

`roughly described by the sentences having the shape ExP(x) with P(x)`

`decidable. Their negation are already not computable and are called`

`Pi_1, they have the shape AxP(x). Example: Riemann hypothesis (this is`

`equivalent with a P1_1 arithmetical sentence, as shown by Turing).`

`Then you have the Sigma_2 and Pi_2, with the shape ExAyP(x,y) P`

`decidable, and AxEyP(x,y) respectively. Etc.`

`Most truth about numbers and machines are not algorithmic (we assume`

`Church Thesis 'course).`

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.