On 8/22/2014 4:43 AM, Bruno Marchal wrote:
On 22 Aug 2014, at 04:18, Pierz wrote:On Wednesday, August 20, 2014 6:04:44 AM UTC+10, Bruno Marchal wrote: Sorry for being again a bit out of phase. On 18 Aug 2014, at 15:15, Pierz wrote: What I mean is, your formulation, the words you use, add a certain numinous quality to the description of what seem (to a non-mathematician) to be dry abstract numerical transformations. Do they truly develop a discourse about the transcendant? Good question. The fact is that I could explain to you the notion of arithmetical truth. I can define it in the same sense that I can define you what is an Hilbert space. Arithmetical Truth, although not definable in the arithmetic language admits definition in slight extension of arithmetic, on which machines can points correctly too. yet, as far the very notion of arithmetical truth is unnameable (Tarski theorem, also found by Gödel). Nor can the machine generates, even working an infinite time, the whole set of arithmetical truth. If she tries, she will be lead to adding recurrently new axioms. There are no finite or constructively-infinite machine/theory capable of unifying the "simple" arithmetical reality.
Isn't the UD a constructively-infinite machine that will generate all arithmetical truths, including all those additional axioms?
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