On 3/5/2010 11:58 AM, Bruno Marchal wrote:
In this list I have already well explained the seven step of UDA, and one difficulty remains in the step 8, which is the difference between a computation and a description of computation. Due to the static character of Platonia, some believes it is the same thing, but it is not, and this is hard to explain. That hardness is reflected in the AUDA: the 'translation' of UDA in arithmetic. The subtlety is that again, the existence of a computation is true if and only if the existence of a description of the computation exist, but that is true at the level G*, and not at the G level, so that such an equivalence is not directly available, and it does not allow to confuse a computation (a mathematical relation among numbers), and a description of a computation (a number).

This mixing of existence and true in the context of a logic confuses me. I understand you take a Platonic view of arithmetic so that all propositions of arithmetic are either true or false, even though most of them are not provable (from any given finite axioms), so true=/=provable. But what does it mean to say a computation is true at one level and not another? Does it mean provable? or it there is some other meaning of true relative to a logic?


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