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?
Brent
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