On 15/10/2015 2:10 am, Bruno Marchal wrote:
You talk like if I have claim knowing some truth. I do not. You are
doing philosophy of comp-theology. That belongs to the field of
philosophy of science, which is not my expertise. You cannot use
philosophy for making people doubting a logical argument.
..........
of course if you doubt the truth of RA axioms, then I can't explain.
Above you claim that you do not know some truth. So how do you know the
truth of the RA axioms?
Of course, you are just being cavalier with your use of the word
'truth'. Axioms are not things which can be said to be either true of
false, at best they are only useful and productive, or not.
If arithmetic is false, Church-Turing thesis makes no more sense. You
will have difficulties in defining computable function from N to N.
See above. Arithmetic is neither true nor false, it is only useful or
not, depending on the context.
All proof of negative results are argument from incredulity. Proving
~p is the same as proving p -> f.
This is just nonsense. An argument from incredulity is an argument that
claims that the difficulty of believing a conclusion (incredulity) is a
valid reason for rejecting the argument. Proofs are things that happen
in formal systems -- starting from axioms and following pre-defined
rules of inference. So the proof of ~p is simply a sound demonstration
that ~p follows from the axioms according to the rules of inference. It
is not a 'proof' that p is false. As I must stress again, truth and
falsity are not words that can be applied within the context of
axiomatic systems.
Bruce
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