[FOM] Certainty in mathematical proofs, part 2

[Vladimir Sazonov]

On 21 Oct 2007 at 0:41, Arnon Avron wrote:

while everything
> provable in PA *is* absolutely certain (I simply  find it hard to 
> believe someone who denies the latter. I think
> that s/he is fooling herself/himself).

In the line of my reply to you  
http://www.cs.nyu.edu/pipermail/fom/2007-October/012084.html
there is no need to mention here absolute certainty. Say, you could 
write: "Let us consider what is predicativity over the natural numbers 
as formalized in PA (or may be in its reasonable extension to be 
understood later) in the following way using such an such novel 
approach and ideas". I am sure you will loose nothing, except doubtful 
usage of term "absolute" (which you seemingly cannot explain himself - 
you express only feeling or belief, and appeal to the community). Of 
course, in further steps and argumentation you will probably use the 
term "absolute" in its known set theoretic technical and simultaneously 
intuitive sense which probably will give you the possibility to express 
whatever you want essential on absoluteness and predicativity, now 
quite legally and avoiding any mysticism.


Vladimir


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