[FOM] Short technical questions about meaninfulness, truth, and induction

[Arnon Avron]

Here are some related questions to those who express (very doubtful
in my eyes) doubts about the validity of the induction principle of PA (and 
so of the consistency of PA).


Consider the following sentence:

"No recursive consistent extension of PA can prove its own consistency"

1) Is the above sentence true?
2) Is the above sentence meaningful?
3) What is the place in the \Sigma-\Pi hierarchy of  the (*direct*
   translation into the language of PA of the) above sentence?
4) Assuming that the answer to the second question is "yes", 
   are we allowed to use induction in proving the (direct
   translation into the language of PA of the) above sentence,
   and if so - induction on what type of formulas? 


Arnon Avron