FOM: Is every provable theorem capable of an elementary proof?

[Robert S Tragesser]

Subject:  A foundationally/philosophically important question(is it?):  Is
every provable theorem  
capable of an elementary proof? 


In view of Steve Simpson's remarks,  I thought I should post a distinct
message to say:
        
        I came to see that what I was trying to point toward with the
meaning/significance distinction conicides with the distinction between
elementary and nonelementary proof.
        This distinction is importantly connected with meaning and
analyticity -- as suggested by Gian-Carlo Rota in INDISCRETE THOUGHTS chpt7
(Birkhauser Boston 1997),  that elementary proofs somehow arise out of the
concepts involved in the theorem at issue.  (Though I am open to the
suggestion that elementary proof be characterized independently of the
notion of analyticity. . .perhaps Reverse Mathematicians might argue so?)
        Then I wanted to make the point that the topic of elementary proof?
is philosophically and foundationally important,  as for example in the
question of whether CH might have a nonelementary (but perhaps not an
elementary) proof/disproof.
        Is there a reasonable explanation of "elementary proof" that would
allow some sort of decisive answer to the question:::
                Is every provable theorem capable of an elementary proof?
                                      rbrt tragesser