[FOM] Deflationism and the Godel phenomena

Neil Tennant neilt at mercutio.cohums.ohio-state.edu
Mon Feb 14 22:56:55 EST 2005

G"odel wrote

"...it turns out that in the systematic establishment of the axioms of
mathematics, new axioms, which do not follow by formal logic from those
previously established, again and again become evident."
(Collected Works III, p. 385)

Reflection principles, I submit, are examples of new axioms that "become
evident", without need for any recourse to a substantial theory of truth.
Any substantially truth-theoretic "justification" of a
reflection principle R, conceived of as an priori argument whose
conclusion is R, therefore faces three epistemological challenges:

i) Is such justification really needed in order to convince us that we may
assert R?
ii) What are the basic principles (axioms and/or rules) on which this
"justification" of R rests?
iii) Why are these principles more convincing/easier to justify/more
basic/... than R itself?

I would be interested to hear from Torkel Franzen and Jeffrey Ketland, in
particular, how they would answer (i)-(iii).

Neil Tennant

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