FOM: Do We Need New Axioms? Upcoming Panel Discussion

Andrew Boucher Helene.Boucher at
Thu Feb 17 16:54:43 EST 2000

Harvey Friedman wrote:

> "Do We Need New Axioms?" is the title of a panel discussion between Sol
> Feferman, Harvey Friedman, Penelope Maddy, John Steel at the Annual Meeting
> of the ASL, June  3-7, 2000, in Urbana.

Is "Do We Need New Axioms?" really the best way of introducing the underlying
issue?  It seems almost to lead to a trivial response, "Of course." 
After all,
if we want to prove CH (for instance), then yes of course we need a new
axiom--because ZFC doesn't allow us to prove it.  The question then merely
resolves down to, "What do we want to prove?"  Since the answer is
likely to be
"As much as possible" (even without recourse to Maddy's MAXIMIZE), this
is not
very interesting.

The sense of Friedman's real question seems more like, "*Should* we
state new
axioms?"  (And if so, which?)  Perhaps this phrasing is avoided because it
raises that troubling issue of values--and whether some axiom systems
have more
value than others.

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