FOM: Re: V=L vs. PD

Neil Tennant neilt at
Sat May 13 20:45:26 EDT 2000

John Steel wrote:

> Large cardinal hypotheses flow from general foundational
> considerations, and by developing the extensive theory around them in a
> natural way, we only make important applications more likely. 

Are these "general foundational considerations" able to provide intrinsic
justifications in Penelope Maddy's sense, or only extrinsic ones? It would
seem, ironically, that the more one disagrees with Harvey Friedman about
how important it is for new set-theoretic axioms to speak to the concrete 
concerns of core mathematicians, the less "extrinsic" the justifications
of those axioms will be.  If the choice of those axioms is to be guided
only by considerations internal to abstract set theory, could their
justifications be claimed to be anything other than "intrinsic", in
Maddy's sense?

Neil Tennant

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