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    $\begingroup$ Do you happen to know where to find this paper (or perhaps the title)? $\endgroup$ Commented Jun 24, 2010 at 2:09
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    $\begingroup$ Here's the header from the MathSciNet review: MR0401475 (53 #5302) Reinhardt, W. N. Remarks on reflection principles, large cardinals, and elementary embeddings. Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part II, Univ. California, Los Angeles, Calif., 1967), pp. 189--205. Amer. Math. Soc., Providence, R. I., 1974. $\endgroup$ Commented Jun 24, 2010 at 2:17
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    $\begingroup$ Andreas, I worry about the very-smart-people argument. After all, before Wiles, very smart people had looked seriously and been unable to refute FLT, but $\neg$FLT turned out to be inconsistent anyway... $\endgroup$ Commented Jun 24, 2010 at 4:00
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    $\begingroup$ Joel, I agree that the smart-people argument is not very strong, and I should have phrased my answer to make that clear. I didn't mean "I believe that very large cardinals are consistent, and the reason is ..."; rather I meant "To the extent that I believe that very large cardinals are consistent, the only reason I have is ...." In the case of small large cardinals (inaccessible, or even indescribable of various levels), I think the reflection idea gives some additional plausibility to the axioms (though I don't think it makes them "clearly true"); I don't see that for measurables and up. $\endgroup$ Commented Jun 24, 2010 at 6:43
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    $\begingroup$ Without implying anything about my personal beliefs, I'm surprised no one has yet mentioned Penelope Maddy's pair of papers called "Believing the Axioms" (I and II), which I enjoyed as a discussion of reasons to believe (or not believe) in various axioms beyond ZFC. $\endgroup$ Commented Jun 25, 2010 at 5:22