Notre Dame Journal of Formal Logic 35 (3):458-463 (1994)

Abstract
We show that the following conjecture about the universe V of all sets is wrong: for all set-theoretical (i.e., first order) schemata true in V there is a transitive set "reflecting" in such a way that the second order statement corresponding to is true in . More generally, we indicate the ontological commitments of any theory that exploits reflection principles in order to yield large cardinals. The disappointing conclusion will be that our only apparently good arguments for the existence of large cardinals have bad presuppositions
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DOI 10.1305/ndjfl/1040511351
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References found in this work BETA

Proper Classes.Penelope Maddy - 1983 - Journal of Symbolic Logic 48 (1):113-139.
Some Impredicative Definitions in the Axiomatic Set-Theory.Andrzej Mostowski - 1951 - Journal of Symbolic Logic 16 (4):274-275.
On a Set Theory of Bernays.Leslie H. Tharp - 1967 - Journal of Symbolic Logic 32 (3):319-321.
Prädikative Klassen.Ralf-Dieter Schindler - 1993 - Erkenntnis 39 (2):209 - 241.

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Citations of this work BETA

E Pluribus Unum: Plural Logic and Set Theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
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