This volume consists of the first of the John Dewey Lectures delivered under the auspices of Columbia University's Philosophy Department as well as other essays by the author. Intended to clarify the meaning of the philosophical doctrines propounded by Professor Quine in 'Word and Objects', the essays included herein both support and expand those doctrines.

In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK∞+. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK∞+ interprets the Kelley Morse class theory. Here we prove that GPK∞+ + ACWF and the Kelley-Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK∞+ + ACWF is a “strong” theory since “On (...) is ramifiable” implies the existence of a proper class of inaccessible cardinals. (shrink)