1 Quine, W. V., "New Foundations for Mathematical Logic," American Mathematical Monthly, 44, 70-80 (1937). 2 Curry, H. B., review of same, Zentr. Mathematik, 16, 193 (1937). 3 Rosser, Barkley, "On the Consistency of Quine's 'New Foundations for Mathematical Logic,' "J. Symbolic Logic, 4, 15-24 (1939); Rosser, Barkley, and Wang, Hao, "Non-Standard Models for Formal Logics," Ibid., 15, 113-129 (1...

The limitations of mathematical logic either as a tool for the foundations of mathematics, or as a branch of mathematics, or as a tool for artificial intelligence, raise the need for a rethinking of logic. In particular, they raise the need for a reconsideration of the many doors the Founding Fathers of mathematical logic have closed historically. This paper examines three such doors, the view ...

03D15 (Mathematical logic and foundations / Recursion theory / Complexity of computation), 03E40 (Mathematical logic and foundations / Set theory / Other aspects of forcing and Boolean-valued models), 68Q15 (Computer science / Theory of computing / Complexity classes).