Second-Order Positive Comprehension and Frege’s Basic Law V

Abstract

Richard Heck and John Burgess have shown that Frege’s Basic Law V is consistent with predicative comprehension and that the resulting theory interprets Robinson Arithmetic. There are also many other ways to keep Frege from being contradictory. This paper shows that Basic Law V is also consistent with positive comprehension and that the resulting theory also interprets Robinson Arithmetic. In addition, the theory of positive Frege provides a new understanding of Dummett’s “indefinitely extensible concepts.”

Keywords

predicative comprehension / positive comprehension / Basic Law V

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2014 Higher Education Press and Brill