Assertion and denial: A contribution from logical notations

Abstract

This paper presents two major aspects of Frege's and Peirce's views on assertion and denial: first, their arguments for the notational choices concerning the representation of assertion and denial in Begriffsschrift (BS) and Existential Graphs (EGs), respectively; and second, those properties of BS and EGs which reflect their inventors' views on assertion and denial. We show that while Frege's notation has an ad hoc sign of assertion and an ad hoc sign of negation, Peirce has a sign of assertion which is also a sign of logical conjunction, and a sign of scope which is also a sign of negation.