Free of Detachment: Logic, Rationality, and Gluts

Abstract. I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b),the logic LP (Asenjo, 1966; Asenjo Priest, 1979) is roughly right as far aslogic goes.1 But logic cannot go everywhere; we need to provide nonlogical axioms to specifyour (axiomatic) theories. This is uncontroversial, but it has also been the source of discomfort forLP-based theorists, particularly with respect to true mathematical theories which we take to be consistent. My example, throughout, is arithmetic; but the more general case is also considered.