. I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b),
the logic LP (Asenjo, 1966; Asenjo & Tamburino, 1975; Priest, 1979) is roughly right as far as
logic goes.1 But logic cannot go everywhere; we need to provide nonlogical axioms to specify
our (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.

Two Flavors of Curry’s Paradox

Free of Detachment: Logic, Rationality, and Gluts

This paper is a sequel to Beall (2011), in which I both give and discuss the philosophical import of a ‘classical collapse’ result for the propositional (multiple-conclusion) logic LP+. Feedback on such ideas prompted a spelling out of the first-order case. My aim in this paper is to do just that: namely, explicitly record the first-order result(s), including the collapse results for K3+ and FDE+.

/pdf/lp-k3-fde-and-their-classical-collapse-3cr9oon7qh.pdf

Lp + , k3 + , fde + , and their ‘classical collapse’

A simple approach towards recapturing consistent theories in paraconsistent settings

Fil: Da Re, Bruno. Instituto de Investigaciones Filosoficas - Sadaf; Argentina. Universidad de Buenos Aires. Facultad de Filosofia y Letras. Departamento de Filosofia; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina

/pdf/theories-of-truth-based-on-four-valued-infectious-logics-428jtbf4vs.pdf

Theories of truth based on four-valued infectious logics

Philosophical applications of familiar paracomplete and paraconsistent logics often rely on an idea of ‘default classicality’. With respect to the paraconsistent logic LP (the dual of Strong Kleene or K3), such ‘default classicality’ is standardly cashed out via an LP-based nonmonotonic logic due to Priest (1991, 2006a). In this paper, I offer an alternative approach via a monotonic multiple-conclusion version of LP.

/pdf/multiple-conclusion-lp-and-default-classicality-2eg7nt3fmm.pdf

Jeffrey Charles Beall

Papers

Multiple-conclusion lp and default classicality