Paraconsistency and its Possibilities: a personalised and partial perspective of the past

I take paraconsistent logic to be one of the most important and significant developments in logic and metaphysics in the last ۱۰۰ years, challenging, as it does, one of the deepest dogmas entrenched in Western philosophy: that consistency is a sine qua non of rational thought. This paper looks back at the modern development of the subject. It is partial, in that it concerns only what one might call the formative years of the subject. It is personal, in that I describe my own involvement in some areas. The first part of the paper concerns paraconsistency as such. It starts with the name itself, its origin and its meaning. After a brief look at the history before the ۲۰th century, it notes the work of the early pioneers: Orlov, Jaśkowski, Halldén, Smiley, Val and Richard Routley, and da Costa. For each of these, it describes both what motivated them, and the techniques they used in their constructions. It then describes the early reception of paraconsistency, and the way that it became a global movement.  Next, the paper turns to dialetheism, again starting with the name itself and its meaning. After a brief look at the history of the notion before the ۲۰th century, it describes the origin of the modern subject in the work of Richard Routley/Sylvan and myself. Finally, it turns to one of the major applications of paraconsistency: inconsistent mathematics—and specifically set-theory, arithmetic, and geometry. It notes the work of da Costa, Routley/Sylvan, Meyer, Mortensen, and others, describing some of the results concerning the mathematical theories they investigated.

Keywords:

Paraconsistency , Consistency , Dialetheism , Inconsistent Mathematics , Newton Da Costa , Richard Routley/Sylvan