Reflections on Routley's Ultralogic Program

Abstract

In this paper, I take up three tasks in turn. The first is to set
out what Routley thought we should demand of an all-purpose universal
logic, and some of his reasons for those demands. The second is to
sketch Routley's own response to those demands. The third is to explore
how else we could satisfy some of the theoretical demands Routley
identified, if we are not to follow him in endorsing Routleyan
Ultralogic as a foundational logic. As part of this third project, I
articulate what seems to me a preferable way of going to respond
to the challenges Routley correctly identifies: and while I doubt what I
will have to say would have convinced Routley himself, I will try to
show that the approach I prefer has several advantages over Routley's.