Is logic universal or hierarchical?

Ivor Grattan-Guinness

pp. 307-318

in: Arnold Koslow, Arthur Buchsbaum (eds), The road to universal logic II, Basel, Birkhäuser, 2015

Abstract

Some conceptions of logic claim that they are universal. By contrast, I assume that the applications of any logic are central to its conception, so that it has to comprise a hierarchy of its metalogics, metametalogics, …, indefinitely extended but never capped off with some universal logic. I also advocate for the distinction between parts and moments of a multitude as key to this conception, and I query the assumption that set theory provides the most general means of handling collections of objects.