Some Remarks on the Definition of Lehrer’s Ultrasystem

Abstract

According to the analysis of knowledge proposed by Lehrer, knowledge equals undefeated justified acceptance. Undefeated justification is then spelled out as coherence with every element of theultrasystemas Lehrer calls it. The question arises how this key-notion should be defined. Two definitions of the ultrasystem which have been proposed by Lehrer are investigated. An argument is presented that both definitions are flawed. A formal proof is given that a third and simpler way to define the ultrasystem is preferable.

An earlier draft of this paper has been presented to Keith Lehrer. I am indebted to him for his helpful comments. It is worth mentioning that Lehrer welcomed the proposal of this paper. An earlier version of this paper was also read at the Lehrer-workshop in Konstanz in 2000 . I wish to express my indebtedness to the participants of the workshop for the helpful discussion, in particular to Wolfgang Spohn and Erik Olsson who also read a first version of the paper. 2 See [2], p. 149 and also p. 194 (n.11) where Lehrer defines the ultrasystem exactly as in (DefUltra’) [where I added the italics].