- Hartley Slater “A Poor Concept Script”, in: Australasian Journal of Logic, vol. 2, 2004
The formal structure of Frege’s ‘concept script’ has been widely adopted in logic text books since his time, even though its rather elaborate symbols have been abandoned for more convenient ones. But there are major difficulties with its formalisation of pronouns, predicates, and propositions, which infect the whole of the tradition which has followed Frege. It is shown first in this paper that these difficulties are what has led to many of the most notable paradoxes associated with this tradition; the paper then goes on to indicate the lines on which formal logic—and also the lambda calculus and set theory—needs to be restructured, to remove the difficulties. …
- ditto “Frege's Hidden Assumption”, in: CRÍTICA, Revista Hispanoamericana de Filosofía, vol. 38, no. 113, agosto, 2006
This paper is concerned with locating the specific assumption that led Frege into Russell’s Paradox. His understanding of reflexive pronouns was weak, for one thing, but also, by assimilating concepts to functions he was misled into thinking, one could invariably replace a two-place relation with a one-place property.
- ditto “Logic and Arithmetic”, in: P. Joray, ed., Contemporary Perspectives on Logicism and Constructivism. Travaux de Logique, vol. 18, 2006
Since there are non-sortal predicates Frege’s attempt to derive Arithmetic from Logic stumbles at its very first step. There are properties without a number, so the contingency of that condition shows Frege’s definition of zero is not obtainable from Logic. But Frege made a crucial mistake about concepts more generally which must be remedied, before we can be clear about those specific concepts which are numbers.