# On Logicist Conceptions of Functions and Classes

## Abstract

John Bell arrived in “new” London in 1989, a refugee from the academy under Margaret Thatcher. We soon became good friends, and during the early years of our friendship we collaborated on two papers (Bell and Demopoulos, 1993, 1996). The first of these collaborations was a paper on the foundational significance of results based on second-order logic and Frege’s understanding of his Begriffsschrift; the second was on various notions of independence that arise in connection with elementary propositions in the philosophy of logical atomism. I retain fond memories of both collaborations; they proceeded quickly and almost effortlessly. In this contribution to John’s Festschrift, I propose to revisit our paper on Frege. That paper was occasioned by (Hintikka and Sandu, 1992), which questioned whether Frege’s understanding of second-order logic corresponded, in his framework of functions and concepts, to what we would now regard as the standard interpretation, the interpretation that takes the domain of the function variables to be the full power-set of the domain of individuals. Hintikka and Sandu maintained that it did not on the basis of a number of arguments, all of which they took to show that Frege favored some variety of non-standard interpretation for which the domain of the function variables is something less than the characteristic functions of *all* subsets of the domain over which the individual variables range.

## Keywords

Disjunctive Normal Form Propositional Function Transcendental Argument Combinatorial Possibility Logical Atomism## Bibliography

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