The Propositional Logic of Frege’s Grundgesetze / Reply to Hunter on Anscombe and Davidson on Practical Knowledge

Volume 5.6 of the Journal for the History of Analytical Philosophy is now online, with full open access.

It features an article by Eric D. Berg and Roy T. Cook entitled, “The Propositional Logic of Frege’s Grundgesetze: Semantics and Expressiveness”. Here is an abstract:

In this paper we compare the propositional logic of Frege’s Grundgesetze der Arithmetik to modern propositional systems, and show that Frege does not have a separable propositional logic, definable in terms of primitives of Grundgesetze, that corresponds to modern formulations of the logic of “not”, “and”, “or”, and “if…then…”. Along the way we prove a number of novel results about the system of propositional logic found in Grundgesetze, and the broader system obtained by including identity. In particular, we show that the propositional connectives that are definable in terms of Frege’s horizontal, negation, and conditional are exactly the connectives that fuse with the horizontal, and we show that the logical operators that are definable in terms of the horizontal, negation, the conditional, and identity are exactly the operators that are invariant with respect to permutations on the domain that leave the truth-values fixed. We conclude with some general observations regarding how Frege understood his logic, and how this understanding differs from modern views.

The volume also contains a discussion piece by Olav Gjelsvik entitled “Anscombe and Davidson on Practical Knowledge. A Reply to Hunter”. Abstract:

David Hunter has recently argued (in this journal) that Donald Davidson and Elizabeth Anscombe were in basic agreement about practical knowledge. In this reply, it is my contention that Hunter’s fascinating claim may not be satisfactorily warranted. To throw light on why, a more careful consideration of the role of the notion of practical knowledge in Anscombe’s approach to intentional action is undertaken. The result indicates a possible need to distinguish between what is called ‘practical knowledge’ and ‘(non-observational) knowledge of what one is doing’, and shows that Hunter’s claim concerning the closeness of Anscombe to Davidson only has plausibility for knowledge of what one is doing. Contrary to an interesting suggestion by Hunter, the paper argues that it is hard to see how Davidson’s position can benefit substantially from making use of the notion of knowledge of what one is doing.

JHAP is a free, open-access peer reviewed journal. It is available at https://jhaponline.org/. Submissions welcome!

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