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date: 17 November 2019

Abstract and Keywords

One of the most famous of Gottlob Frege’s mature views is that there is a fundamental difference between objects and functions (among which are concepts). It is also among the most puzzling of Frege’s views. This chapter suggests that this doctrine is not only easy enough to understand, it is also in some sense so deeply embedded in contemporary logic and semantics that it is hard to imagine life without it. That is the reason for our perplexity: We do not understand the view Frege was opposing. To understand the doctrine of unsaturatedness, we must thus uncover its origin. The notion of function with which Frege operates in 1879, in Begriffsschrift, is rather different from what we find in Grundgesetze in 1893. The evolution of Frege’s mature conception begins soon after the publication of the former volume, and is largely in place by 1882. What drives this development is Frege’s confrontation with the work of George Boole.

Keywords: Gottlob Frege, objects, functions, concepts, logic, semantics, unsaturatedness, Begriffsschrift, Grundgesetze, George Boole

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