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Frege's logicism: Getting an insight into what we grasp. An inquiry into the intended relation between the content of our arithmetic, and the content of Frege's logically perfect language.

Jennings, Mark Richard John; (2002) Frege's logicism: Getting an insight into what we grasp. An inquiry into the intended relation between the content of our arithmetic, and the content of Frege's logically perfect language. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

This thesis is an inquiry into whether Frege intended his logicist reduction to be an explication of the content of ordinary arithmetic, or whether he conceived of it as a replacement, or indeed as something in between those two possibilities. In other words, did Frege seek to capture in Concept Script the Sinn and Bedeutung of our ordinary arithmetical language? Or did he seek to capture none, or just one of those things-Bedeutung? On the face of it, Frege himself is not altogether transparent on the matter: he appears at best unclear, and at worst inconsistent. I argue that Frege sought to uncover both the Sinn and Bedeutung of our arithmetical language. This in itself is not a new thesis, though few subscribe to it. Those who do subscribe to it argue that, for Frege, we have a defective or partial grasp of the content of ordinary arithmetic, which deficiency Frege sought to make good by constructing a logically perfect language in which the full contents of ordinary arithmetic are revealed. I reject the view that our grasp is defective, this on exegetical and non-exegetical grounds. Distinguishing between defective understanding, and defective grasp, I claim that Frege took our grasp to be full, if to some extent tacit and unperspicuous. The methodology of my inquiry lies in the main on a reappraisal of Frege's text. But it lies also on the fruitfulness of the claim that the doctrine of the recovery of tacit grasp informs Frege's logicism. Not only does this doctrine help to make plausible the above claim regarding the relation between our arithmetic and Concept Script arithmetic. It helps to resolve other issues, which arise in the course of arguing for that claim. These other issues are of an independent interest. One such issue concerns what Frege meant by the claim that, by means of fruitful definitions, analytic truths can extend our knowledge, and how this relates to the notion of carving up a proposition already grasped. Another issue concerns whether and in what sense we should regard Frege's logicism as epistemologically motivated.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Frege's logicism: Getting an insight into what we grasp. An inquiry into the intended relation between the content of our arithmetic, and the content of Frege's logically perfect language.
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
Keywords: Philosophy, religion and theology; Pure sciences; Logicism
URI: https://discovery.ucl.ac.uk/id/eprint/10106101
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