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- Added by: Simon Fokt, Contributed by: Alexander Yates
Abstract: Controversy remains over exactly why Frege aimed to estabish logicism. In this essay, I argue that the most influential interpretations of Frege’s motivations fall short because they misunderstand or neglect Frege’s claims that axioms must be self-evident. I offer an interpretation of his appeals to self-evidence and attempt to show that they reveal a previously overlooked motivation for establishing logicism, one which has roots in the Euclidean rationalist tradition. More specifically, my view is that Frege had two notions of self-evidence. One notion is that of a truth being foundationally secure, yet not grounded on any other truth. The second notion is that of a truth that requires only clearly grasping its content for rational, a priori justified recognition of its truth. The overarching thesis I develop is that Frege required that axioms be self-evident in both senses, and he relied on judging propositions to be self-evident as part of his fallibilist method for identifying a foundation of arithmetic. Consequently, we must recognize both notions in order to understand how Frege construes ultimate foundational proofs, his methodology for discovering and identifying such proofs, and why he thought the propositions of arithmetic required proof.
Comment: A nice discussion of what sort of epistemic status Frege thought axioms needed to have. A nice historical example of foundationalist epistemology - good for a course on Frege or analytic philosophy more generally, or as further reading in a course on epistemology, to give students a historical example of certain epistemological subtleties.Export citation in BibTeX formatExport text citationView this text on PhilPapersExport citation in Reference Manager formatExport citation in EndNote formatExport citation in Zotero format
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- Added by: Berta Grimau, Contributed by: Matt Clemens
Abstract: This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic – what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics – Logicism, Intuitionism, Formalism, Realism – and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam are among the philosophers considered along the way.
Comment: This is a survey article which considers positions within philosophy of logic analogous to the views held by the various schools of the philosophy of mathematics. The article touches briefly on many positions and authors and is thus an excellent introduction to the philosophy of logic, specially for students already familiar with the philosophy of mathematics. The text is informal and it does not involve any proofs.Export citation in BibTeX formatExport text citationView this text on PhilPapersExport citation in Reference Manager formatExport citation in EndNote formatExport citation in Zotero format