Intuition and Russelin Paradox (original) (raw)
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Erkenntnis, 1979
May I always speak of the extension of a conceptspeak of a class? And if not how are the exceptional cases recognized ?
Russell's Paradox: A Historical Study about the Paradox in Frege's Theories
Revista Brasileira de História da Matemática, 2020
For over twenty years, Frege tried to find the foundations of arithmetic through logic, and by doing this, he attempted to establish the truth and certainty of the knowledge. However, when he believed his work was done, Bertrand Russell sent him a letter pointing out a paradox, known as Russell’s paradox. It is often considered that Russell identified the paradox in Frege’s theories. However, as shown in this paper, Russell, Frege and also George Cantor contributed significantly to the identification of the paradox. In 1902, Russell encouraged Frege to reconsider a portion of his work based in a paradox built from Cantor’s theories. Previously, in 1885, Cantor had warned Frege about taking extensions of concepts in the construction of his system. With these considerations, Frege managed to identify the precise law and definitions that allowed the generation of the paradox in his system. The objective of this paper is to present a historical reconstruction of the paradox in Frege’s p...
Philosophia Mathematica, 2015
This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in (HP). It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neo-logicist position on the issues of: (i) what's required for proofs of existence; (ii) the connection between models, consistency, and existence; and (iii) the prospects for a logical grounding of arithmetic in the wake of the paradox.
Reflections on Russell's antinomy
ArXiv http://arxiv.org/abs/2409.05903, 2024
We present Russell's antinomy using three distinct deductive systems, which are then compared to deepen the logical deductions that lead to the contradiction. Some inferential paths are then presented, alternative to the commonly accepted one, that allow for the formal assertion of the antinomy without deriving the contradiction, thus preserving the coherence of the system. In light of this, the purpose of this article is to propose a review of the consequences of asserting Russell's antinomy and, by extension, the widespread belief that any attempt to resolve a paradox is doomed to failure.
The Paradox of Knowability from an Intuitionistic Standpoint
An intuitionistic solution to the Paradox of Knowability is given. It consists (i) in accepting α→Kα, the ordinary formalization of the principle of Radical Anti-Realism (RAR) that “Every truth is known”, since, intuitionistically understood, it means that proofs are epistemically transparent; and (ii) in accepting (RAR) itself, on the basis of the fact that knowledge is an intuitionistic internal truth notion. Some neo-verificationist approaches are criticized. Finally the problem of how to frame a rational discussion between Classicism and Intuitionism is briefly discussed.
Problems of Philosophy (Russell) - A critical Review/Essay (Phil.2) [Jun 2017]
This is a review of this very influential “little” book by a man who was one of my early heroes but who fails to deliver convincing argumentation in this (therefore) disappointing book. Professional philosophers like to define philosophy as “thinking about thinking” [see “The Oxford Companion to Philosophy” p. 666 – referred to later as ‘Oxon’] but the practice of philosophy has been an extended attempt by western intellectuals to construct verbal models of the world we live in. Historically, philosophy has focused on three key areas: the nature of the world (metaphysics especially the theory of existence – ontology), the justification of belief (theory of knowledge – epistemology) and the conduct of human affairs (the theory of value – ethics).