Anacletus, I. Ogbunkwu and Isife, Liberatus and Obasi, Samuel Ugochukwu and Okafor, Polycarp (2020) THE LOGIC OF RUSSELL’S PARADOX AND THE SYNTHESIS OF TYPE THEORY. JOURNAL OF CRITICAL REVIEWS, 7 (1). pp. 2658-2665. ISSN 2394-5125
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Abstract
This paper explores the logical and philosophical meaning of the Russell paradox, and follows the intellectual path according to which the Russell paradox led Russell to one of the most impactful advances of the foundations of logic and mathematics: the theory of types. This paper rebuilt the original finding of Russell of the paradox in 1902, its destructive influence on the logicist programme of Frege, and the subsequent efforts to overcome it which have led to the ramified theory of types published in Principia Mathematica (1910-13). This article then proceeds to develop the history of type theory beginning with the simplification of type theory by Ramsey and its formalisation by Church, the Curry-Howard correspondence, the intuitionistic type theory based on Martin-Lof, the Calculus of Constructions and most recently, homo-type theory and the development of univalent foundations. In this article, it is argued that the paradox Russell had found was not a wholesome and irresolvable anomaly but a prodigal crisis that forced the re-examination of the nature of predication, collection and logical stratification by logicians and mathematicians, leading to a family of type-theoretic systems on which modern proof assistants, programming language theory and the future re-conceptualisation of the foundations of mathematics is now based.
| Item Type: | Article |
|---|---|
| Subjects: | B Philosophy. Psychology. Religion > BC Logic |
| Divisions: | Faculty of Arts > Faculty of Law > Faculty of Management and Social Sciences |
| Depositing User: | mrs chioma hannah |
| Date Deposited: | 11 Jun 2026 08:16 |
| Last Modified: | 11 Jun 2026 08:16 |
| URI: | http://eprints.gouni.edu.ng/id/eprint/5789 |
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