Relevant bibliographies by topics / Russell's paradox

Academic literature on the topic 'Russell's paradox'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Russell's paradox.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Russell's paradox"

1

Coury, Aline Germano Fonseca, and Denise Silva Vilela. "Russell's Paradox: A Historical Study about the Paradox in Frege's Theories." Revista Brasileira de História da Matemática 19, no. 37 (October 16, 2020): 95–116. http://dx.doi.org/10.47976/rbhm2019v19n3795-116.

Full text
Abstract:
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 publications and discuss it considering the correspondences exchanged between him and Russell. We shall take special attention to the role played by each of these mathematicians in the identification of the paradox and its developments. We also will show how Frege anticipated the solutions and new theories that would arise when dealing with logico-mathematical paradoxes, including but not limited to Russell’s paradox.
APA, Harvard, Vancouver, ISO, and other styles
2

Levine, James. "On Russell's vulnerability to Russell's paradox." History and Philosophy of Logic 22, no. 4 (December 2001): 207–31. http://dx.doi.org/10.1080/01445340210154312.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Orilia, Francesco. "A Contingent Russell's Paradox." Notre Dame Journal of Formal Logic 37, no. 1 (January 1996): 105–11. http://dx.doi.org/10.1305/ndjfl/1040067319.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Pal, Jagat. "Balzer's solution to Russell's Paradox." Journal of Value Inquiry 27, no. 3-4 (December 1993): 539–40. http://dx.doi.org/10.1007/bf01087703.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Moorcroft, Francis. "Why Russell's Paradox Won't Go Away." Philosophy 68, no. 263 (January 1993): 99–103. http://dx.doi.org/10.1017/s0031819100040080.

Full text
Abstract:
In ‘The Mind's I is Illiterate’, G. S. Miller discusses several paradoxes and paradoxical sentences which Miller claims are related by a common abuse of language. The Whiteley sentence ‘Lucas cannot consistently believe this sentence’ fails to be meaningful for want of a referent outside of the sentence for the phrase ‘this sentence’; the Liar Paradox when formulated as ‘I am lying’ is similarly disposed of when it is seen that the verb is defective and the sentence fails to refer to anything outside of itself. The same point is made concerning the Russell Paradox of the set of all sets that do not belong to themselves. The moral made is that philosophers are simply to be more careful about the laneuaee that thev are usine and then the paradoxes will go away.
APA, Harvard, Vancouver, ISO, and other styles
6

Urbaniak, Rafal. "Leśniewski and Russell's Paradox: Some Problems." History and Philosophy of Logic 29, no. 2 (May 2008): 115–46. http://dx.doi.org/10.1080/01445340701550817.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Pinheiro, I. M. R. "Concerning the Solution to the Russell's paradox." E-LOGOS 19, no. 1 (June 1, 2012): 1–15. http://dx.doi.org/10.18267/j.e-logos.335.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Cocchiarella, Nino B. "Russell's paradox of the totality of propositions." Nordic Journal of Philosophical Logic 5, no. 1 (January 2000): 25–37. http://dx.doi.org/10.1080/08066200050217977.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Orilia, Francesco. "Type-free property theory, exemplification and Russell's paradox." Notre Dame Journal of Formal Logic 32, no. 3 (June 1991): 432–47. http://dx.doi.org/10.1305/ndjfl/1093635839.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Fuhrmann, André. "Russell's way out of the paradox of propositions." History and Philosophy of Logic 23, no. 3 (September 2002): 197–213. http://dx.doi.org/10.1080/01445340210161017.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Russell's paradox"

1

Eldridge-Smith, Peter, and peter eldridge-smith@anu edu au. "The Liar Paradox and its Relatives." The Australian National University. Faculty of Arts, 2008. http://thesis.anu.edu.au./public/adt-ANU20081016.173200.

Full text
Abstract:
My thesis aims at contributing to classifying the Liar-like paradoxes (and related Truth-teller-like expressions) by clarifying distinctions and relationships between these expressions and arguments. Such a classification is worthwhile, firstly, because it makes some progress towards reducing a potential infinity of versions into a finite classification; secondly, because it identifies a number of new paradoxes, and thirdly and most significantly, because it corrects the historically misplaced distinction between semantic and set-theoretic paradoxes. I emphasize the third result because the distinction made by Peano [1906] and supported by Ramsey [1925] has been used to warrant different responses to the semantic and set-theoretic paradoxes. I find two types among the paradoxes of truth, satisfaction and membership, but the division is shifted from where it has historically been drawn. This new distinction is, I believe, more fundamental than the Peano-Ramsey distinction between semantic and set-theoretic paradoxes. The distinction I investigate is ultimately exemplified in a difference between the logical principles necessary to prove the Liar and those necessary to prove Grelling’s and Russell’s paradoxes. The difference relates to proofs of the inconsistency of naive truth and satisfaction; in the end, we will have two associated ways of proving each result. ¶ Another principled division is intuitively anticipated. I coin the term 'hypodox' (adj.: 'hypodoxical') for a generalization of Truth-tellers across paradoxes of truth, satisfaction, membership, reference, and where else it may find applicability. I make and investigate a conjecture about paradox and hypodox duality: that each paradox (at least those in the scope of the classification) has a dual hypodox.¶ In my investigation, I focus on paradoxes that might intuitively be thought to be relatives of the Liar paradox, including Grelling’s (which I present as a paradox of satisfaction) and, by analogy with Grelling’s paradox, Russell’s paradox. I extend these into truth-functional and some non-truth-functional variations, beginning with the Epimenides, Curry’s paradox, and similar variations. There are circular and infinite variations, which I relate via lists. In short, I focus on paradoxes of truth, satisfaction and some paradoxes of membership. ¶ Among the new paradoxes, three are notable in advance. The first is a non-truth functional variation on the Epimenides. This helps put the Epimenides on a par with Curry’s as a paradox in its own right and not just a lesser version of the Liar. I find the second paradox by working through truth-functional variants of the paradoxes. This new paradox, call it ‘the ESP’, can be either true or false, but can still be used to prove some other arbitrary statement. The third new paradox is another paradox of satisfaction, distinctly different from Grelling’s paradox. On this basis, I make and investigate the new distinction between two different types of paradox of satisfaction, and map one type back by direct analogy to the Liar, and the other by direct analogy to Russell's paradox.
APA, Harvard, Vancouver, ISO, and other styles
2

Studd, James Peter. "Absolute and relative generality." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:9bb22c54-e921-420f-acdc-aee0828bdea8.

Full text
Abstract:
This thesis is concerned with the debate between absolutists and relativists about generality. Absolutists about quantification contend that we can quantify over absolutely everything; relativists deny this. The introduction motivates and elucidates the dispute. More familiar, restrictionist versions of relativism, according to which the range of quantifiers is always subject to restriction, are distinguished from the view defended in this thesis, an expansionist version of relativism, according to which the range of quantifiers is always open to expansion. The remainder of the thesis is split into three parts. Part I focuses on generality. Chapter 2 is concerned with the semantics of quantifiers. Unlike the restrictionist, the expansionist need not disagree with the absolutist about the semantics of quantifier domain restriction. It is argued that the threat of a certain form of semantic pessimism, used as an objection against restrictionism, also arises, in some cases, for absolutism, but is avoided by expansionism. Chapter 3 is primarily engaged in a defensive project, responding to a number of objections in the literature: the objection that the relativist is unable to coherently state her view, the objection that absolute generality is needed in logic and philosophy, and the objection that relativism is unable to accommodate ‘kind generalisations’. To meet these objections, suitable schematic and modal resources are introduced and relativism is given a precise formulation. Part II concerns issues in the philosophy of mathematics pertinent to the absolutism/relativism debate. Chapter 4 draws on the modal and schematic resources introduced in the previous chapter to regiment and generalise the key argument for relativism based on the set-theoretic paradoxes. Chapter 5 argues that relativism permits a natural motivation for Zermelo-Fraenkel set theory. A new, bi-modal axiomatisation of the iterative conception of set is presented. It is argued that such a theory improves on both its non-modal and modal rivals. Part III aims to meet a thus far unfulfilled explanatory burden facing expansionist relativism. The final chapter draws on principles from metasemantics to offer a positive account of how universes of discourse may be expanded, and assesses the prospects for a novel argument for relativism on this basis.
APA, Harvard, Vancouver, ISO, and other styles
3

Pérez, Bernal Ángeles Ma del Rosario, and María Luisa Bacarlett. "From the Crisis of the Community to the Community of the Crisis. Some Paradoxes of the Being in Common." Pontificia Universidad Católica del Perú - Departamento de Humanidades, 2013. http://repositorio.pucp.edu.pe/index/handle/123456789/112836.

Full text
Abstract:
This paper explores the idea of community through the proposals of some contemporary thinkers who have tried to rethink the concept of being in common assuming some of its paradoxes. For authors like Roberto Esposito, Jean-Luc Nancy and Giorgio Agamben, thinking the community” implies reflecting on it from the paradoxes and contradictions it contains, both conceptually and in terms of everyday reality. The central paradox that sums such contradictions is stating that the community is feasible only to the extent that it is not. Close to Russell’s paradox, such aporia allows us to recognize the difference between the community that takes care of its contradictions and inconsistencies, the community of the crisis, and the one that, conceived in absolute and unequivocal terms, is not responsible for their antinomies and contradictions, and leads to what we call the community crisis.
En el presente artículo se hace un recorrido por la idea de comunidada través de algunos pensadores contemporáneos que han tratado de repensar el estar en común asumiendo algunas de sus paradojas. Para autores como Roberto Esposito, Jean-Luc Nancy y Giorgio Agamben, pensar la comunidad” implica reflexionarla a partir de las paradojas y contrasentidos que contiene, tanto anivel conceptual como a nivel de la realidad cotidiana. La paradoja central que resume tales contrasentidos es la que afirma que la comunidad es realizable solo en la medida en que no lo es. Cercana a la paradoja de Russell, tal aporía nospermite reconocer la diferencia entre una comunidad que se hace cargo de sus contrasentidos e incoherencias, la comunidad de la crisis, y otra que al concebirse en términos unívocos y absolutos, es decir, que no se hace cargo de sus antinomias y contradicciones, nos lleva a lo que hemos llamado crisis de la comunidad.
APA, Harvard, Vancouver, ISO, and other styles
4

Mora, Ramirez Rafael Félix. "La evolución de la paradoja de las clases propuesta por Bertrand Russell." Master's thesis, Universidad Nacional Mayor de San Marcos, 2016. https://hdl.handle.net/20.500.12672/5197.

Full text
Abstract:
Rastrea las posibles fuentes de las que se nutrió Russell para poder elaborar su conocida paradoja: la teoría conjuntista de Georg Cantor, la fundamentación lógica de la aritmética de Gottlob Frege y el desarrollo histórico de la paradoja de El Mentiroso. Explica el hallazgo de la paradoja de Russell por lo que da cuenta las actividades este filósofo realizaba al formularla. Así, constatamos que Russell estaba intentando solucionar la paradoja de Cantor sobre la cardinalidad del conjunto potencia del conjunto universal. Asimismo, también le hacía frente a la paradoja de Burali-Forti sobre el mayor número ordinal. Sin embargo, a pesar de que Russell no tuvo éxito intentando solucionar estas paradojas matemáticas, consiguió diseñar una paradoja más simple y preocupante: la paradoja de las clases. Da a conocer también las tesis planteadas por Kleene y Kilmister acerca de cómo probablemente Russell procedió a descubrir su paradoja. Expone el impacto que esta paradoja causó en la discusión acerca de los fundamentos de la matemática.
Tesis
APA, Harvard, Vancouver, ISO, and other styles
5

Rouilhan, Philippe de. "Catégories logiques et paradoxes recherches à partir de Frege, Russell et Tarski /." Lille 3 : ANRT, 1989. http://catalogue.bnf.fr/ark:/12148/cb37618277n.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Ertemiz, Nusret. "Some Set-theoretical Traces In Leibniz&#039." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12612860/index.pdf.

Full text
Abstract:
The purpose of this dissertation is to search the primitives of Axiomatic Set Theory in Leibnizian Philolosophy, nourishing, roughly, from Platonic idea of universal-particular distinction, Aristotelian syllogistic propositions of Organon-Categoria and Euclidean Methodology in Elements. The main focus of the dissertation intends to examine the analyticity of Leibnizian Metaphysics and the anologies between the subject-predicate relation in The Philosophy of Leibniz and Axiomatic Method in general and Set Theory in particular. In doing this, special emphasis will be ascribed to the notion of sets as to universality and/or nullness of a class, probable causes of paradoxes and in this context a critical analysis of Russell Paradox.
APA, Harvard, Vancouver, ISO, and other styles
7

Łukowski, Piotr. "Paradoksy." Thesis, Wydawnictwo Uniwersytetu Łódzkiego, 2006. http://hdl.handle.net/11089/3121.

Full text
Abstract:
Książka "Paradoksy" jest monografią poświęconą tym argumentacjom logicznym, które prowadzą, albo do sprzeczności, albo do wniosków niezgodnych z oczekiwaniami. Prawie wszystkie są do dziś źródłem kontrowersji i sporów zarówno wśród logików jak i filozofów. Szczególnie interesującymi są paradoksy o starożytnym rodowodzie. Książka zawiera prezentację wszystkich najważniejszych pradoksów logiki wraz z krytyczną analizą najpopularniejszych propozycji ich rozwiązań. W przypadku antynomii kłamcy, Newcomba, kół Arystotelesa, Trójcy Świętej, Protagorasa, kamienia, Kata i krokodyla autor proponuje własne, oryginalne propozycje rozwiązań. Układ treści monografii "Paradoksy" reprezentuje zaproponowaną przez autora klasyfikację paradoksów.
APA, Harvard, Vancouver, ISO, and other styles
8

Coury, Aline Germano Fonseca. "Frege e as Leis da Aritmética: do ideal de fundamentação ao paradoxo." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/7513.

Full text
Abstract:
Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-09-26T14:58:18Z No. of bitstreams: 1 DissAGFC.pdf: 1978531 bytes, checksum: e57d2335b2038eca2d8a6468869e05fa (MD5)
Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-27T19:36:51Z (GMT) No. of bitstreams: 1 DissAGFC.pdf: 1978531 bytes, checksum: e57d2335b2038eca2d8a6468869e05fa (MD5)
Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-27T19:36:56Z (GMT) No. of bitstreams: 1 DissAGFC.pdf: 1978531 bytes, checksum: e57d2335b2038eca2d8a6468869e05fa (MD5)
Made available in DSpace on 2016-09-27T19:37:02Z (GMT). No. of bitstreams: 1 DissAGFC.pdf: 1978531 bytes, checksum: e57d2335b2038eca2d8a6468869e05fa (MD5) Previous issue date: 2015-07-08
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Since the end of the nineteenth century and early twentieth century, some scholars such as Frege, Russell, Dedekind, Wittgenstein, among others, started to seek the foundations of the mathematics. Specifically, Frege developed studies in order to build the arithmetic foundation based on classical logic, i. e., using logic, he intended to build a system capable of formalizing mathematical definitions and proof methods. These works resulted in the publication of The Foundations of the Arithmetic in 1884 and subsequently in 1893 and 1902, The Basic Laws of Arithmetic. However, Frege’s attempt to reduce arithmetic to logic was inadequate due to a paradox discovered by Bertrand Russell in 1902. The aim of this research was to reconstruct mathematically and logically the Russell paradox in its original formulation in the Frege’s The Basic Laws of Arithmetic. This study had as primary bibliography Frege’s works and as secondary bibliography, works of his commentators, as well as the correspondence between Frege and Russell. This research provides a logical, philosophical and mathematical formation for the educator who is in contact with this event that covers both the areas that is disciplinary today. It is a fertile moment in the history of philosophy of mathematics and logic, configured as a watershed for mathematical theories since it enabled Gödel's incompleteness theorems and non-classical logics to be formulated, and also has repercussions in contemporary philosophy and which is of unquestionable value for the teacher formation.
A partir do fim do século XIX e início do século XX, alguns estudiosos, como Frege, Russell, Dedekind, Wittgenstein, dentre outros, buscaram alcançar os fundamentos últimos para a Matemática. Especificamente, Frege desenvolveu trabalhos a fim de fundamentar a Aritmética tendo como base a Lógica Clássica, ou seja, utilizando a lógica ele pretendia construir um sistema capaz de formalizar definições matemáticas e métodos de prova. Esses trabalhos culminaram na publicação de Os Fundamentos da Aritmética em 1884 e, posteriormente, em 1893 e 1902, em As Leis Básicas da Aritmética. No entanto, a tentativa proposta por Frege de reduzir a Aritmética à Lógica se mostrou inadequada, devido a um paradoxo na teoria apontado por Bertrand Russell em 1902. Assim sendo, o estudo aqui proposto tem como objetivo reconstruir lógicomatematicamente o paradoxo de Russell em sua formulação original nas Leis Básicas da Aritmética de Frege. Para realização deste estudo, o presente trabalho fundamentou-se numa pesquisa bibliográfica englobando, como bibliografia primária, as obras de Frege e, como bibliografia secundária, as obras de seus comentadores, assim como a correspondência entre Frege e Russell. A pesquisa proporciona uma formação lógica, filosófica e matemática para o educador que percorre este evento de fronteira entre as áreas que se configuram disciplinares na atualidade. Este é um momento fecundo na história e filosofia da Matemática e da Lógica, configurando-se como um divisor de águas para as teorias matemáticas, já que abre espaço para os Teoremas da Incompletude de Gödel e as lógicas não clássicas, possuindo também desdobramentos na Filosofia Contemporânea e que é de inquestionável valor nessa formação.
APA, Harvard, Vancouver, ISO, and other styles
9

Rouilhan, Philippe de. "Catégories logiques et paradoxes : recherches à partir de Frege, Russel et Tarski." Paris 1, 1988. http://www.theses.fr/1988PA010521.

Full text
Abstract:
Les recherches qui composent cette thèse, menées à partir de Frege, Russell et Tarski, sont consacrées à la notion de catégorie logique en relation avec le problème des paradoxes. Leurs titres, donnes ci-après, suggèrent plus précisément, au-delà de leur triplicité, l'unité organique du tout qu'elles constituent, si l'on ajoute que les "paradoxes de la représentation" dont fait état le premier sont, d'une part, le paradoxe de Russell, paradoxe logique par excellence, et, d'autre part, le paradoxe de Frege, que l'on peut considérer comme une sorte de paradoxe sémantique: -première recherche (à partir de Frege): sur les paradoxes de la représentation, deuxième recherche (à partir de Russell): sur la résolution commune des paradoxes logiques ou sémantiques par la théorie des types ramifiée, troisième recherche (à partir de Tarski): sur la résolution séparée des paradoxes logiques par la théorie des types simple ou par la théorie des ensembles, et des paradoxes sémantiques par la distinction des niveaux de langage. La visée ultime de cette thèse est quelque chose comme une résolution simultanée des paradoxes logiques et sémantiques, y compris, sous une forme ou sous une autre, le paradoxe de Frege, mais une résolution qui n'implique pas l'ordinaire distinction des niveaux de langage. La thèse ne produit pas une telle résolution, peut-être hors de portée dans l'état actuel de la logique, du moins tente-t-elle de réactualiser la valeur paradoxale du paradoxe de Frege sous une forme généralisée, de faire la critique en règle de la distinction des niveaux de langage, et de rappeler la communauté des logiciens a l'urgence de ladite résolution.
APA, Harvard, Vancouver, ISO, and other styles
10

Eldridge-Smith, Peter. "The Liar Paradox and its Relatives." Phd thesis, 2008. http://hdl.handle.net/1885/49284.

Full text
Abstract:
My thesis aims at contributing to classifying the Liar-like paradoxes (and related Truth-teller-like expressions) by clarifying distinctions and relationships between these expressions and arguments. Such a classification is worthwhile, firstly, because it makes some progress towards reducing a potential infinity of versions into a finite classification; secondly, because it identifies a number of new paradoxes, and thirdly and most significantly, because it corrects the historically misplaced distinction between semantic and set-theoretic paradoxes. I emphasize the third result because the distinction made by Peano [1906] and supported by Ramsey [1925] has been used to warrant different responses to the semantic and set-theoretic paradoxes. I find two types among the paradoxes of truth, satisfaction and membership, but the division is shifted from where it has historically been drawn. This new distinction is, I believe, more fundamental than the Peano-Ramsey distinction between semantic and set-theoretic paradoxes. The distinction I investigate is ultimately exemplified in a difference between the logical principles necessary to prove the Liar and those necessary to prove Grelling’s and Russell’s paradoxes. The difference relates to proofs of the inconsistency of naive truth and satisfaction; in the end, we will have two associated ways of proving each result. ¶ ...
APA, Harvard, Vancouver, ISO, and other styles

Books on the topic "Russell's paradox"

1

Godehard, Link, ed. One hundred years of Russell's paradox: Mathematics, logic, philosophy. New York: Walter de Gruyter, 2004.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Link, Godehard, ed. One Hundred Years of Russell´s Paradox. Berlin, New York: Walter de Gruyter, 2004. http://dx.doi.org/10.1515/9783110199680.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Rheinwald, Rosemarie. Semantische Paradoxien, Typentheorie und ideale Sprache: Studien zur Sprachphilosophie Bertrand Russells. Berlin: de Gruyter, 1988.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Bertrand Russell and the origins of the set-theoretic 'paradoxes'. Basel: Birkhäuser Verlag, 1992.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Dantan, Alejandro Ricardo Garciadiego. Bertrand Russell y los orígenes de las "paradojas" de la teoría de conjuntos. Madrid: Alianza Editorial, 1992.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Link, Godehard. One Hundred Years Of Russell's Paradox: Mathematics, Logic, Philosophy (De Gruyter Series in Logic and Its Applications). Walter De Gruyter Inc, 2004.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Simmons, Keith. Paradoxes of Definability, Russell’s Paradox, the Liar. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791546.003.0005.

Full text
Abstract:
Chapter 5 moves beyond the simple paradoxes discussed in Chapters 2-4. The chapter applies the singularity approach to the traditional paradoxes of definability (or denotation), associated with Berry, Richard, and König. The chapter goes on to argue that there are two settings for Russell’s paradox, one in terms of the mathematical notion of set, and the other in terms of the logico-semantic notion of extension. The chapter then applies the singularity approach to Russell’s paradox for extensions. The chapter moves on to the case of truth, and applies the singularity approach to various versions of the Liar paradox, paying particular attention to the so-called strengthened Liar.
APA, Harvard, Vancouver, ISO, and other styles
8

Simmons, Keith. The Theory at Work. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791546.003.0007.

Full text
Abstract:
Chapter 7 puts the singularity theory to work on a number of semantic paradoxes that have intrinsic interest of their own. These include a transfinite paradox of denotation, and variations on the Liar paradox, including the Truth-Teller, Curry’s paradox, and paradoxical Liar loops. The transfinite paradox of denotation shows the need to accommodate limit ordinals. The Truth-Teller, like the Liar, exhibits semantic pathology-but, unlike the Liar, it does not produce a contradiction. The distinctive challenge of the Curry paradox is that it seems to allow us to prove any claim we like (for example, the claim that 2+2=5). Paradoxical Liar loops, such as the Open Pair paradox, extend the Liar paradox beyond single self-referential sentences. The chapter closes with the resolution of paradoxes that do not exhibit circularity yet still generate contradictions. These include novel versions of the definability paradoxes and Russell’s paradox, and Yablo’s paradox about truth.
APA, Harvard, Vancouver, ISO, and other styles
9

Pruss, Alexander R., and Joshua L. Rasmussen. From Necessary Abstracta to Necessary Concreta. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198746898.003.0007.

Full text
Abstract:
An argument for a necessary being is developed on the basis of the existence of abstracta. This argument has two parts. First, reasons are put forward in support of the necessary existence of abstracta. These reasons include (among others) an argument for the necessary existence of necessary truths and arguments for the necessary existence of certain properties and mathematical entities. Second, reasons are given for thinking that if there were necessary abstracta, they would be grounded in necessary concreta. Included is an Aristotelian argument and a conceptualist‐based argument supported by Russell's paradox of propositions. It is suggested that the arguments of both parts are independently plausible, and thus that the arguments together could move one to accept the conclusion: abstracta depend on a necessary being.
APA, Harvard, Vancouver, ISO, and other styles
10

Tennant, Neil. Core Logic and the Paradoxes. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198777892.003.0011.

Full text
Abstract:
The Law of Excluded Middle is not to be blamed for any of the logico-semantic paradoxes. We explain and defend our proof-theoretic criterion of paradoxicality, according to which the ‘proofs’ of inconsistency associated with the paradoxes are in principle distinct from those that establish genuine inconsistencies, in that they cannot be brought into normal form. Instead, the reduction sequences initiated by paradox-posing proofs ‘of ⊥’ do not terminate. This criterion is defended against some recent would-be counterexamples by stressing the need to use Core Logic’s parallelized forms of the elimination rules. We show how Russell’s famous paradox in set theory is not a genuine paradox; for it can be construed as a disproof, in the free logic of sets, of the assumption that the set of all non-self-membered sets exists. The Liar (by contrast) is still paradoxical, according to the proof-theoretic criterion of paradoxicality.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Russell's paradox"

1

Wolf, Michael P. "Russell's paradox." In Philosophy of Language, 132–37. New York: Routledge, 2022. http://dx.doi.org/10.4324/9781003183167-26.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Fitting, Melvin. "Russell’s Paradox, Gödel’s Theorem." In Raymond Smullyan on Self Reference, 47–66. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68732-2_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Novak, Peter. "The Tale of Russell’s Paradox." In Mental Symbols, 225–42. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5632-5_10.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Tobias, Michael Charles, and Jane Gray Morrison. "Russell’s Paradox as Ecological Proxy." In On the Nature of Ecological Paradox, 129–34. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-64526-7_14.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Anellis, Irving H. "The First Russell Paradox." In Perspectives on the History of Mathematical Logic, 33–46. Boston, MA: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4769-8_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Moore, Gregory H. "The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number." In From Dedekind to Gödel, 215–39. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8478-4_9.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Hinkis, Arie. "The Role of CBT in Russell’s Paradox." In Proofs of the Cantor-Bernstein Theorem, 165–70. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0224-6_16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Garciadiego, Alejandro R. "Russell’s discovery of the ‘paradoxes’." In Bertrand Russell and the Origins of the Set-theoretic ‘Paradoxes’, 81–130. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-7402-1_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

McCain, Kevin. "Is the Past Real? (Russell's Five Minutes Old Universe)." In Epistemology: 50 Puzzles, Paradoxes, and Thought Experiments, 66–70. New York: Routledge, 2021. http://dx.doi.org/10.4324/9781003121091-15.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Castañeda, Hector-Neri. "Negations, Imperatives, Colors, Indexical Properties, Non-Existence, and Russell’s Paradox." In Philosophical Analysis, 169–205. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2909-8_11.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Russell's paradox' for particular source types:
Journal articles Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography