Relevant bibliographies by topics / Set-theoretic paradoxes

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Set-theoretic paradoxes'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 January 2023

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Journal articles on the topic "Set-theoretic paradoxes"

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Forster, Thomas, and Thierry Libert. "An Order-Theoretic Account of Some Set-Theoretic Paradoxes." Notre Dame Journal of Formal Logic 52, no. 1 (January 2011): 1–19. http://dx.doi.org/10.1215/00294527-2010-033.

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van Aken, James. "Axioms for the set-theoretic hierarchy." Journal of Symbolic Logic 51, no. 4 (December 1986): 992–1004. http://dx.doi.org/10.2307/2273911.

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The axioms for Zermelo-Fraenkel (ZF) set theory are an appealing but somewhat arbitrary-seeming assortment. A survey of the axioms does not suffice to reveal the source of their attraction. Accordingly, attempts have been made to ground ZF in principles whose appeal can be felt immediately. These attempts can be classified as follows. First, some of them propose to rest the ZF axioms directly on informal doctrine. The others propose to ground the ZF axioms in other formal axioms that can be regarded as more basic. When the latter approach is taken, ZF continues to draw on informal support, but
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LINNEBO, ØYSTEIN. "THE POTENTIAL HIERARCHY OF SETS." Review of Symbolic Logic 6, no. 2 (March 14, 2013): 205–28. http://dx.doi.org/10.1017/s1755020313000014.

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AbstractSome reasons to regard the cumulative hierarchy of sets as potential rather than actual are discussed. Motivated by this, a modal set theory is developed which encapsulates this potentialist conception. The resulting theory is equi-interpretable with Zermelo Fraenkel set theory but sheds new light on the set-theoretic paradoxes and the foundations of set theory.
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DEAN, WALTER. "INCOMPLETENESS VIA PARADOX AND COMPLETENESS." Review of Symbolic Logic 13, no. 3 (May 23, 2019): 541–92. http://dx.doi.org/10.1017/s1755020319000212.

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AbstractThis paper explores the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various “paradoxical notions” for first-order languages can be formalized. I will first discuss the setting in which this result was originally presented by Hilbert & Bernays (1939) and also how it was later adapted by Kreisel (1950) and Wang (1955) in order to obtain formal undecidability results. A generalizatio
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BRADY, ROSS T. "METAVALUATIONS." Bulletin of Symbolic Logic 23, no. 3 (September 2017): 296–323. http://dx.doi.org/10.1017/bsl.2017.29.

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AbstractThis is a general account of metavaluations and their applications, which can be seen as an alternative to standard model-theoretic methodology. They work best for what are called metacomplete logics, which include the contraction-less relevant logics, with possible additions of Conjunctive Syllogism, (A→B) & (B→C) → .A→C, and the irrelevant, A→ .B→A, these including the logic MC of meaning containment which is arguably a good entailment logic. Indeed, metavaluations focus on the formula-inductive properties of theorems of entailment form A→B, splintering into two types, M1- and M2
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Shaposhnikov, Vladislav. "Theological Underpinnings of the Modern Philosophy of Mathematics." Studies in Logic, Grammar and Rhetoric 44, no. 1 (March 1, 2016): 31–54. http://dx.doi.org/10.1515/slgr-2016-0003.

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Abstract The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern is nineteenth-century mathematics. Theology was present in modern mathematics not through its objects or methods, but mainly through popular philosophy, which absolutized mathematics. Moreover, modern pure mathematics was treated as a sort of quasi-theology; a long-standing alliance between theology and mathematics made it habitual to view mathematics as a divine knowledge, so when theology was discarded, mathematics naturally took its place at the top o
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Urbaniak, Rafal. "Stanisław Leśniewski: Rethinking the Philosophy of Mathematics." European Review 23, no. 1 (January 29, 2015): 125–38. http://dx.doi.org/10.1017/s1062798714000611.

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Near the end of the nineteenth century, a part of mathematical research was focused on unification: the goal was to find ‘one sort of thing’ that mathematics is (or could be taken to be) about. Quite quickly sets became the main candidate for this position. While the enterprise hit a rough patch with Frege’s failure and set-theoretic paradoxes, by the 1920s mathematicians (roughly speaking) settled on a promising axiomatization of set theory and considered it foundational. In parallel to this development was the work of Stanislaw Leśniewski (1886–1939), a Polish logician who did not accept the
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Bodanza, Gustavo. "Yablo’s Paradox, the Liar, and Referential Contradictions from a Graph Theory Point of View." Логико-философские штудии, no. 1 (September 15, 2021): 101–4. http://dx.doi.org/10.52119/lphs.2021.32.43.005.

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F -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘... affirms the falsity of...’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. C
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"Bertrand Russell and the origins of the set-theoretic 'paradoxes'." Choice Reviews Online 31, no. 01 (September 1, 1993): 31–0236. http://dx.doi.org/10.5860/choice.31-0236.

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Priest, Graham. "What If? The Exploration of an Idea." Australasian Journal of Logic 14, no. 1 (April 11, 2017). http://dx.doi.org/10.26686/ajl.v14i1.4028.

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A crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay is to investigate Stragey 1. It is not to advocate it. The work is simply an extended exploration of the str
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Dissertations / Theses on the topic "Set-theoretic paradoxes"

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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.

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

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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 di
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Books on the topic "Set-theoretic paradoxes"

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

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Garciadiego, Alejandro R. Bertrand Russell and the Origins of the Set-theoretic ‘Paradoxes’. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-7402-1.

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GARCIADIEGO. Bertrand Russell and the Origins of the Set-Theoretic 'Paradoxes'. Birkhäuser Boston, 2012.

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GARCIADIEGO. Bertrand Russell and the Origins of the Set-Theoretic 'Paradoxes'. Birkhauser Verlag, 2013.

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

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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 el
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Williams, Donald C. The Bugbear of Fate. Edited by A. R. J. Fisher. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198810384.003.0013.

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This chapter begins with a critique of David Lewis’s ontology of concrete possible worlds. One argument that has been given in support of such an ontology is that possible worlds are needed to uphold our best analysis of counterfactuals. In response to this argument it is objected that we do not need to postulate possible worlds as truthmakers for counterfactuals. It is further argued that Lewis’s ontology of concrete possible worlds leads to set-theoretic-like paradoxes, and that it fails to explain our motivation to eradicate evil in our world. Nelson Pike’s argument that if God exists our a
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Florio, Salvatore, and Øystein Linnebo. The Many and the One. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198791522.001.0001.

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Plural logic has become a well-established subject, especially in philosophical logic. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has
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Book chapters on the topic "Set-theoretic paradoxes"

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Priest, Graham. "Set Theoretic Paradoxes." In In Contradiction, 35–48. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3687-4_3.

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Garciadiego, Alejandro R. "The ‘Semantic Paradoxes’." In Bertrand Russell and the Origins of the Set-theoretic ‘Paradoxes’, 131–50. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-7402-1_5.

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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.

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Garciadiego, Alejandro R. "Antecedents." In Bertrand Russell and the Origins of the Set-theoretic ‘Paradoxes’, 1–17. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-7402-1_1.

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Garciadiego, Alejandro R. "A standard interpretation." In Bertrand Russell and the Origins of the Set-theoretic ‘Paradoxes’, 19–40. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-7402-1_2.

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Garciadiego, Alejandro R. "The philosophical and mathematical background to The Principles of Mathematics, 1872–1900." In Bertrand Russell and the Origins of the Set-theoretic ‘Paradoxes’, 41–79. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-7402-1_3.

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Garciadiego, Alejandro R. "Conclusions." In Bertrand Russell and the Origins of the Set-theoretic ‘Paradoxes’, 151–53. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-7402-1_6.

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Priest, Graham. "Set Theoretic Paradoxes." In In Contradiction, 28–38. Oxford University Press, 2006. http://dx.doi.org/10.1093/acprof:oso/9780199263301.003.0003.

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"Cantor, Russell, and Zermelo and the Set-Theoretic Paradoxes." In Quine, New Foundations, and the Philosophy of Set Theory, 33–58. Cambridge University Press, 2018. http://dx.doi.org/10.1017/9781316591321.004.

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Studd, J. P. "Russell, Zermelo, and Dummett." In Everything, more or less, 21–60. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198719649.003.0002.

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Concerns about generality in the context of set theory are not new. Russell seeks to resolve the set-theoretic antinomies by maintaining that we cannot legitimately speak of ‘all classes’. Zermelo attempts to avoid the paradoxes without ‘constriction and mutilation’ by adopting an open-ended conception of the cumulative hierarchy of sets. Dummett takes the indefinite extensibility of concepts such as set and ordinal to impugn absolutism about quantifiers. But not every paradox-inspired argument is an argument for relativism about quantifiers. This chapter aims to fill in the logical and philosophical background to the contemporary absolute generality debate, with an eye to disentangling my favoured indefinite-extensibility-based argument from others in its vicinity.
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