Relevant bibliographies by topics / Set-theoretic paradoxes

Academic literature on the topic 'Set-theoretic paradoxes'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 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 'Set-theoretic paradoxes.'

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 "Set-theoretic paradoxes"

1

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.

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

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.

Full text
Abstract:
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 the draft is made at a more basic level.The same research can be classified in another way, according to the informal diagnosis offered for the paradoxes of set theory. In some cases, the diagnosis is that the paradoxical sets (such as the Russell set) fail to exist only because they would have to be too large; a set that would be sufficiently small must always exist. This is the doctrine of limitation of size. In other cases, the diagnosis is that the paradoxical sets fail to exist only because they would have to lie too high in a certain hierarchy of sets; a set that would lie sufficiently low in the hierarchy must always exist. This is the doctrine of the hierarchy. The present paper will investigate the latter doctrine, with the doctrine of size making a brief appearance at the end.
APA, Harvard, Vancouver, ISO, and other styles
3

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.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
4

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.

Full text
Abstract:
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 generalization of this method will then be presented whereby Russell’s paradox, a variant of Mirimanoff’s paradox, the Liar, and the Grelling–Nelson paradox may be uniformly transformed into incompleteness theorems. Some additional observations are then framed relating these results to the unification of the set theoretic and semantic paradoxes, the intensionality of arithmetization (in the sense of Feferman, 1960), and axiomatic theories of truth.
APA, Harvard, Vancouver, ISO, and other styles
5

BRADY, ROSS T. "METAVALUATIONS." Bulletin of Symbolic Logic 23, no. 3 (September 2017): 296–323. http://dx.doi.org/10.1017/bsl.2017.29.

Full text
Abstract:
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-, according to key properties of negated entailment theorems (see below). Metavaluations have an inductive presentation and thus have some of the advantages that model theory does, but they represent proof rather than truth and thus represent proof-theoretic properties, such as the priming property, if ├ A $\vee$ B then ├ A or ├ B, and the negated-entailment properties, not-├ ∼(A→B) (for M1-logics, with M1-metavaluations) and ├ ∼(A→B) iff ├ A and ├ ∼ B (for M2-logics, with M2-metavaluations). Topics to be covered are their impact on naive set theory and paradox solution, and also Peano arithmetic and Godel’s First and Second Theorems. Interesting to note here is that the familiar M1- and M2-metacomplete logics can be used to solve the set-theoretic paradoxes and, by inference, the Liar Paradox and key semantic paradoxes. For M1-logics, in particular, the final metavaluation that is used to prove the simple consistency is far simpler than its correspondent in the model-theoretic proof in that it consists of a limit point of a single transfinite sequence rather than that of a transfinite sequence of such limit points, as occurs in the model-theoretic approach. Additionally, it can be shown that Peano Arithmetic is simply consistent, using metavaluations that constitute finitary methods. Both of these results use specific metavaluational properties that have no correspondents in standard model theory and thus it would be highly unlikely that such model theory could prove these results in their final forms.
APA, Harvard, Vancouver, ISO, and other styles
6

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.

Full text
Abstract:
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 of the system of knowledge. It was that cultural expectation aimed at mathematics that was substantially responsible for a great resonance made by set-theoretic paradoxes, and, finally, the whole picture of modern mathematics.
APA, Harvard, Vancouver, ISO, and other styles
7

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.

Full text
Abstract:
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 existence of abstract (aspatial, atemporal and acausal) objects such as sets. Leśniewski attempted to find a nominalistically acceptable replacement for set theory in the foundations of mathematics. His candidate was Mereology – a theory which, instead of sets and elements, spoke of wholes and parts. The goal of this paper will be to present Mereology in this context, to evaluate the feasibility of Leśniewski’s project and to briefly comment on its contemporary relevance.
APA, Harvard, Vancouver, ISO, and other styles
8

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.

Full text
Abstract:
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. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of F -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory.
APA, Harvard, Vancouver, ISO, and other styles
9

"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.

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

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.

Full text
Abstract:
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 strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented. In the first part of the paper I will set up the appropriate background details. In the second, I will look at the strategy as it applies to the semantic paradoxes. In the third I will look at how it applies to the set-theoretic paradoxes.
APA, Harvard, Vancouver, ISO, and other styles

Dissertations / Theses on the topic "Set-theoretic paradoxes"

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

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 "Set-theoretic paradoxes"

1

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

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

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.

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

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

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

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

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

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
6

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.

Full text
Abstract:
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 actions are fated is rejected, and Peter Geach’s argument that if time travel is possible we can change the past is refuted. These responses to Pike and Geach constitute a further defense of the pure manifold theory of time.
APA, Harvard, Vancouver, ISO, and other styles
7

Florio, Salvatore, and Øystein Linnebo. The Many and the One. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198791522.001.0001.

Full text
Abstract:
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 great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic’s applications than has been given so far. Questions about the correct logic of plurals play a central role in the last part of the book, where traditional plural logic is rejected in favor of a “critical” alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes.
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Set-theoretic paradoxes"

1

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.

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

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.

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

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
4

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.

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

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.

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

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.

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

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.

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

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.

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

"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.

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

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.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
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