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Published: 4 June 2021
Last updated: 29 January 2023

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1

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

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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.

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3

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

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4

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

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5

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

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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.

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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.

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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.
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8

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

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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.
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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.

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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.
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10

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 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.
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11

Simmons, Keith. Semantic Singularities. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791546.001.0001.

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This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by the concepts of reference or denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions ‘denotes’, ‘extension’, and ‘true’ are context-sensitive. The second, inspired by a brief, tantalizing remark of Gödel’s, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities is presented and applied to a wide variety of versions of the definability paradoxes, Russell’s paradox, and the Liar paradox. The book argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski’s intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. The book examines the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism.
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12

Link, Godehard. One Hundred Years of Russells Paradox: Mathematics, Logic, Philosophy. De Gruyter, Inc., 2004.

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13

Bell, John L., Ulrich Blau, Godehard Link, Solomon Feferman, and Andrea Cantini. One Hundred Years of Russell´s Paradox: Mathematics, Logic, Philosophy. de Gruyter GmbH, Walter, 2008.

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14

Rheinwald, Rosemarie. Semantische Paradoxien, Typentheorie und Ideale Sprache: Studien Zur Sprachphilosophie Bertrand Russels. De Gruyter, Inc., 2016.

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15

Bakken, Tore. George Spencer-Brown (1923b). Edited by Jenny Helin, Tor Hernes, Daniel Hjorth, and Robin Holt. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199669356.013.0030.

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George Spencer Brown is a British mathematician and logician, whose book Laws of Form (1969) tackles the very foundation of development of knowledge. An abstract and bold ‘calculus of indications’, Laws of Form was even praised by Bertrand Russell. It presents a calculus that seeks to clarify the laws governing the formation of forms. This chapter examines Spencer Brown’s form calculus and its implications for the study of organizations. After providing an overview of mathematics as a cognition theory, it describes some basic main points of Spencer Brown’s form calculus and its implications for process philosophy. It then discusses the two ‘arithmetic axioms’ developed by Spencer Brown in Laws of Form: the law of calling and the law of crossing. Finally, it shows how the calculus can help elucidate self-reference and paradoxes.
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16

Studd, J. P. Everything, more or less. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198719649.001.0001.

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Almost no systematic theorizing is generality-free. Scientists test general hypotheses; set theorists prove theorems about every set; metaphysicians espouse theses about all things regardless of their kind. But how general can we be? Do we ever succeed in theorizing about ABSOLUTELY EVERYTHING in some interestingly final, all-caps-worthy sense of ‘absolutely everything’? Not according to generality relativism. In its most promising form, this kind of relativism maintains that what ‘everything’ and other quantifiers encompass is always open to expansion: no matter how broadly we may generalize, a more inclusive ‘everything’ is always available. The importance of the issue comes out, in part, in relation to the foundations of mathematics. Generality relativism opens the way to avoid Russell’s paradox without imposing ad hoc limitations on which pluralities of items may be encoded as a set. On the other hand, generality relativism faces numerous challenges: What are we to make of seemingly absolutely general theories? What prevents our achieving absolute generality simply by using ‘everything’ unrestrictedly? How are we to characterize relativism without making use of exactly the kind of generality this view foreswears? This book offers a sustained defence of generality relativism that seeks to answer these challenges. Along the way, the contemporary absolute generality debate is traced through diverse issues in metaphysics, logic, and the philosophy of language; some of the key works that lie behind the debate are reassessed; an accessible introduction is given to the relevant mathematics; and a relativist-friendly motivation for Zermelo–Fraenkel set theory is developed.
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17

McDonagh, Josephine. Literature in a Time of Migration. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895752.001.0001.

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Literature in a Time of Migration rethinks British fiction in the light of new practices of human mobility that reshaped the nineteenth-century world. Building on the growing critical engagement with globalization in literary studies, it confronts the paradox that at a time at which transnational human movement occurred globally, on a scale before unknown, British fiction appears to turn inward to tell stories of local places, in which stability and rootedness are rewarded. On the contrary, Literature in a Time of Migration reveals how literary works, from the end of the Napoleonic Wars to the advent of the New Imperialism, were active components of a culture of colonization and emigration. Fictional texts, as print commodities, were enmeshed in technologies of transport and communication, and innovations in literary form were spurred by the conditions and consequences of human movement. Works by canonical writers (Scott, Charlotte Brontë, Dickens, and George Eliot), and other popular contemporaries (Mary Russell Mitford, John Galt, and Thomas Martin Wheeler), examine issues that overlap with an agenda set in public discussions of colonial emigration, which they also helped to shape. Debates concerning, for example, assisted emigration, ‘forced’ and ‘free’ migration, colonization, settlement, and the removal of native peoples, figure in complex ways in fictions. Read alongside writings by emigration theorists, practitioners, and enthusiasts, fictional texts reveal a sustained engagement with British migratory practices and their worldwide consequences. Literature in a Time of Migration is a timely reminder of the place and importance of migration within British cultural heritage.
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