Bertrand Russell on Modality and Logical Relevance

Second Edition

Jan Dejnožka

summary, praise,

and ordering information



Jan Dejnožka's book, Bertrand Russell on Modality and Logical Relevance, is the only exhaustive study of Russell on modality and logical relevance ever written. This is the second edition. It took twenty years to write, including minor corrections to 2019. It is over twice as long as the superseded 1999 Ashgate first edition, which was republished by Routledge in 2017.

This is the only edition in which Dejnožka creates three entire new book-length fields of logical study: Russell on modality, Russell on deductive logical relevance, and Russell on inductive logical relevance. Before this book, there were only brief scattered writings on these topics, because most philosophers wrongly thought Russell's modern classical logic was against modality and logical relevance. Dejnožka shows that Russell was in fact deeply concerned with modality and relevance, and can be formalized.

Many philosophers seem unaware that Russell had any views on these subjects, or think he disliked them. There are two reasons for this. First, most philosophers, even many of those who write on his logic, have read few of Russell's nonlogical works, and those are the works in which Russell most often discusses modal issues. Second, Russell's seminal paper on modality, "Necessity and Possibility," read to the Oxford Philosophical Society in 1905, was not published during Russell's lifetime.

Russell's logic has been universally criticized by modal logicians and relevance logicians for being too limited to accommodate their ideas. Their criticism has been supported by Russell scholars, who agree with Russell's critics that Russell rejects or avoids such ideas.

Obviously, Russell does not expressly state any modal logics. But Dejnožka finds texts in Russell which imply the axioms of S5. Dejnožka paraphrases these texts into the formal axioms of various formal modal logics one axiom at a time. Thus Dejnožka imputes seven implicit S5 logics to Russell: FG-MDL (full generality), FG-MDL* (truth in virtue of form), FG-MDL**implicit (synthetic a priori), MDL-C (Humean causal), MDL-E (epistemic), and MDL-D and MDL-D* (deontic or moral).

Dejnožka shows that despite a brief initial phase of denial that any logical analysis of modality is possible, Russell expressly states a logical analysis of basic modal notions in at least eight works over a period of at least thirty-six years. Indeed, it is the same analysis Russell proposed but rejected in his seminal paper. He develops it from the ideas of Hugh MacColl, now widely recognized as the first formal modal logician. Russell's express idea is to use notions of quantificational logic to define and analyze away basic modal entities, much as he defines and analyzes away numbers. Modal notions are eliminated across the board. The individual and universal quantifiers are used to simulate the basic modal notions. Literally speaking, Russell banishes modality from logic, much as he banishes numbers from arithmetic. That is, for Russell modalities and numbers alike are logical fictions. Yet functionally speaking, Russell implicitly has an S5 modal logic based on a rich and sophisticated theory of modality, much as his logic can also function as an arithmetic.

Russell's implicit alethic modal logics anticipate Carnap, Tarski, McKinsey, Almog, and Etchemendy, and has predecessors in Bolzano and Venn. Dejnožka argues that Russell implicitly anticipated Kripke's modal logic by over seventy years, and even indirectly influenced Kripke via Carnap and Beth. Dejnožka shows that Russell's logically proper names are in fact rigid designators, and that Russell developed a causal reference theory of naming not far from Kripke's own.

Based on Russell's repeatedly stated whole-part containment theory of logical deduction, Dejnožka shows that Russell is implicitly a relevance logician with three progressively stronger forms of entailment. By 1921 Russell expressly adopts Wittgenstein's equation of following from with containment of truth-grounds, which is visibly shown by truth-table diagrams, in the Tractatus Logico-Philosophicus. Such relevant containment can also be visibly shown by Venn-like diagrams. With either sort of diagram, to diagram the premisses of a valid argument is already to diagram its conclusion. This validates modus ponens and disjunctive syllogism as relevantist on the level of containment of truth-grounds. And that refutes the view, advanced by Anderson and Belnap in their book, Entailment, that Russell was anti-relevance. Their requirement of variable-sharing emerges as a Procrustean technical solution not based on what relevance most deeply is, and ignores the well-known development of diagrams of relevant containment from Euler through Venn to Wittgenstein.

Thus Dejnožka explains Russell as implicitly having a unified account of deductive logic in which his implicit analyses of modality and relevant containment are implicit interpretations of his quantificational logic. The implicit necessity operator and the implicit relevant containment operator are the Principia thesis assertion sign.

Last, Dejnožka shows that the concept of logical relevance in English evidence law by far the most likely origin of Russell’s logical theory of probability, indirectly through John Maynard Keynes’ theory of probability as degree of logical relevance. Dejnožka argues that John Maynard Keynes inspired the 1912 Russell to adopt a theory of probability as degrees of logical relevance, that Keynes was inspired in turn by the 1903 Russell and by the legal concept of logical relevance, and that Aristotle's theory of induction is Keynes's ancient antecedent. (Keynes discusses Aristotle on induction, but considers Aristotle's theory of probability to be an alternative to his own.) The interdisciplinary argument involves both legal and philosophical scholarship. Thus Russell is an implicit relevantist with respect to deductive and inductive logic alike. Keynes was a member of the Inner Temple, one of the four English bars; and his work on probability was arguably better researched than his more famous work in economics.

Like the rest of the book, the chapter on Russell, Keynes, and evidence law upends received thinking. The noted legal scholar William Twining denies that some of the great evidence law writers had relevance rules. Dejnožka quotes and discusses the relevance rules of those writers. The famous Keynes scholar, Robert Skidelsky, holds that Keynes himself discovered the relation between probability and logical relevance. Dejnožka quotes and discusses that relation as affirmed throughout the last five centuries of English evidence law. Most relevantists were members of the Inner Temple law bar, and Keynes was too.

Before this book, no one even imagined that evidence law was the origin of the Keynes-Russell theory of probability. But the author has two doctorates, one in philosophy and the other in law, and simply put two and two together. Perhaps no one else could have done this interdisciplinary work on the Keynes-Russell theory; certainly no one else has done it. It is practically a small book in its own right. In fact, here Dejnožka creates a fourth entire new field of study, the history of logical relevance in evidence law. Of course, many scholars have written in that field for centuries, and Dejnožka discusses many of them. But their writings are generally brief and scattered, as opposed to the chronologically unified and developmental book length treatment given here. And Dejnožka’s work should be easily readable “law for philosophers.” It should also be philosophically interesting. For logical relevance is the defining feature of probable evidence. Certainly it is for Russell and Keynes, and also for the last five centuries of English evidence law. If it's not relevant, it's not evidence. If it's not evidence, it's not relevant. You will not find this study on the legal origins of the Keynes-Russell theory of probability anywhere else.


Praise for the Second Edition

"It shows originality and great care." —Jon Michael Dunn

Looks like a seminal work.” Paul Nascimbene


Excerpt from Published Review of the Second Edition:

"As the title indicates, Bertrand Russell on Modality and Logical Relevance investigates two main topics: modality and logical relevance in the work of Bertrand Russell. It claims to be the only study of Russell’s views about modality and logical relevance ever written (p. xi) and as such deserves attention of anyone interested in the magnum opus of the philosopher. In the scope of more than six hundred pages, Dejnožka brought to light many aspects of Russell’s philosophy which, implicitly or explicitly, record Russell’s interest in modal matters. Dejnožka’s strategy is quite straightforward: to gather together relevant quotations including modal notions and, consequently, interpret them in a systematic and ‘Russell friendly’ way. [S]uch a comprehensive overview is unique and of interest [to] a wider group of philosophers.

"Historically oriented reader[s] will definitely find interesting Dejnožka’s ‘History Chart of Relevance Rules’ (p. 480), ‘History Chart of Common Terms for Relevance’ (p. 481) and the ‘Relevantist Members of the Inner Temple['] (p. 481).

Bertrand Russell on Modality and Logical Relevance is literally a full-length study of Russell’s views on modality. It does both, highlight the ‘modality bearing’ passages in which Russell implicitly or explicitly comments on the problems of modality, and interprets them in a spirit of the overall unity, systematicity and Russell’s ingenuity. [I]t is always a hard and risky enterprise to find... important, although ignored, features in the life works of the most influential philosophers of [the] 20th century. But Dejnožka’s book does present one such enterprise and as such is a stimulative and worthy contribution to (the history) of philosophy."

Martin Vacek, Organon F 24/2 (2017), pp. 261-266.


Praise for the First Edition

"In the twenty-five years since Russell's death, much of the major scholarship has drawn heavily on his manuscripts and unpublished correspondence. The author shows that the published Russell is capable of new interpretations; in particular, that modal notions such as possibility have a greater place in various aspects of his logical and philosophical thought than has previously been imagined."

Ivor Grattan-Guinness

Ivor Grattan-Guinness was Emeritus Professor of the History of Mathematics and Logic at Middlesex University, Visiting Research Associate at the London School of Economics, sometime fellow at the Institute for Advanced Study in Princeton, New Jersey, and a member of the Academie Internationale d’Histoire des Sciences. He was the founding editor of History and Philosophy of Logic and was the editor of Annals of Science and associate editor of Historia Mathematica journals. He was the founding editor of the Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences series (Routledge), and was an advisory editor for several other book series, including editions of the works of Peirce and of Russell. His books include Dear Russell-Dear Jourdain (1977) and The Search for Mathematical Roots 1870-1940: Logics, Set Theories, and the Foundations of Mathematics from Cantor through Russell to Gödel (2000).


"Jan Dejnožka's book, Bertrand Russell on Modality and Logical Relevance, has earned a place of prominence in the literature."

--Panayot Butchvarov

Panayot Butchvarov has been President of the Central Division, American Philosophical Association, and the editor of Journal for Philosophical Research. He was professor and chair of the philosophy department at the University of Iowa for many years. His books include Resemblance and Identity: An Examination of the Problem of Universals (Indiana University Press), The Concept of Knowledge (Northwestern University Press), Being Qua Being: A Theory of Identity, Existence and Predication (Indiana University Press), Skepticism in Ethics (Indiana University Press), Skepticism about the External World (Oxford University Press), and Anthropocentrism in Philosophy: Realism, Antirealism, Semirealism (Walter de Gruyter).


"While Chapter 9 on logical relevance pits Russell squarely against the recent research of Anderson and Belnap, Chapter 10 construes Russell's theory of probability in terms of Keynes's degrees of logical relevance. How one might thus combine philosophy proper (in the analytical mode) with highly nuanced history of philosophy in the grand tradition, Dejnožka vindicates on a page-by-page basis. Because Dejnožka can even conclude by imaginatively asking if there is 'room for a concept of partial relevance' where 'premise and conclusion are at least partly connected or related', and include 'inductive kinds of partial relevance' that recall Aristotle for whom induction is the same intellectual activity as clearly passing from a single instance to a universal truth, the only difference being that in induction the subject-matter is less intelligible, I am encouraged to believe that the full sweep of history of philosophy may yet be recovered under analytical auspices."

José Benardete

José Benardete was a professor of philosophy at Syracuse University for many years. He was the author of Metaphysics: The Logical Approach (Oxford) and Infinity (Clarendon).


Excerpt from Published Review of the First Edition:

"Dejnožka's book is the first full-length study of modality in Russell. It is useful for its very full survey of passages in which Russell makes use of or alludes to modal notions. Dejnožka's command of Russell's huge output is indeed impressive and his utilization of it thorough...."

Nicholas Griffin, Studia Logica 68/2 (July 2001), p. 294.

Nicholas Griffin is professor of philosophy at McMaster University in Ontario, Canada, and is the Director of the Bertrand Russell Research Centre there. He is also the General Editor of The Collected Papers of Bertrand Russell, a series of volumes published by Routledge. His books include Relative Identity (Oxford, 1977), Russell's Idealist Apprenticeship (Oxford, 1991), Selected Letters of Bertrand Russell: The Private Years, 1884-1914 (Allen Lane/Houghton Mifflin, 1992), and Selected Letters of Bertrand Russell: The Public Years, 1914-1970 (Routledge, 2001).


Excerpt from Published Review of the First Edition:

"Dejnožka's book raises a very important point in the history of formal logic. Until now the major studies on this topic have drawn heavily on the development of classical logic as standardized by Gottlob Frege and Bertrand Russell. Dejnožka challenges the reader to open his mind for a new interpretation of Russell's work, in particular that modal and relevance notions have a greater place in his philosophy of logic than has been stressed before....

"Dejnožka rightly observes that many of Russell's insights on modality are a result of his discussions with Hugh MacColl, who was indeed the first to seriously attempt to develop formal modal logic. This particularly applies to Russell's conception of a modal logic without modal operators....That is, classical logic can be used to simulate modal expressions. Thus, the notions of (logical) necessity and possibility are not 'fundamental notions'....On this basis, Dejnožka develops a higher level of modality, where the quantification scope extends to the predicates yielding what Russell calls 'fully general propositions'....

"The best studied translation method is known as the standard translation, and it is quite compatible with Dejnožka's suggestions....

"Dejnožka's book is full of material which stimulates [one] to rethink Russell's philosophy of logic is greatly to the author's credit that he brings to light such a wealth of crucial issues in the history and philosophy of logic."

Shahid Rahman, History and Philosophy of Logic 22 (2001), 99-112.

Professor Rahman teaches at the Université de Lille (France). Recently he has served as dean and supervised many dissertations. He is the author of: The Logic of Connexive Statements in the Early Work of Hugh MacColl, (English version of Rahman's Habilitationsschrift) (Dordrecht: Kluwer, to appear 2002); Philosophie Pragmatique et les Logiques Non-classiques (Pragmatic Philosophy and Non-Classical logics (Paris: Kime, Philosophia Scientiae, in preparation); and, with Emmanuel Genot and Laurent Keiff, Logique Modale et Dialogues: Une Introduction (Modal and Dialogic Logic: An Introduction) (in preparation). He is a co-editor of: New Perspectives in Dialogical Logic, Synthése 127/1-2 (2001) and several articles on logic and the history of logic. He is also a co-editor of several works: Wege zur Vernunft: Philosophieren zwischen Tätigkeit und Reflexion (Ways to rationality: Philosophy between Doing and Reflecting)York: Campus (1998); New Perspectives in Dialogical Logic, special issue of Synthése 127/1-2 (2001); Logic, Epistemology and the Unity of Science, Kings College-Paris, Cognitive Sciences Series (in preparation). He has contributed to several anthologies: W. Carnielli, M. Coniglioi, and I. M. Loffredo D'Ottaviano, eds., Paraconsistency: The logical way to the inconsistent (New York: Marcel Dekker, 2002); J. Gasser, ed., A Boole Anthology. Recent and Classical Studies in the Logic of George Boole  (Dordrecht: Kluwer, 2000 (Synthése Library)); M. Beaumont Wrigley, eds, Festschrift para Marcelo Dascal (Campinas: Manuscrito); with Walter Carnielli, in D. Krause, Hg., Festschrift in honor of Newton C. A. Da Costa on the occasion of his seventieth birthday, Synthése 125/1-2 (2000), 201-231; H. Wansing (Hg.), Essays on Non-Classical Logic (London: World Scientific, 2001); with John Symons, in Gabbay, Rahman, Symons, Van Bendegem, eds., Logic, Epistemology and the Unity of Science (Kluwer, in preparation). He has also written several articles and reviews, and read papers at various congresses.


Excerpt from Published Review of the First Edition:

"[B]y far the most comprehensive discussion yet published."

Gary Ostertag, Russell 20/2, Winter 2000-2001, p. 166.

Professor Ostertag teaches at New York University, and is the editor of Definite Descriptions: A Reader (M.I.T. Press).


Excerpt from Published Review of the First Edition:

"As a survey of Russell's use of modal notions in his philosophical language, this is a valuable project."

Bernard Linsky, The Bulletin of Symbolic Logic 6/1, March 2000, p. 96.

Professor Linsky teaches at the University of Alberta in Edmonton, Canada, and is the author of Russell's Metaphysical Logic (Center for the Study of Language and Information, distributed by Cambridge University Press).


Excerpt from Published Review of the First Edition:

"Surprising many by showing that Russell did in fact have views on modality, though scattered through his writings, Dejnožka (philosophy and law, U. of Michigan-Ann Arbor) explores what he thought about logical necessity, and also causal, epistemic, and moral necessity. He describes how the 20th-century philosopher functionally accepted and assimilated modality into his philosophical system even as he rejected what he considered certain more primitive accounts of it."

Book News 14, November 1999, p. 4

Ordering information and publishing history

The second edition is sold on and other sites. Do not buy the first edition or its republication by Routledge. The second edition is greatly superior to the first, and contains over twice the material. The first edition was published by Ashgate Publishing Ltd in the Avedale Series in Philosophy. It was clothbound, viii + 241 pages, ISBN 1-84014-981-7, and published in February 1999. The book sold out. Later, Ashgate discontinued their entire philosophy line and returned all rights to me. Then Ashgate went out of business completely, and was bought out in 2017 by Routledge. Routledge then republished the book in the Routledge Revivals Series.

There is also a free download of the second edition on ResearchGate..

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