**Second
Edition**

**Jan
Dejnožka**

**summary,
praise,**

**and****
****ordering
information**

**Summary**

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 over
seventeen years to write, and is over twice as long as the first.

Dejnožka creates three entire new 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. Each field receives its first book-length treatment here. I show 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.

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**

“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 to...date
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 and...it 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.),

**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**

The second edition can be ordered at Amazon.com. Do not order the first edition. It is superseded by the second edition, which is over twice as long. The first edition publisher was Ashgate Publishing Ltd, Avedale Series in Philosophy. There was a single clothbound edition, viii + 241 pages, ISBN 1-84014-981-7, published in February 1999. It is no longer available from the publisher. The book sold out and the publisher returned all rights to me. In fact, Ashgate discontinued their entire philosophy line, no doubt due to the Great Recession of the 1990s, which hurt many publishers.