**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.

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 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.

**Praise for the Second
Edition**

“Looks like a seminal work.” -- Paul Nascimbene.

**Excerpt from
Published Review:**

"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*.

**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 is the author of *Skepticism about the External World*
(Oxford University Press), *Skepticism in Ethics*
(Indiana University Press), *Being Qua Being: A Theory of Identity,
Existence, and Predication* (Indiana
University Press), *The
Concept of Knowledge* (Northwestern
University Press), *Resemblance
and Identity: An Examination of the Problem of Universals* (Indiana University Press), and *Anthropocentrism
in Philosophy* (Walter
de Gruyter). He was professor and chair of the
philosophy department at The University of Iowa for many years.

"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 is the
author of *Metaphysics: The
Logical Approach* (Oxford)
and *Infinity*
(Clarendon).

**Excerpt from
Published Review:**

"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:**

"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:**

"[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:**

"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**

"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 CreateSpace and Amazon.com. Do not order the first edition. It is totally superseded by the second edition, which is over twice as long. The first edition publisher was Ashgate Publishing Ltd, and the series was 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. Ashgate in fact discontinued their entire philosophy line, no doubt due to the Great Recession of the 1990s, which hurt many publishers.