summary, praise, and ordering information
Jan Dejnožka
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 construct or even describe 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 BERTRAND RUSSELL ON MODALITY AND LOGICAL RELEVANCE
"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 is founding editor of the journal History and Philosophy of Logic and also of the Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (Routledge). He is the author of Dear Russell-Dear Jourdain (Columbia) and other books on the history of logic. He has published numerous papers on Russell. He is professor of history of logic and mathematics in Middlesex University, United Kingdom.
"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 is a professor of philosophy at Syracuse University. He is the author of Metaphysics: The Logical Approach (Oxford) and Infinity (Clarendon).
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). 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:
"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:
"[B]y far the most comprehensive discussion yet published. Moreover, his interpretation of Russell, if correct, would require a radical reconception of the logic of Principia Mathematica."
--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 as quoted by Barnes and Noble Online Bookstore.
Ordering Information
The publisher is Ashgate Publishing Ltd, and the series is Avedale Series in Philosophy. There is a single clothbound edition, viii + 241 pages, ISBN 1-84014-981-7. The book was published in February 1999. No new editions or corrections are contemplated by the publisher. Thus there is no book history to speak of.
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