The Concept of Relevance and

the Logic Diagram Tradition

Jan Dejnožka

summary, praise,

and ordering information



Summary

The book reconciles Peirce-Frege-Wittgenstein-Russell modern classical logic with the relevantists by showing that modern classical logic is relevantist at the deepest level, which is that of truth-ground containment entailment. Wittgenstein was quite explicit about it, and Russell expressly and repeatedly endorsed it, starting with his introduction to Wittgenstein’s Tractatus. Thus the book is written toward reunion in contemporary logic. But its main argument is based on the ancient diagram tradition, which can be traced to texts in Aristotle, and which is logically most deeply concerned with truth-ground containment, not just class containments and exclusions pursuant to Aristotelian classificatory science.

The main argument of the book is very simple in form. 1. If the premisses of an argument contain its conclusion, then the argument is relevantly valid. 2. If in the very act of diagramming all the premisses of an argument we also diagram its conclusion, then the premisses contain the conclusion. 3. Modus ponens, disjunctive syllogism, and all modern classical-valid arguments that violate relevantist variable sharing can be and have been so diagrammed. 4. Therefore all such arguments are relevantly valid.

Thus in their critique of modern classical logic, the relevantists overlook the very deepest relevantism.

Current relevantist logics emerge as mere species of the truth-ground containment genus. I suggest five filters or constraints which most modern classical logicians would find plausible, and which both vitiate the main relevantist objections and bring modern classical logic far closer to the relevantists.


Praise for the book:

"Dejnožka's erudition continues to astound me." — Nicholas Griffin

As Canada Research Chair and Director of the Bertrand Russell Research Centre at McMaster University, Professor Griffin directs the editing of the ongoing editions of The Collected Papers of Bertrand Russell, currently at 16 volumes. He also edited The Cambridge Companion to Bertrand Russell, and has written several books and articles.


"Dejnožka challenges the reader to open his mind for a new interpretation of Russell’s work, in particular that relevance notions have a greater place in his philosophy of logic than has been stressed before. Dejnožka’s work 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

Professor Rahman teaches at the Université de Lille (France). He has served as dean and supervised many dissertations. He is the author of several books and the editor of several anthologies in logic and the philosophy of logic. He recently edited a book on Hugh MacColl. He has also written many articles and reviews, and read papers at various congresses.


Excerpt from Published Review:

This book offers a new interpretation of relevance logic. It does so by reuniting two areas of logical research that have been historically unrelated: diagrammatic logic and relevance logic.” Francesco Bellucci, Studia Logica (2019).


Excerpt from Published Review:

"Dejnožka's defense of his view is well articulated and strongly supported by citing thinkers of the caliber of Quine, Russell and Wittgenstein, among others. Moreover, the defense is presented in a clear and explicit way, making evident the role played by relevance logic and diagrams.... Finally, a very positive aspect is the presence of many explanatory notes, placed at the end of the book, that shed light on the discussion in the text." Edgar L. B. Almeida, Logic and Logical Philosophy (2013).


Excerpt from Published Review:

"The main argument of the book is interesting for suggesting that truth ground containment, i.e. the classical notion of consequence, embodies a meaningful notion of a connection between the assumptions and the conclusion of a valid argument.... I do think that the book's main claims hold.... Yes, classical validity can be seen as involving a...notion of containment - containment of truth grounds. Yes, this notion can be found in the writings of outstanding modern classical logicians such as Wittgenstein or Russell. Yes, the relevantist's notion of relevance...can be seen as a species of a broader genus. Perhaps the greatest merit of the present book is that it emphasizes these points explicitly." Igor Sedlár, Organon F (2014).


Ordering Information

The book may be ordered on Amazon.com. I am the publisher and the author. The book supersedes my paper of the same name in Logica Universalis. It is an independent sequel to my book, Bertrand Russell on Modality and Logical Relevance: Second Edition, but was published earlier.

For online readers, the free download of the book on ResearchGate is fully updated to August 31, 2019; see the preface for this date

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