Logical Forms: An Introduction to Philosophical Logic

by Mark Sainsbury

When is a reason for doing or believing something a good reason? Over the past century, logic's contribution to answering this question has typically involved finding "logical forms": that is, using a special notation to bring out logical features more clearly.

The correct identification of logical forms has been held to be important not only to logic but also to philosophy. Bertrand Russell coined the phrase "philosophical logic" to describe an approach to philosophical problems: find the correct logical form of the problematic sentences and the problems vanish. Logical Forms explains both the theoretical underpinnings of the approach and the detailed problems involved in finding logical forms in the languages of propositional logic, classical first order logic, modal logic, and some alternatives such as free logic, binary and substitutional quantifiers.

This revised edition incorporates results of recent work. Chapter 3 on conditionals, and the sections dealing with predicate quantifiers, free logics and subjunctive conditionals have been completely rewritten. The exercises are integrated throughout the book, and each chapter concludes with updated notes to guide further reading. The result is a genuinely interactive introduction which engages the reader in developing the argument.

This book does not presuppose knowledge of deductive methods in formal logic and it will be of immense benefit to those approaching philosophical logic for the first time.

Genres: Philosophy, Logic

436 pages, Paperback

First published January 1, 1991

Reviews

[José Pereira · Rating 3 out of 5]

An (almost) perfect introduction to philosophical logic. Takes you through all the concepts, nomenclature, and argument forms in baby steps and with friendly clarity. Different theories are addressed with neutrality and laid out in dialectical fashion, making each as appealing as it can be in face of its adversaries.
I wish, however, that there were more examples of logical analysis being applied to standard (e.g., ethical, epistemological) philosophical arguments. And that the proposed exercises had solutions.
In addition, one must admit that the book is extremely dry and sometimes hard to follow. But I imagine no one dives into to it expecting a fun, light ride.

[VII · Rating 2 out of 5]

I abandoned it after reading the first chapter as it's impossible to make sure you are learning if you read it on your own. There is one or two examples in every section and ten exercises without solutions anywhere. The last straw was trying to find why this is invalid: “A only if B. It is not the case that B. So it is not the case that A”. It's obvious that if B was the case, it wouldn't mean that A was the case also. But now that B is not the case and A can only be the case if B, how can A be the case? My only guess is that this “only if” is some special term that I can't understand and allows for A to happen for a reason other than B.

[J.]

I'm sorry, but the first thing to notice here is this destructive and arrogant 'preference'. It's a widespread one, but rarely owned with such cynicism.

'My own preference in teaching logic is to begin with the elementary formal part, keeping the students' eyes blinkered to philosophical questions, which are dauntingly hard. In introducing the philosophical issues later on, I am conscious of the width of the gap I expect students to leap, from the drill of truth tables and proofs to discussions of the semantics of names or conditionals. This is the gap this book is intended to fill.' p. 2

[Richard Newton · Rating 4 out of 5]

The first time I read this book I found it seriously hard work, but coming back to it a year later, and a year further into my philosophy degree I found it helpful and reasonably clear. Perhaps there is no easy way into philosophy of logic, and this book reflects that.

At times I felt the text could be shorter, but overall it is good. I also found the constant cross referencing to other parts of the book a little irritating, but not sure there is an easy alternative.

The strength of the book is its explanation of key logical concepts - validity, truth, propositional logic, modal logic, and quantification - all set within in a framework of long exposition of the challenges of formalisation. A good book for an undergraduate philosophical logic course. As a comparison, it is more interesting, but harder work and less easy to follow, than Guttenplan's "The languages of logic".