Formal Logic: A Philosophical Approach

by Paul Hoyningen-Huene

Many texts on logic are written with a mathematical emphasis, and focus primarily on the development of a formal apparatus and associated techniques. In other, more philosophical texts, the topic is often presented as an indulgent collection of musings on issues for which technical solutions have long since been devised. What has been missing until now is an attempt to unite the motives underlying both approaches. Paul Hoyningen-Huene’s Formal Logic seeks to find a balance between the necessity of formal considerations and the importance of full reflection and explanation about the seemingly arbitrary steps that occasionally confound even the most serious student of logic. Alex Levine’s artful translation conveys both the content and style of the German edition. Filled with examples, exercises, and a straightforward look at some of the most common problems in teaching the subject, this work is eminently suitable for the classroom.

Genres: Philosophy

272 pages, Paperback

First published January 1, 2004

Reviews

[E.L. · Rating 4 out of 5]

Note: I’ve read only the Introduction and SL chapters because that’s what I wanted to review after studying formal logic in college.

As opposed to the textbook my introductory class used, The Logic Book by Merrie Bergmann, which is more like “here’s what you need to know for ‘solving’ formal logic; now memorize it and do tons of practice problems,” this book is not as concerned with “solving” formal logic as with understanding the theoretical and philosophical grounds on which it stands. The text, as a result, addresses and explains the most fundamental aspects of formal logic. To name a few:

1. What’s formal logic?
2. If formal logic involves working with statements, what is a ‘statement?’ Verbatim quote: “We are told that statements are the sorts of things that can be true or false—but what *are* these things, exactly?” (18). Logic can’t exhaustively answer this question without breaking something else in its attempt to define the statement; yet somehow it works insofar as our logical needs go.
3. What’s a logical form? How to properly obtain it? (Note the use of the article “a” here, for there are many logical forms for a given statement).
4. What’s the origin of connectives used in SL and PL? (26-37).
5. Why the falsehood of premises cannot be transferred to the conclusion the way truth can? (76-78). Author uses a hypothetical syllogism to illustrate this point.
6. How to come up with the definition of validity from the ground up? (The *definition* for statement validity stays formally undefined until page 87; you can imagine the discourse the book takes to get there).
7. What theorems the formal logic depends on? Why they work? How to prove them?
8. Why tautologies and logical falsehoods really assert nothing?

The book prioritizes theory over solving logic. And because it’s theoretically heavy and not as “practical” in terms of exercises and solving formal logic, I can’t recommend it as a primary resource — only as a secondary. And I especially can’t recommend it as your first logic textbook. It will be overwhelming and confusing to make sense of this book. For even I, a person who’s taken an introductory class under fair guidance, often found myself scratching my head in defeat.

As a nice detail, the author is keen to give historical context where it’s appropriate, which makes you appreciate the subject and its fathers even more. Another plus on the ledger.

Overall, the book is great as a supplementary resource, and it’s worth your time.

L: you love logic
B: you’ve read the book
C: you think the book is crap

(L & B) -> ~C