# A Concise Introduction to Logic

Craig DeLancey, SUNY Oswego

Copyright Year: 2017

ISBN 13: 9781942341420

Publisher: Open SUNY

Language: English

## Formats Available

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

This volume is a well-constructed introduction to logic for undergraduates. It’s depth and breadth are appropriate. read more

This volume is a well-constructed introduction to logic for undergraduates. It’s depth and breadth are appropriate.

The author writes with care and leaves little room for misunderstanding.

Logic is not a perishable subject. Using intellectual history as a foundation gives the book enduring relevance.

The author is painstaking in his quest for clarity,

Logical consistency is the sine qua non of a book of this kind. The style and structure are consistent throughout,

The text can be assigned by individual chapter. The chapter order is approved and cannot be altered. The book concludes with a look forward to advanced topics.

I think I can use the volume as a reference for the occasional coverage of formal logic in my Business Ethics course,

It is a concise volume and proceeds logically.

I see no errors. The negation symbol used is not the one I thought was standard but apparently I was wrong!

I have encountered no serious grammatical errors, or any really.

The volume is clearly written within the “Western” intellectual tradition. It would be fascinating if the author were to consider alternative logical approaches and probably would be unique among texts.

I intend to use this book as a refresher so that I can add more formal consideration of arguments as an element of my teaching.

This text provides a thorough and responsible introduction to symbolic logic from sentential calculus through first-order predicate logic with identity and its application to specific numbers in arguments. While there is no index, this is hardly... read more

This text provides a thorough and responsible introduction to symbolic logic from sentential calculus through first-order predicate logic with identity and its application to specific numbers in arguments. While there is no index, this is hardly necessary in a digital text. In place of a glossary, the text offers a very effective and detailed summary section for each of the two logical languages developed.

I found no errors or biases in the text; it accurately presents its field of logic. Potential readers should be aware, though, that this is a text in symbolic / deductive logic, as such it reflects the conscious decision to exclude informal logic. Closely related to this is the equating of ‘good argument’ with ‘valid argument’ (using the traditional definition of the latter). A ’bad argument’ is, then, simply any invalid argument. While that's fine given that the text concerns only deductive logic, students or faculty expecting discussion of a wider range of logical ‘goodness’ (e.g. strength) may find this jarring.

The portion of logic introduced by this text is very stable. The systems presented are up-to-date and necessary revisions to the core ideas and techniques are unlikely for some time.

The text is well-designed and clearly written for its intended audience. For instance, most of the major concepts are introduced through discussion of concrete examples from the history of philosophy and science. The author is thus able to introduce concepts and techniques while demonstrating their value. Furthermore, instead of burdening the main text with sidebars or esoteric developments of the material, the author relegates these to footnotes, where they are no doubt useful to more advanced students without risking distracting the less well-prepared.

This is a text in logic; as such it makes a virtue of its consistency.

This text is as modular as a systematic introduction to logic can be. One could, for instance, teach/learn the sentential calculus on its own. That said, the nature of the discipline requires careful sequencing of material. A modular deductive logic text is unlikely to be as usable as this text. Furthermore, it is not clear that rearranging the material would be helpful. For logic, I’d call this a feature, not a bug.

In addition to the expected logical sequencing mentioned above, this text presents its material against the backdrop of history. Frederick Douglass, Hobbes, Socrates/Plato, Aristotle, Galileo, Hume, Frege, Russell, Peano, Meinong, Tarski and Carnap all make an appearance. Many students will find this structure helpful in putting flesh on the logical bones.

I found no problems with the interface, navigation or text/image rendering in the pdf version of the text (the only version I read). Any reader comfortable navigating pdf files should have no concerns.

The text is written in student-approachable professional English. I found no grammatical or typpgraphical errors.

I do not think the content or its presentation is likely to be found culturally insensitive or offensive at all (disclosure: I am a Caucasian male). That said, with only a single exception that I could find (Frederick Douglass) the historical examples are representative of the European male dominated philosophical canon.

The text is very comprehensive. It covers each of the main connectives separately, proofs, and an introduction to propositional logic. The index covers each aspect of the text in explicit detail. read more

The text is very comprehensive. It covers each of the main connectives separately, proofs, and an introduction to propositional logic. The index covers each aspect of the text in explicit detail.

The text is accurate, error-free, and unbiased.

The content is up-to-date but there are areas of logic that go largely uncovered. In particular, there is no explicit instruction on the construction of truth table and the usage of truth tables to assess consistency, tautologies, contingencies, and soundness.

The text is clearly organized. A student is able to learn about each main connective in its own chapter. The language in the text is accessible to a wide variety of audiences while ensuring that students become familiar with the technical terminology of logic.

The text is internally consistent.

The text is divided into chapters that individually address each main connective. Additionally, each chapter includes approximately three practice problems. It would be valuable to include additional practice problems given that logic is best learned through solving a wide variety of practice problems. Additionally, it would be helpful to have more problems that teach students how to use the main connectives together and not just independently.

The organization, structure, and flow of the text is impressive.

The text makes great use of colors and charts. It includes a combination of both logical equations and word problems. The problems within the text are presented in a multiple choice format.

The text is free of major spelling and grammar errors.

The text use a variety of contexts for the problems. The problems include both historical figures and contemporary figures, and examples from a variety of cultural contexts.

The text begins with basic definitions and mapping tools for representing propositional logic and for creating truth tables. It then moves through first order logic, quantification, and proofs. It ends with a look forward to more advanced... read more

The text begins with basic definitions and mapping tools for representing propositional logic and for creating truth tables. It then moves through first order logic, quantification, and proofs. It ends with a look forward to more advanced applications. There is neither index nor glossary, but terms are easy to find using the table of contents. Moreover, the chapters are brief, and terms are relatively easy to identify within them.

DeLancey's work is careful and meticulous. Exercises and examples reflect a diversity of situations, viewpoints, and authors. I observed no glaring errors or bias.

The foundational principles of propositional logic aren't particularly new, but as the final section of this volume suggests, there a several advanced and creative ways to apply them. Some early sections point out what current thinking on certain topics is. While these points are unlikely to change, the text is written in such a way that it would be easy to modify later. Also, Part III: A Look Forward is written in a such a way that it could be edited easily to reflect further modifications, changes, or developments.

This book is what it says it is: a concise introduction. DeLancey's writing is brief and methodical. Paragraphs are small and somewhat minimalist. This, however, is not a criticism. Explanations are short and effective. Terms build upon terms and concepts upon concepts. There are not examples for every single instance, but there are always examples to show how the concepts discussed in the chapter work together. Chapters are well-organized and short. Exercises are interesting and challenging (for that matter, the content matter is, too), and they reflect what is discussed in the chapters. I regularly review online course design and textbooks, and while I always find these reviews stimulating, this is the first time in a long time where I really wanted to take a course in this topic and ask questions about the content and application.

The formatting style, complete with chapter and section numbers, is consistent throughout. There is not much color—nor does there need to be—but for what there is, it is also consistent. DeLancey warns the reader of terminology that has different names but refers to the same concept. He even states that he may use certain terms interchangeably; however, these terms were not difficult to follow, and the interchangeable use was minimal.

Most chapters are about ten pages. They include explanations, examples, and problems (exercises). These chapters could be easily assigned to students. It is conceivable that one might assume sections in order to introduce students to certain concepts, but the text is written in such a way that concepts build on one another. In addition, a method for representing logic, which includes signs and symbols, is introduced. With that in mind, unless students had prior experience with the material, it would not be advisable to reorganize the chapters. In my mind, the chapters and sections are very much dependent on their ordering.

The Reviewer's Notes provide an accurate overview of the text's organization. This is also reflected in the Table of Contents. From start to finish, the text introduces concepts and builds on them to move from basic to more advanced applications.

The text is in a Pressbooks style. The PDF was easy to navigate. There appear to be two primary typefaces, a serif and sans serif font. Both were easy to read. Charts, tables, and images have rendered well. I observed no distracting pixelation, blurring, or alignment errors with these visuals.

DeLancey's style is easy to read. I observed no significant errors in grammar or punctuation.

DeLancey has been careful to include examples from various persons, both male and female, from a variety of cultures, races, and backgrounds. He also varies his use of pronouns, sometimes using he or she, sometimes he, sometimes she.

The conciseness of the chapters, sections, paragraphs, and sentences is to be commended. The organization and structure is also easy to follow. I came to this book on the Open Textbook Library looking for a text for my introductory composition and rhetoric students. While I found some things that would be applicable to them, I found that the text was more in line with a philosophy or more traditional course in rhetoric than what I would typically present to first-year composition students. That said, I found the style and content of the book fascinating. I enjoyed doing the exercises, and I can visualize how students could use this text to confidently develop fundamental skills in using logic and representing it in truth tables and proofs.

## Table of Contents

Part I: Propositional Logic

- 1. Developing a Precise Language
- 2. “If…then….” and “It is not the case that….”
- 3. Good Arguments
- 4. Proofs
- 5. “And”
- 6. Conditional Derivations
- 7. “Or”
- 8. Reductio ad Absurdum
- 9. “… if and only if …”, Using Theorems
- 10. Summary of Propositional Logic

Part II: First Order Logic

- 11. Names and predicates
- 12. “All” and “some”
- 13. Reasoning with quantifiers
- 14. Universal derivation
- 15. Relations, functions, identity, and multiple quantifiers
- 16. Summary of first order logic

Part III: A Look Forward

- 17. Some advanced topics in logic

## Ancillary Material

## About the Book

*A Concise Introduction to Logic* is an introduction to formal logic suitable for undergraduates taking a general education course in logic or critical thinking, and is accessible and useful to any interested in gaining a basic understanding of logic. This text takes the unique approach of teaching logic through intellectual history; the author uses examples from important and celebrated arguments in philosophy to illustrate logical principles. The text also includes a basic introduction to findings of advanced logic. As indicators of where the student could go next with logic, the book closes with an overview of advanced topics, such as the axiomatic method, set theory, Peano arithmetic, and modal logic. Throughout, the text uses brief, concise chapters that readers will find easy to read and to review.

## About the Contributors

### Author

**Craig DeLancey** is Professor of Philosophy and Chair of the Department of Philosophy at SUNY Oswego. He received his Ph.D. from Indiana University. His publications include Passionate Engines: What Emotions Reveal about the Mind and Artificial Intelligence, with Oxford University Press. He has been a fellow of the Center for the Philosophy of Science at the University of Pittsburgh, a fellow of the National Endowment of the Humanities, and has received research funding from the Army Institute of Basic Research. When not teaching philosophy or doing research, he writes science fiction.