Preface to This Version,
Matthew Knachel’s Fundamental Methods of Logic is a wonderfully accessible text for use in Introduction to Logic courses. The text benefits from Knachel’s experience teaching the subject in many ways. The text is rich with examples. The subject matter and content are presented with sufficient thoroughness as to ensure students can achieve a substantive familiarity with the topics while not being overwhelmed by complexities. Fundamental skills are given significant attention enabling students to create and retain a strong foundation for the application of logical analysis to matters beyond the course itself.
Fundamental Methods of Logic is published as an open educational resource (OER) with an open Creative Commons license. Knachel gave this book to any student or teacher to use. Not only does the book have an open copyright for use, but Knachel also opened the book to future edits and revisions. This edition is an example of Knachel’s generosity.
This new version comes with two new chapters. A new, fifth chapter now covers formal proofs in propositional logic. Chapter 5 is written as a stand-alone chapter with only non-essential references and cross-citations to the previous chapters. The chapter explains how to construct formal proofs using 19 rules of inference and replacement, as well as conditional and indirect proofs.
A new, sixth chapter introduces predicate logic and quantification. This chapter is also written as a potentially free-standing chapter, with minor references to parallels that occur in Chapter 3 which covers Aristotelian syllogism. Chapter 6 introduces quantification, rules of universal and existential generalization and instantiation, as well as formal proofs using predicate logic. Conditional and Indirect proofs are re-introduced in this new context. The chapter also covers the use of Truth Tables to prove invalidity using models with 1 – n objects.
Both new chapters try, as much as is possible, to match the tone, style, and formatting of the pre-existing chapters so that readers can work through the complete, new version with continuity and congruity.
This new version also includes several non-substantive edits to Knachel’s original work. A few clarifying sentences have been added at various points throughout any given chapter. Some of the tangential footnotes that were lost as the text transferred between file formats during editing were not replaced out of the sake of concision. At other places, some of the potentially more opinionated and expressive examples were neutralized.
Most dramatically, however, this new version avoids the previous version’s use of examples that draw upon U.S. politics. Knachel’s repeated references to the 2016 presidential election, Donald Trump, and Hillary Clinton have been replaced with difference examples. I think that while Knachel’s use of contemporary matters can help engage students. However, in different localities and contexts such examples can also over-engage them and lead to distracting tangential debates regarding politics, rather than logic. For better or worse, it is unclear the extent to which politics and logic mix.
Thank you, Matthew Knachel, for sharing a solid open education resource with the educational community. I could not have written the additional chapters 5 and 6 without using Copi, Cohen, and Rodych’s Introduction to Logic as a guide. Just as Knachel gives credit to his previous logic instructors, I would like to give credit to Erin Anchustegui and Mary Tiles. I would also like to acknowledge Liza Long, Greg Wilson, Anchustegui, and Jean-Louise Zancanella for their support revising and working with this book and OER materials in general. Financial support for my time was provided through funds from the College of Western Idaho’s OER stipend program and an OPAL fellowship from the Idaho State Board of Education.
Sean Gould
Knachel’s Original Preface.
There’s an ancient view, still widely held, that what makes human beings special—what distinguishes us from the “beasts of the field”—is that we are rational. What does rationality consist in? That’s a vexed question, but one possible response goes roughly like this: we manifest our rationality by engaging in activities that involve reasoning—making claims and backing them up with reasons, acting in accord with reasons and beliefs, drawing inferences from available evidence, and so on.
This reasoning activity can be done well, and it can be done badly—it can be done correctly or incorrectly. Logic is the discipline that aims to distinguish good reasoning from bad.
Since reasoning is central to all fields of study—indeed, since it’s arguably central to being human—the tools developed in logic are universally applicable. Anyone can benefit from studying logic by becoming a more self-aware, skillful reasoner.
This covers a variety of topics at an introductory level. Chapter One introduces basic notions, such as arguments and explanations, validity and soundness, deductive and inductive reasoning; it also covers basic analytical techniques, such as distinguishing premises from conclusions and diagramming arguments. Chapter Two discusses informal logical fallacies. Chapters Three and Four concern deductive logic, introducing the basics of Aristotelian and Sentential Logic, respectively. Chapters Five and Six concern inductive logic. Chapter Five deals with analogical and causal reasoning, including a discussion of Mill’s Methods. Chapter Six covers basic probability calculations, Bayesian inference, fundamental statistical concepts and techniques, and common statistical fallacies.
The text is suitable for a one-semester introductory logic or “critical thinking” course. The emphasis is on formal techniques and problem solving rather than analytical writing, though exercises of the latter sort could easily be incorporated.
A note on tone, style, and content. This book is written by an American teacher whose intended audience is American undergraduates; it is based on my lectures, developed over many years. Like the lectures, it assumes that some members of the intended audience lack an antecedent interest in the subject and may have trouble developing and maintaining enthusiasm to study it. It tries to compensate for this by adopting a casual style, using first- and second-person constructions, and by shamelessly trafficking in cultural references, lame jokes, and examples involving American current events. The result is a logic textbook with a somewhat unusual tone and a sometimesnarrow cultural perspective. Neither familiarity with the relevant cultural references, nor amusement at the lame jokes, is a prerequisite for understanding the material, but I thought it prudent to offer an apologia at the outset. Caveat lector.
An acknowledgment of debts. The following books have influenced my teaching, and hence the present work: Virginia Klenk’s Understanding Symbolic Logic, John Norton’s How Science Works, Ian Hacking’s Introduction to Probability and Inductive Logic, Darrell Huff’s How to Lie with Statistics, and Irving Copi and Carl Cohen’s Introduction to Logic. The influence of those last two books is particularly profound, as I note throughout this text. I am indebted to all my logic viii teachers over the years: Kurt Mosser, Michael Liston, Mark Kaplan, Richard Tierney, Steve Leeds, Joan Weiner, Ken Manders, Mark Wilson, and Nuel Belnap. Thanks to J.S. Holbrook for sending me examples of fallacies. For extensive logistical support, I’m indebted to Kristin Miller Woodward; I also thank her for arranging financial support through the UW-Milwaukee Library and Center for Excellence in Teaching and Learning, who have undertaken a project to encourage the development and adoption of open textbooks. My logic students over the years also deserve acknowledgment, especially those who have recently served as guinea pigs, learning from earlier drafts of this book. Without student feedback, there would be no book. Finally, and most importantly, I could not have completed this project without my wife Maggie’s constant support and forbearance.
