# Fundamental Methods of Logic

Matthew Knachel, University of Wisconsin - Milwaukee

Copyright Year: 2017

ISBN 13: 9780996150224

Publisher: A.T. Still University

Language: English

## Formats Available

## Conditions of Use

Attribution

CC BY

## Reviews

The book covers introductory logic exceptionally well. It would be a good introduction to critical thinking, inductive logic, and the basics of deductive logic. It covers the basics of arguments, logical fallacies, Aristotelian logic, sentential... read more

The book covers introductory logic exceptionally well. It would be a good introduction to critical thinking, inductive logic, and the basics of deductive logic. It covers the basics of arguments, logical fallacies, Aristotelian logic, sentential logic, and inductive logic using analogies, causal claims, and statistics. It does not cover logical proofs or predicate logic. As far as I can tell, it does not have an index or glossary.

The book gives an accurate and clear presentation of logical concepts. Some of the examples and problems venture into political territory that I would prefer not to include in my courses (e.g. arguments citing Barack Obama, Hilary Clinton and Donald Trump, etc.). These can be easily altered but they are somewhat numerous. I would like to see more consciousness of student diversity in the examples, problems, and discussion. In the introduction the author acknowledges the existence of diverse logics but does not delve into cultural or social variation of logical approaches. To its credit it is more gender neutral and avoids blatant sexism detectable in other OER logic textbooks I have surveyed.

The textbook promises longevity with the exception of the already dated citation of political figures.

One of the books greatest strengths is its clarity and approachability. It consistently defines terminology and explains the reasons for it. It is unfortunate that these terms are not gathered in an index or glossary.

The book uses a consistent terminology and framework. It uses familiar and standard logic symbols (dot, wedge, horseshoe, tilde, and triple bar) for symbolic logic. Each section is followed by a good number of exercises.

The chapters are divided into manageable sub-sections that can be divided and rearranged if needed. It is easy to download the text, and it is available as PDF and word. But it is not possible to navigate to a section from the table of contents. If a sub-section is desired on its own, it will be necessary to cut and paste it.

The book has four main content areas: introduction to arguments, informal fallacies, deductive logic, and inductive logic.

The text is clear, easy to read, and avoids distortion. Images such as the square of opposition, Venn diagrams, and truth tables are large and discernable. They are not easily cut and pasted into a Powerpoint or other document but would have to be recreated. The 3 ring Venn diagrams are inverse from those I normally use. It is not easy to navigate the text as a PDF, but it can be downloaded as a word document and bookmarked.

The text's grammar is correct and without errors.

The text is not culturally offensive, but neither is it as culturally diverse as I would like. Use of hypothetical names and people are decidedly mainstream White American/European.

The book is lacking ancillary materials such as question banks for quizzes or exams. There is a place to submit these materials from the textbook site. But following the link there is no accessible repository. Perhaps this is being compiled.

There are exercises after each section but no answers are provided. This means that instructors will have to generate these answers, undoubtedly a time consuming process. I will be seeking for ancillaries elsewhere.

In its intended aims, the book is comprehensive. For example, in presenting a system of sentential logic, it gives a complete set of operators and a method for determining validity of arguments using the system. This would work well for a course... read more

In its intended aims, the book is comprehensive. For example, in presenting a system of sentential logic, it gives a complete set of operators and a method for determining validity of arguments using the system. This would work well for a course in which there is to be some formal logic, but where the main emphasis is on informal logic. The coverage is similar to texts like Fogelin and Sinnott-Armstrong's Understanding Arguments. So, there isn't any coverage of natural deduction, nor is predicate logic introduced. This makes the text as it stands unsuitable for the logic course at my institution. Fortunately, however, one could supplement this text with one's own sections on these topics. The text as it stands is comprehensive in the kinds of methods and skills it intends to cover. In addition, it contains more depth on inductive arguments than other texts of its kind.

The coverage of each method and system is accurate. It covers the basics of these systems in an adequate way.

While many of the examples are contemporary, and so will need updating over time, the methods and skills articulated in the text are timeless. In addition, all texts of this sort require the kind of updating of examples in order to engage with students.

The writing style is precise enough to capture formal concepts like validity and those involved in logical operators and casual enough to be readable and engaging. The text really strikes the right balance for an introductory logic text.

The book is entirely consistent in its use of key concepts like validity and soundness and its presentation of methods of representation and reconstruction of arguments.

As mentioned other places in the review, a more formal course could add modules on formal topics without too much difficulty. And, too, cutting particular topics like inductive logic could also be done with little effort. Because of the organizational structure, the chapters are largely modular.

The text begins like many in this genre with representing and diagramming arguments, moves on to informal fallacies, then introduces some formal deductive systems, and concludes with coverage of inductive reasoning. This is a fine way to organize a text like this and instructors will find it familiar. This way of organizing the text lends itself to easily adding or removing modules.

There are really only two minor issues here. One is simply the sheer amount of unbroken text. As screen readers used to social media, many students will have difficulty engaging with text in such large blocks. (This is, of course, a problem with books in general, or rather, a problem with our students and books). The other minor issue involves the truth tables. The spacing in the truth tables could be a bit wider to make absolutely clear what column goes with what operator.

The text is well edited. I did not find any grammatical errors.

The examples in the text should appeal to traditional college students and non-traditional students alike in that they are taken from popular culture and current events, including politics. This style of attempting to engage through reference to these topics, while also, hopefully, getting students to think about, for example, the current political scene, is one that I also use and find effective. It is presented in a way that challenges without being offensive to any political group. The cultural references are appropriate and should be engaging to people from all sorts of backgrounds.

This is an excellent contribution to the open source repository of logic texts. It would be appropriate for anyone teaching a relatively informal logic course. It is especially useful for those who want to emphasize informal reasoning. The inductive logic chapters are particularly impressive.

This text is very well suited to the sort of Introduction to Logic course taught at most state universities. It begins with basic concepts in Logic and then follows up with sections on inductive arguments, categorical logic, truth functionality... read more

This text is very well suited to the sort of Introduction to Logic course taught at most state universities. It begins with basic concepts in Logic and then follows up with sections on inductive arguments, categorical logic, truth functionality and truth tables in the propositional logic, and then finishes with material on causality and probability. If there is a defect it is that some professors or instructors might well prefer a section on natural deduction rather than one on causality and probability - this is particularly true if the class is a feeder class for an upper level course in symbolic logic. Still it is a fairly simple matter for a professor or instructor to provide that material him or herself. Each section is supplemented with a nice selection of exercises.

The content of the book is accurate and without any errors in the presentation of material

The content is up -to-date. The fundamentals of logic change little and so the usefulness of the book promises to be quite long. Some of the exercises and examples may age less well than does the substance of the book as they reference current political figures and events. This, of course, makes the exercises relevant and interesting to current students but, without updated exercises in the future, the text may come off as a bit dated.

The text is clear and accessible and well pitched to its audience which would primarily be college students in their first or second year of study. Logic is a definition driven discipline but care is taken at every step to ensure students understand each definition and understand it's significance in the body of the course.

The book is consistent. Definitions are appropriate and consistently used and applied. The book itself is nicely structured with each topic well developed and presented in an orderly fashion.

The text lends itself well to the classroom. Sections are easily divisible into manageable reading blocks and classroom sessions. I see no foreseeable difficult in using the text easily and effectively in a semester long introductory logic course. There is also some flexibility as there is probably a section more than one might get through in a semester and so one could for example do the material on causality without doing the material on probability or vice versa allowing the individual professor or instructor some discretion in terms of his or her class.

The text is organized as most introductory logic books are. It is certainly organized as I would have chosen to organize it. Each section is appropriate in terms of its placement and the books flows well from one section to the next.

I have only looked at the electronic version of the text on a computer and so I can't really speak to interface issues on a tablet or, what I think is increasingly common, a cell phone. On a computer the text is free of any significant display issues. Charts and venn diagrams and truth tables all maintain their original formatting and display properly and are large enough to be easily read and followed.

The author's writing and grammar are without noticeable errors. The text is well written and written in a grammatically correct and accessible manner.

I saw no evidence of the text being culturally insensitive or offensive. I would not hesitate to use it in a class and, in fact, have plans to do so starting next semester. Examples are and exercises are all appropriate to the course and the college setting.

I think this text does a great service. Introduction to Logic is class that, along with Introduction to Ethics, serves as a sort of bread and butter course for many philosophy departments. That is, it is a course that sees high enrollments and many students every semester. It is also a course where the price of traditional textbooks has skyrocketed with the purchase costs of some now approaching $200. I think it is fair to say that no single text in philosophy could save more students more money than this one does. Teaching at a regional campus of a state university with many place bound and economically strapped students, I am grateful to the author for having invested his time and effort to produce such a needed text.

## Table of Contents

Chapter 1 - The Basics of Logical Analysis

- I. What is Logic?
- II. Basic Notions: Propositions and Arguments
- III. Recognizing and Explicating Arguments
- IV. Deductive and Inductive Arguments
- V. Diagramming Arguments

Chapter 2 - Informal Logical Fallacies

- I. Logical Fallacies: Formal and Informal
- II. Fallacies of Distraction
- III. Fallacies of Weak Induction
- IV. Fallacies of Illicit Presumption
- V. Fallacies of Linguistic Emphasis

Chapter 3 – Deductive Logic I: Aristotelian Logic

- I. Deductive Logics
- II. Classes and Categorical Propositions
- III. The Square of Opposition
- IV. Operations on Categorical Sentences
- V. Problems with the Square of Opposition
- VI. Categorical Syllogisms

Chapter 4 – Deductive Logic II: Sentential Logic

- I. Why Another Deductive Logic?
- II. Syntax of SL
- III. Semantics of SL
- IV. Translating from English into SL
- V. Testing for Validity in SL

Chapter 5 – Inductive Logic I: Analogical and Causal Arguments

- I. Inductive Logics
- II. Arguments from Analogy
- III. Causal Reasoning

Chapter 6 – Inductive Logic II: Probability and Statistics

- I. The Probability Calculus
- II. Probability and Decision-Making: Value and Utility
- III. Probability and Belief: Bayesian Reasoning
- IV. Basic Statistical Concepts and Techniques
- V. How to Lie with Statistics

## Ancillary Material

## About the Book

*Fundamental Methods of Logic* is suitable for a one-semester introduction to logic/critical reasoning course. It 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. 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.

## About the Contributors

### Author

**Matthew Knachel** is a Senior Lecturer in the Philosophy department at University of Wisconsin - Milwaukee, Milwaukee, WI.