Learning Logic: Critical Thinking With Intuitive Notation

By Stephen Plowright

This book is intended to serve as a compact manual of concepts and symbols used in critical thinking and formal logic. While most people believe that they can present a sound argument, or spot a faulty one, the majority are often unaware of the errors they make. This is particularly true when numbers or statistical evidence areinvolved.

Logic is a valuable skill explicitly required in many pursuits including higher education, the sciences, law, engineering, security, medicine, information technology, and mathematics, to name a few. However it is often not formally taught in these fields.

The aim of this book is to provide a basic but firm foundation in the concepts and symbols of formal reasoning for those who may want to take this study further, or who are pursuing studies or vocations that require logic. To make learning easier, the notation used has been chosen to be consistent, symmetrical, intuitive, and widely used.

• Language: English
• Publisher: Lulu.com
• Release date: Nov 27, 2015
• ISBN: 9781329694934

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Learning Logic: Critical Thinking with Intuitive Notation

Stephen Plowright

Reviews

The theory of logic, the meaning of logic, the study of logic, and the practice of logic are all dependent upon the language of logic.  Without a uniform language, logical discourse is fraught.  This book is not only a clear, straightforward text on the building blocks of logic, but also a handbook which proposes a standardised means of describing those building blocks.  As such it is the sort of publication that will be used frequently and well thumbed.  Plowright has taken a commonsense approach to developing a clear, intuitive and well explained uniform terminology for the language of logic.  The significance of this book is that it enables logical argument with common understanding, thus facilitating sound, well-reasoned logical conversation.  That is a major contribution to the field for a humble little book.

-- Associate Professor Brad Mitchell

  Principal Research Fellow

  Federation University Australia.

"Plowright has succeeded admirably in achieving his aims of writing this book.  He has whetted the appetite of a thinking person to further explore the tools of formal logic. The range of situations he has selected illustrates the need for critical thinking in almost every area of human endeavour. His introduction to techniques such as Venn diagrams and truth tables is clear enough for the reader to follow, and with a little work, be convinced of their validity in solving logical conundrums. His brief introduction to basic probability theory convinces the reader that further study in this area will be invaluable in refuting claims often based on misleading evidence, particularly where statistics is involved.

In all, a worthwhile and informative read which opens the door to an area of mathematics of great value but as yet, undiscovered by many."

-- Michael Fenelon

Senior High School Mathematics Teacher

Victoria Australia

In a world where politicians and celebrities have elevated fuzzy thinking to an art form, this book will show you how to cut through the fog, sharpen your critical thinking skills, and avoid the logical pitfalls that lie in wait for us every day.

-- R. S. Radford

The Radford Center for Law

History & Economics, California USA

Copyright © 2015 by Stephen Plowright

All rights reserved. This book or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permission of the publisher except for the use of brief quotations in a book review or scholarly journal.

First Printing: 2015

ISBN 978-1-329-69493-4

Acknowledgements

I would like to thank and acknowledge the unfailing support and advice of my wife Jodie. I am also grateful to my colleagues and managers at IBM, who were the guinea-pigs who test-drove the short course upon which this book was based, and to the Ulysses motor cycle club for their support and proof reading.

In every country, we should be teaching our children the scientific method and the reasons for a Bill of Rights. With it comes a certain decency, humility and community spirit. In the demon-haunted world that we inhabit by virtue of being human, this may be all that stands between us and the enveloping darkness.

Carl Sagan

Introduction

Logic is the study of the mechanics of reasoning. It is a method of understanding how we make sense of the world. To some extent, the ability to think logically is innate, or at least seems to be. Thus, our ability to understand arguments, or puzzles, is often taken for granted.

However, the more complex, or unfamiliar the reasoning becomes, the more mistakes we make by relying on our intuition or intelligence alone.

Formal logic provides an x-ray view of the skeleton of a line of reasoning. It does this by stripping away the content and representing the relationships between the elements of the argument with symbols.

These symbols and their usages are what we call the notation. The intention of this book is to present an intuitive and consistent notation that follows from one area of logic to another, while being consistent with the familiar notation of mathematics.

By optimising the flow of the notation, the underlying principles of logic are more easily assimilated. The familiar aspects and simple mnemonics make learning and remembering the symbols easy, which in turn makes the underlying logic easier to perceive.

To assist further with the understanding of principles, logical components will be illustrated, where possible, in several contexts:

Reviews for Learning Logic

[sal_paradise-1 · Rating: 5 out of 5 stars]

Seventy years ago, George Orwell warned that the progressive deterioration of the English language had led to such imprecision of expression that words often “fall upon the facts like soft snow, blurring the outline and covering up all the detail.” This vagueness of language was, Orwell maintained, both the effect and a cause of vagueness of thought, which in turn facilitated political manipulation and intellectual passivity. Given the lack of evidence of any improvement in the precision of our language since Orwell’s day, what can be done to develop and strengthen the faculties of logical analysis and critical thinking, especially among young persons still undergoing, or just emerging from, the often brain-deadening process euphemistically called public education? One possibility is advanced by Stephen Plowright in his latest book, Learning Logic: Critical Thinking with Intuitive Notation.The book’s objective is straightforward: “to provide a basic but firm foundation in the concepts and symbols of formal reasoning.” But is such a book really necessary? Wouldn’t only pointy-headed professors ever need to learn the formal rules of logic? Can’t the rest of us just skate by on the seat-of-the pants reasoning skills we pick up from life? Plowright thinks not. Although most people seem to be hard-wired to employ what might be called practical logic in relatively simple contexts like solving puzzles or arranging itineraries, this innate skill breaks down as the complexity of the context increases. The unique value of formal logical analysis is that it provides a tool for stripping away the welter of confusing detail (not to mention intentional obfuscation) in evaluating any statement or situation, reducing a problem to its essential elements and illuminating the relationship of those elements to one another. To this end, Plowright employs a formal yet intuitive symbolic notation that can be applied consistently across all fields of logical analysis. The symbols and their usage are related to similar, familiar examples from outside the realm of formal logic. Consistency is promoted by utilizing similar symbols for similar operations across all the topics covered in the book.In two introductory chapters, Plowright emphasizes the importance of having a sound grasp of logic in everyday life, and reviews a rogue’s gallery of logical fallacies we routinely encounter, although may not recognize. “We are surrounded by illogical claims,” Plowright observes. “Pseudoscience, fundamentalism, advertising, and politics inject emotion-laden messages to appeal to our fears and desires.” Even a basic familiarity with syllogisms can often lay bare the logical flaws in these routine promotions, but a close study of the formal properties of logical analysis is essential if we hope to participate meaningfully in such fields as science, medicine, engineering, information technology or the law.Plowright begins his systematic presentation of symbolic notation and formal analysis in a chapter on propositional logic. Here, the reader is introduced to the fundamental building blocks of logical statements, or propositions. The notation for such familiar operations as conjunction (and), disjunction (or), negation (not), and equivalence will reappear in various contexts throughout the book. The reader is also introduced to the concept of Boolean variables – the interface between mathematics and logic that is indispensable to computer programming. Finally, the author demonstrates how to construct a formal proof of any proposition, to verify whether the underlying argument is logically sound.Moving on to predicate logic, Plowright develops and expands his notation to encompass more general statements and operations involving groups of things. This leads directly and naturally into a chapter on set theory. The author carefully relates the symbols denoting set operations back to the notation previously developed, thereby emphasizing the close connection between set theory (normally regarded as a branch of mathematics) and formal logic. Plowright makes judicious use of Venn diagrams in this chapter, to illustrate his points visually as well as with the corresponding notation.“People tend to think of logic and science,” Plowright notes, “as dealing with, or at least aiming for, certainty. In fact, the opposite is more often true. It is more about how to deal with uncertainty.” This observation introduces the reader to a chapter on hypothesis testing and probability – again, topics not commonly associated with formal logic, although they fit well with Plowright’s overall theme. The material on set theory from the previous chapter flows smoothly into the author’s presentation of conditional probability, concluding with an introduction to Bayes’ Theorem.In a final chapter, Plowright offers a series of puzzles comprising practical applications of the analytical tools presented in the text. He concludes with a short but thought-provoking essay entitled, “Common Sense and Science.” Here, the author stresses that a basic grasp of logic and logical operations is a necessary, but not sufficient condition for avoiding error. Logic is an indispensable tool, but its utility depends upon a sound understanding of reality. “If we are to act capably and successfully, dealing with the challenges of the future,” Plowright says, “we need to be able to identify the best sources [of] information, and be able to reason and plan. This requires the elements of logic, reliable common knowledge, and a basic high-school level of scientific literacy, for a majority of the population.” Many would find such a goal unrealistic. Albert Jay Nock famously asserted that the majority of Americans are uneducable, which he thought accounted for the emphasis on training instead of education in the public schools of his day. Until recently, California withheld high school diplomas until students could demonstrate a grasp of sixth-grade arithmetic. That standard was eventually deemed too rigorous, however, and students now graduate and move on to college based on time served, even if they lack the calculation skills of an average twelve-year-old. Needless to add, the standard for competence in logic is nonexistent. Fortunately, however, the value of Learning Logic to the individual reader does not depend on widespread scientific literacy – or literacy of any kind, for that matter. Indeed, the more popular thought and language descend into Orwellian vagueness, the more important it is to provide ourselves and our loved ones with the sort of intellectual survival manual Plowright has written. In a world where politicians and celebrities have elevated fuzzy thinking to an art form, this book will show you how to cut through the fog, sharpen your critical thinking skills, and avoid the logical pitfalls that lie in wait for us every day.