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: Apr 9, 2019
• ISBN: 9781329694934

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.