An Introduction to Formal Logic

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Logic is an intellectual defense against such attacks on reason, as well as a quality control mechanism for determining the truth of your own beliefs. Beyond these extremely practical benefits, informal logic—the sort we use in everyday life—is the entryway to formal logic, a beautiful and intriguing discipline of philosophy that is philosophy’s counterpart to calculus. Formal logic is an astonishingly flexible instrument. It is a potent technique of inquiry that may lead to startling and paradigm-shifting insights, much like a Swiss army knife for the astute mind.

An Introduction to Formal Logic, 24 engaging half-hour lectures that teach logic from the ground up—from the fallacies of everyday thinking to cutting edge ideas on the frontiers of the discipline—guides you through the full scope of this immensely rewarding subject with wit and charm by award-winning Professor of Philosophy Steven Gimbel of Gettysburg College. Professor Gimbel’s research investigates the nature of scientific thinking and the interactions between science and culture, putting him in an ideal position to make highly abstract topics obvious and accessible.

This course is ideal for everyone, from beginners to expert logicians, because it is packed with real-world examples and thought-provoking activities. The concepts are extremely obvious because to copious on-screen pictures and explanations of symbols and evidence.

For the Logical Thinker in All of Us

The same rational skills that help you spot flaws in a sales pitch or your child’s excuse for skipping homework will lead you to some of our times’ most profound discoveries, such as Kurt Gödel’s incompleteness theorems, which shook the foundations of philosophy and mathematics in the twentieth century and can only be compared to thought revolutions such as quantum mechanics. But Gödel didn’t require a lab to make his discovery; all he needed was logic.

A course with an unexpected range and depth of applications.

An Introduction to Formal Logic will be of interest to:

critical thinkers who want to make better judgments, whether as physicians, attorneys, investors, managers, or anyone who must consider competing possibilities
students of philosophy, for whom logic is the gold standard for evaluating philosophical arguments and a required course for mastery of the discipline students of mathematics, who want to understand the foundations of their field and glimpse the machinery that drives every mathematical equation ever written anyone curious

Your ally is logic.

Professor Gimbel begins by stating that people are hardwired to believe falsehoods. For example, we have a tremendous temptation to adjust our perspective to match that of a group, especially if we are the lone holdout—even if we are confident that we are correct. These and other examples of cognitive bias, where our instincts operate against logical thinking, demonstrate how logic is a wonderful correction that shields us from ourselves. An Introduction to Formal Logic begins with this fascinating premise and proceeds as follows:

Logical concepts: You will learn about deductive and inductive arguments, as well as the standards used to evaluate them (validity and well-groundedness). Then you discover that arguments are made up of two parts: conclusions (what is being argued for) and premises (the support given for the conclusion).
Informal logic: Also known as critical thinking, this sort of logical examination examines characteristics other than the structure of an argument—hence the term “informal.” Here, you concentrate on demonstrating the validity of the premises as well as identifying common rhetorical devices and logical fallacies.
Inductive reasoning: Next, you will study how to evaluate the validity of an argument using induction, which investigates several situations and then produces a general conclusion. Inductive arguments are common in science because they take what we already know and give us logical license to accept something new.
Formal symbolic deductive logic: This family of approaches, known as “formal” logic because it concentrates on the form of arguments, employs symbolic language to analyze the validity of a wide range of deductive arguments that infer particulars from general laws or principles.
Modal logic: After a thorough examination of formal logic, you go on to modal logic, where you learn how to handle statements dealing with possibility and necessity, known as modalities. Modal logic has had a significant impact on ethical philosophy.
Recent developments: You conclude the course by discussing contemporary advances in logic, such as three-valued logical systems and fuzzy logic, which broaden our ability to reason by contradicting what appears to be the foundation of all reasoning—that statements must be either true or untrue.

Learn the Logic Language

One of the most intimidating parts of formal logic for many people is its use of symbols. You’ve probably heard logical arguments presented with these arrows, v’s, reverse E’s, upside down A’s, and other perplexing symbols that may be as perplexing as higher arithmetic or an old language. However, An Introduction to Formal Logic demonstrates that the symbols compactly represent simple ideas and become second nature with practice. In example after instance, Professor Gimbel shows how to break down a confusing English statement into its component premises, which are expressed in symbols. This makes it obvious what is being claimed.

Consider the following two sentences: (1) “A man’s best buddy is his dog.” (2) “There’s a dog in the front yard.” They appear to be extremely similar at first glance. Both state “A dog is x” and appear to differ only in the dog’s attribute. However, in these two examples, the noun phrase “a dog” denotes two very different things. In the first case, it refers to dogs in general. In the second case, it refers to a specific dog. These opposing ideas are represented as follows:

1. “x(Dx→Bx)

2. $x(Dx&Fx) (Dx&Fx)

Many crucial disputes in daily life are based on ambiguity, which disappears when translated into the straightforward language of logic.

Professor Gimbel compares logical thinking to riding a bicycle; it requires talent and practice, but once you learn, you can go a long way! Philosophy, mathematics, and science all rely on logic. There would be no electronic computers or data processing without it. It examines patterns of behavior and reveals societal blind spots in social science—assumptions we all make that are entirely wrong. You can use logic to win an argument, organize a meeting, negotiate a contract, raise a kid, serve on a jury, or purchase a shirt and avoid losing it at the casino. Logic dictates that you take this course.

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