An Introduction to Formal Logic

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An Introduction to Formal Logic

Flawed, misleading, and false arguments are everywhere. From advertisers trying to separate you from your money, to politicians trying to sway your vote, to friends who want you to agree with them, your belief structure is constantly under attack.

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Logic is intellectual self-defense against such assaults on reason and also a method of quality control for checking the validity of your own views. But beyond these very practical benefits, informal logic—the kind we apply in daily life—is the gateway to an elegant and fascinating branch of philosophy known as formal logic, which is philosophy’s equivalent to calculus. Formal logic is a breathtakingly versatile tool. Much like a Swiss army knife for the incisive mind, it is a powerful mode of inquiry that can lead to surprising and worldview-shifting conclusions.
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Award-winning Professor of Philosophy Steven Gimbel of Gettysburg College guides you with wit and charm through the full scope of this immensely rewarding subject in An Introduction to Formal Logic, 24 engaging half-hour lectures that teach you logic from the ground up—from the fallacies of everyday thinking to cutting edge ideas on the frontiers of the discipline. Professor Gimbel’s research explores the nature of scientific reasoning and the ways in which science and culture interact, which positions him perfectly to make advanced abstract concepts clear and concrete.

Packed with real-world examples and thought-provoking exercises, this course is suitable for everyone from beginners to veteran logicians. Plentiful on-screen graphics, together with abundant explanations of symbols and proofs, make the concepts crystal clear.

For the Logician in All of Us

You will find that the same rational skills that help you spot the weaknesses in a sales pitch or your child’s excuse for skipping homework will also put you on the road to some of the most profound discoveries of our times, such as Kurt Gödel’s incompleteness theorems, which shook the foundations of philosophy and mathematics in the 20th century and can only be compared to revolutions in thought such as quantum mechanics. But Gödel didn’t need a lab to make his discovery—only logic.

A course with a surprising breadth and depth of applications, An Introduction to Formal Logic will appeal to:

critical thinkers who aspire to make better decisions, whether as doctors, lawyers, investors, managers, or others faced with the task of weighing conflicting options
lovers of intellectual history, who wish to trace one of the most influential and underappreciated currents of thought from antiquity to the present day
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 about how computers work, for programs know nothing about words, sentences, or even numbers—they only comprehend logic
those fascinated with language, the brain, and other topics in cognitive science, since logic models grammar, meaning, and thought better than any other tool

Logic Is Your Ally

Professor Gimbel begins by noting that humans are wired to accept false beliefs. For example, we have a strong compulsion to change our view to match the opinion of a group, particularly if we are the lone holdout—even if we feel certain that we are right. From these and other cases of cognitive bias where our instincts work against sound reasoning, you begin to see how logic is a marvelous corrective that protects us from ourselves. With this intriguing start, An Introduction to Formal Logic unfolds as follows:

Logical concepts: You are introduced to deductive and inductive arguments and the criteria used to assess them—validity and well-groundedness. Then you learn that arguments have two parts: conclusions (that which is being argued for) and premises (the support given for the conclusion).

Informal logic: Often called critical thinking, this type of logical analysis looks at features other than the form of an argument—hence “informal.” Here, you focus on establishing the truth of the premises, as well as spotting standard rhetorical tricks and logical fallacies.
Inductive reasoning: Next you learn to assess the validity of an argument using induction, which examines different cases and then forms a general conclusion. Inductive arguments are typical of science, taking what we already know and giving us logical permission to believe something new.
Formal symbolic deductive logic: Known as “formal” logic because it focuses on the form of arguments, this family of techniques uses symbolic language to assess the validity of a wide range of deductive arguments, which infer particulars from general laws or principles.
Modal logic: After an intensive exploration of formal logic, you venture into modal logic, learning to handle sentences that deal with possibility and necessity—called modalities. Modal logic has been very influential in the philosophy of ethics.
Current advances: You close the course by looking at recent developments, such as three-valued logical systems and fuzzy logic, which extend our ability to reason by denying what seems to be the basis of all logic—that sentences must be either true or false.

Learn the Language of Logic

For many people, one of the most daunting aspects of formal logic is its use of symbols. You may have seen logical arguments expressed with these arrows, v’s, backwards E’s, upside down A’s, and other inscrutable signs, which can seem as bewildering as higher math or an ancient language. But An Introduction to Formal Logic shows that the symbols convey simple ideas compactly and become second nature with use. In case after case, Professor Gimbel explains how to analyze an ambiguous sentence in English into its component propositions, expressed in symbols. This makes what is being asserted transparently clear.

Consider these two sentences: (1) “A dog is a man’s best friend.” (2) “A dog is in the front yard.” Initially, they look very similar. Both say “A dog is x” and seem to differ only in the property ascribed to the dog. However, the noun phrase “a dog” means two completely different things in these two cases. In the first, it means dogs in general. In the second, it denotes a specific dog. These contrasting ideas are symbolized like so:

1. “x(Dx→Bx)

2. $x(Dx&Fx)

You will discover that many consequential arguments in daily life hinge on a similar ambiguity, which dissolves away when translated into the clear language of logic.

Professor Gimbel notes that logical thinking is like riding a bicycle; it takes skill and practice, and once you learn you can really go places! Logic is the key to philosophy, mathematics, and science. Without it, there would be no electronic computers or data processing. In social science, it identifies patterns of behavior and uncovers societal blind spots—assumptions we all make that are completely false. Logic can help you win an argument, run a meeting, draft a contract, raise a child, be a juror, or buy a shirt and keep from losing it at a casino. Logic says that you should take this course.

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