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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 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.

An Introduction to Formal Logic is a series that is currently running and has 1 seasons (23 episodes). The series first aired on November 1, 2016.

An Introduction to Formal Logic is available for streaming on the The Great Courses Signature Collection website, both individual episodes and full seasons. You can also watch An Introduction to Formal Logic on demand at Amazon Prime, Amazon, Kanopy online.

The Great Courses Signature Collection
1 Season, 23 Episodes
November 1, 2016
Cast: Steven Gimbel
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An Introduction to Formal Logic Full Episode Guide

  • See what happens if we deny the central claim of classical logic, that a proposition is either true or false. This step leads to new and useful types of reasoning called multi-valued logic and fuzzy logic. Wind up the course by considering where you€™ve been and what logic is ultimately about.

  • Delve deeper into the effort to prove that the logical consistency of mathematics can be reduced to basic arithmetic. Follow the work of David Hilbert, Georg Cantor, Gottlob Frege, Bertrand Russell, and others. Learn how Kurt Godel€™s incompleteness theorems sounded the death knell for this ambitious project.

  • See how all that you have learned in the course relates to mathematics-and vice versa. Trace the origin of deductive logic to the ancient geometrician Euclid. Then consider the development of non-Euclidean geometries in the 19th century and the puzzle this posed for mathematicians.

  • Still missing from our logical toolkit is the ability to validate identity. Known as equivalence relations, these proofs have three important criteria: equivalence is reflexive, symmetric, and transitive. Test the techniques by validating the identity of an unknown party in an office romance.

  • Hone your skill with first-order predicate logic by expanding into relations. An example: €œIf I am taller than my son and my son is taller than my wife, then I am taller than my wife.€ This relation is obvious, but the techniques you learn allow you to prove subtler cases.

  • Study two techniques for demonstrating that an argument in first-order predicate logic is invalid. The method of counter-example involves scrupulous attention to the full meaning of the words in a sentence, which is an unusual requirement, given the symbolic nature of logic. The method of expansion has no such requirement.

  • For all of their power, truth tables won€™t work to demonstrate validity in first-order predicate arguments. For that, you need natural deduction proofs-plus four additional rules of inference and one new equivalence. Review these procedures and then try several examples.

  • Complete the system of natural deduction by adding a new category of justification-a justified assumption. Then see how this concept is used in conditional and indirect proofs. With these additions, you are now fully equipped to evaluate the validity of arguments from everyday life.

  • Using truth tables, test the validity of famous forms of argument called modus ponens and its fallacious twin, affirming the consequent. Then untangle the logic of increasingly more complex arguments, always remembering that the point of logic is to discover what it is rational to believe.

  • Truth-functional logic provides the tools to assess many of the conclusions we make about the world. In the previous lecture, you were introduced to truth tables, which map out the implications of an argument€™s premises. Deepen your proficiency with this technique, which has almost magical versatility.

  • Having looked at validity in inductive arguments, now examine what makes deductive arguments valid. Learn that it all started with Aristotle, who devised rigorous methods for determining with absolute certainty whether a conclusion must be true given the truth of its premises.

  • Turn from informal fallacies, which are flaws in the premises of an argument, to questions of validity, or the logical integrity of an argument. In this lecture, focus on four fallacies to avoid in inductive reasoning: selective evidence, insufficient sample size, unrepresentative data, and the gambler€™s fallacy.

  • Learn how to keep a discussion focused by recognizing common diversionary fallacies. Ad hominem attacks try to undermine the arguer instead of the argument. Straw man tactics substitute a weaker argument for a stronger one. And red herrings introduce an irrelevant subject. As in other lectures, examine fascinating cases of each.

  • Deepen your understanding of the fallacies of informal logic by examining five additional reasoning errors: appeal to authority, appeal to common opinion, appeal to tradition, fallacy of novelty, and arguing by analogy. Then test yourself with a series of examples, and try to name that fallacy!

  • Practice finding the logical arguments hidden in statements by looking for indicator words that either appear explicitly or are implied-such as €œtherefore€ and €œbecause.€ Then see how to identify the structure of an argument, focusing on whether it is deductive or inductive.

  • Influential philosophers throughout history have argued that humans are purely rational beings. But cognitive studies show we are wired to accept false beliefs. Review some of our built-in biases, and discover that logic is the perfect corrective. Then survey what you will learn in the course.