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24. Three-Valued and Fuzzy Logic

November 1, 2016

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.

23. Modal Logic

November 1, 2016

Add two new operators to your first-order predicate vocabulary: a symbol for possibility and another for necessity. These allow you to deal with modal concepts, which are contingent or necessary truths. See how philosophers have used modal logic to investigate ethical obligations.

22. Proof and Paradox

November 1, 2016

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.

21. Logic and Mathematics

November 1, 2016

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.

20. Introducing Logical Identity

November 1, 2016

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.

19. Relational Logic

November 1, 2016

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.

18. Demonstrating Invalidity

November 1, 2016

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.

17. Validity in First-Order Predicate Logic

November 1, 2016

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.

16. First-Order Predicate Logic

January 1, 1970

So far, you have learned two approaches to logic: Aristotle’s categorical method and truth-functional logic. Now add a third, hybrid approach, first-order predicate logic, which allows you to get inside sentences to map the logical structure within them.

15. Conditional and Indirect Proofs

November 1, 2016

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.

14. Logical Proofs with Equivalences

November 1, 2016

Enlarge your ability to prove arguments with natural deduction by studying nine equivalences-sentences that are truth-functionally the same. For example, double negation asserts that a sentence and its double negation are equivalent. €œIt is not the case that I didn€™t call my mother,€ means that I did call my mother.

13. Natural Deduction

November 1, 2016

Truth tables are not consistently user-friendly, and some arguments defy their analytical power. Learn about another technique, natural deduction proofs, which mirrors the way we think. Treat this style of proof like a game-with a playing board, a defined goal, rules, and strategies for successful play.

12. Truth Tables and Validity

November 1, 2016

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.

11. Truth Tables

November 1, 2016

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.

10. Truth-Functional Logic

November 1, 2016

Take a step beyond Aristotle to evaluate sentences whose truth cannot be proved by his system. Learn about truth-functional logic, pioneered in the late 19th and early 20th centuries by the German philosopher Gottlob Frege. This approach addresses the behavior of truth-functional connectives, such as €œnot,€ €œand,€ €œor,€ and €œif€ -and that is the basis of computer logic, the way computers €œthink.€

9. Introduction to Formal Logic

November 1, 2016

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.

8. Induction in Polls and Science

November 1, 2016

Probe two activities that could not exist without induction: polling and scientific reasoning. Neither provides absolute proof in its field of analysis, but if faults such as those in Lecture 7 are avoided, the conclusions can be impressively reliable.

7. Inductive Reasoning

November 1, 2016

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.

6. Fallacies of Irrelevance

November 1, 2016

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.

5. Fallacies of Cause and Effect

November 1, 2016

Consider five fallacies that often arise when trying to reason your way from cause to effect. Begin with the post hoc fallacy, which asserts cause and effect based on nothing more than time order. Continue with neglect of a common cause, causal oversimplification, confusion between necessary and sufficient conditions, and the slippery slope fallacy.

4. Fallacies of Faulty Authority

November 1, 2016

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!

3. Informal Logic and Fallacies

November 1, 2016

Explore four common logical fallacies. Circular reasoning uses a conclusion as a premise. Begging the question invokes the connotative power of language as a substitute for evidence. Equivocation changes the meaning of terms in the middle of an argument. And distinction without a difference attempts to contrast two positions that are identical.

2. Introduction to Logical Concepts

November 1, 2016

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.

1. Why Study Logic?

November 1, 2016

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.

Description

Where to Watch An Introduction to Formal Logic

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 Apple TV Channels, Amazon Prime, Amazon and Kanopy.