Why Study Logic?

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Modal Logic
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.
Three-Valued and Fuzzy Logic
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…
Truth Tables and Validity
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
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 "not," "and," "or," and "if"…
First-Order Predicate Logic
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.
Demonstrating Invalidity
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.
An Introduction to Formal Logic
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…
Logic and Mathematics
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.
Fallacies of Faulty Authority
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!
Truth Tables
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.
Relational Logic
Hone your skill with first-order predicate logic by expanding into relations. An example: "If 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.
The Big Questions of Philosophy
We have all pondered seemingly unanswerably but significant questions about our existence - the biggest of all being, "Why are we here?" Philosophy has developed over millennia to help us grapple with these essential intangibles. There is no better way to study the big questions in philosophy than to compare…