An Introduction to Formal Logic

Logic is the key to philosophy, mathematics, and science. Learn logic from an award-winning professor of philosophy.
  • bvseo_sdk, p_sdk, 3.2.1
  • CLOUD, getAggregateRating, 9.59ms
  • bvseo-msg: HTTP status code of 404 was returned;
  • bvseo_sdk, p_sdk, 3.2.1
  • CLOUD, getReviews, 4.6ms
  • bvseo-msg: HTTP status code of 404 was returned; HTTP status code of 404 was returned;


From advertisers trying to separate you from your money, to politicians trying to get your vote, to friends who want you to agree with them, many people use flawed and misleading arguments to sway your behavior. Formal logic is intellectual self-defense and the key to clear thinking, good planning, and sound reasoning. Learn the principles in 24 lucid lectures taught by a professor who practices what he teaches.


Steven Gimbel
Steven Gimbel

Scientists give us new accounts of how the universe works, and philosophers unpack those theories to see what they tell us about what is real.


Gettysburg College
Professor Steven Gimbel holds the Edwin T. Johnson and Cynthia Shearer Johnson Distinguished Teaching Chair in the Humanities at Gettysburg College in Pennsylvania, where he also serves as Chair of the Philosophy Department. He received his bachelor's degree in Physics and Philosophy from the University of Maryland, Baltimore County, and his doctoral degree in Philosophy from the Johns Hopkins University, where he wrote his dissertation on interpretations and the philosophical ramifications of relativity theory. At Gettysburg, he has been honored with the Luther W. and Bernice L. Thompson Distinguished Teaching Award. Professor Gimbel's research focuses on the philosophy of science, particularly the nature of scientific reasoning and the ways that science and culture interact. He has published many scholarly articles and four books, including Einstein's Jewish Science: Physics at the Intersection of Politics and Religion; and Einstein: His Space and Times. His books have been highly praised in periodicals such as The New York Review of Books, Physics Today, and The New York Times, which applauded his skill as "an engaging writer...[taking] readers on enlightening excursions...wherever his curiosity leads."

By This Professor

Redefining Reality: The Intellectual Implications of Modern Science
An Introduction to Formal Logic
The Great Questions of Philosophy and Physics
Take My Course, Please! The Philosophy of Humor
An Introduction to Formal Logic


Why Study Logic?

01: Why Study Logic?

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....

26 min
Introduction to Logical Concepts

02: Introduction to Logical Concepts

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

30 min
Informal Logic and Fallacies

03: Informal Logic and Fallacies

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....

30 min
Fallacies of Faulty Authority

04: 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!...

33 min
Fallacies of Cause and Effect

05: Fallacies of Cause and Effect

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....

28 min
Fallacies of Irrelevance

06: Fallacies of Irrelevance

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....

28 min
Inductive Reasoning

07: Inductive Reasoning

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....

31 min
Induction in Polls and Science

08: Induction in Polls and Science

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....

32 min
Introduction to Formal Logic

09: Introduction to Formal Logic

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....

29 min
Truth-Functional Logic

10: 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" -and that is the basis of computer logic, the way computers "think."...

31 min
Truth Tables

11: 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....

28 min
Truth Tables and Validity

12: 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....

26 min
Natural Deduction

13: Natural Deduction

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....

34 min
Logical Proofs with Equivalences

14: Logical Proofs with Equivalences

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. "It is not the case that I didn't call my mother," means that I did call my mother....

33 min
Conditional and Indirect Proofs

15: Conditional and Indirect Proofs

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....

35 min
First-Order Predicate Logic

16: 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....

29 min
Validity in First-Order Predicate Logic

17: Validity in First-Order Predicate Logic

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....

35 min
Demonstrating Invalidity

18: 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...

31 min
Relational Logic

19: 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....

31 min
Introducing Logical Identity

20: Introducing Logical Identity

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....

33 min
Logic and Mathematics

21: 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....

34 min
Proof and Paradox

22: Proof and Paradox

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....

33 min
Modal Logic

23: 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....

32 min
Three-Valued and Fuzzy Logic

24: 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 about....

29 min