An Introduction to Formal Logic

Rated 5 out of 5 by from Very Good I wish I had taken this course during the first year that I was a mathematics undergraduate student. It would have given me a much stronger hold on my intuitive approach to understanding and proof. Dr. Gimbel takes a very orderly approach (one might say a “logical” approach) to presenting the concepts of logic. He starts very intuitively and slowly builds concept upon concept, usually in response to shortcomings of what he has built thus far, and he builds with it increasing rigor. He ends with logic as applied to quantum mechanics. Quite a journey for something that started with a simple question of “Why should I believe that?” I thought that Dr. Gimbel was an entertaining lecturer. Of course, I liked his course Take My Course, Please! The Philosophy of Humor, so let that temper this opinion. The visual aids are absolutely essential in this course. It does not work in audio only such as while jogging or commuting in a car.
Date published: 2021-04-20
Rated 3 out of 5 by from Lectures: Professor Gimbel presents the concepts of logic slowly and gradually, often repeating points made earlier. This piecemeal, reverting approach is presumably of benefit for the novice. For those with greater understanding or of quick learning, the method might prove tedious. Additionally, the professor's diction often jars and distracts, as is often felt by his repetitive usage and stressing of the word 'but'. Coursebook: The book is riddled with typos. What's more, readers would greatly benefit by more thoughtful and extensive use of tables or images to consolidate and help the learning of the codified proofs, rules, inferences, and equivalences. Course substance: The ideas presented in this course are of much use for work in philosophy.
Date published: 2021-03-03
Rated 3 out of 5 by from Silly Request I can't do a review if I haven't received the order yet!
Date published: 2020-12-08
Rated 5 out of 5 by from One of the best I’ve taken I’ve taken a lot of The Great Courses, and this was one of my favorites. The material was interesting, the professor was superb, and the lectures were very well organized and presented. I should add, however, that this course made me work a lot harder than most of the courses I’ve taken from TGC. I have a fair amount of training in math and science, but none in formal logic, and I think I would have been hopelessly lost, especially in the second part of the course, if I had just passively listened to the lectures. The material is simply too dense and comes at you too fast for that. I found I had to first read the written materials and work the examples before I listened to the lecture in order to really get a handle on what he was saying. Even then, I found that sometimes I had to back up the lecture in some places and listen two or three times to what he said to make sure I was with him. This is no ding on Professor Gimbel. This is just tough stuff. Without in any way detracting from my 5 star rating, I will say there are a couple of things that would have improved the course for me. First, many of the proofs presented in the lectures were not in the written materials. This made it hard to go over those proofs in a careful step by step manner. This problem was exacerbated by the fact that the video format used in the lectures only made a few of the lines of a proof visable on the screen at any one time. Sometimes a line of the proof that Professor Gimbel was referencing was hidden on the screen, which was a bit annoying. Second, I think the written materials could use some closer editing. I found two or three places where I am pretty sure that the written materials were in error. That can make you a little crazy when you are trying to wrap your arms around something this new and difficult. Of course, I might just have only thought there was a mistake! I could be the one whose wrong! Don’t think so, but maybe.
Date published: 2020-07-16
Rated 5 out of 5 by from Tools for Dealing with Life’s Issues Interesting, informative, and challenging but requiring intense communication at times. Missing a glossary of terms and symbols which would have made understanding easier and quicker. After viewing the lessons on logical fallacies, I concluded which two groups which were by far the worst offenders were (1) commercial on tv and (2) politicians, starting at the highest level
Date published: 2020-07-15
Rated 4 out of 5 by from Introduction to Formal Logic I have had this course long enough now to be to the sixth lesson. The Professor is good and knowledgeable. I have other course with him and respect his teachings. This course would have been better adapted for an audio presentation, since the video is almost exclusively of the Professor talking. Unfortunately, audio is something the Great Courses no longer does. I find the fact that the Professor goes back to summarize what he has talked about several times in each lecture to be a bit trying. I love a summary, but the points made early in the lecture are summarized, then new points are made and all of the points to date are summarized, then final points are made and the whole lecture is summarized. It becomes just a bit redundant. On the other hand, the subject material is worthy and merits close examinatioin and some level of rummarization is very appropriate, so this is clearly more about me than about him.
Date published: 2020-06-28
Rated 5 out of 5 by from Reminds me of my college experience. I've just started this as a review. Right off the bat, the professor brought back memories of fifty years ago. Just as then, I could actually feel my imagination swirling to the suggestion of heights that I'm still amazed that I would possibly achieve and share with others twenty years later. Thank you Professor and The Great Courses for bringing back the magic of logic. Let's wff and proof it together. Enjoy.
Date published: 2020-06-28
Rated 5 out of 5 by from Fabulous Professor Excellent presentation...engaging, well organized and paced. Who knew logic could be so entertaining, as well as useful?!?!
Date published: 2020-05-24
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An Introduction to Formal Logic
Course Trailer
Why Study Logic?
1: 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
2: 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
3: 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
4: 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
5: 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
6: 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
7: 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
8: 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
9: 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
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.


Johns Hopkins University


Gettysburg College

About Steven Gimbel

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."

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