An Introduction to Formal Logic

Rated 5 out of 5 by from Amazing Professor This instructor is so very engaging. From the very first lesson he is able to capture attention and hold it through even the most complex of ideas. His dry humor is especially hilarious to me and I look forward to my daily lessons. I highly recommend this course. In fact I have already talked it up to friends and family.
Date published: 2020-02-25
Rated 5 out of 5 by from Your courses are just absolutely fantastic. I would continue to purchase your very fine courses.
Date published: 2020-01-15
Rated 5 out of 5 by from great content and presentation Course was well presented and I will need to go back and do several lectures given the depth of the subject matter. This course will definitely get you thinking.
Date published: 2019-11-17
Rated 5 out of 5 by from This professor explains very clearly Just in lesson 16. Challenging for me. Love it. Professor's quirky humor and lucid explanations keep my head above water. Thanks Professor Gimbel.
Date published: 2019-07-20
Rated 2 out of 5 by from Beware! This course begins in a user-friendly fashion, but after about Lecture 7, it quickly becomes very challenging. The ordinary person without any background in logic, such as my husband and myself, simply cannot understand it.
Date published: 2019-07-19
Rated 5 out of 5 by from An Introduction to Formal Logic Professor Gimbel is knowledgable and concise in his presentations. Someone without basic knowledge in logic might not comprehend everything in lesson ten concerning truth-functional logic. Much difficult material was covered quickly. The advantage of the course is that one can stop the video and review the problematic parts.
Date published: 2019-07-07
Rated 5 out of 5 by from Having some fun will learning formal logic I like his reference to the wizard of oz and his jokes subtle and otherwise always got me laughing. The few commentaries on formalism, logicism, intuitionism, Hilbert and Godel were especially good, and even a moment of dark comedy related to Godel. Not for anyone who does not enjoy an half hour or so of syntactic detail, so be warned that reference to lines in a natural deductive proof that have scrolled off screen can often be annoying. One thing for sure, I learned a lot about truth functional combinations, fundamental form and then categorical or basic form, and that is certainly saying something, especially coming from a fuzzy prof with an inclination to tell fuzzy jokes while explaining fuzzy logic.
Date published: 2019-05-29
Rated 5 out of 5 by from Excellent Course! This course definitely lives up to its name -- it is truly a great one! Every new idea introduced is clearly illustrated by a thoughtfully chosen example. And the examples are just right -- as simple as they can get, without forfeiting any of the substance of what needs to be explained. (One example of many: DeMorgans identities can be thought of through a little story involving `Bob enjoying his coffee with cream and ...or... sugar by the coffee machine'; think through this example, and you will likely never forget what DeMorgans laws are all about. (And, incidentally, if you ever wondered what the real, real difference between Captain Morgan and DeMorgan is, be sure to watch the lectures on deductive validity.).) Moreover, the exercises are just as carefully chosen as the lecture examples. Be sure to spend time with those - working through them will ensure that you can confidently follow the subsequent lectures. (Finally, I should mention that Dr. Steve clearly has some serious acting talent. Not only is the content of the course right on the spot, but the presentation is also superb. But be glad that the Prof. didn't follow an acting career because that would be a huge loss to philosophy and logic.)
Date published: 2019-05-27
Rated 5 out of 5 by from Complex subject well explained Formal logic is a difficult subject for most of us, including myself with a science degree. Professor Gimbel made this subect overview, both interesting and entertaining. Building from a general description through the stages of logic using clear examples, interspersed with humor, it was of great benefit to me.
Date published: 2019-05-23
Rated 5 out of 5 by from Review #2? Not sure if more than one review is allowed, we shall see, but wish to conclude by saying that it was an absolute privilege and pleasure to observe Professor Gimbell's two dozen lectures on Formal Logic, providing "good rigorous ways of defining what it is that we should believe" and, by extension, "who we are." I was also pleasantly reminded of my college years where it was my experience that classes in the Philosophy Department (e.g. Logic, Linguistics and MetaLogic) were marked by humility and wisdom as opposed to the arrogance within the Computer Science Department, albeit the Department of my Major. Also totally enjoyed the Professor's priceless and ever front-and-center (East Coast?) sense of humor.
Date published: 2019-05-19
Rated 5 out of 5 by from Seemed more than an introduction I purchased this course based on the description. While Professor Gimbel introduced the various methods for proving or disproving arguments, I found the later lessons to be quite complex. Especially when defining parameters as all or some, and the addition of operators. I did enjoy some of his anecdotal arguments whereby he shared some humorous results and warnings. I will say some of what he defined as arguments that could be proved, were not the type I would bother with determining the proof. Unless I really disliked the person presenting the argument, and felt mean spirited. Having the DVD, I will be reviewing the lessons a few more times.
Date published: 2019-05-17
Rated 5 out of 5 by from I have purchased courses for the last 10 or so years and have been very satisfied and am very satisfied with our recent purchases that I sent to our daughter who is homeschooling 6 children. I only wish that I could have online access to the courses i have purchased in the past. before digital that possible?
Date published: 2019-04-22
Rated 5 out of 5 by from What a Great Teacher! This is the second Great Course I've purchased taught by Dr. Steven Gimbel (see also "Take My Course, Please, The Philosophy of Humor") and he continues to be my favorite teacher. Dr. Gimbel presents subject matter in a style that enables all viewers to understand the most abstract of academic principles. He's a brilliant academician who is also a spectacular performer!
Date published: 2019-02-11
Rated 5 out of 5 by from Wish I had a few Dr. Gimbel's when I was a student Dr. Gimbel is an excellent presenter. He keeps the lecture interesting and does an great job presenting the material. I found it easy to follow and most enjoyable. My one recommendation would be to suggest a workbook that would allow the student to work through an assortment of statements. There weren't enough in the course book.
Date published: 2018-12-11
Rated 4 out of 5 by from Thick, but delectable Prof. Guelzo is animated, and very long-winded. At first I found it too hard to keep up, and so I started over, re-hearing the beginning of the first "class" numerous times until I started to feel I had actually heard and understood what he was saying. Once I got to that point, then I found that not only is he setting forth a fundamental definition of history and using the history of history to illustrate the various stages of its development, but he is also inviting us to swoon at the delectable details of this magnificent thing, this human thing, history. And he is profoundly prosaic, and at times I have to stop and do something else. But I love this class, and I have only studied the first class. I give it only four stars because, for me, without digging in deeply, I was not enjoying the surface of his presentation. It was too challenging to follow, at first. Here's a tip: Prof. Guelzo is actually a lot of fun, and is quite funny. But you have to listen closely to catch it...
Date published: 2018-12-05
Rated 5 out of 5 by from Dr. Gimbel is Awesome I found that Dr. Gimbel's combination of subject knowledge and humour made for a very enlightening course which held my attention at all times. I will definitely watch it many times.
Date published: 2018-07-27
Rated 5 out of 5 by from Great examples! Gimbel's presentation is lucid and keeps you interested! There are certainly places where it gets a little dense, but I'm not sure how you'd avoid that in a course this short. Possibly there should be more lessons in the sections toward the end -- that is, they should be covered more slowly.
Date published: 2018-06-04
Rated 5 out of 5 by from This course is superb! With his flawless presentation Professor Gimbel takes you through – step by step – the basics , first of informal logic and then the intricacies of formal logic. This course provides a very accessible introduction for the first time student of logic and is also a great review for the more experienced. I especially enjoyed his two later lectures on logic and mathematics. This course is excellent! Professor Gimbel’s other philosophy course called Redefining Reality is equally as well done.
Date published: 2018-02-19
Rated 1 out of 5 by from Stop the Madness! STOP THE MADNESS! This is really a bad course, I had to stop before the 11th minute mark! Let me start at the very beginning. "IN the beginning God created heaven, and earth." (Genesis 1:1) God created all things. Things didn't evolve themselves from nothing by their own effort. The Bible REJECTS evolution. "You shall be as Gods, knowing (gnostically deciding) good and evil." (Genesis 3:5) "And to Adam he said: Because thou hast hearkened to the voice of thy wife, and hast eaten of the tree, whereof I commanded thee that thou shouldst not eat, cursed is the earth in thy work; with labor and toil shalt thou eat thereof all the days of thy life." (Genesis 3:17) "LET every soul be subject to higher powers. For there is no power but from God: and those that are ordained of God." (Romans 13:1) In other words, the individuals, states and governments legislated laws are subjected to Christ. The allegation that "from the people" or the "consent of the governed" is a claim of authority, is a refusal of being subject to Christ. Psychology doesn't mean the study of human behavior and psychology isn't a science, it is more like a religion with different sects. Psychology: Greek - Psyche and logos Psyche means soul. Logos generally means, any organized body of knowledge contains logos in its name. Hegelian dialectics: Thesis meets antithesis to produce a new thesis (synthesis) which, in turn, will meet another antithesis, and so on. Bertrand Russell's first cause argument fails! God is independent of causes and is independent of the LIMITATION which causes impose. Therefore, God the first cause is FREE from limitation; in other words, God is infinite. There can be only ONE NECESSARY BEING, because a necessary being is infinite. Therefore, the necessary first cause MUST be ONE and INFINITE. (RT. REV. MSGR. PAUL J. GLENN, Ph.D., S.T.D.) LOGIC: is the science and art of correct reasoning. THE TWO MAIN BRANCHES OF LOGIC: FORMAL (minor Logic) and MATERIAL (major logic). In formal logic, the purpose is not to discover truth, but to lead us from one truth to another. THREE KINDS of LOGICAL PROCESSES (Formal Logic): MENTAL ACT: 1) Simple Apprehension VERBAL EXPRESSION: 1) Term MENTAL ACT: 2) Judgment VERBAL EXPRESSION: 2) Proposition MENTAL ACT: 3) Deductive Inference VERBAL EXPRESSION: 3) Syllogism ARGUMENT: 1) Premise 2) Premise 3) Conclusion What is man? A substance that is material, living, sentient and rational. What is the extension of man? All the men who have ever lived, who are now living and who will live in the future. What is an animal? A substance that is material, living and sentient. What is the extension of animal? All the animals (including men, lions, dogs, fish, insects, etc.) that have ever lived, are now living, and that ever will live. It is called the Porphrian Tree because it was invented by the 3rd-century logician Porphyry.
Date published: 2018-02-13
Rated 5 out of 5 by from Informative and convincing presentation I am just a few lessons into the course but so far am very pleased with it.
Date published: 2017-12-17
Rated 4 out of 5 by from Well Presented... Anyone considering a career in law or debate should watch the first 8 lectures. As a high school mathematics instructor who teaches discrete math, I enjoyed the formal aspects of the course and found parts that I could incorporate in my lessons. Formal proofs can be followed if you focus on the flow of the logic; you may have to pause now and then.
Date published: 2017-11-23
Rated 4 out of 5 by from Good logic course Very good course and instructor. Subtracted one star for 2 reasons : 1) the course guidebook cries out for an index at back to quickly find items for review, and 2) imho the last few lectures go beyond what I consider intro to formal logic material, and this time could have been better spent on review on previous covered material.
Date published: 2017-11-02
Rated 5 out of 5 by from Well Presented Excellent course, I purchased the transcript as I prefer to 'read' the course material and write notes in margins.
Date published: 2017-09-22
Rated 5 out of 5 by from A Powerful Tool for Life One of the best courses I have ever seen. The professor is hilarious, the explanations relatable, and the ideas clear. This course is exactly what he promises: powerful.
Date published: 2017-09-21
Rated 5 out of 5 by from Comprehensive It was an excellent adjunct/aid for college logic class.
Date published: 2017-08-11
Rated 4 out of 5 by from Very Helpful I purchased this as a companion to watch along with a symbolic logic class I was taking at the local community college. Very helpful, the lectures helped me to grasp what I missed in the classroom. Sometimes 2 instructors are better than one. The professor is easy to understand and seems to really enjoy logic. I would recommend the video version (assuming there is an audio only option.)
Date published: 2017-06-22
Rated 5 out of 5 by from Money Well Spent I am ecstatic with my initial purchase and know this will not be my last. The course is professionally presented in a layman's format that allows for easy comprehension, but with adequate 'in-depth' information to make one feel educated on the topic.
Date published: 2017-05-03
Rated 4 out of 5 by from Introduction to formal logic Good course , well presented. Too much "Junk Mail" after purchase. Also I wanted to buy another course; however the $29.95 sale price listed was always $49.95 at the checkout. So I dropped the issue.
Date published: 2017-04-29
Rated 5 out of 5 by from Excellent presentation I bought this course to complement "Argumentation: The Study of Effective Reasoning" and particularly enjoyed its scope and sequence. Together, these courses give me a one-two punch. I like debating with my friends, and "Formal Logic," in particular, has helped me look at subjects with a new eye, allowing me to zero in on dubious claims with a laser like accuracy which helps me score points. Highly recommended!
Date published: 2017-04-12
Rated 5 out of 5 by from Informal to Fuzzy or Aristotle to Russell & Godel Professor Gimbel, begins this course simply, asking why we should study logic and then moving to discussing Informal Logic (All men are mortal; Socrates is a man; therefore Socrates is mortal). Things go along smoothly for several lectures, as we learn about logical fallacies and move from deductive to inductive reasoning. The course material provided thankfully includes some exercise in the form of questions at to be answered at the conclusion of each lecture. While the first few are easy, being able to be answered without much thought, they become increasingly more difficult and by the end of the course require (at least for me) a great deal of though and also some review of the presented material. The second third of the course begins an excursion into Formal Logic, Professor Gimbel once again starting with some easy ‘Truth Table” concepts and Natural Deduction to the more difficult to grasp equivalences and indirect proofs. For me, the later lectures beginning with “First Order Predicate Logic” is where the course takes off. At least for me these lectures required quite a bit of thought and some considerable review in order to grasp the concepts. All along Professor Gimbel adds new operators to First Order Predicate Logic, so be the time he reaches the penultimate lecture on Modal Logic, we have a very large set of operators and conditions that are available to be used in solving logic problems. The final lecture introduces “Fuzzy Logic”, a relatively new construct. Along the way Professor Gimble introduces various logicians, philosophers and mathematicians who have been instrumental in developing informal and formal logic. For example we get Aristotle and Bertrand Russell, Euclid and his geometry and non-Euclidian geometry. All-in-all, a treat, albeit one requiring a deal of consideration. Dr. Gimbel (normally he refers to himself as ‘Steve’) has a rapid-fire delivery style, especially when going through a proof. He is much more measure when introducing a new concept. I agree with other reviewers that it was bothersome to have sections of a proof scroll off the screen, but I suppose that is a limitation of the technology. ‘Steve’ has a very dry sense of humor, usually just making a quip in the same tone of voice and style of delivery that he uses when discussing ‘Invalidity’, leaving it up to the student to get the joke or not. An excellent, though difficult course.
Date published: 2017-03-21
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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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