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.
An Introduction to Formal Logic
Logic is the key to philosophy, mathematics, and science. Learn logic from an award-winning professor of philosophy.
Rated 4 out of
5
by
DaGeek from
Very technical in the middle
I spent the last 30 years of my working life, first as a programmer, then a programmer/analyst and finally as a systems analyst. As such I worked in more programming languages than I can remember and multiple different computing platforms. I frequently made the comment when changing languages that the syntax and symbols changed, but the logic stayed the same. Watching this course, I was having flashbacks to Boolean logic and various types of case/if-then-else structures. Apparently I could have been a philosopher also.
The professor is very good and has a deep knowledge – and love – for his subject, and a bit of a sense of humor. I think I read somewhere, maybe on another one of his courses, that he is an amateur comedian.
The first part of the course was very enjoyable, as was the last few lectures. The middle part of the course got deep into the weeds of formal logic, with the professor working through many examples. If I was taking a course in Formal Logic, this might have been helpful, but since I was not I found it more than a little tedious. To have really appreciated this part, it would have been necessary to work through many examples yourself. Since I was only “auditing” the course I was not going to do this.
Whether you will enjoy this course depends on what you want to get out of it. As I said, it is very technical in the middle. I found it interesting though as I have always thought of philosophy as a bit of a soft or fuzzy subject, even knowing that the sciences evolved from philosophy. It was interesting to see a more “rigorous” side to the subject.
Date published: 2024-05-30
Rated 5 out of
5
by
B Ford from
Quite technical, yet entertaining
This course about formal logic is valuable because it’s important for everyone to understand their reasons for determining whether a statement is true and why they choose to believe it. Professor Gimbel’s sense of humor and creative use of analogy are entertaining, especially considering the material seems somewhat technical for a philosophy course. The concepts are presented in a continuum that generally progresses gradually from simple to more complex. The guidebook exercises for each chapter help to reinforce understanding as most lectures build on previously presented material. I finished the course a few weeks ago, and now looking at a few notes I made then I seem to have been confused by what I thought might be a few errors. One instance has something to do with the graph of a function in lecture 10 (which I don’t have time to revisit) where an equation at the bottom of a diagram said “y=x+1” and for some reason I thought it should have been “y=x+2”. Another example is in the guidebook chapter for lecture 9 on page 85 in the answer for question 3 (there’s no answer provided for question 4) where the “E sentence” is referred to as the “minor premise” and the “I sentence” is referred to as the “major premise”, when I wondered whether it should be the other way around, based on the definition of major and minor premises on page 78. Another example is in the guidebook chapter for lecture 15 on page 150 in the answer for question 2 where the first 2 lines didn’t make sense to me. Lastly, in the guidebook chapter for lecture 19 on page 189 in the answer for question 2 it seemed to me statement 14 should be “Conj 8,13” rather than “Conj 12,13”. Not necessarily concluding the text is wrong, but seemed to be so based on my understanding, although it could just be me being confused.
Date published: 2024-04-15
Rated 5 out of
5
by
Robert42 from
wow - a powerful course
I'll be turning 62 in 2 months. I wish I had taken this course when I was 12. lol, A fantastic course. Thank you
Date published: 2023-10-27
Rated 1 out of
5
by
tarski from
logic, really?
The prof wants to show an invalid argument. He proposes 1) some frogs are green, 2) some frogs can hop, then 3) some green things can hop. He then rejects this as an example of an invalid argument! So, consider a universe of 2 frogs. One frog is red and can hop and the other is green and cannot hop. Both premises are true and the conclusion is false. Seems invalid to me.
Date published: 2023-07-14
Rated 1 out of
5
by
MarkG Ohio from
Overly Complicated
I loved Dr. Gimbel's highly informative class on Great Questions of Philosophy and Physics. I did not like this class. It has useful insights, until after chapter 8, when it descends into lengthy and nearly incomprehensible algebraic-like notation. In real life, no reasonable person would make any decision by using the time consuming system that is described. Would you really want to use a 22 step calculation to prove what was obvious in one simple paragraph? Why exchange clear ordinary language for confusing abstract symbols which are manipulated through a bizarre sets of rules? Further, substantial judgments about what is true or false are made before using the complicated calculus of “truth-functional logic” and “first-order predicate logic.” My ethical duty is to suggest that most potential listeners avoid this class. This is a class for philosophy graduate students.
Date published: 2023-01-19
Rated 1 out of
5
by
jklnaba from
Challenging to follow (not because of content)
I found the instructor's speech pattern to be particularly distracting. I don't know the precise cause for it; I imagine it has to do with a frequent fluctuation in tone and/or the stressing of words. This, combined with adequate visual aid (I much prefer the use of chalkboards, btw), made the course challenging to follow. Be sure to buy the transcript. As for the content itself, I did not have much issue with it.
Thankfully, this was only meant as a refresher for me. Overall, I appreciate the effort.
Date published: 2022-11-04
Rated 5 out of
5
by
Harun from
Well done
So far I have watched the first 6 lectures. They are very clear with clear outline text. The lecturer uses graphics to show the thinking process for good logic and faulty logic. He then summarizes with several example and show the process for determining the soundness of the logic. It would be hard to avoid improving your logical thinking and spotting the faulty logic around you in daily life.
Date published: 2022-01-10
Rated 5 out of
5
by
Talken49 from
Excellent. Highly Recommended.
I was a philosophy major in college at the undergraduate level. I bought this course for two reasons: 1) as a refresher and 2) to see if the presentation in this course might be a more complete introduction to the topic.
It turns out didn't forget much of the topic and, Steven does an excellent job of covering this topic in a clear, comprehensive manner. Of benefit to the new learner is Steven breaks out the topic in concise but thorough segments. This is a more comprehensive approach than one might get in a college course.
If you would like to learn more about this subject and not take a college course about this subjec to do so, this course is a great start.
Warning note: As the department head of philosophy at my college told me 50-years ago, once you take this course (and/or major in philosophy) you'll spot irrational arguments all around you all of the time. He was right. Take this course and at the very least, you'll spot elements of the "Matrix" all around you as politicians, the media, marketers, co-workers, relatives -- almost everyone you encounter -- besiege you all day long with irrational arguments as they advocate their views.
Date published: 2021-12-27
Overview
About
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."
Trailer
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
