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Rated 5 out of 5 by 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 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 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 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 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 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
Date published: 2021-12-27
Rated 5 out of 5 by from Excellent supplementary video The quality of the speaker is key to the quality of great courses. Professor Gimbel is first rate. This course carefully layers technical detail, one lecture at a time. I am no longer intimidated by modal logic. Just as with all other logical structure, without true premises, an argument, not about logical form, can never (could this be the makings of an axiom for a sixth level of modal logic?) make the jump from validity to soundness. Dr. Gimbel cut through the confusing symbols to set up my deepening of this understanding, extending this understanding to modal logic. Every explanation and every proof is presented in complete detail, so repeating the lecture will eventually lead to mastery. This course is a superb preliminary for taking any college course in logic.
Date published: 2021-11-21

Overview

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.

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.

INSTITUTION

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."

#### 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

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