I have received several inquiries regarding other possible solutions to the syllogism translations in Introductory Logic Exercise 27. Though the Teacher’s Edition offers only one solution per problem, there are in fact many possible correct answers to each question.
Here is one more reasonable possibility for each: Continue reading Alternate Answers for Exercise 27
Logic students sometimes struggle with understanding and remembering immediate inferences. The more opportunities they have to see them used, the more likely they are to grasp them. Consequently, I want to give some examples of immediate inferences used in the Bible. Two equivalent immediate inferences for categorical statements are obverse and contrapositive. Continue reading Some Uses of Immediate Inference in Scripture
While teaching through Exercise 25, I was challenging my students on problem 3 to identify every possible syllogism making the fallacies of Two negative premises, and negative premise and affirmative conclusion, and no other fallacies. I had original concluded that there were 32 such forms: EEA, EEI, EOA, EOI, OEA, OEI, OOA, OOI — all four figures of each.
Suddenly one of my students said, “But don’t some of those forms make others fallacies as well?” I realized he was right, and together we followed this rabbit trail, carefully working through the question to determine that, in fact, six of these forms do make additional fallacies: EOA-1, 2 and OOA-1, 2 have an Illicit Minor, and OOA-3, OOI-3 have an Undistributed Middle. Consequently, I have corrected my previous post on this topic.
I have some truly impressive logic students!
One of the difficulties in writing a textbook like Introductory Logic is that, for most of the questions, there are often several possible correct answers. Rather than writing “Answers may vary” every time, I elected in the answer key to give a typical correct answer to each question that could have more than one possible answer.
But all the possible correct answers for Exercise 25 are worth a little more thought. In this exercise, I ask students to write schemas of syllogisms that have a given set of fallacies. If for each problem I only allow those fallacies and no others, there are a reasonably small number of identifiable answers for each problem. Here they are (for the sake of space, I gave the answers as mood & figure, rather than schema): Continue reading More Answers for Exercise 25
Mr. Nance,
I am loving Logic, and have understood the lessons up until now, but the syllogisms and validity has me a bit overwhelmed.
You lost me in the 256 challenge when you started using the same term (dogs) for the major, minor and middle terms. I thought we needed to use different terms when testing for validity. I went back and tried putting dogs into Exercise 22 to see how that worked, and now I’m even more confused. It looks to me that it doesn’t prove the syllogisms to be valid or invalid (when using only one term).
Could you also let me know if I am on the right track on somethings else? Can you test for validity by using the relationships between statements when going from the minor premise into the conclusion? For example, in exercise 22, #1 would be false by contradiction, #2 would be false by contrariety, #3 would be false by superimplication etc…#5 would be true by subimplication.
Thank you for considering my questions! Continue reading Two questions on Intro Logic Exercise 22
Mr. Nance,
On Test 2b there were two questions on the issue of statements being logically independent that I found myself tripping on a little. Can you help me understand them more clearly?
The first is Test 2b, 11a: “It is later than 1:00 pm. / It is later than 2:00 pm.”
The next is Test 2b, 11c: “Some siblings are twins. / Some siblings are not twins.”
Both are said to be not logically independent. I would appreciate if you could help me see that more clearly than I do.
Thank you! Continue reading On Logical Independence
Mr. Nance,
My question has to do with Lesson 24. Exercise 22 has the students do a challenge, testing the validity of all 256 forms. I understand it’s to practice counterexample. Is there another reason not to put this challenge after lesson 26 after they’ve learned all the rules? (Which I think would make it easier.) Continue reading Counterexample challenge
Introductory Logic Lesson 23 introduces the concepts of validity and soundness. The lesson says that a syllogism is valid if and only if the premises imply the conclusion. If a syllogism can have true premises and a false conclusion, the argument is invalid. A sound argument is a valid argument with all true statements.
The only purpose of Lesson 23 is to introduce the concepts of validity and soundness. This lesson does not explain how to determine validity. So if after studying this lesson you have trouble knowing whether a given syllogism is valid or invalid, don’t worry about it. You will learn how to do that in the next three lessons. Lessons 24-26 are dedicated to teaching the methods for determining the validity of a syllogism.
Mr. Nance,
It is said that the key exercise of the Poll-parrot (grammar) stage is Latin Grammar, and of the Pert (dialectic) stage is Formal Logic. What is the key exercise of the Poetic (rhetoric) stage?
Thank you. Continue reading Extrapolating Sayers
Teaching students how to translate syllogisms into standard categorical form occupies several lessons in Introductory Logic. Lessons 11 and 12 explain how to translate categorical statements into standard form, which is then emphasized while learning about the Square of Opposition in Lessons 13-18. Lesson 19 teaches students how to distinguish premises and conclusions, in part so that in Lesson 20 they will understand how to identify the major and minor premises, so that they may know how to arrange a syllogism in standard order. Finally, Lessons 21 and 22 teach them how to identify the syllogism form using mood and figure. All this occurs before the students begin to learn how to determine the validity of a syllogism. Continue reading Why Standard Form?