Tag Archives: Categorical Logic

Caught by my students: Errors in my fallacies!

Introductory Logic, , , , ,

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!

More Answers for Exercise 25

Introductory Logic, , ,

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 →

Counterexample challenge

Ask-a-question, Introductory Logic, , ,

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 →

Common errors to avoid: Don’t sweat Lesson 23!

Introductory Logic,

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.

Why Standard Form?

Introductory Logic, Why learn logic?, , ,

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? →

The Square of Opposition (for logic nerds only!)

Intermediate Logic, Introductory Logic, ,

The Square of Opposition is a useful tool for representing and understanding the relationships between categorical statements with the same subject and predicate:

square-of-opposition

The relationships are defined this way:

Contrariety: The statements cannot both be true, but can both be false.
Contradiction: The statements cannot both be true, and cannot both be false.
Subcontrariety: The statements can both be true, but cannot both be false.
Subimplication: If the universal is true, the particular must be true.
Superimplication: If the particular is false, the universal must be false.

Students might be interested to discover that the square of opposition can be created for non-categorical statements as well. Continue reading The Square of Opposition (for logic nerds only!) →

Invalidity and truth

Mr. Nance,

I have a question on Intermediate Logic, Test 2, Form B, Problem 4. The question says: “An invalid argument can have true premises and a true conclusion, is this true or false?” The answer book says it’s true but the definition of an invalid argument would prove that statement to be false. Is there a typo or is that correct? Continue reading Invalidity and truth →

Shakespeare’s Use of the Liberal Arts: Logic

Classical Education, Logic, Old Western Culture, Poetics, Trivium, Why learn logic?, , , , ,

81Few4FQ9cL[1]The classical Christian school movement is seeking to revive a form of education that helped shape some the greatest minds of western civilization. But how do we know that our father’s were trained according to the Trivium? One delightful demonstration of this is William Shakespeare’s frequent and detailed use of the liberal arts of grammar, logic and rhetoric in his plays and poems,  a use thoroughly identified by Sister Miriam Joseph in her book Shakespeare’s Use of the Arts of Language. In this well-researched book, she argues that Shakespeare’s application of formal logic is evidenced in his use of definition, genus and species, syllogistic vocabulary, applied syllogisms, enthymemes, and more. Let me give some of her clearer examples. Continue reading Shakespeare’s Use of the Liberal Arts: Logic →

The Antichrist and the Beast Syllogism

Mr. Nance,

Regarding question no. 10 on page 252: What is the reason for its invalidity? Does the pure hypothetical syllogism also use the five rules of validity? The argument is:

If he is the Antichrist, then he opposes God’s people.
If he is the Beast, then he opposes Gods people.
Therefore, if he is the Antichrist, then he is the Beast.

Is the Beast major term? And is the Antichrist the minor term? How do we make it into valid categorical syllogism? Continue reading The Antichrist and the Beast Syllogism →