Category Archives: Introductory Logic

Counterexample Challenge

Introductory Logic, ,

Introductory Logic formally teaches two methods for determining the validity of a syllogism: rules of validity, and counterexamples. The rule that tells us that any AAO-4 syllogism is invalid is this: “A valid syllogism cannot have two affirmative premises and a negative conclusion.” But can we show the invalidity of AAO-4 with a counterexample? Here is the schema:

All P is M
All M is S
∴ Some S is not P

I contend that there is only one way to write a counterexample for a syllogism of that form. I challenge you to write a counterexample to AAO-4. Remember that a counterexample must be the same form, and have true premises and a false conclusion.

Good luck!

Four More Informal Fallacies

Introductory Logic, Rhetoric

Formal logic gives us standards by which we can distinguish good reasoning from poor reasoning. Most often, when someone reasons poorly, they are not making an error in formal reasoning, but rather sidetracking their hearers with an informal fallacy. Informal fallacies are less structured errors made in the everyday use of language.

The Introductory Logic text identifies eighteen different types of fallacies, but of course there are many more ways to go wrong than that. My new rhetoric text Fitting Words includes a few popular fallacies not included in Introductory logic. Let me summarize them. Continue reading Four More Informal Fallacies →

An Enthymeme of P. J. O’Rourke

Mr. Nance,

I have a question about enthymemes. When the conclusion is assumed, how do we know which is the major premise and which is the minor premise? I fear there is a simple explanation that I may have missed but when I compare your example in Introductory Logic on page 221 with Exercise 31 #5, I can’t correlate how you knew which was the major premise and which was the minor premise, and therefore, how to write the assumed conclusion in proper form. Continue reading An Enthymeme of P. J. O’Rourke →

Predicate noun in categorical form

Mr. Nance,

One question on 6A, problem #11. My son struggles getting a nominative in the predicate consistently. His current method is to repeat the subject (e.g. No bats are blind bats), which I tell him isn’t allowed (based on example), but he requests a better reason than that. (It being circular didn’t impress him, either.) Help? Continue reading Predicate noun in categorical form →

Help with Hypotheticals

Introductory Logic, Why learn logic?,

One of the more practical parts of Introductory Logic is Lesson 31 on Hypothetical Syllogisms. Hypothetical syllogisms of all kinds are a very common form of reasoning, so we should not only be able to identify them quickly, but we should also learn to use the valid forms confidently.

A hypothetical statement is an “if/then” statement, such as this one: Continue reading Help with Hypotheticals →

Another rule of validity

Introductory Logic

Earlier I explained the fallacies of Undistributed Middle and Illicit Major/Minor. But what about the fallacies regarding the quality of the statements? One such rule of validity states,

A valid syllogism cannot have two affirmative premise and a negative conclusion.

Why is this the case? What prevents two affirmative statements from implying a negative one? The easiest way to show this is to consider counterexamples for syllogisms with two affirmative premises and a negative conclusion, in which the premises are necessarily true, and the conclusion necessarily false. We will do this with a trick. Continue reading Another rule of validity →

Illicit terms

Introductory Logic

In my last post I promised to explain the reasoning behind the rules of validity that relate to the distribution of terms. Recall that a term is distributed in a statement when it refers to the entire extension of the term. This implies, as we saw, that the subjects of universal statements and the predicates of negative statements are distributed.

One related rule of validity says this:

A valid syllogism must distribute in its premise any term distributed in the conclusion.

This syllogism, for example, breaks this rule: Continue reading Illicit terms →