Tag Archives: Categorical Logic

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 →

More than a switching

Mr. Nance,

Tomorrow morning I will be explaining why EIO-2 is valid but IEO-2 is invalid. The only problem is that I think both ought to be valid. I do not understand why reversing the order of the premises invalidates the syllogism, especially when the placement of the middle term remains the same. Thank you in advance. Continue reading More than a switching →

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 →

Distributed Terms

Introductory Logic,

A term is distributed in a statement when the statement makes some claim about the entire extension of the term. For the four types of categorical statements, the highlighted terms are distributed, as shown in this simplified square of opposition:

   All S is P              No S is P

Some S is P     Some S is not P

You should discern two patterns to help you remember which terms are distributed: Continue reading Distributed Terms →

Fixing a counterexample

Mr. Nance,

One of my students came up with a counter-example for OAO-1 (#6 Quiz 9) in class yesterday:

Some fish are not cats.
All catfish are fish.
∴ Some catfish are not cats.

Because of subimplication “NO catfish are cats” is true, would this counterexample be incorrect since “some catfish are not cats” is implied to be true as well? We had several class examples so by the end of the class, we were all a bit bogged down.

Thanks for your help! Continue reading Fixing a counterexample →

A real-life enthymeme

Mr. Nance,

An article included said of the following argument, “That’s a syllogism without a minor premise”:

“[P]olitical decisions in the modern world often concern how to deploy science and technology, so people well-trained in science and technology will be better prepared to make those decisions.”

I would like to give this to my students to work on, but I can’t seem to translate Jacob’s rendering into terms that work formally. Do you have time to take a look?

All the Best. Continue reading A real-life enthymeme →