Monthly Archives: November 2015

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

#17 – On Reading

“Reading without reflecting is like eating without digesting.” – Edmund Burke

“The man who does not read good books has no advantage over the man who cannot read them.” – Attributed to Mark Twain

“Outside of a dog a book is a man’s best friend. Inside of a dog it’s too dark to read.” – Groucho Marx

#16 – Happy Thanksgiving!

“Oh, give thanks to the Lord, for He is good! For His mercy endures forever.” – 1 Chron. 16:34

“Be happy with what you have, and there will be plenty to be happy about.” – Irish proverb

“Baskets of fruit are heavy.” – Doug Wilson

“Wine is bottled poetry.” – Robert Louis Stevenson

“Never eat more than you can lift.” – Miss Piggy

“I’m in shape. Round is a shape.” – Hans Leidenfrost

In which I take issue with Isaac Watts

watts[1]In his excellent Logic: The Right Use of Reason in the Inquiry After Truth, Isaac Watts identifies 14 forms of syllogism that he considers valid and useful:

Figure 1:  AAA, EAE, AII, EIO
Figure 2: EAE, AEE, EIO, AOO
Figure 3: AAI, EAO, IAI, AII, OAO, EIO

From the list that I consider valid, he omits these ten as either invalid or “useless” Continue reading In which I take issue with Isaac Watts

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

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

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

The Square of Eli

One of my greatest delights as a teacher is learning something new from my students. That happened today in my logic class, when Eli, Lily and I wandered down a rabbit trail of immediate inferences. We had used two immediate inferences to write a statement equivalent to some other statement, and realized that we could have gotten to that same answer using two different immediate inferences.  Eli asked if there was some “triangle of immediate inferences” that we could go through and end up where we started. After some playing around, we discovered, not a triangle, but what I will call The Square of Eli: Continue reading The Square of Eli

Another rule of validity

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