Category Archives: Ask Mr. Nance

Mr. Nance,

My son is in high school, and we want to use your Fitting Words curriculum. If he works through the Fitting Words text in tenth grade, would it be appropriate for him to work through it again as a review in eleventh and/or twelfth grade?

What would you advise? Thank you in advance.

Fitting Words: Classical Rhetoric for the Christian Student was designed to be taught as either a one-year intensive course, or a two-year regular course. In the front of the Fitting Words Answer Key are one- and two-year schedules. I would suggest that your son work through the curriculum over two years, tenth and eleventh grade.

In the first year the topics covered are:

Unit 1: Foundations of Rhetoric
Unit 2: Invention and Arrangement
Unit 3: Understanding Emotions: Ethos and Pathos
Unit 4: Fitting Words to the Topic: Special Lines of Argument

In the second year the topics are:

Unit 5: General lines of Argument (a review of logic)
Unit 6: Fitting Words to the Audience: Style and Ornament
Unit 7: Memory and Delivery

For twelfth grade, I would suggest a thesis paper (or papers, perhaps including a research paper) and defense, applying what they have learned in the first two years.

Blessings!

Mr. Nance,

I am using your Introductory Logic course to teach an informal class in logic to four young people in my church. Thank you for creating a rigorous, explicitly-Christian logic textbook!

During a recent class (working through Lessons 6-8), two questions came up. Can I get your thoughts on them?

(1) Nonsense Statements

On page 57 you give the example of the nonsense sentence “The round square sweetly kicked the green yesterday.” A few students began waxing philosophical about what precisely rendered this sentence nonsense. One asked if it was nonsense in virtue of the fact that squares, by definition, cannot be round. If so, they asked, wouldn’t the sentence, “The square sweetly kicked the green yesterday” be eligible for statement-hood? Sure, squares aren’t known to kick, but that only means that the sentence is likely a false statement. Further, “green” might refer metaphorically to the green grass or a public common grassy land.

I love having such inquisitive students, but I’m afraid I wasn’t able to give them a tidy answer to these questions: Instead, I suggested that we take statements like “this statement is false” as clear examples of nonsense and leave the rest for an epistemology class. What would you have said?

(2) Self-supporting statements

There was some consternation about the notion that self-supporting statements are true (p. 61). One student gave the example of James 2:14 where the self-report “I have faith” is false. I answered by saying that, in general, we should give self-reports the benefit of the doubt. That is, we should judge a self-report true, until or unless we have some good reasons or arguments for thinking it false. Of course, this doesn’t mean that all self-reports are true. Categorizing self-reports as self-supporting, I told them, is more a point of intellectual decency and doing-as-you-would-be-done by than of hard logical categories.

I also pointed out that many self-reports fall into the category of incorrigible statements—that is, for some self-reports, we simply will never have any means, whether by authority, experience, or deduction, of proving them false. Most self-reports about mental states fall into this category—for example, “I wish I had purchased Apple Stock five years ago.”

If you can give any general pointers here, I would be grateful. Thank you. Continue reading Re: Nonsense and Self-reports

Christian Logic

I was recently asked the question, is there a distinctly Christian view of logic? I offer here the beginning of an answer to that question. (I am not trying to be original here. These thoughts are from many sources. Just trying to be faithful.)

Laws of Logic

The laws of logic are universal (applicable everywhere), abstract (immaterial, grasped by thought), invariant (not changing), and authoritative (they must be accepted). A non-Christian worldview has a difficult time accounting for such laws. The laws of logic cannot be denied with any kind of consistency, since a denial of logic is tantamount to a denial of truth and reason. But if it is affirmed that the laws of logic are universal, abstract, invariant, and authoritative, yet not “from God,” how can they be justified? Where do such laws come from? They are not invented by men, because they would not then be universal, invariant, or authoritative. They are not material, because they would not then be abstract.

Rather, logic is an expression of God’s unchanging, orderly, truthful, authoritative character.

The Character of God

God Himself is logical; He is a reasoning being: “Come, let us reason together” (Isa. 1:18).  As the ultimate lawgiver He orders His cosmos in a logical way. “God is not a God of disorder” (1 Cor. 14:33). God is orderly, and order implies reason. Where there is no reason, there is only chaos. God’s word is truth (Jn. 17:17), and He would have us be truth tellers (Eph. 4:15). God Himself is non-contradictory. He is truthful (Jn. 3:33), He cannot lie (Heb. 6:18). He does not deny Himself (2 Tim. 2:13). John Frame, in his book The Doctrine of the Knowledge of God, identifies these attributes of God, and then adds: “Does God, then, observe the law of noncontradiction? Not in the sense that the law is somehow higher than God Himself. Rather, God is Himself noncontradictory and is therefore Himself the criterion of logical consistency and implication. Logic is an attribute of God, as are justice, mercy, wisdom, and knowledge.”

The Christian worldview does account for the properties of logical laws. The laws are universal because God is omnipresent; His character is expressed throughout His creation. The laws are abstract, needing no created, material foundation, because they existed before the creation, being attributes within God. The laws are invariant, because God does not change, and neither do His attributes. If the laws of what is true and rational could change, then how could God be trustworthy? How could He keep His covenant promises if truth could be non-truth? He can and does keep His promises, because Christ, the logos, is the same yesterday, today, and forever. The laws are authoritative, because God is the ultimate authority.

A Tool and Gift

God has communicated logic to man as a tool by which we can come to truth. God made us in His image with the ability to reason. We are created as rational beings, and God uses our reasoning ability to speak to us. For example, the giving of law presupposes an ability to reason. Laws are given in the form of universal propositions. “God has commanded all men everywhere to repent.” To obey this, we finish the syllogism: I am a man, therefore I must repent. Without logic, the command could not be applied to particulars. A denial of logic opens the door for disobedience, for without it we cannot obey.

Logic is presupposed, not only in law, but in all revelations of God to men. God gives us minds that reason just as He has given us eyes that see, in order that we may receive His revelation to us. Cornelius Van Til said, “The gift of logical reason was given by God to man in order that he might order the revelation of God for himself.” In order to comprehend any doctrine, we must use logic. The truth that there is one God, eternally existent in three Persons, though clearly contained in the Bible, is not found in any one place in scripture. To see the truth of the Trinity requires a godly, submissive use of logic. If a truth is truly and logically derived from the scripture, we have a divine obligation to believe whatever it is. This is what the Westminster Confession is referring to where it says, “The whole counsel of God concerning all things necessary for His own glory, man’s salvation, faith and life, is either expressly set down in scripture or by good and necessary consequence may be deduced from scripture.” Isaac Watts, the great hymn writer and logician, said it this way in his book on logic: “It was a saying among the ancients, Veritas in puteo, Truth lies in a well; and, to carry on this metaphor, we may very justly say, that logic does, as it were, supply us with steps whereby we may go down to reach the water…. The power of reasoning was given us by our Maker, for this very end, to pursue truth.”

Logic is thus a tool which God has given us in order to understand and obey Him. Like other tools, our grasp of it as humans is no doubt incomplete and imperfect, but it is sufficient for the task for which it is given. And like any other tool, we need to be careful how we use it.

Rhetoric Interview

The following is a slightly edited version of a survey given me by Joshua Butcher – rhetoric instructor at Trinitas Christian School in Pensacola, Florida – regarding the teaching of rhetoric in a classical, Christian setting.

Josh:  How long have you taught rhetoric in a classical education setting?
Jim:  I taught Classical Rhetoric for 18 years at Logos School to 11th graders. I have also written a rhetoric text – Fitting Words: Classical Rhetoric for the Christian Student – and lectured through it.

Josh:  What are the essentials of rhetoric that every classically educated student should have?
Jim:  Do you mean, “What are the essential rhetorical skills that every classically educated student should seek to master?” Continue reading Rhetoric Interview

Digital Logic Q & A

Mr. Nance,

I have an overload of questions on digital logic. Hope that is okay!

1. Truth-functional completeness often makes circuits more complicated than they have to be. Is there anything besides cost-effectiveness that is beneficial about truth-functional completeness?

I assume you are asking “Why do we learn how to use NOR gates or NAND gates exclusively in a circuit?” Primarily, it is just to teach students how the gates work. But in practice, if you are constructing an electronic device, you may not have all the gates available (e.g. Radio Shack ran out and will not get them in for ten days), and so need to use a couple of NAND gates to do the job of one AND gate. Also, you might only use one NOR gate in the circuit, but a chip might contain four NOR gates, so why not just use three of them to replace an AND gate instead of buying one?

2. Since the symbol for NOR is the upside-down triangle, is there a symbol for NAND?

The triangle symbol is largely my own convention. See the Wikipedia page for the standard ways of expressing NOR. I know of no special symbol for NAND.

3. Is there a conditional gate (P ⊃ Q)?

Not that I am aware of. You can make a conditional using other gates.

4. Why do we write the names of logic gates in all caps? ( AND instead of and or And)

Just to distinguish them from the words in a sentence. It would be confusing to read “Take an or gate and an and gate…”

5. Why in K-maps do we circle in groups in powers of two?

Because that’s how they work to correctly simplify propositions. Draw yourself a K-map with 0111 across the top four cells, and 1110 across the bottom four cells. If you made two circles with groups of three across and ask, “What variable stays the same (negated or unnegated)?” the answer is that nothing stays the same, so no proposition can be identified. To get the simplest proposition, you must circle the middle four square, and the two on the top right and bottom left. Spend some time thinking through exactly what the K-map is doing when you circle groups and determine the proposition from the circled group. (See the next question.)

6. Finally, do K-maps eliminate the need for the Algebraic identities? I found that doing the Digital Logic Project didn’t require using them.

Yes, that is their primary benefit. Consider the proposition (p • q) ∨ (p • ~q). This simplifies this way:

  1. (p • q) ∨ (p • ~q)  Given
  2. p • (q ∨ ~q)  Distribution
  3. p • 1  Tautology
  4. p  Alg. identity

Now do a 2×2 K-map for this proposition:

 

 

 

See how it does the same thing in a faster, easier way?

Blessings!

Equivalence w/ Shorter Truth Tables

Mr. Nance,

Within Intermediate Logic Lesson 11, what would keep us from setting up the propositions both being true at the same time, and if there were a contradiction they would not be equivalent? Instead of setting them up one true and one false and if there’s a contradiction then they are equivalent?

That would be checking for consistency, not equivalence. If you set them both as true, and get a contradiction, then they are not consistent (which of course also means they are not equivalent, nor related by implication, per the chart in Introductory Logic, p. 71). But if you get no contradiction, all you have shown is that they can both be true, which is the meaning of consistency. To show equivalence, you have to show that they cannot have opposite truth values: the first cannot be true while the second is false, and vice versa.

Blessings!

Two Strange Proofs

Mr. Nance,

Could you give real-world examples of the arguments to prove in Intermediate Logic Lesson 18, number 7) U / ∴ W ⊃ W, and number 8) X / ∴ Y ⊃ X, showing how they would be used, or explain them a bit? Thank you.

Thanks for the great question! These two arguments are unusual, so I am not surprised that you are asking about them.

A real-world example for #7 might be Esther 4:16, “I will go to the king which is against the law; if I perish, then I perish!” This argument form basically shows that any proposition implies a tautology.

An example for #8 could be, “God created all things. So even if evolution can be used to explain some fossils, it’s still true that God created all things.” The form of this argument shows that if a proposition is given, any other proposition implies it.

To be honest, my purposes for including those two problems were: 1) to show how very strange the conditional proof is, and 2) to show how this method can be used to simplify otherwise difficult proofs.

Blessings!

May Proofs Use the Same Line Twice?

Mr. Nance,

In the answer to Exercise 17a, problem #12, is there a typo? It has row 5 twice.

There is no mistake there. A given line may be used more than once in a proof, as I say at the end of Lesson 15, “Usually, though by no means always, every step in a proof is used and used once.” Line 5 is used twice, once to simplify to get ~L, and once to commute and simplify to get ~M. 

Blessings!

Guessing w/ Shorter Truth Tables for Consistency

Mr. Nance,

Two questions:
1.  If you guess on consistency must you guess again as in validity and equivalence?
2.  If you find it inconsistent once does that trump consistency no matter what?

Thanks so much in advance for your help.

Answers:

1.  If you guess on consistency and get no contradiction, then you do not have to guess again. This is also true for validity and equivalence. In all three, if you guess, fill in truth values, and get no contradiction, then the question is answered (either that they are consistent, as in this case, or that the argument is invalid, or that the propositions are not equivalent).

2.  No, if you guess and get a contradiction (which looks like an inconsistency), then you must guess again, because the contradiction may mean that you just guessed wrong.

If you think about what consistency means, then all this makes sense. Consistency means the propositions can all be true. So if you assume they are true and can fill in the truth values without contradiction (even when you need to guess), then you have shown that they can be true.

Below is a short video in which I explain how shorter truth tables are used to determine consistency. 

Blessings!

Parentheses in Conditionals

Mr. Nance,

Could you please explain how the placement of the parentheses is determined in Test 1, Form A, #12 of Intermediate Logic? My student wrote “(M ⊃ P) ⊃ ~C,” but the answer key says “M ⊃ (P ⊃ ~C).”

The original proposition is,

“If we see a movie then if we eat popcorn then we do not eat candy.”

This proposition has the overall form pq, where p is the antecedent, “We see a movie” (abbreviated M) and q is the consequent. This consequent is another complete conditional: “If we eat popcorn then we do not eat candy.” This is the (P ⊃ ~C). Because it is a complete proposition in itself, this consequent gets placed in parentheses.

It will be important later to note that propositions of the form p ⊃ (qr) are equivalent to propositions of the form (p • q) ⊃ r. The given proposition could be understood in this way. “If we see a movie and eat popcorn, then we do not eat candy.” Notice in this form, “We see a movie and eat candy” is the antecedent, and it is a complete proposition in itself, and thus gets placed in parentheses.

Blessings!