Monthly Archives: August 2017

Knowing the Truth of Statements

Mr. Nance,

Introductory Logic Exercise 8, Question # 9 asks what type of statement this is:

“Jesus is God, and He is man.”

The answer key says “supported, by authority.” Could definition also be a possible answer?

I see what you are thinking. Jesus is both God and man by nature, and definitions are (to a certain extent) trying to get at the nature of the term. But the question is basically asking, “How would you know that this statement is true?” Ask anyone how they know that Jesus is both God and man, and they will point to some authority: the Bible, or a creed, or their pastor tells them, etc. Besides, we don’t really define people.


Differences in the new versions of the Logic texts?

Mr. Nance,

How different is the 2006 version of introductory & intermediate logic to the most recently published version? My friend is selling it, but I need it for Classical Conversations next year and want to make sure it’s close enough to being the same.

And what about the DVDs?

Thanks for your time

The Introductory Logic student text just has cosmetic differences between the fourth and fifth editions: a nicer cover, reformatted style. Most of the improvements are in the additional materials: suggested lesson plans, notes to the teacher, additional tests and quizzes. But the student texts are essentially the same.

Not so with Intermediate Logic. In addition to similar cosmetic changes to the student text and similar additional materials, the student text also has two completely new units, both showing how the tools learned can be applied to real-life, but in different ways. One new unit is designed to teach how to use the tools to analyze chains of reasoning found in real writings: Boethius, Augustine, the Bible, and so on. Another new unit introduces Digital Logic, the logic of electronic devices, as a ubiquitous and powerful application of the tools of Intermediate Logic.

The DVDs are quite different, significantly improved, and professionally filmed. The new DVD lessons are much easier to follow and to navigate. After comparing the two, I am frankly embarrassed by the older version of the DVDs. Look HERE for a side-by-side comparison of the videos on YouTube.


Sayers’ Helpful Summary of Logic

Sayers’ Vision for Logic

In her seminal essay “The Lost Tools of Learning,” the author Dorothy Sayers describes her understanding of the medieval scheme of education, specifically the Trivium — the three liberal arts of grammar, logic, and rhetoric. She argues that students in the Middle Ages were taught the proper use of the tools of learning by means of these arts. Of logic she says,

dorothy[1]“Second, he learned how to use language; how to define his terms and make accurate statements; how to construct an argument and how to detect fallacies in argument.”

As I have taught logic in the classroom, written logic texts (and blog posts), and spoken on logic and classical education around the world, I have regularly returned to this quote. It is for me perhaps the most useful sentence (of the 238 sentences) in the essay.

A Proper Pedagogical Progression

In this sentence Sayers explains what logic is for: logic teaches us how to use language. This reminds us that the liberal arts of the Trivium are language arts (whereas the Quadrivium are mathematical arts). Specifically, logic teaches us how to use the language of reasoning, of disputation and proof.

This sentence also describes a proper pedagogical progression of logic:

  1. We must start with terms: how to define them, relate them, and work with them, including understanding the value of defining terms.
  2. Terms are related in statements (categorical statements connect subject terms with the predicate terms). Logic teaches us “how to make accurate statements”; that is, how to make statements that are true and applicable, as well as understanding how we know that they are true, and how they relate to each other. It teaches how to do this with many different types of statements: simple and compound, categorical and hypothetical, immediate inferences, and so on. Terms are the building blocks of statements.
  3. Statements are the building blocks of arguments, as we connect premises together to draw conclusions. So logic teaches us “how to construct an argument”; that is, how to write a valid argument to establish a desired conclusion.  It teaches how to do this with many types of arguments: categorical and propositional, conditional and disjunctive, symbolic arguments and arguments in normal English.
  4. Finally, logic teaches us “how to detect fallacies in argument,” both the formal fallacies from the rules of validity for categorical syllogisms and propositional arguments, and the informal fallacies of ordinary discourse, like circular reasoning and ad hominem. Logic teaches us not only to detect them, but to name them, and to expose them by means of counterexamples to those untrained in logic.

Were I to add one element to Sayers’ list, it would be “to construct a proof in a step-by-step, justified manner.” With this addition, every page, every concept of both Introductory and Intermediate Logic is covered in Sayers’ helpful description of what is encompassed in learning logic.

Mr. Nance the Younger

“A wise son makes a father glad” (Prov. 15:20)

It is my sincere pleasure to announce that this year for Roman Roads Classrooms, the teacher of Logic and Rhetoric will be my son Josiah. He will also be teaching an Astronomy course (his favorite subject).

Josiah is an experienced teacher, having taught several math and science courses for the last three years at Sequitur Classical Academy in Baton Rouge, before returning to his roots in Idaho this year. He was a very popular teacher at Sequitur among both students and parents.  Roman Roads Classroom is blessed to have him as a teacher.

In his 12  years at Logos School, Josiah was one of my best students. He has a sharp mind, true artistic talent, a fun sense of humor, and a mature sense of the seriousness of life firmly founded on godly joy. He received his bachelor of arts in liberal arts and culture from New St. Andrews College in 2014, before being hired by Sequitur to help develop their math and science program.

If you want to learn logic, rhetoric, or astronomy, I highly recommend this young man!


Don’t Let Your Child Cheat

Dear homeschool parent,

This is something I feel compelled to share. In my 25+ years teaching in a classroom, and my 3+ years teaching online classes for homeschoolers, I have seen a disproportionately large number of homeschooled students cheating in online classes. I have spoken with several other teachers of online courses for homeschoolers, and some have reported cheating by as many as 25% of their students. Most incidents of cheating involve the student either plagiarizing a paper, or looking at the answer key while taking a test unsupervised at home.

Plagiarizing a paper is harder for parents to catch and prevent. But stopping your child from cheating on tests should be easy.

Believe me, I understand how it can happen. An otherwise good child is taking an online course. He is struggling, the other students seem to be understanding the material better than he does, and unlike most of his previous courses, he is (perhaps for the first time) not allowed to learn at his own pace. He is being required to complete a test over material he knows he has not mastered. He also knows where the answer key is kept, and can look at it because his mom is busy and she trusts him. The temptation becomes too strong, he caves and decides to copy the answers, and does not tell anyone.

Thankfully, he is probably bad at it. When children cheat in this way, they tend to use words and phrases directly from the answer key, even when the answers could have been worded in many different ways. They also aim at 100%, of course, not realizing that a perfect score from a struggling student will set off a warning light to the teacher.

Parents, when the teacher claims that your child has apparently cheated on a test or assignment, listen to him! No good teacher will make such an accusation lightly. It is very uncomfortable to charge a student with cheating, and most teachers will err on the side of giving the student the benefit of the doubt.

When I discover a student has cheated on a test, I first send an email to the parent. I express my concern as a possibility, along with the evidence of the cheating. The child is allowed to make a defense, which is usually pretty flimsy. Almost every time, the child admits to cheating. Some confess everything immediately, some at first confess to cheating to a certain degree (“I only looked at the answers for the first few questions”), and some initially deny it, only to admit it later when they realize that the evidence is overwhelming, or (Lord willing) when their conscience smites them. According to other teachers I have spoken with, the only students who steadfastly refuse to confess in the face of overwhelming evidence are those students whose parents “can’t believe Jimmy would do such a thing.” When they are caught and confess their sin, they should be forgiven, fellowship should be restored on all sides, and they should be given a zero on the test or paper.

Here are three easy rules to follow when your child needs to take a test for their online class:

Keep the answer key inaccessible to your children.

Be in the room with them as they are taking a test, and pay attention to what they are doing.

Have them give you the test to send in.

Getting caught cheating is a hard blessing on both parent and child. The child learns that the truth behind the biblical proverb, “Be sure your sin will find you out.” He also learns that there are consequences to cheating. And the parents learn that their child is a sinner who can fall to temptation, just like the rest of us.

Logic: A Science and Art

Is logic a science or an art? Of course, a logician would answer Yes, and here is why.

A science is a systematic study of some aspect of the natural world that seeks to discover laws (regularities, principles) by which God governs His creation. Whereas botany studies plants, astronomy studies the sky, and anatomy studies the body, logic studies the mind as it reasons, as it draws conclusions from other information. Logic as a science seeks to discover rules that distinguish good reasoning from poor reasoning, rules that are then simplified and systematized. These would include the rules for validity, of inference and replacement, and so on.

For example, logic as a science could study the apostle Paul’s reasoning in 1 Cor. 15, “If there is no resurrection of the dead, then Christ has not been raised… But Christ has been raised, and is therefore the first fruits from among the dead.” It then simplifies this into a standard pattern: If not R then not C, C, therefore R. This rule can be further simplified, named, and organized in relation to other rules of logic.

An art is a creative application of the principles of nature for the production of works of beauty, skill, and practical use. The visual arts apply their principles to the production of paintings, sculptures, and pottery. The literary arts produce poems and stories. The performing arts produce operas, plays, and ballets.

Logic is one of the seven liberal arts, which include the Trivium of grammar, logic, and rhetoric. These arts are the skills which are essential for a free person (liberalis, “worthy of a free person”) to take an active part in daily life, for the benefit of others. Specifically, logic as an art seeks to apply the principles of reasoning to analyze and create arguments, proofs, and other chains of reasoning.

In summary:

Logic is the science and art of reasoning well. Logic as a science seeks to discover rules of reasoning; logic as an art seeks to apply those rules to rational discourse.