# 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,

“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.

# What will I learn in Fitting Words – 2nd half?

Fitting Words: Classical Rhetoric for the Christian Student is arranged around the five canons of rhetoric: invention, arrangement, style, memory, and delivery. In the first half of this course, after laying the Christian philosophical and historical foundation of the subject, we concentrated on constructing the first two canons: invention, and arrangement (primarily the six parts of a discourse). We also studied the three artistic modes of persuasion: ethos, pathos, and logos (including the special lines of argument: forensic, political, and ceremonial oratory).

In the second half of this course, we will continue to learn about logos by constructing general lines of argument. In Unit 5 we will review the applicable parts of logic: defining terms, determining truth, employing maxims, and using inductive and deductive arguments. We will also considering the destruction of our opponents’ arguments in refutation, including identifying informal fallacies.

In Unit 6 we will learn about Style: understanding the nature of the soul, speaking with clarity and elegance, the levels of style, and figures of speech and thought. In Unit 7 we will learn the essential skills of memory and delivery.

We will continue to see examples of all of these concepts in historical and biblical speeches and other discourse. Click HERE to learn more.

# Fallacies in Comics

Comic strips are a great place to find examples of informal fallacies. It seems that we tend to find improper reasoning funny. In the “Peanuts” comic strip below, Lucy is ad baculum incarnate.

Note that the fallacy is not really made by Lucy making the threat, but by Charlie Brown, who is convinced by her “argument.”

Here is another example, where Lucy persuades Linus to memorize his lines using “five good reasons”: Continue reading Fallacies in Comics

# Caught by my students: Errors in my fallacies!

While teaching through Exercise 25, I was challenging my students on problem 3 to identify every possible syllogism making the fallacies of Two negative premises, and negative premise and affirmative conclusion, and no other fallacies.  I had original concluded that there were 32 such forms: EEA, EEI, EOA, EOI, OEA, OEI, OOA, OOI — all four figures of each.

Suddenly one of my students said, “But don’t some of those forms make others fallacies as well?” I realized he was right, and together we followed this rabbit trail, carefully working through the question to determine that, in fact, six of these forms do make additional fallacies: EOA-1, 2 and OOA-1, 2 have an Illicit Minor, and OOA-3, OOI-3 have an Undistributed Middle. Consequently, I have corrected my previous post on this topic.

I have some truly impressive logic students!

# More Answers for Exercise 25

One of the difficulties in writing a textbook like Introductory Logic is that, for most of the questions, there are often several possible correct answers. Rather than writing “Answers may vary” every time, I elected in the answer key to give a typical correct answer to each question that could have more than one possible answer.

But all the possible correct answers for Exercise 25 are worth a little more thought. In this exercise, I ask students to write schemas of syllogisms that have a given set of fallacies. If for each problem I only allow those fallacies and no others, there are a reasonably small number of identifiable answers for each problem. Here they are (for the sake of space, I gave the answers as mood & figure, rather than schema): Continue reading More Answers for Exercise 25

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

# One Lesson Logic Students Must Learn!

The most important concepts to understand in Formal Logic is the concept of validity. All logic students should memorize and come to understand these three different (but related) ways of defining validity:

1. In a valid argument, the premises imply the conclusion
2. In a valid argument, if the premises are true, then the conclusion must be true.
3. If an argument has true premises and a false conclusion, then it is invalid.