Category Archives: Trivium

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.

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.

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

After Intermediate Logic?

What is recommended after Intermediate Logic? The short answer is: Rhetoric! But let me give you a bit more than that.

Introductory and Intermediate Logic together provide a complete foundational logic curriculum. Informal, categorical, and modern propositional logic are all included. The next step in a student’s classical education is to begin to apply what they have learned in logic to effective speaking and writing. This means that the student should move on to study formal rhetoric. Rhetoric applies the tools of logic: defining terms, declaring truth, arguing to valid conclusions, and refuting invalid ones. Indeed, of the modes of rhetorical persuasion – ethos, pathos, and logos – one-third is applied logic.

With this in mind, Roman Roads has released a new curriculum, Fitting Words: Classical Rhetoric for the Christian Student. I am the author of this text, and in Fitting Words I work to apply in rhetoric much of what the student has learned in logic. I am very excited about this project, because one significant reason that I wrote this text was to provide a satisfying answer the question of where to go next!

Take a look HERE for the most up-to-date information about Fitting Words.

Shakespeare’s Use of the Liberal Arts: Rhetoric

81Few4FQ9cL[1]In her invaluable book Shakespeare’s Use of the Arts of Language, Sister Miriam Joseph tells us that, according to Shakespeare scholar T. W. Baldwin, William Shakespeare “was trained in the heroic age of grammar school rhetoric in England, and he shows knowledge of the complete system, in its most heroic proportions. He shows a grasp of the theory as presented by the various texts through Quintilian.” In fact, a contemporary reported that Shakespeare was a country schoolmaster before he came to London, and at that time the grammar school would have significantly familiarized him with the arts of language.  Many passages in Shakespeare’s plays show such a familiarity with the technical vocabulary of rhetoric. Continue reading Shakespeare’s Use of the Liberal Arts: Rhetoric

Shakespeare’s Use of the Liberal Arts: Logic

81Few4FQ9cL[1]The classical Christian school movement is seeking to revive a form of education that helped shape some the greatest minds of western civilization. But how do we know that our father’s were trained according to the Trivium? One delightful demonstration of this is William Shakespeare’s frequent and detailed use of the liberal arts of grammar, logic and rhetoric in his plays and poems,  a use thoroughly identified by Sister Miriam Joseph in her book Shakespeare’s Use of the Arts of Language. In this well-researched book, she argues that Shakespeare’s application of formal logic is evidenced in his use of definition, genus and species, syllogistic vocabulary, applied syllogisms, enthymemes, and more. Let me give some of her clearer examples. Continue reading Shakespeare’s Use of the Liberal Arts: Logic