Tag Archives: Propositional Logic

What comes after Logic? Rhetoric!

Introductory and Intermediate Logic together provide a complete foundational logic curriculum. Informal, categorical, and modern propositional logic are all included. The next step in your student’s classical education is to begin to apply what he has learned in logic to effective speaking and writing. This means your student should move on to the study of formal rhetoric, the capstone of a classical education. Rhetoric applies the tools of logic – defining terms, declaring truth, arguing to valid conclusions, and refuting invalid ones – to the persuasion of people. Rhetoric puts flesh onto the bones of logical analysis, that we may breathe arguments into life through the wise use of fitting words.

Fitting Words: Classical Rhetoric for the Christian Student is a complete formal rhetoric curriculum. Presented from a thoroughly Christian perspective, Fitting Words provides students with tools for speaking that will equip them for life. Drawing from Aristotle, Quintilian, Augustine, and others, and using examples from the greatest speeches from history and scripture, this robust curriculum guides Christian students in the theory and practice of persuasive communication.

The complete curriculum includes:

  • Student text with 30 detailed lessons
  • Student workbook with exercises for every lesson
  • Answer key for the exercises and tests
  • Test packet with nine tests, review sheets for every test, and speech judging sheets
  • Video course in which the author introduces and teaches through every lesson

A Simpler Truth Tree

In this video, I decompose a set of propositions from Intermediate Logic, Additional Exercises for Lesson 24. I first decompose the truth tree in the order of the given propositions. I contrast this with a second truth tree that uses the simplifying techniques from Lesson 24.

This shows first, how to use a truth tree to determine consistency, and second, how the techniques from Lesson 24 make the truth tree simpler.

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.

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.


Logic with James B Nance

Introductory Logic Prerequisite for Intermediate Logic?

It is certainly possible for a student who has not taken (or not completed) Introductory Logic to take and successfully complete Intermediate Logic. Though the Intermediate Logic text is designed as a continuation to Introductory Logic, it does not assume a mastery of the concepts in it. Almost all of the concepts from Introductory Logic that are essential for Intermediate Logic are re-taught (the only exceptions being the definitions of logical argument, premise, and conclusion; definitions assumed in Intermediate Logic, Lesson 7, but taught explicitly in Introductory Logic, Lesson 19).

That being said, a new Intermediate Logic student who is familiar with Introductory Logic will have an advantage over a student who is not. The following concepts from Introductory Logic are repeated and re-taught in Intermediate Logic (the concepts are first taught in the respective given lesson numbers): Continue reading Introductory Logic Prerequisite for Intermediate Logic?

The ambiguous OR

Logic is a symbolic language. It is also a very precise language, every term well defined and unambiguous. English, on the other hand, is a somewhat ambiguous language. The same word can have multiple meanings: a pen is a writing utensil and an enclosure for livestock.

One key term in logic is the disjunction “or”. In English, the word “or” has two meanings. The first is the inclusive or, which means basically “this, or that, or both.” If someone said, “Most Bible students read the King James or the NIV,” this statement is still true for a student who reads both the King James and the NIV. The “or” includes both possibilities.

The exclusive or basically means “this or that, but not both.” This is the sense used in this classic argument for the deity of Christ: “Jesus was either God or a bad man.” If Jesus was God, then He was not a bad man. If He was a bad man, then He was not God.

Symbolic logic deals with the ambiguous “or” this way. The logical operator OR is taken in the inclusive sense. “A or B” is true if A is true, B is true, or both A and B are true. To represent the exclusive or, we use the compound proposition “A or B, but not both A and B.”

Question about Conditionals

Mr. Nance,

My student has a question on Exercise 4 number 14.  Her answer for was ~C ⊃ S instead of S ⊃ ~C. Can the statements “I will go swimming only if the water is not cold” be considered logically equivalent to “If the water is not cold, I will go swimming”?

Also, how can I explain the difference between “If the water is not cold I will go swimming” and “I will go swimming unless the water is cold”?

Thank you! Continue reading Question about Conditionals

Logic with James B Nance

What will I learn in Intermediate Logic?

intermediate-logic-complete-program-dvd-course[1]Logic gives us standards and methods by which valid reasoning can be distinguished from invalid reasoning. It teaches students to think in a straight line, and to justify each step of their thought. Intermediate Logic does this using a symbolic language to represent the reasoning inherent in the language of argument. It is more flexible than syllogistic logic, and can thus apply to more real-life arguments.

Intermediate Logic Unit One teaches the powerful method of truth tables to determine the validity of propositional arguments. Unit Two takes these methods and teaches students how to deduce a conclusion from a set of premises, so they are able not only to show that an argument is valid, but also prove why it is valid. Unit Three teaches these same concepts using the modern method of truth trees. Unit Four applies these methods to the analysis of real-life arguments from 1 Corinthians 15, Hebrews 2, Boethius’ The Consolation of Philosophy,  Augustine’s City of God, and more (including a scene from the movie “Get Smart”). Unit Five teaches the fascinating application of these methods to the logic of digital electronics.

Logic with James B Nance

Audit Intermediate Logic

Would you like to be a fly on the wall in my logic class? Want to improve your understanding and/or teaching of logic by watching me teach and interact with my students, discussing the lesson after the class, and having the recorded class sessions available? If so, click HERE to audit Intermediate Logic for the 2017 school year!

What’s included for Auditors? First, you have access to all the live classes. During the discussion, you will not be called upon as I do with my regular students. You are free to watch in the background by muting your mic and camera, but you also have the option of appearing to ask a question or make a comment if you’d like.

After the regular class time has ended, students leave the virtual classroom while auditors are invited to stick around for a few minutes to ask “Teacher Questions”! This is when you would have me all to yourselves as teachers. Turn on your webcams and mics, and discuss the lesson, teaching logic in general, or whatever questions you might have.

We will meet together live for online recitations Monday/Thursday from 8:00-9:30 AM (PST), or Tuesday/Friday from 8:00-9:30 AM (PST). The spring semester starts January 5/6, 2017, and goes to May 18/19, with a Winter Break in mid-February and an Easter Break in mid-April.

I hope to see you there!

The Square of Opposition (for logic nerds only!)

The Square of Opposition is a useful tool for representing and understanding the relationships between categorical statements with the same subject and predicate:


The relationships are defined this way:

Contrariety: The statements cannot both be true, but can both be false.
Contradiction: The statements cannot both be true, and cannot both be false.
Subcontrariety: The statements can both be true, but cannot both be false.
Subimplication: If the universal is true, the particular must be true.
Superimplication: If the particular is false, the universal must be false.

Students might be interested to discover that the square of opposition can be created for non-categorical statements as well. Continue reading The Square of Opposition (for logic nerds only!)