Category Archives: Intermediate Logic

What will I learn in Intermediate Logic?

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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.

Audit Intermediate Logic

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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!)

Intermediate Logic, Introductory Logic, ,

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

square-of-opposition

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!) →

Applying Intermediate Logic

Intermediate Logic, Why learn logic?

The most recent edition of Intermediate Logic has two new sections, Unit 4 and Unit 5. I’ve included these new units in the text because I wanted to answer the important question, “What are some practical applications of the tools that we are learning about, i.e. truth tables, formal proofs, and truth trees?” I believe that the applications of these tools in the new units will deepen and solidify student understanding of the concepts that, up to that point, have been largely theoretical.

Saint_Augustine_Portrait[1]Unit 4 (Lesson 28) gives logic students the opportunity to analyze chains of reasoning. The arguments to be analyzed are taken from Boethius’s The Consolation of Philosophy, the Apostle Paul’s argument proving the general resurrection of the dead in I Corinthians 15, and a section on angelic will from Augustine’s City of God. I work through this last one in full on the DVD.

An exercise not in the text that may be beneficial would be to have students write their own chains of reasoning, arguing for a conclusion of their choosing, in imitation of these authors. Their arguments must include at least one NOT, AND, and OR, and two IF/THENs. Tell them to include a truth-table or truth-tree analysis of their own chain of reasoning.

Digital display 4Unit 5 (Lessons 29-40) teaches students how to apply what they have learned to the fascinating topic of Digital Logic. Do not be intimidated by the 0’s, 1’s, and new symbols. It’s just the same old true, false, and logical operators that they have already learned about presented in a new way. Students often find this a fun application of what they have learned. It helps them to understand the electronic world around them, and it shows that the tools that they have learned apply not only to philosophy and theology, but to digital clocks and iPhones!

Do these truth tree branches close?

truth tree errorMr. Nance,

I have a student asking me if this would be a valid way of completing this truth tree for consistency. She thinks since she already found inconsistency in the branches, that she doesn’t have to do line 3 (per lesson 24). I’m thinking that this thought process only applies if she finds it consistent, not inconsistent. She’s also asking if it matters the order they are done in (I told her non-branching first, then branching, but that I didn’t think the order mattered if it was all branching that was left). Please help me give her direction! Continue reading Do these truth tree branches close? →

Logic & the Resurrection

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Intermediate Logic Unit 4 teaches how to apply the tools we have learned in logic to real-life arguments. One such argument is contained in 1 Cor. 15:12-20, in which Paul argues that Christ has been raised from the dead, and as such He is the firstfruits of the general resurrection to come.

There are many points to Paul’s argument, but the main one is from verses 13, 16, and 20:

“If there is no resurrection of the dead, then Christ is not risen…But now Christ is risen from the dead, and has become the firstfruits of those who have fallen asleep.”

This argument can be symbolized as follows (C = Christ is risen, R = There is a resurrection of the dead):

~R ⊃ ~C    C     ∴   R

You can use the tools of truth table, truth tree, or formal proof to demonstrate that Paul’s argument is valid.

There are several other arguments in 1 Cor. 15:12-20, but the others leave premises assumed, so they take additional effort to analyze. But it is a beneficial exercise to work through them. Look at Exercise 28b.

Have a blessed Good Friday!

Where does the CPA come from?

Mr. Nance,

I’m stumped on Logic lesson 18 #5. We got same answers as answer key until line 7…I can see from line 8 why line 7 is important, but how did we deduce a consequent that was not the original consequent of line 1 (from which we assumed the antecedent in line 3)?

Hope that makes sense! Continue reading Where does the CPA come from? →

Rule of Commutation

Mr. Nance,

I have a question on Intermediate Logic, Exercise 17a, problem 5. To justify the conclusion (L • M) ⊃ N, the answer key says to use the rule of commutation from (M • L) ⊃ N. But the rule of commutation says (p • q) ≡ (q • p). How can I use that rule without switching the propositions, but switching the letters inside of a proposition? For example, in step 3, they are switching the propositions and not the letters inside the parentheses. Continue reading Rule of Commutation →