# What will I learn in Intermediate Logic?

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

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!

# Impressive Logic Students

Those who have taught a subject for many years have occasionally had the blessing of teaching a student who naturally has (or has developed) an intuitive insight into the subject.  I was blessed this way by two of my logic students this morning!

I was teaching Intermediate Logic, Lesson 34, “Converting Truth Tables into Digital Logic Circuits.”  We were going over the exercise, problem 3, for which the final answer in the text is the unsimplified proposition (~A • ~B • C) v (A • ~B • C). One of my students said, “I know that B has to be false and C has to be true, and it doesn’t matter about A. So that would simplify to ~B • C.” When I asked him if he has been reading ahead to future lessons, he said no, “I can just see it by looking at the proposition.” I was very impressed. He just saw future lessons on simplification techniques, without being taught them.

But the surprises for the morning were not yet over. Continue reading Impressive Logic Students

# Do these truth tree branches close?

Mr. 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

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

# Tackling More Difficult Proofs

Mr. Nance,

In our logic studies, my son and I wrestle to work through the proofs, generally together. When we get stuck, really stuck, we go to the answer key, cover the answer, and move through the proof step-by-step until we find where we veered off-track. Then we use that one step to get us back where we need to be; and then, hopefully, we finish the proof. My question is, is this a reasonable approach? Continue reading Tackling More Difficult Proofs

# Shorter Truth Tables for Equivalence

Mr. Nance,

I have a question Lesson 11 of Intermediate Logic. I have all of the right answers to the exercises, but I noticed that on a few of the questions, I wrote more lines in my answers because I thought I had to be exhaustive in my efforts to find no contradiction. A specific example would be #5. I agree that there is only one way for the conditional to be false. But, there are multiple ways the conditional can be true. Why didn’t you try lines with I as true and C false, or C false and I true? Am I misinterpreting the fourth instruction from p.70 to “switch the assigned truth values and try again”? Is this directive leveled at each whole proposition, or at each constant? (I hope this is making sense). Continue reading Shorter Truth Tables for Equivalence