# Parentheses in Conditionals

Mr. Nance,

Could you please explain how the placement of the parentheses is determined in Test 1, Form A, #12 of Intermediate Logic? My student wrote “(M ⊃ P) ⊃ ~C,” but the answer key says “M ⊃ (P ⊃ ~C).”

The original proposition is,

“If we see a movie then if we eat popcorn then we do not eat candy.”

This proposition has the overall form pq, where p is the antecedent, “We see a movie” (abbreviated M) and q is the consequent. This consequent is another complete conditional: “If we eat popcorn then we do not eat candy.” This is the (P ⊃ ~C). Because it is a complete proposition in itself, this consequent gets placed in parentheses.

It will be important later to note that propositions of the form p ⊃ (qr) are equivalent to propositions of the form (p • q) ⊃ r. The given proposition could be understood in this way. “If we see a movie and eat popcorn, then we do not eat candy.” Notice in this form, “We see a movie and eat candy” is the antecedent, and it is a complete proposition in itself, and thus gets placed in parentheses.

Blessings!

# 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?

# Translating “only if”

Mr. Nance,

Question 6 of Intermediate Logic Quiz 2 asks to symbolize this proposition: “The knight attacks the dragon only if the dragon devours the damsel.” The answer key says K ⊃ D (“If K then D”). I would have thought the answer was D ⊃ K (“If D then K”). Am I wrong? Continue reading Translating “only if”

# 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!

# The Antichrist and the Beast Syllogism

Mr. Nance,

Regarding question no. 10 on page 252: What is the reason for its invalidity? Does the pure hypothetical syllogism also use the five rules of validity? The argument is:

If he is the Antichrist, then he opposes God’s people.
If he is the Beast, then he opposes Gods people.
Therefore, if he is the Antichrist, then he is the Beast.

Is the Beast major term? And is the Antichrist the minor term? How do we make it into valid categorical syllogism? Continue reading The Antichrist and the Beast Syllogism

# Help with Hypotheticals

One of the more practical parts of Introductory Logic is Lesson 31 on Hypothetical Syllogisms. Hypothetical syllogisms of all kinds are a very common form of reasoning, so we should not only be able to identify them quickly, but we should also learn to use the valid forms confidently.

A hypothetical statement is an “if/then” statement, such as this one: Continue reading Help with Hypotheticals