Monthly Archives: March 2016

Logic & the Resurrection

Intermediate Logic, Logic, , ,

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!

Conditional Proof and Reductio ad Absurdum

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With the nine rules of inference and the ten rules of replacement taught in Lessons 13-17 of Intermediate Logic, we can construct a formal proof for any valid propositional argument. But for the benefit of the logic student, I introduce two additional rules in Lessons 18 and 19: the conditional proof, and the reductio ad absurdum. The conditional proof will often simplify a proof, especially one that has a conditional in the conclusion, making the proof shorter or easier to solve. The reductio ad absurdum method usually does not shorten a proof or make it that much easier to solve, but understanding the concept of reductio is beneficial for purposes outside of formal logic, such as understanding proofs in mathematics and apologetics.

Both conditional proof and reductio ad absurdum start with making assumptions. I want to clarify what happens with those assumptions. Continue reading Conditional Proof and Reductio ad Absurdum →

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 →