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#173 Argumentation and Logic Exercise

August 09, 2010

Hi Dr. Craig,

My question pertains to your work in Philosophical Foundations for a Christian Worldview. In Argumentation and Logic I was confused by argument B in the first exercise set pg 39.

The argument is as follows:

1. God is timeless only if he is immutable
2. God is immutable only if he does not know what time it is now.
3. If God is omniscient, then he knows what time it is now.
4. God is omnipotent and omniscient.

The assignment is to symbolize each argument and the draw the conclusion stating the rule and the justification of each step.

So, I think the argument should look like the following:

1. P → Q
2. Q → R (MP 1)
3. S → T
4. O & S (MP/Conj. 3)

I am confused by how the argument can go from God's immutability to his omniscience.

I don't know what rule is being used and I was hoping you could help me think better about these nine rules of logic and which ones are used in this argument.

Thank you and God bless!


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Dr. craig’s response


This is a good exercise for our readers. What mistake(s) has Daniel made? Has he correctly symbolized the four premisses? What follows from them? Can you name the rules of inference which are used in this argument? Take a moment to work on this problem before reading on.

So, Daniel, where did you go wrong? First, a couple of minor points: (2) is not an inference from (1) using the rule MP (modus ponens) as your notation indicates. It’s just a premiss in its own right. Modus ponens is the rule that would allow you to infer from P → Q and P that therefore Q. But in this argument P doesn’t appear as a premiss; it’s just the antecedent clause of (1).

Second, premiss (4) is similarly not an inference but just a premiss in the argument. It is a conjunction, but it is not using the rule of inference called Conjunction to infer from O and S that therefore O & S. The argument doesn’t “go from God’s immutability to his omniscience.”

Your main misstep, Daniel, occurs in your symbolization of premisses (2) and (3). Look at the consequent clause of (2) and the consequent clause of (3). The consequent clause of (2) is just the negation of the consequent clause of (3)! So the clause should be symbolized by the same letter with a negation sign “¬” in front of it, so:

2. Q→ ¬R

So (3) should become:

3. S → R

Our symbolization of the premisses should now look like this:

1. P → Q
2. Q → ¬R
3. S → R
4. O & S

OK, now apply your rules of inference and what do you get?

5. S

(Simplification, from 4)

6. R

(Modus ponens, from 3, 5)

7. ¬¬R

(Double negation, from 6)

8. ¬Q

(Modus tollens, from 2, 7)

9. ¬P

(Modus tollens, from 1, 8)

In English: we can infer that God is not timeless. Pretty nifty, eh? Now all we have to do is assess the truth of the premises to see if we have a sound argument for God’s temporality. For that discussion see my Time and Eternity.

- William Lane Craig