Why “Soundness” Is Not Sufficient for Making a Good Argument

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ON ARGUMENTATION AND LOGIC 101

An Exercise in Argumentation and Logic

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:⁶

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!

Daniel

Dr. Craig’s Response

This is a good exercise for our readers. What mistake(s) has Daniel made? Has he correctly symbolized the four premises? What follows from them? Can you name the rules of inference that 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 premise 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 premise; it’s just the antecedent clause of (1).

Second, premise (4) is similarly not an inference but just a premise 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 premises (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 premises 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?

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.⁷

What Is a Criterion for a Good (Apologetics) Argument?

Dear Dr. Craig,

I have a question dealing with what constitutes a good argument. You frequently state in your popular work that a good argument must: be logically valid, be sound, and have premises more plausible than their negations. Now, I know you rightly ignore the popular objections to your work raised by Internet atheists, but regarding your third criterion, I think they raise a valid point. Several atheists and skeptics, both on YouTube and elsewhere, have objected that there exist counterexamples to your third criterion that the premises must be more plausible than their negation. The first one proceeds as follows:

1. If (A & B), then C.

2. A.

3. B.

4. Therefore, C.

Now, suppose we learn that the credence (I’m using this term in a probabilistic sense) for believing (1) is 1, and the credence for believing (2) and (3) are each 0.6. Now, here is the problem: although all three premises are more plausible than their negations (all of them have a credence above 0.5), their conclusion is not, for when the probabilities of the premises are multiplied, the conclusion’s credence is a mere 0.36! So something clearly went wrong, but what?

Another example proffered which does not use probability is as follows:

1. It is raining.

2. My neighbor’s dog is outside.

3. Therefore, it is raining and my neighbor’s dog is outside.

This is a logically valid argument, since the conclusion follows from an inference rule known as conjunction introduction.

So here’s the problem with this argument: (1) might be more plausible than its negation because I might see rain falling through my window, whereas (2) might be more plausible than its negation since I know my neighbor’s dog is always outside. Yet, I am nowhere near as certain about the conclusion! If my neighbor is a good owner, he would bring his dog in when it rains, meaning that the conclusion is less plausible than its negation! Moreover, one cannot say that (2) is implausible because it is raining, for he then is bringing (1) into consideration and is, therefore, commenting on the argument’s conclusion.

So Dr. Craig, these are the main issues raised by atheists and skeptics on the Internet against your third criterion. Is there any way for one to answer them? And if they are right, then how should seekers of truth approach the premises of an argument and how much warrant should they demand of them?

Thank you and God bless,

Pranav

(country not specified)

Dr. Craig’s Response

It’s scary how really desperate these people are becoming! Far from raising valid points, Pranav, these objections are just worthless, based on fundamental misunderstandings of what makes good apologetics arguments. The people who posted these criticisms on YouTube, if they continue their study of philosophy, are going to be very embarrassed someday about these videos.

Let me back up and take a run at your question. What makes for a sound deductive argument? The answer is: true premises and valid logic. An argument is sound if the premises of the argument are true and the conclusion follows from the premises by the logical rules of inference. If these two conditions are met, then the conclusion of the argument is guaranteed to be true.

However, to be a good argument, an argument must be more than just sound. If the premises of an argument are true, but we have no evidence for the truth of those premises, then the argument will not be a good one. It may (unbeknownst to us) be sound, but in the absence of any evidence for its premises it won’t, or at least shouldn’t, convince anyone. The premises have to have some sort of epistemic warrant for us in order for a sound argument to be a good one.

QUESTION-BEGGING

This is why question-begging arguments are not good arguments. A person is guilty of begging the question if his only reason for believing in a premise is that he already believes in the conclusion.

For example, suppose you were to present the following argument for the existence of God:

1. Either God exists or the moon is made of green cheese.

2. The moon is not made of green cheese.

3. Therefore, God exists.

Now, this is a sound argument for God’s existence: its premises are both true and the conclusion follows from the premises by the rules of logic (specifically, disjunctive syllogism).

Nevertheless, the argument is not any good because the only reason for believing the first premise to be true is that you already believe that God exists (a disjunction is true if one of the disjuncts is true). But that’s the argument’s conclusion! Therefore, in putting forward this argument you’re reasoning in a circle or begging the question. The only reason you believe (1) is because you believe (3).

INSIGHT

“Question-begging” is an informal fallacy that pertains to whether a person’s only reason for believing in a premise is that he already believes in the conclusion. Notice one could believe in a premise because he believes in the conclusion and this would not be question-begging unless that reason for believing were the only reason. Bottom line: we want to learn to offer arguments that have reasons for a premise that are “independent” of a conclusion.

So, soundness is not sufficient for making an argument a good one. Something more is needed concerning the warrant the premises have for us. Following the lead of George Mavrodes⁸ and Steve Davis⁹, I’ve argued that what is needed is that the premises be not only true but more plausible than their opposites or negations. If it is more plausible that a premise is, in light of the evidence, true rather than false, then we should believe the premise.

I trust that this clears up the gross misunderstanding propagated in a YouTube video that when I say that the premises of a good argument must be more plausibly true than their negations, I’m positing a range of additional truth values in between true and false. No, I presume the classical Principle of Bivalence, according to which there are only two truth values, True and False. There are different degrees of plausibility, not of truth, given the varying amounts of evidence in support of one’s premises.

THE RELATION OF CONCLUSION TO PREMISES

Moreover, in a valid deductive argument, like the kalam cosmological argument, any probabilities assigned to the premises are not used to calculate the probability of the conclusion.¹⁰ If the premises are true, then it follows necessarily that conclusion is true, period. It’s logically fallacious to multiply the probabilities of the premises to try to calculate the probability of the conclusion. That’s why you wind up with the clearly wrong results that you did. In a sound deductive argument the most we can say about the probability of the argument’s conclusion is that it cannot be less than some lower bound; but it could be as high as 100 percent.

So with respect to your first example, we have here a valid deductive argument, since from (2) and (3), we may infer

3*. A&B

and from (1) and (3*) it follows logically that (4). All we need to find out is whether there are better reasons to believe (1), (2), and (3) rather than their opposites. If there are, then you have a good argument for (4). The probability of (4) doesn’t even enter the picture.

As for your second example, this is also, as you note, a valid argument. So you just need to find out whether the evidence makes each premise more likely to be true than its negation. The misgiving you share is simply evidence that (2) may not be more plausible than its negation. You’re entitled to look at all the evidence relevant to (2). If it’s raining or 40 degrees below zero or you heard your wife say your neighbor was taking his dog to the vet today, etc., you may well have good grounds for thinking (2) is not true. You might know, e.g., 1*. If it is raining, my neighbor takes his dog inside.

It follows from (1) and (1*) that (2) is false. But if, on balance, the evidence supports (1) and (2) rather than their opposites, then you’ve got a good argument for (3).

So you can see that good apologetics arguments are simply those which are sound and whose premises have more warrant than their negations. If these are really “the main issues raised by atheists and skeptics on the Internet against [my] third criterion,” we’re in great shape, and they are in deep trouble.

Why “Soundness” Is Not Sufficient for Making a Good Argument

Hello,

My name is Manol. I am from Albania. I have just graduated in Medicine and Surgery in the University of Bologna in Italy. I am a Christian, and I have been using your arguments many times during evangelism. I am also preparing for teaching others in church about these arguments. I am writing because I have a question on the moral argument. The argument is:

1) If God does not exist then objective moral values do not exist.

2) Objective moral values do exist.

3) Therefore God exists.

I agree with all of that. The first premise seems very obvious to me. And I agree that in our moral experience we do discern a realm of objective moral truth.

But one day as I was thinking about it, considering what an atheist may answer to this argument, it came to my mind that he might answer that the argument is too “simplistic”, or too “obvious”.

Let me explain what I mean. Your argument in support of premise 2 is that in the same way the outer world is objective, in the same way moral values are objective. Our perception of objective moral values is on a par with our perception of the outer world with the five senses.

But if this parallelism between moral values and the outer world is true, then it means that the argument may be turned into something like this:

1) If God does not exist, then an objective outer world does not exist.

2) An objective outer world does exist.

3) Therefore God exists.

But as an argument it doesn’t seem very convincing. Is the parallel correct? If yes, then why not using this second argument in the debates or talks? If this second argument is used and it is proven not convincing, why should the moral argument, which is a parallel argument, be convincing? Or, if you think this second argument is not convincing, why is it so?

Thanks for all you are doing and God bless,

Manol

Dr. Craig’s Response

Manol, I can’t tell you how thrilled I am to receive a question from so articulate and thoughtful a Christian in Albania, a traditionally Muslim and lately Marxist country! With your education and obvious language skills, you are well-prepared to be mightily used of God in your homeland.

I’m impressed that in contrast to so many native English speakers you have correctly grasped the moral argument which I defend. You are spot-on in thinking that the support for the second premise lies in the fact that “in our moral experience we do discern a realm of objective moral truth.” You have correctly grasped the parallel between the deliverances of our five senses about the realm of physical objects and the deliverances of our moral sense about the realm of values and duties. Just as we cannot get outside our five senses to check their veridicality and so prove that we are not the proverbial “brain in a vat” being stimulated by a mad scientist to perceive an external world, so we cannot get outside our moral sense to check its veridicality. But in both cases we are perfectly rational, in the absence of any defeater of our beliefs, to believe that we do apprehend objective realities.

On this basis you construct a parallel argument, which, if dubious, ought to make us think that the moral argument is also dubious. Now, the parallel argument you construct is actually a sort of cosmological argument for God’s existence. In fact, I think it is a sound argument! It is obviously valid, and both the premises seem to me to be true. For the objective outer world obviously exists, and if God did not exist, then no world at all would exist, including an objective outer world! It’s not that if God did not exist, then the outer world would be merely a subjective illusion; rather it’s that there wouldn’t be anything at all!

So why not use this parallel argument in debates or talks? The answer to that question serves to highlight what makes for a good argument. Soundness is not sufficient to make an argument a good one. It’s easy to construct sound arguments for God’s existence. For example:

1. Either God exists or the moon is made of green cheese.

2. The moon is not made of green cheese.

3. Therefore, God exists.

This argument is logically valid, and both its premises are true (a disjunction like (1) is true if one of its disjuncts is true, and in this case the first disjunct “God exists” is true). But I’m sure you wouldn’t recommend my using this argument in debates and talks! Why not? Simply, because no one would believe the first premise unless he already believed the conclusion to be true. The argument is thus circular or, as we say, begs the question.

So being sound is not sufficient to make an argument a good one. The argument must also not commit any informal logical fallacies like begging the question, and the premises must be more plausible than their negations. The first premise of your parallel argument threatens to beg the question and is not apt to appear more plausible than its negation to someone who is not already a theist. By contrast, as you know, the first premise of the moral argument is one that many atheists themselves believe and argue for. Thus, although the premises of your two arguments are parallel, the support for the premises is quite different.

In order to run a good cosmological argument, we need to provide some reason to think that if God did not exist, then the world would not exist. I, myself, like the following version of Leibniz’s cosmological argument:

1. Anything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause.

2. If the universe has an explanation of its existence, that explanation is God.

3. The universe exists.

4. Therefore, the universe has an explanation of its existence. (from 1, 3)

5. Therefore, the explanation of the existence of the universe is God. (from 2, 4)

In this argument, premise (1) is a modest version of the Principle of Sufficient Reason and (2) is logically equivalent to the atheist’s typical claim that if atheism is true, then there is no explanation of the universe’s existence. This argument is, I think, a good one.¹¹

6. William Lane Craig and J. P. Moreland, Philosophical Foundations for a Christian Worldview (Downers Grove, Ill.: InterVarsity, 2003), 39.

7. For that discussion see Dr. Craig’s book Time and Eternity.

8. George I. Mavrodes, Belief in God: A Study in the Epistemology of Religion (New York: Random House, 1970).

9. Stephen T. Davis, God, Reason and Theistic Proofs (Grand Rapids: Eerdmans, 1997).

10. With Dr. Craig, it is preferable to speak of plausibility rather than probability to avoid the problem that it is often difficult to assign probability values to the premises.

11. For more on this, see the question in this book, “On Assessing the Argument from Contingency” (pages 148–53).

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