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#171 Apologetics Arguments

July 26, 2010

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 does 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 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,


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Dr. craig’s response


Apologetics arguments

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 fellas who posted these criticisms on You Tube, 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 premisses and valid logic. An argument is sound if the premisses of the argument are true and the conclusion follows from the premisses 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 premisses of an argument are true, but we have no evidence for the truth of those premisses, 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 premisses it won’t, or at least shouldn’t, convince anyone. The premisses have to have some sort of epistemic warrant for us in order for a sound argument to be a good one.

Apologetics arguments – beware of 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 premiss 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 premisses are both true and the conclusion follows from the premisses by the rules of logic (specifically, disjunctive syllogism). Nevertheless, the argument is not any good because the only reason for believing the first premiss 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).

So, soundness is not sufficient for making an argument a good one. Something more is needed concerning the warrant the premisses have for us. Following the lead of George Mavrodes ( Belief in God , 1970) and Steve Davis ( God, Reason and Theistic Proofs , 1997), I’ve argued that what is needed is that the premisses be not only true but more plausible than their opposites or negations. If it is more plausible that a premiss is, in light of the evidence, true rather than false, then we should believe the premiss.

I trust that this clears up the gross misunderstanding propagated in a You Tube video that when I say that the premisses 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 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 premisses.

Apologetics arguments – the relation of conclusion to premisses

Moreover, in a valid deductive argument, like the kalam cosmological argument, any probabilities assigned to the premisses are not used to calculate the probability of the conclusion. (I actually prefer to speak of plausibility rather than probability to avoid the problem that it is often difficult to assign probability values to the premisses; but never mind.) If the premisses are true, then it follows necessarily that conclusion is true, period. It’s logically fallacious to multiply the probabilities of the premisses 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%.

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 premiss 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 premisses have more warrant than their negations. If these are really “the main issues raised atheists and skeptics on the Internet against [my] third criterion,” we’re in great shape, and they are in deep trouble.

- William Lane Craig