What Makes A Good Argument?

There’s been some recent discussion over at our forum on what constitutes a good argument.  Incorporating some criticisms from some YouTube atheists as well some criticisms from another forum user, one of our members submitted this as a question to William Lane Craig. Lo and behold, he actually answered it! The following is the original post which inspired the question, followed by Craig’s answer (Found in the second half of his answer).

Nocterro wrote: Philosopher William Lane Craig has often stated, as one of the conditions of a good argument, that the premises must be more plausible than their negations. I disagree with this, on the grounds that it does not always apply – there are counterexamples. Consider this:

1. My neighbor’s dog is outside.
2. It is raining.
C. My neighbor’s dog is outside and it is raining.

This argument is valid – the conclusion follows from the inference rule known as “conjunction introduction”: if p is true, and q is true, then the conjunction p and q is true.

Now, it might be quite plausible, when considered alone, that my neighbor’s dog is outside; after all, his dog is almost always outside. It might also be very plausible that it is raining; perhaps I have looked outside and seen that it is raining. However, I might not be very certain at all that the conclusion is true – who would leave their dog outside in the rain? Should I think it’s plausible to accept this conclusion, just because both 1 and 2 are plausible? Surely not.

One might object by saying that 1 is not plausible because it is raining. This, however, is erroneous; and even supports my point. To say such is not to consider the plausibility of 1 at all; rather, one is instead actually commenting on the plausibility of the conclusion.

So, when should we accept the conclusion of an argument? I employ a modification of Craig’s method. First, I check the argument’s validity. If the argument is valid, I put all of the premises on the “left”, and the negation of the conclusion on the “right”. I then ask myself which is more plausible (or, which “side” I am more certain of. If it is the left, I accept the conclusion of the argument. If the right, I do not. For example:

Left:
1. My neighbor’s dog is outside.
2. It is raining.

Right:
C/N. Not (My neighbor’s dog is outside and it is raining).

If I am more certain of the conclusion’s negation (perhaps because I believe that my neighbor is home, and cares for his dog), then I do not accept the argument.

Let’s run through another example, with an argument often proffered by Dr. Craig:

Left:
1. Whatever begins to exist has a cause.
2. The universe began to exist.

Right:
C/N. not (The universe has a cause).

Of course, different people will have many different views on the plausibility of these premises and conclusion. Most people will not be certain at all that “the universe does not have a cause”. However, one may in fact be even less certain of 1. Depending on rough probabilities, one may be justified in rejecting this argument based on the uncertainty of 1 alone. In any case, these subjective probabilities, combined with this analysis of what makes an argument “good”, serve very well to explain why certain arguments are convincing to some but not to others.

Craig responds:

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. 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.

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.

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 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.

Tags: Analytic Theism, good argument, William Lane Craig