So this is something that's been addressed quite a lot on this forum but I've never understood the objections to it. Long ago SolElQoy tried explaining this to me and others but I came away none the wiser. So here's another attempt at getting to the bottom of this.
The idea is that the probability of the premises become multiplied in a deductive argument. This means that if an argument has two premises that have a .6 probability of being true, the conclusion only has a .36 probability of being true.
Let's take the newer version of the KCA (forgive me if I'm not formulating it exactly right):
1. If the Universe began to exist, it had a cause.
2. The Universe began to exist.
C. Therefore, the Universe had a cause.
Now let's say that we give each premise a .6 confidence level. How likely is the conclusion to be true? It seems pretty obvious to me that the answer is .36. There are three possibilities and here's how I'd put the probabilities:
1. The Universe began to exist and had a cause = .36
2. The Universe began to exist without a cause = .24
3. The Universe did not begin to exist = .4
This seems right to me, but Dr. Craig (and others I'm sure) has a standard that says a good argument simply needs to have premises that are more plausible than their negation. But that seems to contradict the above. Somethings gotta give! It's been suggested that the answer lies in the difference between probability and plausibility but I can't understand why that would be. Even if plausibility and probability are different things, I can't see why a plausibility estimate couldn't be roughly translated into a probability estimate. It seems that we do that all the time. Here's another example that has nothing to do with God:
1. If my neighbour's dog is in the park, it's wearing a dog-sweater.
2. My neighbour's dog is in the park.
C. Therefore, my neighbour's dog is wearing a dog-sweater.
Edit: My neighbours dog only wears a sweater if it's in the park (it's not really the same structure otherwise).
Let's say again that we give each premise a .6 confidence level. Is anyone claiming that conclusion is more likely than not in that scenario? If yes, why? Where did I go wrong? If no, does the same reasoning apply to the KCA or is there a relevant difference?
When I've brought this up in the past I've had some accusations of dishonesty and irrationality thrown at me so let me just make it very clear that my reasoning doesn't only apply to arguments for theism. I'm also certainly not claiming to be pwning Craig. I'm guessing there's a good reason for his standard, I'm just not sure what it is. Also, just to show that this isn't an objection the RF atheists have dreamed up, here's Christian philosopher/apologist Calum Miller on Craigs KCA. I get that Miller isn't regarded as an authority on this, but he seems well respected among theists:
"Again, for completeness, I should briefly detail one or two final concerns. These are to do with the framework of the argument as a whole. The first is that in general, I find many deductive arguments unsatisfactory. It is not always clear how the plausibility of the premises is supposed to relate to the plausibility of the conclusion. To secure a conclusion which, given our evidence, is more probable than not, the conjunction of the premises of a deductive argument must have a probability of greater than 0.5. But the fact that each premise is more likely than not, given our evidence, is certainly not sufficient to establish this.
This raises a further problem, something of a “dwindling probabilities” argument: we can only guarantee a probability of the conclusion insofar as the conjunction of the argument’s premises is probable. But if each premise is only somewhat more probable than not, the probability of the conclusion we can derive drops off pretty quickly. Suppose we think that P(P1) = P(P2|P1) = 0.7: then P(P1 & P2) = 0.49. Let P3 be the premise that if the universe has a cause, the cause of the universe is personal. Suppose P(P3|P1 & P2) = 0.7. Then P(P1 & P2 & P3) = 0.343. Of course, some might question these probabilities: but it is clear that the more uncertain steps there are, the more the probability we can guarantee for the conclusion decreases. Since a lot of steps in the KCA are far from certain, and since some seem only slightly more probable than their negations, this presents a serious problem for the KCA."
Sorry for the long post. Looking forward to responses.