Bump.
I'd like to hear from some theists. It seems that if my approach is right, that undermines a big chunk of WLC's case for God.
Something must be missing.
What part of Craig's case for God's existence is undermined by the fact that an argument's being "good" (in the way Craig defines it) does not guarantee the conclusion is more probable than its negation (which I take to be your point)?
If we take the KCA, I could grant that both premises are more likely true than not while still claiming that an eternal Universe is more likely than the Universe having a cause. Surely that undermines the KCA somewhat.
The same thing seems to be true for Craigs version of the MA and the FTA. It puts a heavier burden on Craig in that he needs to show that the premises are quite a lot more probable than not.
... if I'm right that is.
Edit: Now that I think about it, this objection might not apply to Craig's version of the MA. At least not identically.
Well, no. I don't think the mere possibility that one could find the two premises of the kalam more likely true than not and the conclusion more likely false than not undermines the effectiveness of the kalam (or any deductive argument, for that matter) at all. Craig spends an awful lot of time (in his debates and written work) arguing for the truth of the premises of his arguments for God's existence. So it doesn't seem like he's counting on people shrugging and assigning 51% to each of the premises.
That's fair, but I think a lot of people are under the impression that if the two premises are more likely true than not, it would be irrational not to accept the conclusion (unless counter arguments are given). Maybe that's not how Craig presents it, but I do think a lot of his followers interpret it that way.
But, suppose you are one of those people who find themselves in a situation where you think the premises are each more likely true than not, but find the conclusion more likely false than not. The argument is still not ineffective. Suppose, as Craig actually does, multiple arguments are presented for a particular conclusion. For example: A/B//G and C/D//G. And suppose you think the probability of each of the premises is 0.60 (and, following the rest of the thread for simplicity, assume these probabilities are independent). Taken individually, these two arguments only set the minimum probability of the conclusion, G, at 0.36. But, taken together, the minimum probability of the conclusion is 0.59: P((A and B) or (C and D)) = 0.59.
So even if something like your probabilistic scenario is the case with the kalam, it still can play a valuable role in a cumulative case for the conclusion. And that's generally how Craig uses it.
Ok. I don't understand the above. Could you try explaining it in a different way?
I agree that the Kalam could have some force even if we regarded the conclusion as more likely false than true, but I'm not sure how that's explained. I suppose you could say that a "starting point" would be applying the principle of indifference to both premises which would give us a probability of .25 for the conclusion. If we grant a higher probability than that, I suppose that we could say that the argument still works in favor of the conclusion. Is that similar to what you have in mind?
I mentioned above the MA as an example of an argument where this approach works differently. In fact, it seems to me that if we come away with a .01 probability of the conclusion of the MA being true, that still supports the conclusion (although very mildly). Would you agree with that?
Sure, let me try to flesh out that a bit more. (I'm just going to assume the probability of all premises are independent.)
Suppose we have a valid argument:
1) A
2) B
3) Therefore, G
Suppose that we think P(A)=0.6 and P(B)=0.6. Then we can say that the rationally required lower bound of the probability of G is P(G)>=0.36. That is, it may be that the probability of G being true is higher than 0.36, but can be no lower without revising the probabilities we assign to A and B.
Suppose we have a second valid argument:
1) C
2) D
3) Therefore, G
As with the premises in our first argument, we think that P(C)=0.6 and P(D)=0.6. So, when considering this argument alone, the lower bound for the probability of G is 0.36.
Now that we have two independent arguments for the same conclusion, G, we might wonder how our having both of them changes the rationally required lower bound on the probability of G. So we might reason: If both A and B are true, then G must be true. And, if both C and D are true, then G must be true. So, G must be true if (A and B) is true, *or* (C and D) is true. Since we're multiplying probabilities, we know that P(A and B)=0.36 and P(C and D)=0.36.
So, to determine the lower bound for the probability of G, we need to determine the probability of "(A and B) or (C and D)". For any two propositions, X and Y, P(X or Y) = P(X) + P(Y) - P(X and Y).
Plugging our propositions into the formula:
P((A and B) or (C and D)) = P(A and B) + P(C and D) - P((A and B) and (C and D))
P((A and B) or (C and D)) = 0.36 + 0.36 - (0.36 * 0.36)
P((A and B) or (C and D)) = 0.5904
And that gives us, when considering these two arguments, a lower bound for the probability of G of 0.5904. That's how two different arguments can support one another, even though neither one alone is sufficient to guarantee the conclusion is more likely true than not.
Of course, when dealing with actual arguments, it's a lot more complicated. The probabilities associated with the premises will rarely be completely independent. And it may be the case (as with the moral argument, potentially) where the falsity of one of the premises is incompatible with the truth of the conclusion. But this is the gist of it, as I understand it.
