The Christian philosopher Dr. William Lane Craig debated the atheist philosopher Dr. Daniel Dennett some time ago about whether God exists, and by most accounts Dr. Craig won the debate. When all was said and done, Dennett’s conclusion was something like ‘Well, I suppose when you have premises that appear at first to be more plausible than their negations and that logically imply a conclusion that you find to be implausible, you just have to go back and deny one of the premises’. As you can imagine, Dennett took heat for this. On one hand, duh. If you want to deny a validly inferred conclusion the only possible thing you can do is to deny one or more premises. Stating as much at the end of a debate in which you were allegedly going to rebut or undercut your opponent’s position doesn’t really pack a punch. It also seems like it might indicate non-rational motivations on your part. Is it only after you see what your own commitments imply that you are willing to be critical of them? Do you so badly desire that God not exist that you are willing to go back and rework your cosmology and metaphysics to make sure that they cannot be appealed to in a theistic argument? Can somebody say “ad hoc”?
On the other hand, I sympathize with Dennett in a way I didn’t before. One weakness of deductive reasoning is that it does not account for the degree of certainty with which an individual holds the premises of an argument or the intrinsic plausibility one assigns the conclusion of an argument. Perhaps I could agree to two premises because I find them just slightly more plausible than their negations, only to discover that together they imply a conclusion that I find simply unbelievable. It serves as evidence against the probability of both premises being true.
So let’s say you assign the following probabilities:
- 51% – Everything that begins to exist has a cause of its existence.
- 51% – The universe began to exist.
- 95% – The universe does not have a cause of its existence.
In a certain context, if you think about it, you find the causal principle to be reasonable. Probably more likely to be true than not. And similarly with the past-finitude of the universe; it’s more likely the case that the universe had an absolute beginning a finite time ago than that it has existed from eternity. And when you are not holding those things in mind, in some other context, you are very confident that the universe does not have a cause of its existence. (Let’s just say for now that you have your reasons.) What do you do when someone points out that if both of those first items are true, then the last item is false? If everything that begins to exist has a cause of its existence and the universe began to exist, then the universe has a cause of its existence. But you’re pretty sure that the universe does not have a cause! And you were only barely agreeing to the other propositions. Now you feel cornered.
It is this concern that used to motivate another Christian philosopher, Alvin Plantinga, to argue against the utility of theistic proofs. He called it the problem of “dwindling probabilities”. Think of it this way: What are the odds of the result of a coin toss being heads? 50%? But what are the odds of the results of two coin tosses both being heads? To find the answer you have to multiply the probabilities that each of the tosses will be heads. So that would be .5 (for 50%) x .5, which equals .25, or 25%. As one builds a theistic proof, one tries to provide supporting arguments and evidences of each premise. However a reader or listener will not be convinced with 100% certainty of the truth of each premise. Now the likelihood of all the premises being true dwindles just like the likelihood of all of the coin tosses resulting in heads dwindles. While there are some things to say in reply to this, and while I believe Plantinga has abandoned this line of reasoning, the concerns here are important. Logical deduction cannot account for degrees of certainty or the intrinsic plausibility of a conclusion.
One alternative to using the logical structure that Dr. Craig uses when formulating what he calls the “Kalam Cosmological Argument” for God’s existence, which is called “modus ponens”, is to formulate the argument using a logical structure that has a way to account for probabilities. And one guy has attempted to do exactly that.
You can read it here.