This is the sixth installment of my blog series "Mapping the Fine-Tuning Argument" in which I take a look at the notorious Principle of Indifference and how important it is to the argument.
If you take a look at The Argument Stated, you'll see that the premises stated up to this point (if they are valid, but I've shown already that there are doubts about that, see here) establish that only a small set of the different combinations of possible values for the laws of physics make life possible. Picture each physical constant as a dial (like on a radio). The physical constants of the universe can be thought of as dials which can be set to different values. Out of all the concievable dial settings, only a few dial settings make the universe life friendly. But does that mean that a life friendly universe is improbable?
That depends on whether or not we believe the Principle of Indifference (PI) is valid. What is PI? The PI basically states that when we should assign all possibilities an equal probability unless we have evidence/argument to show that the probability assignment should be different. I find this principle highly intuitive, and I also think that it can be shown to be logically valid: If we feel that we should raise the assigned probability of some outcome to a higher (or lower) level when we have evidence that it is more (or less) likely to occur than other possibilities, then the converse of that is the principal of indifference: when we do NOT have evidence that some outcome is more/less likely to occur than others, we do NOT assign it a higher/lower probability than other outcomes, which means that we can only assign it an equal probability.
Now, some have tried to disprove PI by arguing that its application leads to contradictory probability assignments. For example, suppose that I own a square tile making factory. I ask you to guess the length of the side and the area of my tiles. I help you out by telling you that the square tiles have a side length between 1 and 3 inches and an area between 1 and 9 square inches. Applying PI, you realize that there is a 50% chance of the side length being between 1 and 2 inches, which would mean that there is a 50% chance of the area being between 1 and 4 square inches. But wait a minute: if you had applied PI to the area of the square (between 1 and 9 inches) you would have found that there was a 50% chance the area was between 1 and 4.5 inches. So the PI leads to contradictory probability assignments: in this case, it leads you to assign a 50% to square area between 1 and 4 and also a 50% chance to square area between 1 and 4.5. So should we reject PI?
I don't think so. As I've stated before on this blog, I think Ofra Magidor got it right when he characterized the PoI as an action guiding principle and said of it:
"It seems to me perfectly reasonable that an action guiding principle will give me some recommendation as to how to act. It may not suggest a unique course of action, nor does it have to be the only action guiding principle I am using."
Exactly. Using inductive reasoning can lead us to contradictory conclusions too, but we know better than to reject it. For example, someone may reason inductively that the sun always rises and always will rise, because it always has in the past. But we know (from laws of physics that we discovered inductively, through repeated observation) that one day the sun will cease to rise, for it will have burned out. Now, you may argue that elementary physical laws have been observed more than the sun's rising, and therefore there is a stronger case to be made that physical laws are constant. I'd agree with you, but you should concede the point that it is possible, at least in principle, for induction to lead to contradictory conclusions, since we might have an equal amount of inductive evidence in favor of two different, contradictory scenarios.
But there are other problems with the alleged 'disproof' of PI. I won't go into them here, perhaps I will in a later blog post.
Another question that must be asked is, "must the fine-tuning argument assume PI in order to be valid?" One answer is that the fine-tuning argument might appeal to a more well-developed version of PI than the crude version I presented here. Several philosophers have formulated versions of PI designed to avoid paradoxes like the one I described above .
Another answer is that the argument could simply say something like "Theism gives us reason to expect a life-friendly universe as much, much more probable than any other. Atheism does not give us a reason to think a life-friendly universe is probable. Therefore, it seems reasonable to suppose that fine-tuning is more probable (to some unknown degree) on theism than on atheism."
I suppose this is reasonable, the reasoning described here doesn't exactly rely on PI. However, it greatly weakens the argument. Most proponents of fine-tuning try to argue that the odds of a life-friendly universe are damn-near zero unless we suppose God exists. But this modified version of the argument only claims to have given the God hypothesis some vague and undetermined degree of support. We can't determine whether fine-tuning adds a neglible amount of support to the God hypothesis or an enormous amount. And that doesn't make the argument look strong at all.
Of course, my conclusion is that the Principle of Indifference is right. Fine-tuning proponents will recieve no complaint from me in their use of it. Besides, it's going to come back and bite them in the ass in a later post. ; )
 For example, Paul Castell "A Consistent Restriction of the Principle of Indifference" British Journal for the Philosophy of Science 49 (3):387-395. (1998).