Reply to Second Objection to Fine-Tuning Argument


This objection wonder how it could be that an infinite number of possible universes permit like, but that they still make up only a "tiny proportion" of the total number of possible universes.

The answer is that mathematicians have (evidently) worked out a way to make sense of the idea that one infinite set (in this case, the set of life-permitting
universes) can be a tiny proportion of another infinite set (in this case, the set of all possible universes).

Consider an analogy. Suppose we have a huge dart board with a tiny bull's eye. Suppose we also have darts whose tips are no bigger than a point in diameter. Now, the whole huge dart board itself contains an infinite number of points (an infinite number of places a dart could land). Likewise, the tiny bull's eye in the middle also contains an infinite number of points. By the reasoning above, we could therefore conclude that it is just as easy to hit the bull's eye as it is to hit outside the bull's eye. But, of course, this is absurd. The bull's eye is just a tiny proportion of the possible places a dart could land.  It's very hard to hit.

This analogy is meant to show that there is sense to be made of the idea that one set can be a "tiny proportion" of another set even when the sets are exactly the same size.

So this is how a defender of the fine-tuning argument would reply to this objection.