This is the third installment of my blog series "Mapping the Fine-Tuning Argument" in which I examine the notion that there might just be one type of universe that is mathematically consistent.
Let's take a look at the first four statements of the fine-tuning argument:
1. It is conceptually possible to change physical laws and constants from observed values.
2. Conceptually changing some constants from their observed values (independently) would make the universe uninhabitable for life as we know it. NOTE: What I mean by changing "independently" is when someone changes the constant value in their equation without changing the value(s) of any other constants.
3. The constants have an extremely large range of conceptually possible values.
4. Therefore, the number of values that permit life is very small.
The problem with this argument lies with (4) being drawn from (1), (2), and (3). Although it may be conceptually possible (premise one) to change physical values from their observed values, that does not imply that it is logically (or physically) possible (as stated in premise 4). Here's an example: If I ask you what 1048 plus 69 is, you probably would not know off the top of your head, and so it would seem "possible" in your mind that the correct answer is 1107 when actually the answer is 1117 and could not be otherwise out of mathematical necessity. Likewise, the values of the constants might be what they are out of mathematical necessity (what if there is some fundamental mathematical principle that determines them all?) even though we don't see how. Of course, we have no proof that this is the case, so perhaps it would better to think of what I just stated as the "mathematical necessity" hypothesis (a possible explanation which may or may not be true) and to compare it to the God hypothesis at a later date. Nevertheless, we still have a valid objection to the fine-tuning argument, even if it is somewhat weak, in my opinion.
Robin Collins, a well-known proponent of the fine-tuning argument, has this to say about the above objection:
"[T]he problem with postulating such a law is that it simply moves the improbability of the fine-tuning up one level, to that of the postulated physical law itself. As astrophysicists Bernard Carr and Martin Rees note 'even if all apparently anthropic coincidences could be explained [in terms of some grand unified theory], it would still be remarkable that the relationships dictated by physical theory happened also to be those propitious for life'" (1979, p. 612). [See his paper "God, Design, and Fine Tuning"].
I find this response faulty on several grounds: first, God is improbable, and so attributing the fine-tuning to God also transfers the improbability upwards. So, if the "mathematical necessity" hypothesis suffers from the flaw of not resolving the improbability of the universe, then so does Collins' alternative proposal (God).
Second, we must live in a universe that is logically possible, and so if there is only one kind of universe that is logically possible it would have to be our kind. Why is it that Collins missed this objection? Maybe he is thinking that, if we ignore the fact of our own existence momentarily, then it would seem improbable that any one type of universe is logically (or mathematically) necessary (as long as we have no mathematical proofs that one type of universe actually is necessary). The a priori probability of our universe being the only mathematically possible one does indeed seem low. However, the fact that we know our universe exists means that it must be completely logically and mathematically consistent. We do not know this about the other "universes" scientists might describe in their equations. If we grant the hypothesis that only kind of universe is consistent, then our universe must be of that kind. So the only question of probability is this: what are the odds that only one kind of universe is mathematically consistent? I cannot for the life of me think of how probable or improbable this proposal is, or even how to go about putting a probability on this hypothesis. So, in my eyes, the mathematical necessity hypothesis has an unknown initial probability.
Another point against Collins' objection is that if there is some mathematically necessary way that the universe must be, then not even God could have any leeway in altering that fact, since logically impossible and mathematically impossible feats cannot be done, period (this, by the way, is conceded by most theologians nowadays). So "transferring the improbability" to a mathematically necessary principle is not something that theists can use to their advantage, since God could not explain the percieved improbability of this anyway.