By my lights, the following considerations are sufficient to show that the argument from fine-tuning fails to make theism more likely than not.
There is an equally good, rival explanation of the apparent fine-tuning of our universe. For the fine-tuning for life would be equally well explained if our universe were embedded in a vast “sea” of infinitely many other universes. Imagine a natural process or mechanism that continually generates universes (call it a 'cosmos generator') – perhaps something like a giant quantum field. Each time it pumps out a universe, it gives a random combination of values to its fundamental constants of nature. So on this hypothesis, infinitely many other universes exist – or at least lots and lots – and each one has a different set of values for its fundamental constants. Most of these universes have no life, since only a few possible combinations of values of the constants are life-permitting. But some do (e.g., ours). If so, then the explanation for why our universe is "fine-tuned" for life is that we exist in one of those few cosmoi – out of the trillions upon trillions of cosmoi that exist -- that has the “right” combination of values. This hypothesis is just as good as the hypothesis of intelligent design, since it's a hypothesis that explains all of the same data; so we have no persuasive reason to prefer the hypothesis of intelligent design to this one.
Objection 1: We've never seen such a multiverse, and we have no good evidence that it exists.
Reply: This objection fails to see that the point of constructing these theories in the first place is precisely because we have no way of directly observing the cause of the apparent fine-tuning of the fundamental constants of our universe. And it's just part of the nature of such theories that they accrue probability just to the extent that they can explain the range of data in question. Thus, it's not true that we have no evidence that a multiverse exists. Rather, the extent to which it can explain the data *just is* the grounds for according it some degree of probability. And the same is true of the theistic hypothesis, of course -- we only have reason to think that *it* is probable to the extent that it can explain the data of apparent fine-tuning. That's what the theory-data relationship is all about.
Obection 2: The hypothesis of a cosmos generator only pushes the problem of apparent fine-tuning back a step. For a cosmos generator would be a very complex and intricate process/mechanism. If so, then we would need an explanation for the fine-tuning of the cosmos generator itself.
Reply: (i) Of course, we can just stipulate that, as a part of our hypothesis, the cosmos generator has its laws and constants *of necessity*, i.e., that there is only one possible set of laws and constants for the cosmos generator. It’s not important that this stipulation is independently known to be true; it need only be a hypothesis with no features for which we have independent reason to think false or impossible. Why is it ok to make these stipulations? Because it's a *theory* constructed to explain a range of data, and that's just the way it is with theories in general. And notice: This is both true of this hypothesis and the designer hypothesis -- both theism and naturalism are treated in the argument as sort of large-scale scientific hypotheses that were generated to explain some fundamental features of the universe. (ii) But even if one rejects the "necessary laws" stipulation -- i.e., that the laws governing the nature and functioning of a cosmos generator must be contingent -- the objection is still pretty dubious. For it's an objection that applies equally well to the theistic hypothesis. For both hypotheses grant that there is some brute, unexplained order that can have no further explanation -- the structure and the laws governing the cosmos generator on the naturalistic hypothesis, and the intellect and will of God on the theistic hypothesis.
Objection 3: OK. But even if we grant that both hypotheses are saddled with some brute order that can have no further explanation, still, the theistic hypothesis is *simpler* than the naturalistic “cosmos generator” hypothesis. For on the cosmos generator hypothesis, the explanation of the apparent fine-tuning of our universe requires that there are lots and lots of other universes -- perhaps infinitely many. By contrast, the theistic hypothesis explains the apparent fine-tuning of our universe in terms of just a single entity: the god of traditional theism. Thus, even granting that theism leaves unexplained and brute at least *some* order (God's intellect and will), it's a much more economical/parsimonious explanation of the data of apparent fine-tuning.
Reply: The objector mistakenly assumes that there is only one kind of theoretical parsimony, viz., *quantitative* parsimony (i.e., the explanation postulates fewer entities). However, as David Lewis has taught us, another type is *qualitative* parsimony (i.e.,the explanation postulates fewer *kinds* of entities). And while the theistic hypothesis is a much more *quantitatively* parsimonious explanation of the data (it explains all of the data in terms of just one entity, viz., a god), the naturalistic cosmos generator hypothesis is a more *qualitatively* parsimonious explanation of the data (since it explains all of the data solely in terms of one *kind* of entity, viz., material objects). And it's not clear which type of theoretical parsimony is more important here.
Thus, it seems to me that the theistic and multiverse hypotheses are roughly equally likely given the data of fine-tuning.
 This line of reasoning is based on Peter Van Inwagen's in his Metaphysics, 2nd edtion (Westview, 2002).
 Notice that this is precisely the naturalistic version of the objection to the design argument that the theist is unwilling to countenance as legitimate to her own hypothesis of design (i.e., the "who designed the designer?" objection).
 This seems to me where the real force behind the "who designed the designer?" objection lies: both theism and naturalism are saddled with at least *some* brute order; so why fault naturalism with a "problem" that applies equally well to theism?
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