tl;dr: The extremely low probability of a life-permitting universe points to design rather than chance. Appealing to infinite time or a multiverse to explain fine-tuning is an ad hoc move to rescue naturalism, not unlike a "God of the gaps" argument. Positing a purposeful God as the cosmic designer is a simpler and more illuminating explanation for the extraordinary fine-tuning of our universe than an infinite multiverse generator. The "God of the gaps" charge cuts both ways, and "God of the system" is the more parsimonious and compelling explanation given the evidence.
“We know the probability of an intelligible, life-enabling, finely-tuned universe is essentially 0, given the amount of time evidence, so we fill the gap with more time.”
The extraordinarily low probability of a life-permitting universe by chance alone seems to point to design or intention rather than mere happenstance. Physicist Roger Penrose calculated the odds of a low-entropy initial state of the universe conducive to life as 1 in 10 ^ 10 ^ 123 - a vanishingly small probability. In the face of such staggering improbability, appealing to infinite time is basically a special pleading to make chance a more plausible explanation and avoid the implication of design.
Invoking a multiverse of infinite universes to explain the fine-tuning is essentially an ad hoc hypothesis aimed at dodging the conclusion of a Cosmic Designer. An ad hoc argument is one that is introduced to save a theory from being falsified, without having independent empirical support of its own. In this case, an unimaginably vast number of unseen universes are posited to account for the apparent design of our universe, without independent empirical evidence that these other universes exist. This is really no different than invoking an supernatural God to explain the design - both are naturally unverifiable explanations introduced to reinforce a worldview.
However, philosopher Richard Swinburne argues that a good explanation should have the characteristics of simplicity and specificity. A single logically omnipotent God is a simpler explanation for apparent cosmic design than a multiverse generator churning out infinite unseen universes. And a purposeful God is a more specific explanation for why our universe in particular is finely tuned for intelligent life than a sea of random universes where we just happen to find ourselves in one of the extremely rare life-enabling ones.
A commitment to naturalistic materialism forces science to stick to explaining things based on known natural laws and chance, without introducing supernatural causes. But this presupposes that natural laws and chance are ultimately sufficient to explain the deepest layers of reality. The fine-tuning of the cosmos is the very kind of evidence that should lead us to question that presupposition and consider that a supernatural Intelligence might be the best explanation for why the universe is intelligible and life-enabling.
Positing infinite time or infinite universes to dissolve the fine-tuning problem is really just an ad hoc move to paper over a gaping explanatory hole in the naturalistic worldview. Theists are often accused of making a "God of the gaps" argument, but the "multiverse of the gaps" or "infinity of the gaps" arguments are no less a case of reaching for a speculative and empirically unsupported notion to save one's paradigm. And at least with God there is an inherent explanatory power to the notion of an intentional, omnipotent being as a cause for the cosmos, unlike a purposeless multiverse generator.
Given the evidence, “God of the system” is a much more elegant solution.
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