Here are three well known speculations about the nature of reality, implicitly or explicitly Bayesian, followed by my discussion.
(1) The fine-tuned universe. Quoting Wikipedia,
The Fine-tuned Universe is the proposition that the conditions that allow life in the Universe can occur only when certain universal dimensionless physical constants lie within a very narrow range of values, so that if any of several fundamental constants were only slightly different, the Universe would be unlikely to be conducive to the establishment and development of matter, astronomical structures, elemental diversity, or life as it is understood.Assume this is true. What can we infer? As the Wikipedia article shows, many writers claim one can infer X or Y, giving arguments that may appear superficially different, but which implicitly start with the assertion
it is unlikely that this fine-tuning occurred just by chanceso instead X or Y is likely true. Most commonly, X is some version of the multiverse idea, and Y is some version of "design" by a God or other entity. Now I agree this topic is interesting and worth thinking about, but I disagree that one can make any probability calculation that makes sense of "unlikely".
(2) The simulation hypothesis.
Again quoting Wikipedia, the simulation hypothesis
proposes that reality is in fact a simulation (most likely a computer simulation).
The simulation argument (ignoring any invented numbers) rests on comparing (i) and (ii):
(i) A hypothetical universe in which aliens simulate an arbitrarily large number ("many") of virtual universes
(ii) our one apparent real universe
and then argues:
many is more than one, so the former is more likely.
Discussion. There are many other ways in which reality might be different from what we perceive. Maybe I am dreaming. Maybe I am the only real entity. But the 3 speculations above suffice to illustrate my basic objections to any such argument.
(a) The string "8 + 1 = 9" is symbolic manipulation. It is a fallacy to believe that one can just plug into such formulas without thinking what the terms mean; it requires an intelligent entity (our hypothetical observer) to connect formulas to reality --- see further discussion here (xxx draft magical.html) especially if you believe "8 + 1 = 9" is invariably true. The same holds for Bayes formula. In everyday cases -- no worries. But in these speculations it is a serious issue: where is the observer and what information does the observer have? In the first two speculations it seems impossible to get started on an analysis: whether you posit the observer is in the perceived universe or outside it, either case begs the question.
(b) Within any alternative explanation one can multiply possibilities indefinitely -- there are many possible Gods other than the Christian one.
(c)
My take on the simulation argument.
Humans find it fun to simulate hypothetical universes, so let us assume the hypothetical aliens do, too.
As above, the simulation argument rests on comparing (i) and (ii):
(i) A hypothetical universe in which aliens simulate an arbitrarily large number ("many") of virtual universes
(ii) our one apparent real universe
and then argues that many is more than one, so the former is more likely.
One reason this is ridiculous is that, because once one envisages hypothetical universes one can replace (ii) by
(iii) an arbitrarily large number ("many") of hypothetical universes in which we would be real, not simulated, inhabitants.
And we now have no way to compare many with many.
(4) Not fantasy: chance of intelligent life in Earth. To illustrate where I draw the line between fantasy and non-fantasy, one portion of the large circle of questions around the Fermi paradox can be expressed as follows.
Given the physical nature of planet Earth shortly after its formation, what is the probability that a technological civilization (as we perceive such) would arise there sometime?Here I am imagining a hypothetical alien with our current knowledge of science, observing at the time of formation and seeing what we currently believe. (I have no objection to hypothetical aliens as observers, the issue is to specify the information they have). So I regard this as a non-fantasy question. It also satisfies the second test, in that as we learn more about the origins of life on Earth (see Nick Lane's fascinating The Vital Question) we can presumably improve improve our estimate. The practical difficulty is the third test -- what is the data or knowledge by which we assign specific numbers to some variant of the Drake equation (see this recent popular discussion), and how to account for possible alternate paths to a technological civilization? No numerical estimate I have seen is remotely convincing, but I am open-minded that future estimates might be.