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The problem is that the AP ansatz uses Bayesian inference which relies on degrees of belief, or subjective probabilities, in the induction process, and doesn’t provide an objective method of induction. Hence, provides no objective probabilities.
Thus the probability of intelligent life in the cosmos is based on an "observed: one sample set- the Earth, and Homo Sapiens. This is totally artificial and not even random, since it is predicated on wild assumptions – including that the absence of contact signals from ETs constitutes “evidence of absence”. But as Carl Sagan once pointedly noted, “absence of evidence is not evidence of absence”. There could be hundreds of reasons why we have received no signals from advanced extraterrestrial civilizations.
One of the most compelling I can think of is based on what I call the brain divergence factor: the ETs that do exist are so radically advanced beyond us, they regard us akin to cockroaches or termites and not worth communicating with. On Earth, do you see any sane humans trying to communicate with roaches and termites? Hardly! Do you see sane humans transmitting radio messages across their yard to the termite nest yonder? Nope. It simply isn’t worth the effort because no possible meaningful exchange can result.
(Yeah, as some perspicacious poster said, cockroaches have been here longer than we have - hence merit some grudging respect for their evolutionary adaptative success and longevity. Right, but you still wouldn't invite a pack of them over for afternoon scones and tea and pleasantries!)
Thus, the absence of intelligent ET signals cannot be interpreted as an absence of intelligent life in the universe. In addition, the only means a genuine assay may be done – using interstellar spacecraft- isn’t available to us technologically. Thus, we cannot obtain any true sampling of actual planets in a direct sense, only use crude proxies and hunches based on them.
Thus, we are in a somewhat similar position to the Arawaks of Barbados who believed nothing sentient existed- no intelligent human life- beyond the “great Sea” (Atlantic). Because they had – up to the 15th century- beheld no evidence of such, they concluded no other humans existed in that direction. Of course, once Columbus and his lot arrived those delusions were forcibly dispelled. (Even then, tribal “sacred” leaders had to communicate the reality of the ships coming in because the Arawaks couldn’t believe their own eyes)
In this sense, one can even assert – analogous to the Arawaks’ – that AP is a childish and naïve belief based on inadequate evidence.
The argument that “we are here because the constants of nature are so and so” is also circular and ignorant. Of course we are here! BUT there may also be thousands of OTHER civilizations around too, so that it is the height of human parochialism to assert because we haven’t found them the specificity of the constants is all about “us”. This is terrestrial solipsism writ large, on the cosmic scale.
Another basis for non-visitation of ETs is based on what I call “entropic containment”. ETs aren’t visiting us because interstellar distances are so vast, and require such expenditures of energy – that the conversions needed to achieve (including manufacture of structures) results in an undesirable entropic additive that can’t be tolerated on assorted home worlds or even in their space vicinities. Hence, the really advanced and intelligent species have learned to stay put – conserve their enegies for more proximate uses, and cease any extravagant space-faring ambitions.
One can perhaps, despite these issues, make a case for what is needed for a genuine “anthropic principle” to be accepted, as opposed to an artificial ansatz. I believe the way to set this out is by using “necessary and sufficient conditions”.
For example, when a car crashes and the driver is killed, one can examine the necessary and sufficient conditions for that to have occurred.
Obviously, the “necessary condition” is that the car and driver had to be out on the highway in the first place. The ‘sufficient” conditions might have included: the driver’s blood alcohol level over 0.2, black ice on the roads near the intersection where the crash occurred, and the failure of the brakes at that instant.
Further scrutiny may isolate one of the above as a single sufficient conditions.
Now, in the analogous context, what would be the necessary condition(s) for a genuine anthropic principle? There is really only one: Humans would have to be the only species in the cosmos. If that is so, then ancillary and derivative conclusions can be drawn, otherwise not.
The problem is there is no way to establish such a condition with any real confidence (as I noted above), similar to the fact of establishing the necessary condition in the auto crash (that the car had to be on the road with its driver). If one cannot first establish the “necessary” condition(s), it makes no sense to move on to the designation of sufficient conditions.
Thus, until such time it can be ascertained (via genuine tesability and sampling - not proxy indices and hunches) that humans alone exist in the cosmos, there is no way to proceed with a genuine principle.
Hence, the really advanced and intelligent species have learned to stay put – conserve their enegies for more proximate uses, and cease any extravagant space-faring ambitions.
There is one exception I can see to this: a civilization that has developed the ability to fold brane-space and hence render actual enormous traversals of 4-D space-time unnecessary. There have been some physicists who written a lot about these possbilities, even published some intriguing papers - one of them is Jack Sarfatti.