Dear Alexey, dear Lev,
I read your very impressive article several times, there are so many things to say.
First, it is highly pertinent to recall Descartes' dualism while showing that the "refutation" of the latter would need a lot of farfetched, hypercomplex and self-refuting presuppositions. The established mainstream thinking says that dualism is "scientifically outdated." Well, let us accept that "the human brain is a set of neurons, the consisting of molecules and so of atoms." In other words, let us accept that "the brain is matter." Yes, but we do not need be great neuro-scientists to see an obvious problem neurosciences en vogue, despite its obviousness or rather because of it manifestly do not want to consider: even if neurons are "matter" - nobody denies it - the relations between these neurons making that a brain is a brain and not just an fortuitous conglomeration of matter , these relations are governed by an immaterial logic. So, far from showing that dualism is "scientifically outdated", a functioning brain in turn expresses dualism in a particularly intuitive way difficult to deny. It would be hard to deny the immateriality of logic, given that the the latter is interpreted by immaterial data as well as by very different material phenomena. The mainstream argument that logic - immaterial or not - "is created by the human brain" leads to circularity: the functioning of the brain being governed by a logic created by the brain logic governs. Of course, logic is just a restrictive aspect of the functioning of brains, but even this point remaining reducing per se shows that there is a gap between matter and immaterial preconditions for the occurrence of mind and thought. So, saying that the emergence of life and the emergence of mind/thought from matter cannot be considered as the same, you are absolutely right. Indeed, the mainstream conception of evolution according to the schema "inert matter 竊' living matter 竊' human mind comprising self-consciousness" manifestly is undermined by grey areas and misses the essential.
Your analysis in terms of Epimenidic structure - a striking formulation; with your permission, I will quote you in a paper on serious lacks in evolution theory I am finishing - is really impressing. I think, under a given criterion leading to Platonism, Epimenidic self-refutation is equivalent to circularity used in my own paper as an argument going in the same sense. (i) By definition, circularity, to be broken, needs references exterior to the considered system. It is the same for Epimenidic self-refutation. It is the same for circularity. Stated by a on-Cretan, the proposition "All Cretans are liars" - true or false - would be formally consistent. The the non-consistency of the liar paradox results from the fact that Epimenides is a Cretan and so belongs to the "considered system." In our context, this first equivalence leads to Platonism required in the name of consistency. As I tried to explain it in my own paper, within a historical process, the sole way to escape the circularity of laws occurring "with" the first phenomenon governed by them is to admit the objective existence of immaterial laws preceding ontologically the phenomena expressing them. The immaterial aspect of these laws per se is underlined by the fact that these laws can govern materially different phenomena. Now, it is the same for Epimenidically self-refuting systems. Breaking the Epimenidic self-refutation of this system requires an logically external reference, and if the system in question is a "historical" one, this logically external reference in turn must precede ontologically the system to explain.
Your article and mine, beyond their differences, are complementary, and further discussions certainly will confirm it.
Here I would just highlight that both papers, each one in its own way but in an equivalent manner go against mainstream evolution theory founded on presuppositions which never would be tolerated in any other scientific area.
Concerning Epimenidic self-refutation, you know that since Gﾃｶdel's second theorem, a plethora of voices evoking "Turing machines" and so on abundantly recall that the consistency of a system cannot be founded on the sole resources proper to the system to be founded. This familiar refrain certainly is right, and even so obvious that it seems not necessary to repeat it in all occasions. Hence it is all more surprising that mainstream evolution theory is the great exception neglecting the foregoing and the cognitively and otherwise absurd consequences of this choice you describe so well in your paper.
My own approach ultimately is based on irreversibility, knowing that the latter - certainly "familiar", but "familiarity" does not necessarily mean "understanding" - generates philosophical problems probably unsolvable. The issue whether irreversibility is law-like or only fact-like remains controversial, but until further notice irreversibility is a fact and must be accepted as such. There is no way to way to escape irreversibility. The principle of generalized irreversibility says that for any system which apparently violates irreversibility, there is a wider system reestablishing irreversibility in its standard form. Here the notion of "wider system" can denote very different, divergent configurations. The impossibility of building a perpetuum mobile represents a good example summarizing all the extent of the issue. Whatever could be the - per se unpredictable - attempt to construct perpetuum mobile, there will be in one way or another a detail preventing the system from functioning. Or, if the system apparently does function, there is still in one way or another a detail connecting it with a wider system so that irreversibility is reestablished.
Usually, a given "scientific" approach whose consistency requires a "functioning perpetuum mobile" or any other form of absolute violation of
never is taken seriously.
So, once again it is all more surprising that mainstream evolution theory is the great exception presupposing absolute violations of irreversibility as the very foundations of the approach.
In my own paper, I show that "cumulative selection" categorically defended by Richard Dawkins, far from circumventing irreversibility, does confirm in it generalized formulation, but in the context of our discussion here, it is not the most important point. The main issue is: why does evolution theory join so farfetched adventures like the denial of Epimenidic self-refutation as well of generalized irreversibility? And I think, in both cases, it is to avoid at all costs Platonism, i.e. to avoid at all costs the idea of immaterial factors behind the material expression of biological evolution.
I suppose, above we agreed that the unique way to escape Epimenidic self-refutation within a historical process passes by Platonism, and it is the same if you want to escape generalized irreversibility. Indeed, since (i) any material system apparently going against irreversibility must be supported by a wider system, and (ii) a circularity-free explanation of a historical process refusing the idea of laws occurring "with" the phenomena they govern,
necessarily implies immaterial laws preceding ontologically the corresponding phenomena.
It would be hard to grasp the significance of the concept of mathematical beauty without referring to Platonism. From a Platonist standpoint, it is easier, I think, you agree. Here the best way probably is to come back to Plato's original thought, even if it often had been said that Plato would not recognize himself in modern mathematical Platonism. Perhaps it is true, but anyway, according to Plato himself, beauty is nearly the same as truth. In fact, it is a triad with a moral dimension, but here we can neglect this point. By contrast, it is important to point out that for Plato beauty as well as truth are on the top of immaterial, immutable and eternal "ideas" which, existing objectively, independently of human thought, constitute the "intelligible world" or "heaven of ideas", knowing that our material world we take for "reality" or "world" tout court is just a rough and imperfect representation of the "intelligible world" as the authentic reality. So, on the one hand, "beauty" according to Plato has nothing to do with material objects common sense finds "beautiful".On the other hand, Platonist beauty must be seen in relation with truth and eternity. Your quote of Dieudonnﾃｩ is highly significant. The unity of mathematics mysteriously half-seen ((I am trying to translate "entrevoir"; not being satisfied by "to half-see" found on Linguee", I appeal to your intuition focusing on "mysteriously.")) through partial but consistent and so distortion-free discoveries necessarily presupposes the existence of an absolutely consistent global mathematical edifice preceding ontologically any perhaps contingent human discovery, in other words, the transcendent existence of a perfect mathematical edifice beyond space and time, so inscribed in eternity.
But now there is a further question. The contest subject concerns "aims" and "intentions", so something essentially temporal. Between eternity and temporality, a gap opens up. The standard discourse sees problems how to imagine the passage from "familiar" temporality to eternity. Personally, I think that in the eyes of convinced Platonists should not feel troubles with eternity. The real problem is the inverse: how to position a temporal/contingent world in respect of eternity? (Always, from my personal standpoint, I do not find "mysterious" the unity of mathematics.) Christian theology with its essentially Platonist roots rightly considers the relations between eternity and temporality - implying de facto matter or equivalent - as a fall. But in the context of the fqxi subject, we have to try to explain how eternal mathematics can lead to temporality. At the end of your essay, you quote "Beauty is the Moira and Eileithyia for birth.", whereas your own words "As
we cannot conclude from "stoneness" about the essence of a sculpture, so from the formality of mathematics, its mere material, one cannot deduce its ontological essence or espy that essentially it is the universal beauty of all worlds." express in an impressive way the gap between eternity and temporality. But how to explain the threshold crossing of between eternity and temporality having nevertheless led to humans like you and me able to discuss about temprality and eternity?
Looking forward to further discussions,
All the best