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Every object is the combinatorial combination of atoms (or quarks/gluons/leptons if we dive deeper to the elements). Is there formal definition which combinations of atoms are "natural" and which are not "natural"? And which combinations of primitive motions are "natural behavior" and which are "unnatural behavior"? This is the question of my question. The remainder of my question just gives explanation of notions and sketches some initial arguments and reasoning - i.e. in the spirit of stackoverflow which requires to demonstrate what I have done myself to arrive at the answer.

One can say that such combinations of atoms which form the living matter that can not reproduce - such combinations are not natural. Or one can be more exact and say, that such combinations are natural but their behavior is unnatural if such behavior does not lead to reproduction.

E.g. notion of "unnaturalness" of same-sex marriage (by conservative thinkers) is one example of such definition.

But such definition is called into question if we invoke the modern technologies that - in principle (and philosophy is about principles) - allows one-parent babies or babies whose both parents are men. https://www.theguardian.com/science/2018/oct/14/scientists-create-sperm-eggs-using-skin-cells-fertility-ethical-questions is popular summarization of this research effort:

Making artificial gametes could introduce new permutations into how we reproduce. The somatic cells of both men and women could in principle be transformed into eggs and sperm. So gay couples of both sexes could have babies that were genetically related to both parents, although male couples would need a surrogate mother. Rather more challenging is the notion of a single individual conceiving a child from eggs and sperm both made from his or her cells, what Greely calls the “unibaby” of a “uniparent”, which could become some grotesque vanity project. Equally disturbing is the prospect that genetic parents could include, say, the very elderly, children or even foetuses. The ability to make gametes from any bodily residue we leave lying around – “like cells you leave on beer bottles and wine glasses,” says Greely – opens up other alarming scenarios. You can imagine the celebrity paternity suits already.

One can argue that the use of technologies delineates the boundaries between natural and unnatural. But the reproduction question (matter of 6th commandment) is the example again. E.g. computer science (and evolutionary programming specifically) explore the mathematical nature of reproduction and genetic inheritance and recombination during this process. The framework is quite general - it considers s.c. orgies as well which is the term for multi-parent recombination https://link.springer.com/chapter/10.1007/978-3-642-18965-4_6. One can build models that try to explain why the existence of exactly 2 sexes is the most optimal balance. Because 3+ sexes can speed up evolution, but 3+ sexes involves more complex physical implementation and mating behavior. This can explain why we have seen 2 sexes up to now, but this does not prevent the emergence of life forms with 3+ sexes.

So - again. If theory and general framework gives explanation of existence and possibility of 2 or 3+ sexes then why should be call some combinations (2 sex life forms) natural and some combinations (3+ sex life forms that could emerge in the future during the evolution process) unnatural? Why we should call some combinations natural only because they have emerged up to date in the evolutionary process and why we should call some combinations unnatural only because they have been created in the lab (e.g. by genetic engineering) to speed up the processes but they could also emerge "naturally" (i.e. outside the lab and human intervention) at some point in the future?

Should we approach the notion of "naturalness":

  • from the probability point of view? Those combinations are natural whose probability is the most likely? But creativity (e.g. sacral art by Giotto) can be rare, but it is considered somehow good or natural in many cases?
  • from the fitness point of view? Those combinations are natural whose fitness to survive and reproduce is the highest? But cyborgs and transhumans can be extremely fit to survive and reproduce but one can hardly call them "natural"?

My understanding, based on examples mentioned in this question, is that there is no fundamental or transcendental meaning of "natural" and hence there is no meaning for the "natural law". But is there some more conscise and more professional insight into this matter? Are there formal definitions of "naturalness" that considers the objects/subjects as the combinations of elements and their behavior as the combinations of elementary movements?

I predict that many can argue against may mechanistic understanding of the existing objects/subjects, many can argue that living creatures or intelligent creatures are something beyond this mechanistic interpretation and hence my call for the delineation between "natural" and "unnatural" combinations of elements or movements - such framework is not appropriate.

But can we stick - during this question - to the framework that we are considering such combinations.

I argue that the modern "combinatorial" views is quite sophisticated. I can use 2 arguments for this:

And to add more confusion - my question assumed that there are some unchanging elements, movements and the rules of their combination. But current view of the physical sciences does not prevent the slow change of fundamental constants. Even more https://arxiv.org/abs/2104.03902 article considers the Universe as the neural network that can learn its own rules gradually and so - we are living in the universe which learns its own rules how to exist in the future. So - this is additional argument against the "natural" and "natural law" again.

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    "Natural" as used in social arguments of the kind used to deny some rights is usually a fallacy that some times appeals to what is traditional, some times to what is popular and some times to what is usual in some other parts of the world. In all cases it is a fallacy.
    – Nikos M.
    Jun 30, 2022 at 22:53
  • If there is no philosophical meaning to the term "natural", then the natural law is just special case of positive law. I opened Law Stackexhange question about that law.stackexchange.com/questions/81642/…
    – TomR
    Jun 30, 2022 at 23:10
  • I don't think anyone argues against same-sex marriage on the grounds of what is natural. I have seen arguments against homosexuality on those grounds, but not without an extensive discussion of what "natural" means and why "unnatural" is to be avoided. What particular author do you have in mind here? A link would help. Jul 1, 2022 at 4:54
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    @TomR I am not aware of a "formal" definition of natural. In an intuitive sense we have an understanding. Next we can say natural is anything realizable not in conflict with other natural processes (of higher value). I would use this as a tentative definition. Although others might disagree.
    – Nikos M.
    Jul 1, 2022 at 13:05
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    @TomR for example, in this sense, a machine that sucks all the oxygen and produces carbon dioxide, although realizable is unnatural (eventually it will suffocate all life). Homosexuality on the other hand, is realizable and doesn't conflict with other natural processes in this sense.
    – Nikos M.
    Jul 1, 2022 at 13:30

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