Hi Peter,
In Section 1.3, you mention that natural law, must first exist in an immaterial manner, "...preceding its first 'materialization' not only temporally but also ontologically".
Agreed that the notion of Scientific Platonism -- the idea of an objective immaterial reality -- is controversial. At first, identifying the 'objective immaterial' as mathematics, and that in turn as 'being objective' makes good sense, insofar we -- multiple diverse people -- experience mathematics in a way that is both repeatable and surprising (ie, it feels scientific).
However, there is also implication that the mental (ie, the idealism of mathematical models, etc) ontologically precedes the physical realism (ie, an actual 1st person experience of material causality, reality, etc). That latter aspect seems invalid -- to not be the case -- insofar as the experience of the physical consistently includes elements that we could not have predicted in advance, on the basis of any deterministic theory currently available, or even on the basis of *any* possible/potential future theory that could be proposed, even in principle.
The idea that 'reality' 'consistently includes inherently unpredictable measurement aspects' is well modeled by QM, as a theory of evolving potentials, as long as we do not attempt to go too far and moreover posit a 'determinism' of 'hidden variables' -- re-introducing the same old problems all over again by continually trying to model all that is real with only mathematics.
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In section 2.1, you write "Irreversibility cannot be reduced to the sole fact that the corresponding system never returns to its states occupied in the past".
This is a claim. Why is it true? Why *not* posit a basic and irreducible asymmetry in the relation between observer and observed, when measuring -- gaining information about -- some inherently random process, as a axiom?
Perhaps the actuality of objective potentiality -- unpredictability -- is the very thing that separates that which is completely model-able in system terms and that which is real, in actual terms.
You might want to see my one page summary of why a basic fundamental temporal state asymmetry might be "built in".
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In section 3.2, the notion of 'potential' and 'energy degradation' both refer, inherently implicitly, and moreover inevitably, to an entropic arrow of time. However, this in itself, in turn, depends on a notion of 'randomness' as being inherent in the 'real', even though there is no corresponding characteristic in the lawful substrate of the platonic ideal (ie, the symmetrically reversible mathematics, models, etc). As such, the dis-connect is actually between how the 'real world' cannot not have some type of embedded randomness, (potentiality) whereas the group theory models simply/ultimately do not.
As such, it can be argued that the ontology of the real is actually based on the mixture of the random and the pure, rather than just on the basis of what can be fully and completely predicted as an outcome of theory, no matter how modeled, what mathematical forms are used, etc.
The notion of 'ordered to disordered' (as entropic arrow of time) is considered as 'objectively meaningless', insofar as fully/absolute lawful causation/determinism can contain no new information (no novelty). This is in clear contrast with, and distinct from 'life', 'alive', etc, insofar as the notion of 'choice' is regarded (subjectively at least) as 'meaningful' in direct proportion to the degree that it is novel, contains new information not derivable from prior states, etc, (ie, it in at least some irreducible way is in-deterministic, non-rational, random).
Thanks,
Forrest