I’ve been writing about this more today in another venue, and will try to answer this last one , because You have given me more than I can answer at this late hour. So to further this, St. James intimated as such. as to the reasons why the relationship between Reality and Perception is better untangled , at least from an analytical mind’s point of view , from general to specific propositions.
I think Reality can be taken as a given, and work itself down to perceptions, in spite of , and we talked of this previously here, mistaken notions between precepts and sense data.
Given what we know about the logical basis of modeling in general, it can be safely said that any model needs reconstruction based vestiges , which had at one point cohesive qualities to form such a model.
Such a reconstruction must follow the probable type of the deconstructed ‘original’ or becomes virtually bound more to probable formal arranged centers of operation, which adhere tacitly(Polanyi) to embedded ones,with it’s structural patterns of mathematical notation.
This is merely a derivation more from more general or hidden particulars for processing more identifiable
patterns.
I must excuse myself for this intuitive approach relqted to philosophical underpinnings , whereas it may have relevance as well to mathematical abstraction.
I agree with St.James that reality consists of precepts of posited bits but such position is not some juxtaposition of formal and substantial elements, but of interaction between them , not as some form of transcendent. Although a precept appears as priority , it is only by conventional meaning does it appears as such.
Reality vs perception is not a priorotozation of the shift from a deductive logical sequencing of meaning bits to an inductive ones, since modeling reconstructs reality through changeless bits of information which are brought together by the most probable patterns toward saturation of redundant bits.
This process goes on until a successfully modeled reconstruction is achieved, where its sequentially repeated through varying integrative cycles.
This is based on the most general philosophic notions , and therefore hypothetical.
The trend in computation is less and less reliance for proofs and more and more reliance on the presumptive integrity of the hypothetical acceptance reality as a given.
There is a time approaching when only very complex computers can prove the various levels of lesser computer generated sub-programs. This time ideal is fast approaching. , The objective integrity will need to be confirmed by the operational coherence of all subsequent systems. But here I feel I am not saying anything new.