Hi Tim, having fun yet...? The 'background problem', or 'landscape problem' is the most difficult to theorize about, to the point of fully understanding this concept's necessary mechanics. Instead of me going through my entire system, let me attempt a straight symbolic logic explication of the 'background problem'__if possible__as I see all arguments are going to come back to this most fundamental of problems...
First, here's a few of your quotes, related to the problem, and my comments:
Btw, I’m not sure that I was using math to refute math in that quote you were debating. I was simply suggesting that macro systems are functioning as a product of micro interactions as described earlier. Thus, any macro math is a product or extension of the math which represents what is going on at the micro scales. Without the micro interactions we wouldn’t have the macro outcomes we witness.
Tim, the problem here is one of foundations of math and logic. There's two major math foundations; 1. Build up of numbers from the smallest to the largest. 2. Build down from the largest to the smallest. Both math foundations are correct uses, but if you'll more thoroughly notice, the most infinitesimal maths are actually build downs from some higher product, even if only the products between 0 and 1. The build downs at the larger end of the scale are actually foundations from rational infinities, or actual infinities represented by equilibriums and identities at massive scales, such as 10^900 = 10^900 representing the massive identities and equalities of two distinct sides, or just a random number chosen to found such formal math systems from/on. Of course the same can be done from the smallest up, also, as per 10^-900 and add or multiply and such__but how would we know of such math, unless we'd first discovered the large numbers to divide to such infinitesimal entities__as the large is what we as humans actually saw first(just a fact of Nature's evolution). The point is, the foundations just happened to have been discovered, top-down, or large to the smallest... Tim imo, any comparison of ideas is really a mathematical comparison, of some sort__No...?(as to the point of math unknowingly being represented in your ideas, as mentioned above.)
Though I may stand at risk of taking your statement slightly out of context, isn’t such a relational background independent model subject to having to internally prove all of its validity by such means as using the aspects it establishes such as math, science, logic, etc, within itself to establish its own validity?
Tim, many systems' uses is not one system, within itself… You can not deduct, deduction from deduction, to achieve the background of the ‘deducted from’__It’s still the original ‘deducted from’__Circular logics are not allowed. A –B, when B is A, is still A…(I'll explain below, if possible, since it's extremely complex to explain, understanding-wise, a singularity of logic, about itself.)
Tim, my statement was the singular subject of 'math' could not be used to prove the validity of the singular subject of such 'math', in and of itself. Logic, philosophy and semantics are additional singular subjects__which when combined with math, science and experimental evidence__can prove math, but outside of the subject of math__with extra-relational ideas and logics, etc. Imo, it always takes extra entity subjects to prove any statements or maths, such as experiments, etc. The singularities are not all, yet the problem is, one of em is all__The Universe... Now, as to more easily see the Universe's 'background problem', take the simple symbolic logic stated above; A -B, when B is A, is still A... What this means is that when we deduce the Universe's entire particle field, down to its absolute fundamental field or FS__We have A, and in order to stipulate what is to be distinguished from this most fundamental A(FS), we must name another A, a B, as it's actually the same exact field FS, therefore A becomes B, for clarity's sake, yet is still understood as the fundamental substance A, i.e., still the FS Field__as we have no other language when dealing with an absolute singularity__until volumes, frequencies, velocities, etc., are added. Yes we can write it A -A' = A'' = part of A, with a different volume as per Av, but the first Av must be specified, and it's a true and possible variable unknown__so, do you see what I'm getting at here, Tim?__Logic itself has a major problem of self-distinguishment/ability, at its most fundamental level__the logic singularity. Yes, we can say A and A + PSF, but what would we use to distinguish the naked A FS-substance as__where even the naked A must be A + PSF, at all times, so it's all a matter of wording and understanding of supervenience, or how A(the fundamental FS) itself, depends on the PSF for definition, and the PSF(A +PSF) depends on A to be itself. Tim, it's simply an abstraction to separate A and PSF to discuss what is actually A__so A -A, being a reduction of part of A' from A is a reduction of part-self from self__yet having no true definition of difference possible, as we have no definition of the initial Universal volume__unless we abstractly set it at some tremendously high value such as 10^80 solar masses, or some other arbitrary number like 10^900kg, etc__as there are no known factuals of A(thus the independence of true background), at either end of the measurement spectrum(there's also no knowledge of how small the PSF actually goes). All measurement is a created system, at limits, and the higher we set these limits__or the lower in the case of infinitesimals__the more accurate we can make our math and measurement systems__This is why its oh so important to fully understand limits, as there's also the great problem of the limits to our logic and understandings if not fully interpreted. Reduction from the self-same singularity of Universe A, to a part of Universe A, when A is only a blind black-box unknown, is a bit confusing, unless one uses symbolic logic to distinguish what one is actually relating to. Therefore, generally stated; A -A' = A'' or A -B = C, as the same__since the FS mechanics is always FS -FS represented by different volumes, times, distances, temps, velocities, frequencies and such or whatever... Tim, it's just if you don't use symbol logic or semiotics(sign systems) to talk about such singularities, ones terms and meanings become far too confusing and conflating to interpret between different interpreters__and this is why symbolic logic and semiotics were created, in the first place__to make explanation even possible, at the singularity's 'background independence' level...
One volume of FS is or can be totally different(unstructured vs. structured) as you already know, but we must stipulate these exact differences when speaking of all the physical state differences, so's understanding between different parties is possible__it's that simple, Tim__Accurate language, maths and logics are always required. Now, as to discreteness and deterministic states__How would such states be proved, when we are only viewing the entire Universe, which is really a singular continuum, as per information flows, of superfluid states__anyway?__The state of A, when we don't actually know much about the state of A, except that A Exists__The Universe...? If you state that PSF applies to the entire states of the Universe, you have no possible method to prove this, even though it may be the state we find QM in, by way of present scientific measurement(except for superfluids), but there's nothing to prove the FS Universe doesn't exist in fluidic states far exceeding the minimals of the stated PSF's, as per Planck's present scales, and there's actually no absolute evidence as to the state of our Universe being finite, infinite, expanding forever, or possibly contracting at some date in the future. There's a lotta' guesswork in physics__but when one thoroughly investigates the whole of it, there's a lotta' false guesswork__and it's our job to separate the wheat from the chaff. This is why we always must state whether we are stating and using abstract ideas and theories, or they have been scientifically experimentally proven.
Yes, c seems to force the quantum world to have some relationship to a PSF grid of interpretation of volumes, masses and such__but I can't find the math necessary to match it up__yet__since it needs to cross the 'math gaps'. And, I full well realize there are many 'gaps' in our logic and knowledge systems, also__that create the present states of incompletenesses. I'm just simply trying to show you, we can't know as much as you are quite often stating about the absolute FS mechanics, determinism and discreteness__especially since A is always necessitated to be a property of A, which just as easily interprets to a fluidic FS-Substance Field, and more-so, than any discrete substance field(As such would seem to destroy the very meaning of the em-field.), since all He4 is known to be superfluidic, with no discreteness known to exist in its most fundamental states. The individual fermion and boson states seem to blend into a super-flowing single state__indistinguishable to present science, at the best resolutions of QM__so far... The question then becomes, Tim__Is A, A...? Or, is A, -A...? Or is A, A and -A...? And herein is the most fundamental abstract problem of both logic and math__the para-consistencies of both math and logic in relation to identities and non-contradictions... Ever since the Non-Euclidean and Non-Aristotlean Logics and algebras/maths were invented by Boole, Lobchevsky, Grassmann, DeMorgan, Clifford, Peirce, Vasiliev and company__we've been left in the interpretation problem pool of 'Peirce Abduction' to figure it out, and btw, Peirce is the first of the relational logic and algebra books ever written, which all these modern singularity interpretation problems, pool around__He wrote the first theses about relational-extended logics and maths, in 1869 and 1870__not Frege, as much of the academic world falsely thinks...
Tim, in the end__The Universe is a single atom, we abstractly subtract from itself__yet it's always that same single atom__as far as our logic, math and science can tell__And our fundamental modal logics of possibility, impossibility and necessity__absolutely necessitate this__or we have no truth systems possible, as all full quantification logic is dependent on modal existence and non-existence proofs, all the way from the early Greeks to today. Discreteness's and determinism's are no more than our abstractions ascribed onto the singularity atom of the logical continuum interpretations, and when you go down to the bottom measurement of QM, you always find the superfluids acting as a highly complex super-positioning singularity__and we possess no science to measure any differently__no matter how much abduction is thrown at it__He4 tells another story, as does all the math and logic, at that level...
The experiments, to date, prove non-discreteness and non-determinism or indeterminism, uncertainty and incompleteness... That's the science of the maximum and minimum levels of all measurement__to date... Iff you stay within sound and 'necessary' logic and math, you have no other necessary truths even possible... Now say; "But absolute discreteness and absolute determinism are counter-intuitive, and not easily grasped by classical, relative or quantum logic and mechanics." But, such thinking is simply going beyond any conception of classical, relative or quantum science, logic and math__we actually have access to, imo Tim...
May not be the best of explanations Tim, but it's the best I can put together, for the simplest and easiest understanding of these ideas__though they be extremely complex to understand... The way I most easily understood it from David, was to see the entire Universe as a marble, as a single atom, then I was able to see all motion contained within itself__self-containing the marble as a FS-Continuum of FS-Motion__as the Universe has no__'absolutely zero'__outside information. We are in the Universal FS-Motion__The FS-Motion is also inside us, but 'us' is still in the Universal Motion's FS-Singularity of Non-Singularity, by Abstraction__Only__The Human Observer Position...
Abstraction is not 'The Reality', only 'The Universe' Is 'The Reality...'
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