Marcel,
There are so many things I can discuss with you, but I'll pick and choose what I think are the most important differences between our views.
"Because all truth system are logically incompatible with each other, the axiomatization of all of physics is, in my opinion, impossible ( i.e. no physical TOE) On the other hand, the underlying reality can be axiomatized under natural metaphysics, as the unreachable cornerstone of all our experiences."
Indeed, all truth systems are logically incompatible with each other and this is the essence of Gödel's result about the impossibility to have a TOE of math. However, a TOE of physics is an entirely different matter. Find one logical inconsistency in nature. There is none. Order the platonic world of math in a way that avoids all contradictions and you get the necessity of time (among other consequences). Time is a necessary condition to avoid self-referencing contradictions.
lebel:1)"Find one logical inconsistency in nature. There is none" The universe obeys logic-is operational on logic = only one substance allowed!
2)"Time is a necessary condition to avoid self-referencing contradictions." it has to be so in all points, everywhere.
1) + 2) = universe all made of time operating on logic
"[The first thing you want is to have existence independent of context (see the universal truth property] Why in the world would you want this? We make this distinction/ partition; the universe doesn't."
There are two definitions of truth: (1) the mathematical definition: a statement is true if it can be derived from the axioms (2) the physical definition: true is something corresponds to reality. The mathematical definition is very narrow and the same statement is true or false depending on the axiomatic context. 2+2 = 4 is true in the usual arithmetic, but it is false in the addition modulo 4 for example. But in nature, truth has a much larger reach and this is remarkable. It is this larger reach which gives reality its ontological value independent of any observers.
lebel: Again, it is a matter of definition: For me a truth is an absence of choice. A most certain truth is an impossibility. My essay is based on that definition.
"We could not have more opposite ideas! I say that the whole universe is made of an explosive process/substance that we call the passage of time. Incidently, I show in my essay the logical creation of the universe and it allows only one substance to exist; the passage of time. Just try to create the universe out of nothing without resorting to the logical rule of non-contradiction! Good luck!"
Not quite, I use to think in the past along your lines, but time by itself while necessary, it is not sufficient.
The key of explaining the birth of our universe is in an acausal domain and I think is linked with the multiverse idea. If the 3 principles guarantee the uniqueness of our universe, then to get to the multiverse scenario we need to break this uniqueness, meaning removing one or more of the 3 principles. And indeed there is a mathematical solution called split-complex (or hyperbolic) QM which has inequivalent representations (unlike standard QM). There are no logical contradictions, everything is consistent within a representation, and I believe this is the mathematical starting point of the multiverse investigation.
"1) I think that in general, we have a poor semantic use of some terms carrying multiple meanings and that need constant limiting adjectives, like time, nature, reality, empirical, truth, substance, cause, etc. For example, time means many things and if unspecified, it means everything and nothing specific."
This was the main point of Wittgenstein.
"2) Natural metaphysics can be built in a bottom-up approach as I did in my essay. It doesn't require one reject anything from physics. It explains logically what is observed empirically, the cause but not the metric."
As Wittgenstein put it, philosophy is mainly playing with words. What we need is unequivocal mathematical proof of our statements, in other words, we need physics axiomatization. A proof, is a proof, is a proof. When axiomatization is achieved, then anybody, even a machine can mechanically check the validity of the proof. No more fuzzy semantics.
lebel: "philosophy is mainly playing with words" which is what gave philosophy a bad name in the first place...
I believe I showed the way of how to do it. Compare math and reality. Extract core characteristics of reality: (independent ontology, unrestricted interaction, and infinite complexity). Then derive mathematical consequences from them. Prove the necessity of time, quantum mechanics, space-time in 4 dimensions, electroweak symmetry. This is already done. To do: Eliminate all supporting assumptions. Attempt to prove the rest of nature: strong force, standard model, quantum gravity, cosmology. Then physics axiomatization will be complete.
lebel: Philosophy and science used to be one and the same (PhD). This present schizo approach leaves pieces of the puzzle in the hands of two different group of people. Science build truth systems by adding truths. Philosophy produces opinion that add up only to more opinions. This means that in metaphysics, you get it all in one shot, or you don't. It must be self sustaining and cannot use any previous work or be based on citations. This is how it works. The core question is always the same; What do you want? Create one more description or to understand the meaning of all descriptions. You look for description, I look for the real stuff; substance and cause of the universe.
What I propose is first and foremost a paradigm. The existing mathematical results were all obtained as part of various unrelated research programs with their own motivation. But together they enforce the hope that the rest of the program will be ultimately successful.
lebel: Your essay could win for summarizing well the work on the subject. But your goal is that of a physicist. You are condemned to the hopes of a physicist, hopes that share the limits of physics. The exercise of finding the limits of physics was not to find more physics but rather to find out what comes next, after physics. What is physics missing and in need of?
I wish you well, Marcel
Florin