on Full theories of time, existence and qualia

So, suppose there is no fully-communicable "full" theory of time. Call a theory T₁ about something full if it accounts for everything I know about the something, but I *necessarily* cannot communicate the entire theory to you, and you have an analogous theory T₂.

The initial idea was that I can't write down a full theory of time and thereby communicate all of it to you.

Let T₁ be person 1's full theory involving time, and suppose it has atomic elements/operations {x, y}. Let T₂ be person 2's full theory involving time with atomic elements {x, z, w}, so they're not isomorphic. In this case we can utter truths (or think of them), but sometimes we literally won't know what the other is talking about because we don't have the same referents (y versus z and w). T₁ could be isomorphic to a person 3's theory T₃ which has atomic elements {x, v}, but this de-emphasizes that they are not ontologically equal to each other so I'll ignore it. But suppose T₁ has a well-defined sub-theory T₁', and T₂ has a well-defined sub-theory T₂' such that:

(1) T₁' is isomorphic to T₂'

This isomorphism is the part of our theories where we can agree, in some sense, about "objectively true" stuff. Namely, the isomorphism, in practice, warrants the ontological assumption that T₁', T₂', and the definians or objects they use/assert to exist, such as the number 5, are independent of who or what system or whether there is anyone/thing at all instantiating/conceiving of it. Which interpretation you use for the number 5 doesn't matter, you can just as well take the set {0, {0}} as given by ZFC.

What's going on seems to be for a full T₁ the disjoint elements that "exist", according to T₁, are necessarily the only perspectives from which T₁ can be defined. A difference with set theory is that in set theory it's irrelevant what the elements {a, b, c, ...} of a set s "really are", you just assume the existence of the power set P(s), or at least some constructive schema independent of the content of s. On the other hand, suppose you have a set theory S that's "full". Suppose that, according to S, there exist two urelements a and b. Then there doesn't exist the set {a, b}, but rather the two set theories

(2) S_a = {a, 'b'} and S_b = {b, 'a'}

'b' is in a's theory (i.e. a's theory of a and b), 'a' is something in b's theory (i.e. b's theory of a and b). S_a exists in the same way a does, and S_b exists in the same way b does.

Suppose we start with elements a, b, and c. a and b exist, but c is a purple unicorn, and doesn't exist. The possible set theories are S_a, given in terms of {a, 'b', 'c'}, and S_b given in terms of {b, 'a', 'c'}, and that's all. There is no fact of the matter in terms of {a, b} or {a, b, c}. If c did exist it would only add S_c to the mix given in terms of {c, 'a', 'b'}. An iteration gives the four set theories from the perspective of a, b, S_a, and S_b, since each of these exists. Another iteration gives

(3) S_a(a, 'b', 'c', 'S_a(a, 'b', 'c')', 'S_b(b, 'b', 'c')'), ... S_Sb(S_b(b, 'a', 'c'), 'a', 'b', 'c', 'S_a(a, 'b', 'c'))

Existence

Since a full theory seems to have this ontologically-self-referential behavior it's reasonable you could have a "full" theory of ontological existence, independently of any considerations about time.

Let F_a, F_b, F_c, ... be full theories of existence of a, b, c, ... Then F_a's assertion that b exists is true only if it's symmetric in some way with F_b, or in the same equivalence class, or something.

Qualia.

That you can't communicate them is paradigmatic of qualia. One could argue the reason for this is the necessarily-exesitentially-self-referntial behavior again. Consider three theories of qualia

(4) the set s = {this experience of green}

(5) this experience of green is neuronal processes X, or else is correlated to neuronal processes X

If these theories are going to be full (and refer to qualia), then the variable this experience of green doesn't range over my experience of green *and* your experience of green (i.e. each instantiation of green in the universe). There is a different variable in some sense for each person, and there may not be, in the ontology of the theory, a variable in existence that ranges over both our greens. (It doesn't really matter you define a "person" to be, it could be a person, an information-bearing agent, a Super Universal Turning Machine, a donkey, or, on some accounts, a rock. The points are the same.)

Let green₁ be green as perceived by person1 and green₂ be green as perceived by person2. The set {green₁, green₂} is ontologically inconsistent, if the set is supposed to exist in the same way that green₁ does to person1, and green₂ does to person2, i.e. fully.

Instead the total information of the situation is given by two weaker theories with (2nd-order?) interrelations:

(6) s_person1 = {green₁, 'green₂'}, s_person2 = {green₂, 'green₁'},

w/relations between 'green₁' and green₁, etc. In (6) 'green₂' is person 1's theory of person 2's green₂. (A "theory" could be a conceptual referent, an unspecified representation, the concurrent physical instantiation of my theorizing, the set of possible interactions between person1 and person2, etc. The idea is that ) Since iterating the process never yields a legitimate assertion that green₁ = green₂, the ontology is underdetermined, in the sense that for all we know my green could be your red (spectrum inversion!). This is consistent with the laws of physics from each person's perspective. Schematically, the idea is

(7) person1(green₁, 'green₂', physics) [physics] person2(green₂, 'green₁', physics)

The physics in this case are the isomorphic subtheories mentioned in (1). This is a very different kind of model than either (physics) or _x(green₁, green₂, physics), where x ranges over everything in the universe.

So, there is a calculus of qualia there. But, more-or-less, it's based on the single property of the ineffability of qualia. A more sophisticated treatment would account for other properties. The place to start is Lormand's list of 6 properties of qualia: Intrinsicness, Directness, Reliability, Unanalyzability, Ineffability, Privacy. Other properties should be considered, whether they turn out to be properties of qualia or not. For example, for quale q,

(8) q is a property of q

and

(9) q is epistemologically objective and ontologically subjective (and exists)

I'm told Searle also considers (9) (references welcome to all the ideas of these posts.)

The question is, which of these 8+ properties do qualia have, does time have, and does existence have? For example, it is perfectly reasonable to wonder, as in (8), if existence exists, whatever the eventual consensus turns out to be. Also, is (8) true of time? Temporal flow seems to be a property of time itself. I would also argue that being green is an ontological property of green itself... In fact it's plausible that time and existence are special cases of qualia (ones that are more public than green, but still basically have most of the properties of qualia).