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# The Problem with Science

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Buffy Ho! Nice to see to here, but watch what you say about Kurt, I don't think that's quite what the trouble is.

Dick, the definitions I was talking about were what you mention in parentheses:

The statements you quote are the exact reason that I must leave the sets A, B, C and D undefined (defining only the relationships between the sets; which is, once again, and analytic truth).
which is why I had said "By the time I get to sets C and D...".

Sodann, any hope of clearing up what you call "the relationships between the sets"?

First, there's a slight problem with $\norm B(t_k)$, which you define to be "a finite unordered collection of elements of A" which (strictly) is neither a set (as you later specify "Since all explanations must be modeled, B may contain the same element of A more than once") nor an ordered n-ple. I think I can gloss over this by assuming each $\norm B(t_k)$ to be a sequence, since I get the impression you mean k to be a natural number. This would mean it's a map from 0 < k < n into A. C isn't troublesome once one has cleared up B, although having many of these would imply the need to label them with a further index in order to make it possible to specify which of the various $\norm B(t_k)$ when necessary.

Now comes D. It absolutely isn't clear and I find no hint nor clue whether the elements of D may be elements of A (meaning $\norm D\subseteq A$), or of the type $\norm B(t_k)$ or what. In appendix 2 you have the Dirac delta symbol with arguments $\norm\vec{x_i}$ and $\norm \vec{x_j}$ but give no idea of what each of these two is supposed to be. I might suppose one of them is meant to be an element of D, I'm not sure if the other is meant to be an element of C, or of one of the B in C or what, you seem to pull the x out of a hat when defining the $\norm\Psi$ functions, without much clarity and the appendices don't tell me much to get it straight.

Then, after defining the commutation relations with the $\norm\alpha$ having two indices x and $\norm\tau$, you define $\norm\vec{\alpha_i}$ and $\norm\vec{\nabla_i}$ using the mysterious $\norm\hat{x_i}$ and $\norm\hat{\tau_i}$ which is not clear at all.

Without greater clarity about such things, I don't think you'll find many people making the effort to piece the puzzle together. You may say "nothing (except a rather trivial set of internal relationships) in the equation is defined" but I'm still stumped on that "rather trivial set of internal relationships". :shrug:

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Thanks Qfwfq, I think you have made your difficulties a little clearer to me. I will admit that my knowledge of set theory may not be up to snuff and I may not be using the terms correctly; however, in my head, “set” seems to be the most applicable word to use for what I am talking about.

First, there's a slight problem with [imath]norm \left(B(t_k)\right)[/imath], which you define to be "a finite unordered collection of elements of A" which (strictly) is neither a set (as you later specify "Since all explanations must be modeled, B may contain the same element of A more than once") nor an ordered n-ple.
The set B is nothing more then a specific finite collection (you could call it a sampling if you wished) of elements of A. I hate to call it a list as “a list” implies order and I specifically wish to embed all cases where “order” is significant to the explanation into different k indices.

It seems to me that your complaint that B is not a set stems from the idea that a set cannot contain identical elements as a set consists of different elements. Perhaps I am wrong but I think that depends upon the definition of difference. If one allows the definition of difference to change from set A to set B then they can both be sets without generating any logical conflict. (After all, the set of socks in my drawer can be described as a selection from the set of socks in the catalog.) The only constraints I want to put on B is that the individual elements of B were chosen from the elements of A and that the number of elements in a given B is finite.

What B stands in for is a change in information available to be used to create our explanation. If order in some of the elements is significant to the explanation, I would want to consider the changes different: i.e., referred to via a different k. That mechanism simply puts all order effects into the k index.

I think I can gloss over this by assuming each [imath]norm\left( B(t_k)\right)[/imath] to be a sequence, since I get the impression you mean k to be a natural number.
C is a finite collection of sets B: i.e., the elements of C are specific sets B. Again, I wish to allow the possibility of C containing more than one copy of any specific set B. Since the number of elements in C is finite, they may be ordered. This order (and the k index indicating that order) is a free prerogative of the explainer: i.e., k is defined by “the explanation” and is not information derived from A except by implication (the implication being implied by the explanation). If this violates the definition of a set then please give me a name you feel is more representative.

In my initial write up of the thing, the index k began in the form [imath]B_k[/imath]. The specification k was later changed to [imath]t_k[/imath] in order to allow the explainer to introduce time and associate a particular B to that time but not necessarily in the same order that the information became available to him which seemed to be what was implied by k. When I condensed the thing down, I ended up putting down the final definition [imath]B(t_k)[/imath] (it is written in functional notation because most all explanation presume time is a continuous variable and thus there exists unobserved information between the explicit B's). It is most definitely not a map from 0<k<n into A and is actually exactly the label you refer to as “a further index” in your comment:

C isn't troublesome once one has cleared up B, although having many of these would imply the need to label them with a further index in order to make it possible to specify which of the various [B] when necessary.
A residue of the original presentation remains in the “Solution to Sub Problem number 2”. I apologize for the rather confusing notation. I will see if I can do a better job of defining the four sets A, B, C and D,

The complete set D which would be the collection of all sets D) would be quite analogous to the set C and the specific sets D themselves are analogous to the sets B. There are two major differences: between B and D. First, the elements of D are definitely not taken from A (they are totally fictional and part and parcel to the explanation) and second, their number is not constrained to be finite (we can dream up lots and lots of infinite sets). D consists of information presumed to be valid and thus likewise consists of presumed changes in information which the explanation being modeled would include in B.

Again, I apologize for the confusion caused by my sloppiness. I was in the process of editing that document when I first posted it on the web. Since no one seemed to be following any of it and I didn’t know what they didn’t follow, I pretty well ceased trying to fix it up (seemed at the time to be a pretty worthless task).

D is only in there for a very specific purpose; any explanation may have in it presumptions which are in error. In order to be valid, the explanation must explain both those aspects which are correctly known, C and those aspects which are presumed to be known D. Failure to explain either destroys the validity of the explanation no matter which set is incorrectly predicted; notice that although the set D is totally fabricated, its existence is nonetheless confirmed by the correct expectations of C implied under the assumption that the explanation is valid. So, as long as the explanation is valid, it makes little difference which is which (the explanation must be consistent with the entirety). However, there is a distinct difference between the way C and D are to be handled by my model and thus by the implied constraints. In the evolution of the explanation, D can change whereas C cannot. This introduces some subtle consequences. That is really the only reason I maintain the differentiation. Actually, in the derivation of my fundamental equation, this difference in inconsequential as it must be or one could determine which was which from the model.

Finally, the anti-commutating matrices serve only one purpose. By including them one can represent the three totally independent constraints in what appears to be a single functional relationship: my fundamental equation. Appendix 3 is a proof that the explicit independent differential constraints required by symmetry (deduced earlier) can be directly extracted from any solution to that fundamental equation which obeys the constraints:

$\sum_i \vec{\alpha}_i \vec{\Psi} = \sum_{i\not= j}{\beta}_{ij} \vec{\Psi} \;=\; 0$

Then, after defining the commutation relations with the [imath]\alpha[/imath] having two indices x and [imath]\tau[/imath], you define [imath]\vec{\alpha}_i[/imath] and [imath]\vec{\nabla}_i[/imath] using the mysterious [imath]\hat{x}[/imath] and [imath]\hat{\tau}[/imath] which is not clear at all.
I think your confusion here arises from your misunderstanding of [imath]t_k [/imath]. If you examine the paragraph immediately following “Sub Problem number 2”, you will see the line, “The model consists of points in a real (x,tau,t) space where "real" means that x, tau and t are taken from the set of real numbers.” When I was a student, the mysterious [imath]\hat{x}[/imath] and [imath]\hat{\tau}[/imath] would have been seen as unit vectors in the x and tau directions within the (x,tau) plane, that two dimensional Euclidean space just mentioned. By the way, those hats are terrible and hypography's latex apparently does not allow an argument for "\rightharpoon" a "\vec" would probably be better:

$\vec{\alpha}_i \;\;and \;\; \vec{\nabla}_i$

Also, you left out the "i" index on the x and tau.

Without greater clarity about such things, I don't think you'll find many people making the effort to piece the puzzle together. You may say "nothing (except a rather trivial set of internal relationships) in the equation is defined" but I'm still stumped on that "rather trivial set of internal relationships". :shrug:
The “trivial set of internal relationships” are explained in appendix 1 and appendix 2. And I agree with you about the clarity but, without any feedback, the lack of clarity is hard for me to spot since I know exactly what I mean and seldom notice any alternate interpretations.

Have fun -- Dick

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Hi Buffy, I would have completely missed your post had it not been for hypography sending me a note in my e-mail as you apparently posted while I was commenting on HydrogenBond’s post and that ended up on the next page. Since I presumed his post was the last post on the previous page, I never looked back. Let us see if we can get this communication problem straightened out. (By the way, I don’t think either you or Qfwfq are simpletons; I merely think you are misinterpreting what I am presenting.)

I *think* I understand that you're proposing a "model" of explanations, and I'd agree that a "method for constructing an instance of that model" is a different thing. Having such a method is not necessary to formulating a valid model, however having a well defined model is a necessary prerequisite to constructing a method that creates an instance!
Exactly what do you have in mind as “an instance“? Are you thinking of “an explanation” or are you thinking of an exact analytical description of “an explanation”?

Look at my question this way: are you asserting above that you need a well defined analytical model of the concept, “an explanation”, in order to create an instance of an explanation? I would deny any assertion of that kind of expectation in a heartbeat. People explain things all the time without giving the first thought as to exactly what an explanation is. Your comment about the private message, "I'm really looking forward to Dr. Dick explaining how to explain an explanation." implies that you are presuming my model is designed to produce explanations. If that is indeed what you think, you have utterly no comprehension of what I a doing at all. And certainly your comment, “Incompleteness is specifically relevant to your desire to construct a model” makes no sense at all unless you are presuming my work is intended to provide explanations..

That is, for your model, either there is at least one instance that cannot be proven within the model, or the model is inconsistent.
An instance of my model would be “an explanation”. Thus you are saying that there is at least one explanation which cannot be “proven” within the model, or the model is inconsistent. I never said the first word about proving any explanation. I am talking about “modeling" an explanation (the explanation to be modeled is taken as given; that is why the set C is defined to be an unknown). Now if you had said that there exists an explanation which cannot be represented by my model, that would be an entirely different issue; but I am afraid any attempt by you to present such an argument without understanding the model would be rather futile.
You are claiming that the model is complete yet has no unprovable instances.
Just exactly what is an “unprovable instance” of an interpretation or an “unprovable instance” of a description or an “unprovable instance “ of an understanding? I am modeling ones “interpretation/description/understanding” of an explanation based on my definition of "an explanation".
Except that your affirmative data …
What “affirmative data” are you talking about. What I have presented is a simple deduction of the consequences of my definition of “an explanation”. It is a pure tautological construct. There is no such thing as “affirmative data”. My fundamental equation is a tautological consequence of that definition and nothing more.
But you must recognize that this *still* does not constitute finding "methods for constructing explanations."
Once again you directly confirm the fact that you think the purpose of the model is to construct explanations. It is not! It is nothing more or less then “a model for” any conceivable finite explanation of anything. Each and every explanation anyone will ever come up with will most definitely be finite by the very definition of infinity. It provides constraints in exactly the same way that, "the explanation has to be logical", provides a constraint on acceptable explanations.
And there you have it: a tautological model is always true no matter what the inputs are. I don't actually need to even refer to a specific instance let alone a method for constructing it to "explain" that this implication is entirely fallacious. A tautology is always true! How could it possibly imply anything!
If it reproduces in detail what some presumed science produces, it “implies” that science is a tautology. Even if you do not believe my interpretation of that tautology represents anthropomorphic reality, I have still shown that it is possible that modern physics is true by definition as my definitions have led to exactly that result. If you consider your definitions to be sufficiently different from mine that they do not predefine the results of your experiments, I suggest that you need to prove your case. :)

And you should check my definitions carefully before you make such a claim. I don’t think Scholars in the dark ages thought they were constructing tautologies either. :shrug:

Have fun -- Dick

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Exactly what do you have in mind as “an instance“? Are you thinking of “an explanation” or are you thinking of an exact analytical description of “an explanation”?
If you are constructing a "model of explanations" then yes, an "instance" is "a particular explanation." Now your second statement is curious though: what do you see is the difference between "an analytical description" and "a model"? Is there a difference? If so, what is it? Your followup seems to create quite a conundrum:
Look at my question this way: are you asserting above that you need a well defined analytical model of the concept, “an explanation”, in order to create an instance of an explanation? I would deny any assertion of that kind of expectation in a heartbeat.
I would argue that if you are describing a "model" the first and most useful operation is the "is a member of" operation. Now be VERY careful in how you read this because I have said *nothing* about how you "CREATE" an instance, only how you can establish membership of a GIVEN instance handed to you on a silver platter, that is, whether a particular instance does or does not follow the rules (description) of the model. So, again:
And certainly your comment, “Incompleteness is specifically relevant to your desire to construct a model” makes no sense at all unless you are presuming my work is intended to provide explanations.
You seem to be obtusely unclear about this distinction between "establishing membership" as opposed to "rules for creating" or "methods of construction" which I'm happily separating out so that you can get on with your explanation of explanations.

Conversely, if you are saying that you are creating a model that leaves the "membership" operator undefined, I'll strongly argue that your model is incomplete. Its vague handwaving that leaves everything tautologically undecideable, and is pretty much worthless. Thus, either

An instance of my model would be “an explanation”.
in which case your model should have something to say about whether or not a given instance is a member of the "explanations" set or not, OR
the explanation to be modeled is taken as given
in which case you are not creating a model of explanations, but rather a model of how explanations ARE USED. That is it would be a model of Reasoning GIVEN Explanations which I would call "axioms." That would be fine too, but that's not what you've said. The only thing that I have objected to here is that *you* are mixing these two concepts up, and most importantly, you insist on saying that the explanations are not axioms, and only pure logic is required. I really don't care if you call them tunaburgers, you need to stop flipping back and forth by insisting that "givens are not axioms." And here's an example of that:
Each and every explanation anyone will ever come up with will most definitely be finite by the very definition of infinity. It provides constraints in exactly the same way that, "the explanation has to be logical", provides a constraint on acceptable explanations.
So here you are defining an explanation, rather than a model for how they are used. The interesting thing about this definition of course is that it does indeed hint that you want to define a membership function. That's what I'm talking about! Yet in order not to disturb your insistence that your model requires no external assumptions, you do not pursue the full definition of the decidability of an instance of an explanation. It seems to me that by not doing so, conclusions drawn from your model of usage of explanations will produce fallacious conclusions because membership in the set of explanations fully allows for invalid explanations to be included as true statements.

The core of this issue is really that by saying "I will not deal with decidability of the validity of an explanation instance" you open yourself wide open to the fact that all explanations make assumptions--that is they themselves have a set of axioms--upon which they depend. All you have done in order to justify that your model "does not depend on outside assumptions" is to hide them semantically under a rug.

Obviously I completely misunderstand what you're talking about, but until you get that this issue of membership and decidability is NOT about "constructing" or "defining algorithms for creating" explanations, we're stuck in a circle. If you keep insisting that I'm doing the latter, then you'd better ask me some more question so we can get past that one.

And you should check my definitions carefully before you make such a claim.
I'm trying, Dick! The fact that you seem to be unable to understand my question only helps to confirm my feeling that your definitions are not very definitive!

Now just to jump ahead, what I've come to believe about your model here is that you think that 1) decidability of valid explanations is not possible nor interesting, 2) reasoning based on explanations whose validity is undecidable may be termed valid nonetheless by finding no internal contradictions in their logic, and 3) reasoning thus found consistent is valid irrespective of the validity of its underlying explanations. Now I can't argue with that at all, but I can't find any reason to find this useful in any practical way (in fact this would show that at least some false theories of physics are internally consistent: so what?), and it *still* uses axioms that are defined outside the model to determine consistency! :shrug:

Having lots of fun,

Buffy

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Hi Buffy, you make it quite clear that you have no understanding at all of what I am doing. I credit that problem to the fact that the current scientific model of “an explanation” is so crude as to elude recognition as a model. A model is a construct which displays the properties of the thing being modeled. In this case, both the construct and the model are abstract entities. I define what I mean by an explanation and then construct a general model of such a concept.

[it is nothing more or less then “a model for” any conceivable finite explanation of anything.] Each and every explanation anyone will ever come up with will most definitely be finite by the very definition of infinity. It provides constraints in exactly the same way that, "the explanation has to be logical", provides a constraint on acceptable explanations.
So here you are defining an explanation, rather than a model for how they are used. The interesting thing about this definition of course is that it does indeed hint that you want to define a membership function. That's what I'm talking about! Yet in order not to disturb your insistence that your model requires no external assumptions, you do not pursue the full definition of the decidability of an instance of an explanation.
Before you can understand what I am doing, you need to get in your head around exactly what the currently accepted scientific model of “an explanation” is. The current model, accepted by the scientific community, is that “an explanation” is a collection of words, symbols and concepts which provide some causal connection between different events and/or circumstances. The constraints on the model are very vague and not really clarified anywhere. In essence the constraint on the model is that “it should make sense” (a rather vague catchall to terminate instances thought to be unacceptable). Explanations are usually deemed to be logical and not to contradict known facts; however, the common definition of “an explanation” does not require these constraints. There exist such things as implausible explanations, silly explanations and invalid explanations. The main central component of a common explanation is that it presents some causal connection. (Such as "God did it!" for example!)

I pick up that causal connection in my definition “a method of obtaining expectations from given known information”. What this method is, is left entirely open as it is to be the “causal connection” itself (what the explanation is to provide). The known information of course includes the different events and/or circumstances. And finally, an issue given no attention in the common model, that collection of words, symbols and concepts referred to as an explanation must also be included in that known information. That fact has sublime consequences. The common model of an explanation makes the explicit assumption that there exists no uncertainty in the meaning of that collection of words, symbols and concepts; a generally false assumption.

The core of this issue is really that by saying "I will not deal with decidability of the validity of an explanation instance" you open yourself wide open to the fact that all explanations make assumptions--that is they themselves have a set of axioms--upon which they depend. All you have done in order to justify that your model "does not depend on outside assumptions" is to hide them semantically under a rug.
Not really, I am facing that issue openly and exactly by noting that there exist no outside assumptions; there cannot be as they must be included in that “known information” (in either C, the valid information, or in D, the information presumed to be valid).
Obviously I completely misunderstand what you're talking about, but until you get that this issue of membership and decidability is NOT about "constructing" or "defining algorithms for creating" explanations, we're stuck in a circle.
Regarding membership in my definition of an explanation, any function (and here you should see the word “function” as defined in the general language: i.e., one thing depends upon another) may be seen as an explanation as it provides a causal connection between the arguments and the result. An explanation is a description of the relationship. Your expectations (based on the explanation) indicate what relationships the explanation provides (which, of course, have to be expressed in terms of known information).
It seems to me that by not doing so, conclusions drawn from your model of usage of explanations will produce fallacious conclusions because membership in the set of explanations fully allows for invalid explanations to be included as true statements.
History is full of explanations deemed valid at the time they were accepted which turned out to include invalid relationships as true statements and there exists no proof that any current explanation is free of the same flaw; that is the reason for the need of set D. Much is made of the supposed fact that useful explanations must predict future experimental results. That is not a valid constraint at all; rather it is a description of the means by which an explanation is invalidated. At the moment the said explanation is invalidated, the information invalidating it is in the past: i.e., it is now part of the known information. Thus it is that all explanations need only explain the past to be qualified as acceptable or “valid”.

The inference that the explanation will yield valid future results is based entirely on the assumption that the future will be similar to the past. Considering the volume of “known information” (the past) compared to the present (a change in that knowledge) it is quite reasonable to expect little change in gross knowledge at any given moment and the probability such an inference is wrong is actually quite small.

If this post makes sense to you we can proceed to other problems you or Qfwfq’s may have with my presentation.

Have fun -- Dick

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Hi Dick,

You make it quite clear that you're not able to understand many of my terms, and since your model is based upon not recoginzing the difference between the definition of an explanation and an instance of an explanation, its not surprising that you don't seem to understand that your model is muddled because you skip back and forth randomly between the model and its meta-model.

Most of what you've written here is somewhat internally consistent, but it lacks certain explanations and makes certain leaps in logic that result in it being hard to make sense out of it at all.

...an issue given no attention in the common model, that collection of words, symbols and concepts referred to as an explanation must also be included in that known information. That fact has sublime consequences. The common model of an explanation makes the explicit assumption that there exists no uncertainty in the meaning of that collection of words, symbols and concepts; a generally false assumption.
First I'll argue that the notion that the "common model...assum[es] that there exists no uncertainty in the meaning of [its] words" is ridiculous: explanations--at least over time if not at first explication--do require many of their terms to be defined. Einstein had to define what Relativity was! To the extent that "common experience" can reduce this "part" of the explanation, there is no explicit *need* to include all of the defintions, but they are certainly *implied*. Now why this is at all sublime, you're going to have to start explaining, because to the rest of us, it may be unstated, but its obvious!

The core of this issue is really that by saying "I will not deal with decidability of the validity of an explanation instance" you open yourself wide open to the fact that all explanations make assumptions--that is they themselves have a set of axioms--upon which they depend. All you have done in order to justify that your model "does not depend on outside assumptions" is to hide them semantically under a rug.

Not really, I am facing that issue openly and exactly by noting that there exist no outside assumptions; there cannot be as they must be included in that “known information” (in either C, the valid information, or in D, the information presumed to be valid).
Here you're completely missing--or choosing to miss--the fact that I'm not talking about the definitions *within* your model, I am talking about the method you are using to *define* your model, that is its meta-definition! Now in my statement here, I'm refering to the assumptions of your model, not of instances modeled by it, but in your response you do not understand this and simply refer to assumptions made by instances being *included* by definition, which is not something that I'd argue about, other that the issue I just mentioned.

But what you are engaging in is an interesting example of an activity known as bootstrapping, which is useful in computer science but usually results in a case of fatal circular logic, as appears to be the case here. The problem:

• You've devised a model of explanations which allows inclusion of any explanation that might in a particular instance produced a correct prediction.
• You've broadened membership in this set by making a small distinction between what Rummy would call "known knowns" © and "unknown knowns" (D), which seemingly removes the time component, but mostly is used in an attempt to "include all assumptions so there are no outside assumptions"
• Finally, you've tripped over the distinction of the model and the meta-model and blythly applied the "lack of assumptions" to the model itself, ergo, the model requires no assumptions.

This is precisely where you can get into trouble with Kurt Goedel, because the applicability of the model to itself IS AN ASSUMPTION THAT IS OUTSIDE THE MODEL! If this is not clear, I'd encourage you to go back and read Kurt some more.

Thus it is that all explanations need only explain the past to be qualified as acceptable or “valid”.
Just to play along with you here, I'd say that your model--as I mentioned above--"removes the time component," thus allowing you to discuss the "set of valid explanations" without reference to time. I get the sense that you're trying to get at this, but honestly, this is hardly sublime...
The inference that the explanation will yield valid future results is based entirely on the assumption that the future will be similar to the past.
Here's where I sense you start to contradict yourself if you understood my previous statement. As far as I understand what you're talking about, once an element is in set C, it can't magically pop back into D or worse be defined as invalid, unless either the physics of the universe change (an assumption of your model!), or you go back in time. As I see it, defining C&D allows time-independent *abstract* definition of membership in the set.
If this post makes sense to you we can proceed to other problems you or Qfwfq’s may have with my presentation.
Oh please proceed! This is so entertaining! :hihi:

Unstuck in time, :Guns:

Buffy Pilgrim

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Buffy,

First, would you clarify to me what you mean by a “meta-model”.

Finally, you've tripped over the distinction of the model and the meta-model and blythly applied the "lack of assumptions" to the model itself, ergo, the model requires no assumptions.
It is certainly unclear to me exactly what you mean here. From my perspective, my meta-model is “logic”, and, with it, mathematics. And, as I have said, I treat mathematics as a well understood language with least opportunity for misunderstanding. I will leave the assumptions internal to that language to others and use the language as I have learned it. The model itself must include modeling the assumptions otherwise it will certainly exclude possible explanations (those with different assumptions).
…it lacks certain explanations and makes certain leaps in logic that result in it being hard to make sense out of it at all.
Then please point out the first “leap in logic”.
First I'll argue that the notion that the "common model...assum[es] that there exists no uncertainty in the meaning of [its] words" is ridiculous: explanations--at least over time if not at first explication--do require many of their terms to be defined.
The problem here is that, when one gets down to fundamentals, defining the terms used in the explanation is part of the explanation. That, in itself (taken as a serious problem) results in reduction ad absurdum. I know of no scientist who would seriously consider that to be a problem: i.e., they make the assumption that the meanings of their definitions can not be misunderstood. Your comment, (i.e., “is ridiculous”) points out that you yourself don’t consider the possibility worth thinking about. QED
As far as I understand what you're talking about, once an element is in set C, it can't magically pop back into D or worse be defined as invalid, unless either the physics of the universe change (an assumption of your model!), or you go back in time.
You seem to misunderstand the purpose of the set C. Our purpose is to explain A under the circumstance that “all of A” is not known. When it comes down to serious objective science, it is clear that there is no way to know for sure what (in our comprehension of A) is or is not real. However, by definition, what is real cannot “magically” change and thus, in the creation and evolution of explanations, the explanation must continue to explain the “real” information or it is invalid even before any assumptions are made. That is an embedded fact and does not require a determination of what is and is not C; however, it does imply some subtle conclusions: in particular, the fact that C must be finite and consequences of that fact.

Regarding any explanation, C constitutes the underlying knowledge of the “truth” and D constitutes “fiction”. The one and only difference between C and D is the fact that D is part of the explanation and not part of “what is being explained”. This fact is important if we are to consider “all possible explanations”. To put it another way, if you have two explanations of the same phenomena which differ only in their ontology, and all known experiments are perfectly consistent with all “accepted” information (information agreed upon as valid by both explanations) and all “argued” information (information specifically implied by the particular ontology) there exists absolutely no mechanism for separating the two (other than Occam’s razor which is, after all, a measure of convenience and not an arbiter of truth).

As I see it, defining C&D allows time-independent *abstract* definition of membership in the set.
Use of the concept, “time” in an explanation, requires the definition of “time” be included as part of the explanation. Membership in C (truth) can not be assumed or you have explicitly excluded the possibility that the concept is fiction.

Have fun -- Dick

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Just another quick comment before I go out of town again. ;)

But what you are engaging in is an interesting example of an activity known as bootstrapping, which is useful in computer science but usually results in a case of fatal circular logic, as appears to be the case here.
I think you are missing the entire central issue. What I am doing is much more analogous to the deduction of the black body radiation spectrum. Internal consistency can be a very powerful constraint on a complex phenomena. I am merely enforcing global consistency on any construct consistent with my definition of an explanation. :pirate:

Have fun -- Dick

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