Your first complaint is, "You are assuming that a particular element of A is referable and this, I think, is an incorrect assumption." Please inform me as to how you intend to explain something you cannot refer to?
You cannot necessarily explain everything Dick. Explanation might only be a human thing, not related at all to what the thing (i.e., set A) is.
A is defined as that which is to be explained (what one has to work with are elements taken from "A"；
This is a complete misrepresentation of set A. Something that which is to be explained does not mean that this something is explainable. This is your mistaken assumption. For example, 'gravity' needed to be explained by the ancients, but that doesn't mean that 'gravity' was explainable with their understanding of the universe. Even today we don't have a full explanation of gravitation, and we cannot say with full honesty that gravitation will ever be explained fully, some aspects of it might be unexplainable.
You keep trying to tell me what "A" is. I defined "A" to be what you are trying to explain: that would be the infinite collection of all possible elements of "B" (which cannot be available to you because "infinite" means there are always more). In your head, "A" seems to be "what you would like to explain", a subtly different concept.
What we are trying to explain or what we would like to explain is only a difference in our interest level. Presumably, if we have enough interest, we will try to explain A. That, however, has no relation to whether A is explainable.
I am asking you to believe that MATHEMATICS is a logical structure: i.e., that any results of any MATHEMATICAL DEDUCTION are as true as is the START POSITION of that DEDUCTION.
Rather than say 'true', then why not say 'as applicable'? I prefer this term since 'true' has ontological implications which I'd like to avoid.
If you want to throw out logic and mathematics, tell me exactly how you intend to explain anything. Show me a useable explanation of something where the explanation does not depend on logic! Until then, I will hold that your explanation can be modeled by my procedure.
Explanations should be based on logical means (or mathematics, if applicable), however the reason is entirely different than the reasons which you utilize logic and mathematics. The use of logic and mathematics is not to necessarily obtain a real/i> explanation of something, rather it is to obtain a useable explanation of something. No one has the slightest idea if any explanation is ontologically true. As I mentioned, a demon might exist which prevents us from ever having an ontologically true explanation.
As for your argument that any explanation can be modeled by your procedure, you aren't specifying which explanations are valid and which are not valid. So, it is sort of like saying that you can spell any label any true statement with a number. Who disagrees with that? But, that doesn't mean you have a method from deciphering which statement is true from that which is false. The same method you use to label a true statement is also can be used to lable a false statement. In fact, if it is a matter of using your model, your model would have its most usage in false explanations (e.g., lies) since presumably there is a higher cardinality of false explanations over true explanations. This all boils down to a big "so what?".
My modeling procedure begins from a state of total ignorance; you on the other hand, are continually trying to start from some position which presumes all kinds of information outside "C". "C" constitutes everything you have to work with.
You are claiming knowledge about set A. The truth of that matter is that you cannot know what patterns might turn up in future insights into what must be explained. How could you? Ignorance of set A does not produce knowledge of set A. The statement itself is ridiculous.
If I am going to model your explanation of "TIDE", I need a definition of "TIDE" plus the definition of every term used in your definition of "TIDE" plus every definition of every symbol used in the continued process. Clearly, you cannot exactly define "TIDE" the process is ultimately infinite; however, there is always a finite cut off point in your presentation: i.e., when I become sufficiently convinced that I understand your explanation of "TIDE". When is that? That occurs when my expectations of your answers to my Questions about "TIDE" and those other underlying definitions are substantially in agreement with your answers (your explanation as far as it is available to me. You are absolutely correct; "A" cannot be explained perfectly without making "C" infinite. This is clearly impossible so my understanding of your explanation must always be based on incomplete information. You call the explanation "technically false"; I call it incomplete. We have no disagreement on this issue. If you wish to consider only "technically true" explanations, then you are dealing with an empty set and no model is necessary. Your whole problem here is that you simply do not comprehend what I am doing. You keep harping on "A" when, in my model, "A" is nothing more or less than the source of the elements of "B". I set up the three sets, "A", "B", and "C", in order to encapsulate the important issues of the problem inherent in understanding an explanation (which is fundamentally equivalent to creating an explanation in your own head).
What you do not apparently see is that set C has no proven relationship to set A. All we can say is that we believe set C has some elements of set A, but that is a belief - which could be entirely false if the demon has his way. So, your only hope of constructing a useful model of explanation is to show how set C is limited by logic (or mathematics), but you have no idea what twists and turns analyzing set A will provide. Even if you have such knowledge, you have almost no evidence to show that humans are limited in set C except from some after the fact equations which have already been produced. You have not shown any future limitations, and certainly the 'limitations' that you have shown were only in physics, not mathematics, not philosphy, not biology, etc. So, here you have a very puzzling situation which you have no answer and one you haven't even really addressed.
There is a great difference between "modeling" an explanation and "communicating" an explanation. I have laid out a specific procedure for creating a model of any explanation (as the explanation, including all underlying components must be a finite communication, the procedure may be accomplished).
Dick, it is you who arbitrarily is saying that you are modeling an explanation. You might as well said that you are modeling lies, or excuses, or analogies, or stories, or jokes, or fairies for that matter. You only select the term 'explanation' in hope that it makes your model more credible. But, if we can model anything, then let's just say we are modeling goblins and fairies, and you can see how it sounds to those who read this.
My model specifically includes some unknown algorithm which will supply you with appropriate expectations. I don't define that algorithm, I just point out that specifying a set of expectations which correspond well with the explainer's efforts constitutes an explanation: i.e., it is nothing more or less than a method of producing expectations. Then, I show that it is always possible to interpret the elements of "C" such that the algorithm must obey a specific differential equation. I am not saying this is the "correct" interpretation of the explanation intended. What I am saying is that it is just as good as it will yield expectations for "B" exactly in line with "C".
Based on what evidence?? Let's talk about astronomy. Can you show one astronomical discovery that your model predicted?? So, why in the heck do you think your model can "supply you with appropriate expectations"?
I do not provide any explanations of anything. I simply notice that all explanations can be interpreted (that is the "fundamental" elements making up the explanation can be seen as entities which behave in a specific way) in a way which requires them to obey that specific differential equation.
Based on what evidence? Aside from physics, what is your evidence? Please share with the rest of us.
That means that there exists no valid explanation "of anything we know" which violates modern physics (at least the parts which can be deduced from my fundamental equation).
Had you been a mathematician and completely unfamiliar with physics, then you would have no knowledge that you discovered anything. I think you put way too much emphasis on physics, and you do not show how it pertains to fields of thought outside of physics. Within physics you make the mistake of providing no tangible evidence or predictions, but you seem to think that is no big deal.
Harv, "But, occasionally someone will come along and talk about set A as something that can be understand in terms of some model, and oh boy, that's what you cannot do." And exactly what do you think scientists are doing when they "explain things"? I think you are confusing "an explanation" with a "correct explanation". An explanation cannot be better than the information on which it is based.
Many physicists believe their models are about set A, and really there's nothing wrong with having a belief. If pushed, though, any honest physicist will just show you their predictions that the model predicted (i.e., before the model was derived this information was not known), and they will ask how it is possible that this knowledge is not about set A if their model is not about set A. That's understandable reasoning on the part of the physicist. The reasoning would look pretty solid if there wasn't a history of constant revision and new theories completely replacing the former theory, in which case the physicists argument starts to look more and more unreliable. There's more to the story of set A than the physicist is saying, and that's why anti-realists do not buy into the tradition of equating models with the operation of reality. BUT, it does not matter as far as physical theory is concerned since the main reason for believing a physical theory is because it is useful for other things besides believing it is about set A. Physics has many applications and even if every physical theory is eventually shown to be technically false, this will not affect the model's usefulness in our given situation (or the given situation of past periods). On the other hand, your model has absolutely no practical merit except by which to discuss here on astronomy.net as an excellent case study for the debate on the philosophy of science (which is why I debate this issue). I don't consider that enough practical merit to justify your model as legitimate since the pool of possible models that could perform the same function are innumerable.