Harv, I don't think it's intentional but you are totally misrepresenting my presentation. I am modeling a general explanation, not providing one! Let us, for the sake of argument apply the model to an explanation by you. If you think about that for a moment perhaps you will comprehend what I am doing.
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?
A is defined as that which is to be explained (what one has to work with are elements taken from "A"; these are used to construct "C" which is exactly what you are going to explain)! "B" is a set, defined to be an unordered finite collection of elements of "A". 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.
Apparently you didn't even bother to read what I asked you to believe! To item one you comment, "I won't say they are 'true' since they may be inventions (e.g., Tide detergent, yellow smiley faces, and those sticky notes that you take messages on)."
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.
Your comments have absolutely nothing to do with mathematical deduction! 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.
Oh, I wouldn't say your disagreement is illogical; it is just based on a very confused idea of what I am talking about. 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.
On two, you once again step off into the microscopic realm and totally omit all the concepts and information which lie behind your symbol "TIDE". 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).
To paraphrase you, "So, how can we really know anything about anything if A is not accessible? Well, fortunately for us we can view "A" not as it is, but as to how it appears [which is called 'C' in my model]".
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). 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".
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.
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).
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.
Try and think about it a little; and read what I say carefully-- Dick