Science Forums 2

[Doctordick]

Originally Posted by modest

What does it mean then, in a practical sense, to assign a value to x, or to map an element of the explanation list into the information list as you indicate here:

It is quite simple actually, anytime one has a theory one must be able to compare the consequences of that theory to the actual information on which it is based. To the casual observer, it might appear that the “i” index is sufficient to that purpose; however, that is not quite true. The problem with the “i” index is that it is defined by the specific theory being examined and that theory could be incorrect. The fact that the theory might be incorrect implies that the “i” index identification could also be incorrect. It should be held in mind that being correct is actually quite a different classification than is “flaw-free”.

If we are to include all possible “flaw-free” theories, we must allow for all possible mappings from each of those theories to the actual information which is to be explained. Our model must allow such a comparison without specifying what the actual labels are.

When we are comparing those theories to the actual information, we do not want to change the labels of that actual information as doing so essentially destroys the comparison: i.e., we want the actual values of the index x to remain unchanged during any such examination. What is important here is that we can cast that requirement into x without knowing what x is.

Originally Posted by modest

All the questions in my mind are centered around what you practically plan to do with them, which I believe will unfold in the natural course of the conversation.

Nevertheless, I doubt it does any harm to know what is going on in my head when I express these things.

Originally Posted by modest

Ok, but, when you introduced the idea you used the term "knowledge list" (unless you were referring to something else).

Sorry about my sloppiness; and it is indeed sloppiness. We all often seem to presume others know what is going on in our minds. You are correct; there are indeed going to be three different lists here serving three very different purposes and it is important that I be consistent with regard to the use of different names. I will try to remain with the following specific names:

The “information list” consists of the information upon which the explanation is based: the entire collection of sets of (x_i)_tq. I might note that the double index t_q serves exactly the same purpose as does the double index x_i.

The “explanation list” (at least initially insofar as the opening ”what is”, is “what is” explanation is concerned) consists of exactly the “information list” but is regarded as a different issue.

The “knowledge list” (as I intended to use it in the quotation you referred to) is an excerpt from the information list which is used for the purpose of analyzing the actual use of the “explanation”.

The fundamental purpose of an explanation is to allow one to deduce the constraints imposed upon the answer to a question when given only small part of the relevant information. The essential situation is that if we actually knew the entire “information list” an explanation is rather beside the point; we could simply refer the questioner to the ”what is”, is “what is” explanation.

What is important here is that other, quite simple, explanations exist. Explanations which do not require memorization of the entire “information list” and it is these explanations which are of interest to us.

I will do my best to be consistent with regard to these three “lists” mentioned here.

Originally Posted by modest

The other was "change".

I am presuming that you now understand that I was referring to “change” in the labels associated with a given comparison of two different “presents” (which are defined to be changes in information upon which the explanation is to be based). Persistence from one present to another is “lack of change”; if the same element appears in different presents, the element is called “persistent”.

In the absence of persistence, I suspect the simple ”what is”, is “what is” explanation is the only possibility: i.e., we have the information list and nothing more. Element persistence is one of the fundamental aspects of any decent explanation.

So, presuming you understand everything up to this point, that brings me back to the question I asked earlier. The one I referred to in post #35.

Originally Posted by Doctordick

Let us go back to that original question, suppose we are given a set of numbers (a supposed “present”) and are asked, “what is the correct t index assigned to that set?” The possibility certainly exists that there are multiple presents with exactly the same set of reference numbers associated with different “t” indices. In that case, our ”what is”, is “what is” explanation (as currently defined) will fail to provide us with an answer.

This thread has now exceeded fifty posts and I was unable to find the post where I originally asked that question which is somewhat troubling. Nevertheless, this is a very important question and resolving it will lead to more subtle issues. We need to be able to handle this kind of question. Let me know that you understand the issue I am bringing up.

Have fun -- Dick