Hi modest, sorry about being slow to answer but the last two days have been somewhat busy and, on top of that, my son-in-laws internet connection has been flaky. It is now up and doing fine. We presume it was a comcast problem.
You do an excellent job of expressing your confusion and I thank you for that. There are a lot of indices flying around here and it is quite easy to get them confused. I will try to be more careful but please don’t be too hard on me (I tend to use context to differentiate between the meanings).
Quote:
Originally Posted by modest
Two lists? The "explanation list" and the "knowledge list"? Yes? (or is it the explanation list and the information list?)
|
At the moment (regarding the
”what is”, is “what is” explanation) the issue you bring up is only beginning to rear its ugly head. I have asked you to consider these two lists to be different because, down the road, an explanation will be quite different from the information upon which it is based. We do have another collection of information, which we might very well call “knowledge”, which certainly does not include all the information upon which the explanation is based. This would be the information given to the person using the explanation as knowledge on which his answer to a specific question is to be based (this presumes his knowledge consists of the explanation plus some other specific detailed information).
At the moment, as long as you can agree to view “explanation” as different from the “information” upon which it is based, I don’t really think the words “information” and “knowledge” are really that different; however, if you don’t mind, I would prefer the term “information” as “knowledge” seems to carry a bit more intuitive baggage with it.
Quote:
Originally Posted by modest
Two indices? x and i, yes? x and i exist in the explanation list?
|
The two indices exist in both the information list and the explanation list. Their purpose has very little to do with the actual lists. They are there merely to assist in the logical mapping of the “explanation list” into the “information list” as these two lists have some fundamental differences when it comes to logical content.
Quote:
Originally Posted by modest
(I feel as if I'm reading the instructions to a game I've never seen played).
|
That is an excellent analogy to the circumstance. Until I define something it will be presumed to have no definition. It is exactly a logical game being laid out. That is essentially what any tautology is. How I define things is very dependent upon the fact that I know where I am going. Sometimes the necessity of defining them the way I do will not be initially evident, but that is not the real issue. This is another characteristic of tautologies in general: things are often defined for reasons which only become apparent later. The real question you should concern yourself with is, do my definitions create any constraint on the problem being examined, not “what requires them to be defined that way?”
Quote:
Originally Posted by modest
I don't understand the difference between the "knowledge list" and the "explanation list" nor the difference between x and i. For all the importance put on it, I don't see a qualitative difference.
|
In a
”what is”, is “what is” there is utterly no difference between the “information list ” and the “explanation list”; however, down the road, that “explanation list” will be transformed into something quite different. The important issue here is that any explanation of any kind can be transformed into a
”what is”, is “what is” explanation if “what is”, is known.
The difference between x and i is very specific. The numerical label of a specific element in information list will be expressed by the number “x”. Is x an integer? At the moment it certainly could be but there is no reason to so constrain it; as the number of elements in the “information list” rises to infinity (something which will happen down the road) x will transform to a continuous variable. The number “x” can be seen as an index used to refer to a specific entry in the “information list”. That same number is used to refer to the same element in the “explanation list”. The index “i” is an index used to refer to a specific entry in the “explanation list”. Of course, since the label “x” appears in both lists, “i” can be seen as attached to x in both lists.
So your real question is, why both x and i? Because different x’s denote different elements in the information list and different i’s denote different elements in the explanation list. But you say, if they are the same in the information list, they are the same in the explanation list. But my answer is, that is not necessarily true. To understand that assertion, let us go back to the definition of the index t.
I defined “the past” to be, “the information on which the explanation is based”. The explanation was created to explain the set of undefined elements which make up that past. What these elements are is left undefined thus to give any two the same label (the same numeric label “x”) is to assert that they are the same element. We can’t know that unless we have already solved the problem: i.e., somehow we have come to know what these elements are. It follows that we must leave them as unknowns until after we have found an explanation.
So, let us presume we have found an explanation. Within the context of that explanation we know what all the elements are so we can assign a specific numerical label to every element. Now, it appears to me that you immediately jump to the conclusion that we can assign a specific value to each numerical label (which references our definition of that particular element). We certainly can; however, that labeling is only valid so long as our explanation is valid.
The problem is, it is always possible that additional information might invalidate that explanation; in that case, the assignment of those labels might be in error. That is the reason I use the term “flaw-free” to describe an explanation which explains all the information upon which it is based: i.e., there exists no information within the set defined as “the past” which contradicts the explanation. That is why I define the index “i” to be the numerical label assigned by the explanation. The numerical label x
i would be “i” (or perhaps some translation of i) if and only if the explanation were valid. Think of x
i as no more than a translation table to be used to translate your presumed elements (presumed in your explanation) into the proper references in the information list.
Now we bring in the possibility of more information: additional undefined elements not in the original past (this additional information is what I call “the present”). As I said the introduction of this idea brings forth the possibility that the past might be seen as a serial accumulation of additional information and that issue brings up the need for another index “t” to allow us to specify exactly which present we are talking about.
We now have an explanation which is flaw-free so long as the past consists of the collection of all presents prior to some specific index t. It consists of a collection of presents, each of which consist of a set of elements (some set of x
i’s) associated with each t
q. Thus, having an explanation, we can assign an “i” to every element in every present (and thus to every x) in both the information list and the explanation list.
This is where the issue of persistence comes into play. If some element, say element 55, (i=55 defined by the explanation) occurs in both presents, t
6 and t
25, then that particular element will have exactly the same “i” assigned to it (in this case, 55) in both t
6 and t
25. But we certainly can not say that x
55 from present t
6 is the same as x
55 from present t
25. That is no more than an assumption we have made in creating our explanation. Put it this way, there may exist another flaw-free explanation which explains exactly that same information where that particular element is not persistent as presumed above.
Fundamentally, we can never assign a numerical label to our information list as that presumes we know what that element is. All we can actually do is use i to indicate our presumptions so that we might compare our explanation with the information list. That is the reason for the double numerical labels.
I hope that is a little clearer than what I said before.
Quote:
Originally Posted by modest
I don't recall where I read these things. You appear to say "different times" ... and "a supposed present" ...
|
I have defined the index “t” on specific presents to be “time”; thus “different times” means different values of that index and a “supposed present” refers to a collection of information (a collection of numerical labels x
i) lacking information as to the proper index “t” which should be assigned. I am proposing a question there as to how our explanation list can be used to determine what that index should be. An issue we would like our explanation to answer.
I sort of balk at the term “instant” because it pretty well implies t is a continuous variable which it certainly is not at this point in the discussion. Time here is no more than a discreet index and is, in this way, not yet equivalent to the common meaning of the term.
Quote:
Originally Posted by modest
Is the past equal to the "information list" ...
|
The past is defined to be the “information list”. The explanation is not yet defined at all except for the specific
”what is”, is “what is” explanation, in which case it is exactly the information list.
The term “knowledge list” is somewhat a dangerous term because I want to use the idea of the “explanation list” as an explanation (separate from the information list). In that case, I can presume someone possesses the explanation and can analyze his ability to answer questions given less than complete “knowledge”: i.e., I would like to use the word “knowledge” to indicate the information given as part of the question asked. This has to do with generating the kind of questions I want an explanation to be able to answer.
Quote:
Originally Posted by modest
I'll again stop and see if you can iron out this confusion. Don't give up on me yet, Dr. D. I just want to be comfortable that I understand what you're saying, and I'm currently not.
|
I think you are doing a good job of pointing out what people find confusing. Let me know it the above clears up the issues you have brought up.
Have fun -- Dick
