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[modest]

Thank you for bumping the thread. Perfect timing as I have a couple hours today to spend on this

Originally Posted by Doctordick

It is quite clear to me that you are missing the very essence of what I am doing. You are thinking in terms of specific explanations; not in terms of the general problem of creating a mechanism capable of representing any and all possible explanations: i.e., not knowing anything about what they are or what is being explained. We have a problem here which absolutely no one (except for myself and Anssi) has made any attempt to come to grips with. The underlying problem is, how does one represent something when they have utterly no idea as to what it is they are talking about. You have to confront that problem before we can even begin to talk about how to solve it.

Perhaps I've not been specific enough with my comments. It's really not the purpose of the model nor the reasons behind the formalism that are giving me pause. I understand that (and even agree with your fundamental motivation) better than you probably think. My lack of footing is situated at the mechanics, the nuts and bolts, of the model and the model's formalism itself. You might say I understand the reasoning behind the things you've done thus far, but don't feel comfortable in my understanding of their execution.

To help solve that problem I'm going to back up and try to make some specific comments on the main developments so far.

Originally Posted by Doctordick

At this point, “the past” (that which is to be explained or the collection of presents) is a labeled set of ontological elements and the explanation itself is that self same set of labels. The first thing I want to bring forth is the fact that the labels of the ontological elements are themselves a fundamental part of any explanation. If you have no way of referring to those ontological elements (or whatever title you wish to place on the known information) then you cannot build a epistemological construct based upon them. In effect, once you tell me we are discussing a specific explanation, you are confirming the existence of a set of specific labels you have placed upon these elements.

The past is a set. It contains ontological elements which are represented, regardless of their nature, with numbers.

The elements of the set P contain labels

Originally Posted by Doctordick

In a ”what is”, is “what is” explanation, that same specific set of labels constitutes your explanation. Using numerical labels is no more than a convenience and constitutes no assumption concerning the character of those elements.

In a “what-is is what-is” ‘explanation’ the “set of labels” are the explanation.

We then have,

where P is the past
is an index which labels elements of P
I is an index set containing .

The index is essentially an index of subsets of P and I.

I am, by the way, trying to put this in the language of set theory in hopes that our communication might be a little more precise (or, at least more-precisely understood).

Your next post:

Originally Posted by Doctordick

Essentially that means that every ontological element in the ”what is”, is “what is” “explanation” requires two indices: one which is consistent with the explanation under examination and another which maintains the generality of the model. Clearly the “past” must actually consist of only the general index (so that all possible explanations are still included) but, for the moment, we are concerned with analysis of the specific “explanation”. I will denote the general index with the number “x” and the "explanation" index (possible presumptive persistence) with the number “i”. Thus it is that every element in the current ”what is”, is “what is” explanation will be represented by the number x_i and each present in that explanation will be represented by a specific collection of numbers. As an example,

I would like to point out that one must include the possibility that the past might actually include real persistence and we don't want to eliminate that possibility from our model: i.e., the same x index might appear at different times.

Ok, the idea is to add another index. If I were to continue with the P example, , I might enumerate this a little differently than your example,

Such a difference may be trivial. I'll see what you have to say.

What we have now is "the past" (P) which is a "set of ontological elements". The elements are divided into subsets which are labeled and . The elements are numbers each of which is labeled by two indices: and . In the what-is is what-is explanation the index makes a set (an index set) which I've called I.

But, having gone through that, I'll say I suspect the explanation list is, in fact, not the set I, but the whole compilation of:

At this point I've probably written enough for a half a dozen you-don't-understand-what-I'm-doing objections, so I will stop and return to the body of your post.

Originally Posted by Doctordick

It is quite clear to me that you are missing the very essence of what I am doing. You are thinking in terms of specific explanations; not in terms of the general problem of creating a mechanism capable of representing any and all possible explanations: i.e., not knowing anything about what they are or what is being explained. We have a problem here which absolutely no one (except for myself and Anssi) has made any attempt to come to grips with. The underlying problem is, how does one represent something when they have utterly no idea as to what it is they are talking about. You have to confront that problem before we can even begin to talk about how to solve it.

We need both x and i for the very simple reason that we have two very different collections of concepts to deal with here. First there are the concepts needed by a specific given explanation. We need an extremely general way of specifying these ideas (concepts, ontological elements, noumenon, ... or whatever you desire to call them) which stand behind our explanations: the things on which the flaw-free theories (or explanations) and their epistemological constructs are built. No explanation serves any purpose if that explanation can not be understood. In order to be understood, the explanation must be expressed in terms of meaningful labels. The first question to be answered is, what mechanism are we going to use to represent these undefined “things”. We need some kind of language to do such a thing: i.e., the definition of the language itself is part and parcel of the explanation. The labeling mechanism must be independent of the language used (this must be so because the language itself, and that would be any language, is a presumed explanation of sounds, marks and ideas). It should be clear that we may use numerical references to identify these “things”. That is the essence of the index “i”.

If we have a specific explanation (which includes everything necessary to understand that explanation) and do indeed understand that explanation, we can specify each and every elemental component of that explanation (and that includes the language necessary to that explanation) with specific numerical values for all references “i”. If you wish, you can think of that collection of numerical references as a computer file containing the entire body of that specific explanation (every document including the descriptions of all phenomena associated with that explanation, including an entire complete presentation of the language necessary to understand the explanation and every bit of information standing behind the explanation.) That is to say that a complete collection of the necessary information requires all connections and relationships within that data to represent a specific pattern: the specific explanation being represented. In essence, the existence of a specific explanation implies possibility of generating a specific set of indices “i”.

Now, under the assumption that you understand what I have just laid out, let me ask you a simple question. Is that collection of indices “i” sufficient to label all possibilities of interest here? When I say “all possibilities” I don't mean “any” specific explanation; I instead mean “each and every possible flaw-free explanation”. I must assume that you are bright enough to realize that the answer to that question is quite clearly “no” as the “i” indices represent a specific (possibly known) explanation.

Try and look at it from the following presumption. Suppose, for the sake of argument, you have a “correct explanation” (that presumes such a thing exists but we really need not worry about that issue for the moment). Clearly, that “correct” explanation could be set forth via some set of indices “j” totally and completely analogous to the index “i” just discussed. The next question which should arise in your mind is, does there exist a one to one correspondence between each and every possible specific index in the set “i” and the set “j”? The answer has to be a resounding no as, if there were, the collection represented by the indices “i” would be exactly that “correct explanation” represented by the set “j”: i.e., all information contained in the complete set "i" would be identical to the set "j".

To go off on a tangent for a moment, I am of the opinion that (among almost all people) there is a major misunderstanding of exactly what the conflict between “science” and “religion” is all about and it has to do with comprehending exactly what a “flaw free explanation” is. An excellent example of what I am talking about is the simple explanation, “It is no more than what God wants it to be!” That is a perfectly flaw-free explanation of everything. There exists not a whit of evidence to counter that assertion. The flaws occur not with the explanation itself but rather with those who claim to know the “will” of God. The real problem with such an explanation is that it is not really a very useful explanation (except perhaps for controlling the behavior of gullible people, but that is not the central issue being discussed here): i.e., scientists perceive scientific explanations as better than religious explanations for the simple fact that they provide much more useful deductions. In fact, I could comment that there exist scientific explanations known to be flawed which are commonly used every day for the simple fact that they are so useful. This is exactly the issue lawcat brings up in the following post (though I wouldn't suggest he understands what I am talking about).
When I was a graduate student, I had many an argument with both other students and with faculty concerning this very issue. I always asserted that, “any theory which, when pushed to the limits of its supposed applicability, gave incorrect answers”, was wrong. They all essentially took the position that I was pushing the said theories outside the realm assigned to them. What they didn't understand (and I guess I never made clear) was that I wasn't saying these theories were not useful (as they were all quite useful); I was simply pointing out that they were wrong (a totally different issue). Science is chock full of “compartmentalized thought”. The first requirement of a valid explanation is that it must start by being flaw free. Otherwise it is actually little more than “a rule of thumb”. Being useful is a totally different issue entirely.

The question here (in the logic of creating a representation of an arbitrary flaw-free explanation) is, can a one to one correspondence between all the elements of the ancient Roman gods (and what consequences can be attributed to them by those who believe such an explanation) be established with all the elements of modern physics? It should be clear to you that we certainly cannot use the same set “i” for every possible flaw-free explanation.

But, back to the set “j” defined to represent that correct explanation. That would appear to be a rather unique set. If that is indeed a correct explanation, then the collection of the entire set of “j” indices is a correct representation. It follows from that assertion that it must be possible to map each and every “i” index contained in a given "present" to a specific “j” index (however, it should be clear that the reverse is not true as the persistence assumed in the flaw free explanation might be in error). Since we clearly do not know this “correct” explanation and its elements are totally unknown, I use “x” to refer to those elements and thus “x_i” refers to the correct unknown element standing behind that reference index “i”.

Is that picture clear to you?

I understand the conceptual difference between and . It’s the functional difference between the indices and the lists which I was asking about. In the quote above you use the term “set of indices ” or just “set ”—is that equivalent to saying “the explanation list”? If so then I think I see where you're coming from.

My only trepidation at this point is the structure you're giving the information list. Am I correct that it is to be represented with subsets ? A change in information happens from one to the next?

If this is the case then it seems you've already given the information list a kind of Euclidean character with a single dimension of time. The rate of change of any element in the information list must be some exact multiple of this index , and there is only one index allowing for change translating into one dimension of time.

Let's see... I guess that's all.

Oh, yeah, the Coptic thing. The Rosetta stone could only be translated because people still spoke modern Coptic. The more modern of the two Egyptian texts on the stone was rather close to this modern language allowing it to be translated with both phonetics and meaning. The Egyptian Hieroglyphs had similar phonetics allowing its translation. Had there been no phonetic connection between the Hieroglyphs and the newer of the Egyptian languages on the stone or had we not known modern Coptic, I don't believe the stone could have been translated.

But, that's immaterial for your purpose in using the example. It was a good example and I understand what you mean to convey. Like I said, I do understand quite well the purpose of the model.

~modest