Hi Steve, I have no idea what is going on here. I posted an answer to your last note to the "wish list" forum (actually, I posted it to the "watercooler" but it was moved. There are very strange things happening because I received a note in my e-mail that you had posted; however, when I went to the thread, your post wasn't there. On the other hand, the e-mail included a copy of your actual post and (except for your quote of my post) it is exactly the same as your message. Tormod says it is the server which is hosting them and they have no control over it. They are currently looking for a new host.
Now, with regard to your message, I think you and I are operating on different levels. Analytically thinking, I operate on a very abstract level; I take logic and mathematics very seriously and very much regard mathematics as a language. Analytically speaking, all the other languages are appallingly vague. In my head, they can only be used as vague signposts toward the underlying concepts of logic and mathematics. In other words, I use English only to develop enough interest in my abstract concepts to get people to think about them. I would never subject my English to analytical analysis as it is not an analytical language. On top of that, I am firmly convinced that it is impossible to make such a language analytical anyway as the number of relationships standing behind those vague definitions is almost beyond conscious comprehension.
Essentially, when you use the term, "an explanation", you have a certain concept in your head. I can not be sure at all of exactly what you have in mind but, if it is in reasonable alignment with the understanding of most people, I suspect that most things you categorize as explanations, I will also so categorize. Mathematics is far different. When it comes to a mathematical expression or a mathematical operation, I can be far more confident that we have the same concepts in mind (that is the issue driving the development of mathematics for many long centuries).
The same thing is true of all the words and expressions you use: if what goes through your mind is in reasonable alignment with the understanding of most people, I suspect that I also will categorize my experiences in a very similar manner. That is what we call "understanding the language". However, as is pointed out by many people these concepts are independently developed by everyone and there is no proof that they are the same. In the final analysis, even mathematics is subject to that same doubt. To quote any intelligent person, "nothing is known for sure."
What I have discovered is that a simple mix of mathematics and my concept of "an explanation" will yield astounding volumes of relationships regarded by physicists to be defining relationships of reality. But in order to understand that, one has to be able to do the abstract logic and mathematics based on that specific concept. Your interest seems to be in analyzing the English I use to construct the concept, not the concept itself.
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Originally Posted by ldsoftwaresteve
I think this is a good place to drill. Let’s take the snippet “an abstract model would be an identification of how”…
‘An’ is a pointer implying a single thing being pointed at.
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The first step required to understand that English sentence would be to understand what a "model" is. The model of anything is something which appears very similar to another thing (the thing which is being modeled); at least sufficiently similar to play the roll of the thing being modeled in some possible circumstance. "Abstract model: identification of how ..." is almost sufficient to communicate the issue being communicated by "that snippet" you refer to. The gramatical purpose of the "An" is little more than an expression of "good grammar". That realization brings us to the adjective "Abstract" and the general consensus is that what ever concept being modified with that adjective is being conceptually modified as to contain no "real" or "physical" components. Thus it is that "an abstract model of an explanation" would be something totally imaginary (having nothing about it which is real or physical) but still able to "play the roll" of an explanation: i.e., act in a manner analogous to an explanation or "obey the same rules an explanation obeys".
That is why I spent so much time establishing the rolls of those various components of an explanation: a component, "what is being explained"; another component, "what is known about what is being explained"; another component, "what does an explanation achieve"; another component, "by what mechanism yields that achievement". Each of these aspects of an explanation are real things so if one wants to fabricate an abstract model, one needs to dream up abstract representations of each of them.
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Originally Posted by ldsoftwaresteve
abstract model is the set, any instance of which constitutes the ‘an’.
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Apparently you think I am talking about a "set" of abstract models" here. What I am talking about are the requirements of "any" abstract model of an explanation. There may vary well be many ways to model the concept of "an explanation" but I am aware of only one. As far as I know, no one else has ever even tried to create an abstract model which had the properties of an explanation. As a matter of fact, I am unaware of any attempt to even examine the properties of "an explanation". All I have ever heard are vague loose requirements of the concept. Perhaps I have misunderstood what you have tried to say but it seems to me that you are trying to complicate a simple issue.
I am going to try and post this to the thread and send it to you as a private message.
Have fun -- Dick
