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The Concepts Of Definition And Assignment!

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Posted by Richard D. Stafford, Ph.D. on March 14, 2002 16:58:51 UTC

Harv,

It is entirely beside the point how we got to where we are, what is significant is that mankind has developed some very useful abstract concepts which make thinking about things much more organized than it was for our ancestors. The purpose of these abstract concepts is to provide us with a clear conceptual base from which to reason things out. Definition is itself one of these abstract concepts.

In order to clarify that concept, let us discuss the nature of definition. To begin with, I think you will agree with me that "dictionaries" are collections of definitions. With regard to that issue, a little serious thought should convince you that it is clearly a mistake to presume that dictionaries provide us with any meaning (consider the problem facing you were I to hand you a dictionary in a foreign language with which you had no prior experience). In fact, presuming dictionaries provide meaning is a common error made by almost everyone.

The confusion herein arises because English (and all the other human languages I am aware of including mathematics) are strongly context sensitive. The definitions themselves do not ever provide any meaning in and of themselves; a dictionary definition can be seen as providing meaning only when meaning has already been assigned to all the other symbols and to the syntax used in that particular definition. That such an assignment of meaning exists is exactly the contextual assumption made whenever one attempts to discover meaning of a symbol from a dictionary. In fact, it is exactly this constraint which generates the rule that a definition cannot contain the symbol being defined (as clearly, such a definition will fail its purpose which is, of course, to provide a mechanism for assigning meaning).

Now "definition" can be seen as a category of information: i.e., it is a word which identifies a particular type of information. Information is also an important abstract concept. Before we can discuss a category of information we need to understand exactly what the concept information refers to. Essentially, everything that you can know is information; when you are aware, information is what you are aware of. As Paul says, "thought happens"; information is no more than a tag word for a particular thought or concept (or any collection of the same) sans meaning. It is very important to realize that the abstract concept "information" need not include the quality of "meaning". Information acquires meaning only after meaning is assigned to it whether that assignment is piecemeal or whole.

Clearly, as a dictionary is a compilation of definitions, definition must be a particular type of information. One of the problems here is that the identification of some piece of information as a definition cannot be made until after some assignment of meaning has been made. Fundamentally, the issue that makes a piece of information a definition is the fact that it assigns a meaning to some symbol (whenever the meanings of the other symbols and the syntax of the remainder of the "information" in the definition are already supplied). That is, before one can categorize a piece of information as a definition, some assignment of meaning must have taken place.

There exists a subtle issue within that last observation, an issue taken full advantage of by anyone versed in the field of mathematics. That issue is that one may assign the meaning "this is a definition" to a piece of information without assigning meaning to any other part of the symbols extant or even to the syntax.

Now there is a distinct difference between a concept and an example of an application of the concept, so information can be much more than the examples I will present; nonetheless, presentation of these examples is made in order to communicate a rather universal concept. The following four things can all be called "information":

1. (00110101001100010101010000001111110101010100010101010)
2. (strilig fandiocuk daturhhig frmainhgte)
3. (123fff4876fff3000---7fff869fff577)
4. I live in the United States.

In fact, it is entirely possible that all four could be classified as "definitions"! I make that comment with clear knowledge that number 4 (by your interpretation ) is not a definition. It is not a definition (in your mind) because you have already assigned meanings to the words (symbols) and to the syntax used in that piece of information. However, the fact that that need not be the case is clearly understood by anyone who has ever broken a code. In fact, the act of breaking a code is exactly the act of assigning internally consistent meaning to symbols and syntax imbedded in information which (prior to that assignment) was without meaning.

The point of the above is that information and meaning are wholly different concepts. In particular, the concept of information in the absence of meaning (no assignments of meaning having been made) is a concept of fundamental significance.

If you are capable of comprehending that concept, then you should also be capable of seeing scientific progress as the phenomena of shifting assignments of meaning applied to the total information available to a thinking mind (the entity in which "thought happens"). If, in fact, learning is indeed little more than the consequence of accumulated shifts in the assignment of meaning of what we know (that underlying undefined information) then it becomes quite reasonable to consider the issue of what constraints those assignments must obey in order to provide an acceptable assignment of meaning. That is the central issue of my work.

If you find problems with the differences I propose for the meanings of definition and assignment in the context of my work, we should discuss issues very carefully.

Have fun -- Dick

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