I'm just back from the tropics... burr.
***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.***
***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.***
What are referring to exactly? Information is usually referred to within the context of a sender, message, medium, receiver, noise, encoding, decoding, etc. When you talk about the difference of definition and assignment, we aren't usually as focused with concepts such as medium, noise, encoding, decoding, etc. I'm guessing that you would like to ignore some aspects of information (e.g.., medium) and focus purely on a theory of meaning and/or theory of understanding? As you suggested, you can't have information unless some more primitive issues are settled first - namely a theory of meaning and a theory of understanding.
What I don't understand from your comment is that you distinguish the assignment from the definition. But, the definition is the assignment of meaning. For example, if a child associates the verbal word 'block' with the cube in front of him, then the child has an 'assignment' between the verbal word and the visual thing (i.e., ostentation). The meaning of the word 'block' is made possible by the verbal-visual heuristic that exists in the child's head. It is an assignment, but it is also a definition. Asking the child to define a 'block' is like asking the child to show you what a 'block' looks like in their heads and asking them to identify that block with items around them. If you want to consider the verbal-visual heuristical structure inside the child's head as information, then that helps me better understand what you mean by information, but I'm not so sure experts in information theory would agree. Information is usually discussed in a different light (not so much in terms of what is happening inside the heads of children).
***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.***
I think we are talking about different issues. When I talk about a definition I am talking about what exists in the heads of people. I am not talking specifically about the content that crosses the air waves in terms of a back and forth communication between sender and receiver. Yes, this is involved in communicating our ideas and definitions to others, but in the context of our discussion we aren't so much discussing this aspect. What I think we have been discussing is whether the terms you identify in your paper mean the same thing as the terms used in many scientific equations. If the meaning - as it exists in the heads of theorists and experimenters who validate or falsify those theories - is different then the meaning of your terms, then the terms used in your paper have not been elucidated in the popular equations of physics. This is, in my mind, directly related to what those terms mean (how they are defined or how they are assigned meaning - which is pretty close to identical issues from what I can tell).
***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.***
This is what Paul and I discussed. I think we can agree on this in terms of formal systems and the fact that meaning is not assigned as part of this formal practice (whether that be mathematics, logic, or any formal system). However, where Paul and I had the controversy is our different way of summarizing our points (or different view since I'm not sure we fully settled on this issue).
My view is that a 'point', for example, can be left undefined (i.e., no abstract or physical association need be made), but it still carries meaning within mathematics in which only a certain range of operations are acceptable. For example, you can't take the squareroot of a 'point' simply because the point is undefined. You can leave the point undefined in terms of coordinates, or you can define the points in terms of coordinates. You can leave the point undefined in terms of physical space, or you can define a point near the center of the galaxy and calculate distances from it. Nevertheless, an undefined point still has an associated meaning within mathematics as being treated within such and such contexts (e.g., no sqrts of undefined points, can't cube undefined points, shouldn't subtract an undefined point from another undefined point, but you can consider vectors beginning at an undefined point, etc).
Perhaps you are treating an assignment and definition as something more technical in terms of mathematics or data processing. For example, in the computer programming language C++ (as well as many others) the assignment occurs after the variable has been defined. Maybe you can elaborate on whether that's what you mean (if so, then our words are carrying different meaning altogether since I am discussing the manner from an epistemological perspective).
***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.***
I can accept it as having a different meaning if we ignore the English language and adopt a language that is English-like but having different meaning for clearly understood English phrases. However, if we do so, then the English-like code has a different meaning and if you see that phrase you cannot associate it with the original Engish language meaning. Similarly, if we see terms used in equations having different meaning then how they are assigned and understood in physics, then those terms no longer have the same meaning. The new definition of terms might look like physics, but it isn't (anymore then the English-like code is English).
***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.***
You can't have information that has absence of meaning (at least outside a formal system). In formal systems (e.g., mathematics) you can leave terms and variables undefined as long as you have rules (axioms) on how to treat those terms and variables and build upon those axioms with your rules of inference (theorems). Outside a formal system, you need to impute meaning to concepts initially so that you aren't talking of meaningless concepts.
A big problem here is that formal systems have no connection to reality. The only connection they have to reality is the rules and terms selected, but for formal purposes these are purely arbitrary. In the case of the real world, you don't have information that carries no meaning. This is a contradiction to what information must have to be information.
***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.***
Lots to say, but I'm tired from my trip. I'm beginning to see a little better of what problems you are trying to solve. I'll take a guess in the dark, and say that you are trying to solve David Hume's problem of induction. The problem affects even science since science relies on induction.
You want to justify scientific inquiry by giving it (induction) a valid basis. Only formal systems via deduction methods are justifiable whereas induction methods are not.
If I'm correct in this surmising, then I congratulate you on at least seeing the induction problem. Most of those who study philosophy of science only learn of it because of the study of philosophy. Even Kant was unaware of the problem until David Hume spoke of it and he said that Hume woke him from his dogmatic slumbers. Kant spent a great deal of effort trying to solve the induction problem, but it is clear that he hadn't solved it. Even today there is no agreed solution as to what solves the induction problem. Science still resides on faith (shhh... this is a secret).
Warm regards, Harv