mosassam said:
Thanks Paul, I was trying to express that, using my own brand of logic, that there must always be some kind of starting point and that this starting point has to be definable. Dr.D's theorem seems to be emerging "from the mists of the undefined" which eradicates the definable starting point I was grasping for.
You're welcome, mosassam. I think you have an excellent brand of logic. You seem to get right to the point using English without the difficult and cryptic symbolism of mathematics or symbolic logic.
Let me try to interpret what you said here using your own brand of logic:
There must always be some kind of starting point -- for anything. In particular, there must be some kind of starting point for existence, which we could call the essence, or the ontologically fundamental stuff. There must also be some kind of starting point for any explanation, or for any other language structure for that matter.
The starting point has to be definable in both cases. In the language case, it is straightforward. Langauge structures, such as explanations, or novels, must have a set of defined words to begin with or they will make no sense. In the ontological case, it is a little more subtle.
The starting point for existence has to be definable, i.e. in the situation (universe, world) in which we find ourselves we must assign tags to things we think exist simply in order to talk about them. The assignment of tags constitutes definition, so anything we can assign a tag to is definable.
But, ... the starting point for existence does not necessarily have to be defined. At least not for the early stages of existence. Definable, yes; defined, not necessarily.
So what, exactly, constitutes a definition? Here's my proposal. If we consider 'information' to mean a difference that makes a difference, then an undefined set of "things", which make up existence or reality, may contain differences among the "things". And those differences could make a difference to other "things". So a rudimentary or primordial "universe" could contain information without any definitions.
If we consider 'definition' to mean the assignment of a symbolic tag to some existing "thing", then in order for there to be a definition, there would have to be some kind of assignment. That is, there would have to be a correspondence between some symbolic tag and some existing "thing".
But what does that correspondence require? We could probably conceive of several sufficient conditions for a correspondence.
One of those conditions might be a physical connection or relationship between a physical, or extant, "thing" and a symbol which is also constructed from physical, or extant, "things". For example, a particular amino acid group, which is a physical, extant, "thing", could have a relationship to a specific sequence, called a codon, (or set of specific sequences) of three nucleotides taken from the set {A, C, T, G}. The relationship between a codon and a particular amino acid group would be specified by another physical, extant, "thing", viz. tRNA. In this example, and in this case, we have a correspondence which involves nothing but physical, extant, "things".
Another condition for correspondence might be between a physically, extant, "thing" and a concept in the "mind" of a "knower". I won't define 'mind' or 'knower' just yet because those refer to the profound mystery of consciousness that we are at work exploring. We have an idea of what we mean by 'knowing', and 'idea', or 'concept', so using your brand of logic, let's just go with our own notions of what we mean by these terms.
So, in this case, and using the previous example, we could imagine a correspondence between an amino acid group and a sequence of three of the letters A, C, T, and G. The triad of letters is the tag. The letters are merely linguistic concepts -- an agreement among users of some languages to use them to refer to some "things" with the expectation that most of the people using them mean the same "things" by each letter.
Now, are those linguistic concepts extant "things"? Well, yes they exist so they must be.
Are they physical things? Well, that is debatable. You could say that the letters are made of ink molecules arranged in a specific pattern on paper. That would make them physical. Similarly, an uttered phoneme, called 'A', would be made of a pattern of vibrating air molecules which is also physical. But if we try to pin down the nature of the idea or the concept of a letter, like 'A', we enter the controversial domain of whether concepts are nothing more than, or are something beyond, mere patterns of physical brain states.
I think we can sidestep this issue for the moment. Just as we can dodge the problem of defining terms like 'I', 'you', 'we', etc., I think we can dodge the question of exactly what constitutes a concept. We know what concepts are so I think it is fair for us to talk about them. (You will notice that the previous sentence is rife with terms that are vague, if not undefined, if not undefinable, but we understand it nonetheless.)
So, to finally get to my point, I think that there are two fundamentally different kinds of relationships that can connect symbols to "things", i.e. there are two fundamentally different ways of defining a "thing". The first way is strictly through physical connections. The second is a conceptual connection of a conceptual symbol and a physical "thing".
If you agree with me so far, the next move I would make would be to define the second of those types to be 'knowing'. That is, given that a conceptual symbol is related to a physical "thing", 'knowing' is defined as the existence of that relationship in whatever it is that constitutes a concept. Without knowing what that is, it will be convenient to assign the tag 'mind' to it so we can talk about it. This yields the claim that a "thing" can be defined by the process of a mind making an assignment of some conceptual symbol to the "thing". When such an assignment has been made, we can say that the mind knows the definition. Or we can say that the mind knows the meaning of the symbol: the symbol means the "thing".
Now, if this makes sense to anyone, I think it can be a starting point for speculating on what the nature of the origin of reality might have been like. I think it would be fun to engage in that kind of speculation. We might even be able to get a glimpse of how reality emerged "from the mists of the undefined" and how the definable starting point was necessarily eradicated.
If, on the other hand, what I said does not make sense, please tell me about it.
Warm regards,
Paul