Saturday, May 10, 2014

About the "meaning" of the element labels

From page 11:
"Thus it is that I propose using the common mathematical notation $(x_1,x_2,...,x_n)$ to represent any specific "circumstance" of interest."

It is common that people raise questions and ask examples about the intended meaning of the $x_i$ elements, because there appears to be little bit too many ways to understand the intent of the author.

In this case the intent is specifically to not define any particular meaning for these elements; the possibilities must be kept completely open. What is being developed is a notation capable of representing any self-consistent explanation of reality in abstract manner. At this junction, it is not important whether or not we know how to actually perform a translation from some existing explanation to the proposed notation. The analysis up ahead does not rely on any specific meanings of the labels, it only relies on self-consistency issues. What is important is to understand in what way the notation itself does not impose constraints on what could be represented in principle.

Any explanation of reality operates under the idea that some collection of (well defined) indivisible elements exists, and the existence of a particular collection of those elements, or particular states of some elements, leads into some expectations about the future as per our beliefs regarding how those elements behave.

Thus, to have a generic notation that does not speculate about the existence of anything in particular at the outset, there needs to be a completely generic way to write down what elements exist (in some relevant situation or circumstance) according to some explanation. Whether or not the explanation conceives reality as collections of elements, or collections of states to some elements, the relevant information can be represented as a collection of numerical $x_i$ labels, where the meaning of each label can only be understood if that specific explanation is understood.

Note; it is natural to the notation defined here, that multiple different understandings of the same collections of elements can potentially exist. That is exactly the issue facing us as we are developing explanations about reality. If we have an explanation for reality that holds any predictive power, then we also have defined some elemental, indivisible entities with more or less persisting identity to themselves. By definition, we cannot write down "noumenal" reality in itself, we can only write down something we have already defined to constitute an element.

It is important the reader understands what is being developed is not an argument about reality, but an argument about our explanations of reality.

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