Actually, I don’t mean it like “=” == “or”, because writing it that way has a different meaning. The quotation marks serve as a type of “not” (which = signs and ‘or’ themselves are a type of, too), and are related to the double-equals sign. Abstraction is an implicit negation.
The purpose of the ===or theorem is to simultaneously explain why ‘=’, ‘==‘, and ‘or’ have subtly different meanings in practice, what we choose to use them for, and how they are directly a consequence of choice in general.
== is the weakest insistence on preference, it means that either the left or right argument are preferable at any time, and could be swapped with one another at whim.
= (and or) are one step stronger than the weakest, and impose a weak preference choice on either the left or the right argument being preferable to the other. They both obtain simultaneously, so we choose to use one to imply that the right argument is preferable (=), the other (or) to mean that the left argument is preferable.
There is only one insistence on preference at the highest level of “ought”, which is that anti is preferable to not. We show that the claim that anti is better than not is equivalent to stating that choosing the better of two things is better, period. We can then opt to use anti-X for not X for any X, which is like saying that I’d opt to use X and something better with it, rather than throw away X entirely if something better were to become available.
Well, firstly, I must assume that I am not completely incomprehensible—if I did, I would not be able to operate at all, so we must assume that I am at least somewhat comprehensible, especially about the claims that have been elevated to “main.”
I assume that symbols are not empty, and that they do contain things. The exterior of the symbol is what gets written down. If it contains something, we say so.
I posit that when we say that two symbols are “equal”, X = Y, for example, that we could be saying one of several things. I narrow this down to saying that X and Y are alternatives for the same underlying meaning, and that we are claiming that one of them is preferable to the other.
I also posit that the symbols we commonly use are to be held with respect unless they are shown to be inherently negative in some way. Furthermore, that symbols ought to, and for the most part, already do, look like what they mean. Thus in some way, perhaps still yet to be fully elaborated, the “X” symbol as a cross of two lines actually implies that it is a variable, and can be replaced with anything else which is desired.
If I understand what I’m talking about, then I assume you do as well, but that you might expect a higher level of formal rigor before you can “accept” my claims. I claim that although you may demand that standard, that I can provably (even in the formal, rigorous sense) accept my claims as true before I have satisfied any arbitrary level of demand.