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.
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.