That’s not true. What I’m doing is I’m treating infinite quantities as if they are quantities.
Maybe you should start with the word “definable”. What does it mean? What does it mean to say that something is not definable?
In most cases, there is absolutely no need for symbols to look like what they represent.
The sentence “infinite line of green apples” looks nothing like the infinite line of green apples and it doesn’t have to. (Indeed, it would be a problem if it looked like the infinite line of green apples.)
If the purpose of symbols is to merely represent something, and not to look like that something, then there is absolutely nothing questionable about the act of symbolization. (Cryptography must be a very questionable practice.)
If there’s an infinite line of green apples in front of you and you say “Look, there’s an infinite line of green apples in front me!” the statement isn’t false by virtue of not looking like what it represents. The word “true” does not mean “a symbol that looks exactly like that which it is trying to represent”. It merely means “a symbol that can be used to represent that which it is trying to represent”.
You didn’t explain why.
Here’s the problem. You’re saying that one can only pretend that the symbol (\infty) can be used to represent infinity. But that’s not true. I don’t have to pretend. The symbol (\infty) CAN be used to represent infinity without any sort of pretense.
So I was right when I said that you’re one of those people who think that the symbol must look like the symbolized in order to be able to say that the symbol represents the symbolized. According to you, if the symbol does not look like the symbolized, you can’t say the symbol represents the symbolized, but you can pretend that it does. Useful contradictions and all. Beside being wrong, what you’re doing here is justifying contradictions in the name of utility.
The symbol (\infty) does not represent undefinability. It represents infinity. Infinity and undefinability are two different concepts.
When I use a symbol to represent something (e.g. an infinite line of green applies), I am not describing what that symbol means, I am simply using a symbol to represent that something.
There is absoultely nothing that cannot be represented using a symbol. All it takes is to pick a symbol (you can literally pick anything) and say “This symbol represents this thing”.
The problem is that you do not understand what it means to say that a symbol is representing something. You have this naive idea that to represent something means to find a symbol that looks exactly like that something. That’s not true.
In other words, you think you’re an expert semiotician while in reality you know nothing about semiotics.
They are different concepts.
That merely means you’re one of those people who do not think but merely follow whatever is popular at the time.
You are deferring to the authority precisely because you have no idea why (0.\dot9 = 1).