[seebs]

Originally Posted by Michali

To seebs: What does it mean for something to have a function? Doesn't it mean that it functions in something?

No.

Not when we're talking about mathematical functions, anyway. You're mistaking mathematical functions for "uses".

Again, you simply don't know the terminology, and because you're not familiar with the field, you're using other meanings some of these words had in other contexts.

What is ice? Well the oxygen molecule functions as one pole and the two hydrogen molecules function as another pole, and then the water molecules align in a crystalline manner to make ice. And you want to say, "Well hydrogen existed in water before it existed in ice", and I'm like, "Well that doesn't matter what it was in water because the function of its polarization is what it is in ice." So "hydrogen's polarization from oxygen" is "ice". Take away the polarization, then no ice. Take away the ice, that entails no polarization. I've been saying it all along, and its that the system is its function, and the function entails its system.

And what you've been saying all along is, so far as I can tell, complete nonsense.

I think what you might be almost sort of getting at is a kind of notion of an equivalence class; if you have two inputs, A and B, and f(A) = f(B), then you're figuring A and B are somehow interchangeable, at least with respect to f(), right?

Now imagine only one system and only one function. The existence of the component parts are irrelevant and only exist because they might function in other systems. Hydrogen functions in water, for instance, and many other things, and that's why we can pull it apart from its function in water. But we see these multiple functions because we cannot grasp the overall function. This is in reference to the fact that we can technically make a law for any state in Conway's life to its total end state. The steps we take are something that we do. So if hydrogen functions as an element. Take away the element, you take away the hydrogen.

There's not necessarily an end state, though.

Furthermore, I think you're massively misunderstanding the term function. It sounds to me like what you need here is some exposure to basic abstract mathematics. You're seeing words which have special meaning in mathematics, and you're using plain English meanings, then expecting mathematical claims to still be true of those meanings too. They aren't.