Ohhhh, after reading the wikipedia article on impredicativity I think I understand the confusion better now! Yes. It is kind of strange, in a way, but it basically collapses to something that’s okay. Let’s take an example.
Suppose I say that “A bachelor is a married man,” this is a fine definition. I could then also say “a man is a bachelor iff he is a married man and he is a bachelor.”
This is indeed a super weird way of defining stuff, and you’d never normally do it (unless you have to because of weird second-order logic things, this is what’s going on in the proof above). But you can recollapse the definition for bachelor to be about everything that doesn’t require you to be a bachelor. So a bachelor is just a married man.
So God is something that has every perfect property except that it doesn’t have to have the property of being God to actually Be God. Once it has all the other perfect properties I say that it also has the property of being God, and that itself is also perfect. And it’s okay. If you like we could define two properties “Being God 1” and “Being God 2“ and then define two properties “perfect 1” and “perfect 2” and separate it all out. But it would be kind of annoying.
EDIT: I’ll leave it as an exercise to the reader to separate it all out ;)
Ohhhh, after reading the wikipedia article on impredicativity I think I understand the confusion better now! Yes. It is kind of strange, in a way, but it basically collapses to something that’s okay. Let’s take an example.
Suppose I say that “A bachelor is a married man,” this is a fine definition. I could then also say “a man is a bachelor iff he is a married man and he is a bachelor.”
This is indeed a super weird way of defining stuff, and you’d never normally do it (unless you have to because of weird second-order logic things, this is what’s going on in the proof above). But you can recollapse the definition for bachelor to be about everything that doesn’t require you to be a bachelor. So a bachelor is just a married man.
So God is something that has every perfect property except that it doesn’t have to have the property of being God to actually Be God. Once it has all the other perfect properties I say that it also has the property of being God, and that itself is also perfect. And it’s okay. If you like we could define two properties “Being God 1” and “Being God 2“ and then define two properties “perfect 1” and “perfect 2” and separate it all out. But it would be kind of annoying.
EDIT: I’ll leave it as an exercise to the reader to separate it all out ;)
Nit: a bachelor is an unmarried man.
My argument has been destroyed, and I am ashamed! (Seriously though, thank you for the correction)