I just tried this 'battleground god' thing and it told me:
'It is strange to say that God is a logical impossibility, but you don’t know whether God exists. If God is a logical impossibility, then surely She can’t exist, and so you know that She doesn’t exist.'
I don't get it. Why can't I be unsure about the truth value of something just because it's a logical impossibility? My understanding of logic isn't exhaustive.
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I feel like I might understand now. Can I represent your points as follows:
Assuming statement 1 is correct, without accepting a further premise I don't feel compelled to accept the second premise. It sounds like things which are logically impossible may in fact be equivelant to things which don't exist, and vice-versa. And that sounds intuitively compelling. If something was logically possible, it would happen. If it is wasn't possible, it's not going to happen. Or, the agent's modelling of the world is wrong.
Importantly, I don't accept premise 1, as I've indicated in another comment reply (something about how I find I'm wrong about the apparent impossibility of something, or possibility of something.)
Well, the conclusion should read not "more things" but "at least as many". Things might accidentally not exist.
I feel the fact that you reject premise 1 just means that you don't really grasp the concept of impossibility, logical or otherwise... Or you have a different concept of existence.
The reason why I used a semi-formal notation was to suggest that if you formalise it all, you can actually prove "P(x doesn't exist) ≥ P(x is impossible)" as a tautology. (Ignoring the issue that with specifically logical impossibility, you get into a bit of trouble with probability assignments to tautologies.)