@Drug Mentor
The way you wrote it totally removes the meaning I was aiming for. I don't claim to have made my point correctly using formal logic. It'd be awesome if I did, but I don't think I've pulled that off.
My reconstructed interpretations of your argument in post #19 were not presented using formal logic, that was informal logic. I certainly wasn't trying to remove your meaning, I was trying to make it more perspicuous. I apologise if I came across as uncharitable in my attempted reconstruction(s) of your argument.
By binary I mean a statement that can be negated. True/False, Exists/Doesn't Exist
Is there such thing as a statement that can't be negated, at least in principle? It's negation might not be correct, but in principle I expect that one can assert the negation of any statement.
God exists is a valid statement, and if existence has two states (Exists/Doesn't Exist) then it is perfectly valid to write the statement God doesn't exist. Well, here's what I'm poking at. God doesn't exist is not a valid statement. Sure you can write it down, but it is a paradox. Kinda like the statement: I don't exist. Well, if I don't exist, then who's the I that is claiming non-existence. I see this mirror the same pattern in Russels paradox. If you disagree I'm interested in your reply.
What do you mean by
valid? In logic when we say a formula is valid (not to be confused with saying that an argument or an inference is valid) this is generally interchangeable with the claim that the formula is tautologous - i.e. true on every possible interpretation. I am guessing this is not what you mean though, because even if the claim 'God exists' is necessarily true, it certainly isn't logically tautologous by virtue of its
form. In fact, if one doesn't presuppose a non-empty domain of discourse then the more general claim that something exists is not valid/tautologous.
Why do you think that asserting God doesn't exist is a paradox? From what I can tell, you aren't suggesting that 'God doesn't exist' logically follows from the assumption that 'God exists'; so, how does the initial assumption lead to a paradox? I am inclined to think you are going to respond that it does not (and I would certainly agree with you on that point!), but, if that's the case, then introducing the proposition that 'God exists' seems entirely superfluous.
You seem to want to say that denying the existence of God is somehow paradoxical, but, you haven't really explained how at all. Assuming that I am correct in thinking you are not claiming that one can derive 'God doesn't exist' from the premise 'God exists' then it is difficult to see what the paradox is. You might say that 'God exists' is a necessarily true statement, so that to assert its negation is necessarily false - but, there is nothing inherently
paradoxical about asserting a necessarily false claim. Moreover, you haven't provided any reason for thinking 'God exists' is necessarily true...
I certainly have a lot of trouble seeing the connection between this idea and Russell's paradox. For one thing, if they were analogous then the assertion 'God exists' would be no more or less paradoxical than the assertion 'God does not exist'; either assumption would logically entail the other and from here it is trivial that by and-introduction one derives an explicit contradiction (a statement which takes the form (
p & ~
p), or, in the case of Russell's paradox ((
R ∈
R) & (
R ∉
R))).