Re "But the "necessary" existence is another "therefore..." that doesn't follow from the previous statement.": The ontological argument re-phrased.
Definition: God = that than which nothing greater can be conceived. Claim: a Being that *cannot* be conceived not to exist is greater than a Being that *can* be conceived not to exist. Muse over that definition and claim and they both sound appropriate to our idea of God, no? An atheist or agnostic is therefore saying: "Well, yes, IF God exists He would be a Being that cannot be conceived not to exist, but as we don't know whether or not He exists we're not getting anywhere." Let's unpack this sentence by our atheist: it comes down to this: "God is a Being that *cannot* be conceived not to exist, but I *can* conceive of Him not existing." That is a flat contradiction. The issue boils down to what Judy calls a "category error". To imagine that God's existence could be doubted is to put God's existence in the same category as the existence of salted popcorn, unicorns or quarks. It's to imagine that if God does exist He just *happens* to exist (like you) and so might *happen* not to exist, but God's existence is super-essential.
