Is Having Properties a Criterion for Existence?

Dear Dr. Craig,
In your most recent post, you wrote, "I'm inclined to say that ... properties don't really exist."
However, if the having of properties is a necessary criteria for being, then it follows that:
1. If something exists, it has one or more properties.
2. If God exists, He has one or more properties.
3. Properties do not exist.
4. God has no properties.
5. God does not exist.
Of course, I don't accept the premise that properties do not exist, so I wouldn't arrive at atheism. But since you deny the existence of properties, aren't you denying the existence of God? In fact, you'd be denying the existence of all things, which is an absurdity, for surely you must exist to deny anything else.
So I can only conclude that your idea of existence doesn't require the having of properties. If that's so, what criteria constitutes existence?
Furthermore, I hope you have a better answer than to just say that properties are "useful fictions". I fail to see how a fictitious something or other can constitute a criteria for existence. One may as well appeal to a "blark" as a criteria for existence. My intent is not to be snarky, because I have the utmost respect for you and your work. However, I find your denial of properties as highly problematic. It appears more reasonable to accept the reality of properties, but to redefine them, if necessary, in a way that doesn't appeal to platonism.
Finally, I realize that the having of properties as a criteria for existence raises a problem of infinite regress (if a property exists, does IT have a property? And does its property have a property, ad infinitum?), but it seems any criteria we suggest will fall prey to the problem of self-reference.
United States

Click HERE to read Dr. Craig's answer