The Stanford Encyclopedia of Philosophy’s Russell’s Paradox entry has the following.

Russell’s paradox is the most famous of the logical or set-theoretical paradoxes. Also known as the Russell-Zermelo paradox, the paradox arises within naïve set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself. Hence the paradox.

Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves “R.” If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself.

Did Russell’s paradox exist before he . . . discovered it? Or . . . invented it? Which is it, discovered or invented? If discovered, then yes, the paradox was there since before the Big Bang, just waiting to be found. If invented, then no, the paradox came into existence the moment Russell first thought of it.

The paradox exists. For how much longer? Can an idea stop existing? That doesn’t seem right. It seems if all humanity vanished tomorrow, Russell’s paradox would still exist. But if an idea cannot cease to exist, then it obviously must exist for all eternity into the future. If Russell created the paradox, that would mean the idea is half-eternal, having a start time in the finite past but no end time in the future. It seems rather odd to say a mortal human being can create something which will exist for all eternity. It seems to make more sense to say that Russell’s paradox was discovered, not invented; that it has always existed.

Existed where? One answer is: in the mind of God. But this answer assumes an all-good, all-powerful, all-knowing being, which are more assumptions than we need. The minimum is merely to stipulate a place where all thoughts exist, without saying anything more about the place. I call the place the “mindscape.” I discussed the mindscape in another thread: https://thephilosophyforum.com/discussion/14133/where-do-thoughts-come-from-are-they-eternal-does-the-mindscape-really-exist.

I don’t claim the above is a proof; any of the steps in thinking can probably be disputed. But it’s a train of thought—an interesting train, at least, for me—that leads to the idea of the mindscape.