Roger Penrose is a hack

[Belacqua]

then the mental and abstract would be by definition SUPER-natural or transcendental in the sense that they're not of physical reality. Now go watch the video.

I don't know about Craig, but as Penrose formulates the Three Worlds (following Popper) the world of commonly held intellect isn't what I'd call supernatural. Maybe transcendental, depending on how you're using it.

So as I understand it, World 1 is the concrete, tangible world. World 2 is mental phenomena, which is largely the internal representation of World 1, plus our personal experiences of emotion, thought, etc. 

World 3 is where it gets tricky. This includes things that are made up by people but exist in some way independent of particular minds. One example Popper gives is that of a symphony. The symphony was written by someone. It is sometimes performed by people or printed on paper. But it has an independent existence in a sort of non-particular mental realm. It continues to exist even if it isn't being played. It isn't equivalent to the scores it's written on. I suppose that as long as there is someone in the world who remembers it, or some creature in the world capable of recreating it from the score or the CD, it continues to exist.

A lot of things are like this. For example Sherlock Holmes. And one of the main points about objects in this world is that while they can't be quantified or measured by science-type objective methods, nonetheless we can say things about them which are true or false. For example, if I said that Sherlock Holmes lives in Peru and drives a taxi, this would be incorrect for the Sherlock Holmes that we know. We know what the "real" Sherlock Holmes is like, so we can recognize a parody or a "reboot," even though he never had a physical existence. Likewise we are able to say objective statements about a symphony, including whether a particular performance is good or bad, although the issue is not a scientific one.

Numbers are also in this category, which is what Penrose is most interested in. 

As far as I can tell, this is Popper's attempt to deal with numbers and other non-physical objects which are perhaps eternal but not limited to individual minds. It is a way to adapt Plato to a non-supernatural view. 

But I may be wrong. And as I say, I don't know Craig's take on all this.