Interesting. I haven't read Popper. Of his three "worlds":
1) the physical worldI humbly suggest that only world one exists. I suppose now we need a definition of what it means "to exist." I think it means that it has objective existence -- external to our private conceptions of what's out there. Worlds two and three are the same thing -- abstractions in our minds, and they "exist" (so to speak) only subjectively. The difference between worlds two and three is that world two is a reasonably accurate conception of world one, and world three is fantasyland, as can be determined by reference to the reality of world one.
2) the imaginary world that tries accurately to describe relationships in the real world and
3) the imaginary world that does not try to be an accurate reflection of the physical world.
So, for example, you believe Aristotalian logic does not exist?