In my humble opinion, much of the unsatisfactory vagueness that always seems to hover about ontological discussions on this subject is alleviated by sharply differentiating these three worlds, as Popper did in his fairly famous 3-worlds paper, which I recommend.
It is, I submit, the tendency to implicitly resolve the middle world (accurate imagination) with either the physical world (raising type conflicts for the formal crowd) or with the purely imaginary world (thereby unfairly yielding the tar brush to banish it from objective existence) that leads these discussions into infertile territory.
I've had a sudden impulse of delight which has led me to suggest a modified platonist position: as a new & improved modern platonist, I subscribe to the theory that world-1 objectively exists, world-3 subjectively exists and world-2 plows a middle ground we have not named, and which is neither entirely objective nor subjective. I'm going to call it "conditionally exists" or interjective. The condition being, of course, that world-1 behavior is close enough to world-2 descriptions to qualify as existing, for whatever purposes we have to hand. Something that cannot be guaranteed to be permanent or completely reliable. As an example--Ptolomaic astronomy is an interjective (world-2) reality of less reliable existence than Einsteinian astronomy. Nobody really thinks epicycles are an essentially explanatory orbital description, even though they accurately describe orbits. And nobody knows if Einsteinian astronomy is the final story. So there's an intractibly subjective element to world-2, even though it is objective in intent.
I call it the toe-in-the water school of platonism.
Well done, donh! And thank you for the heads up!
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.
"As far as Ortega is concerned,
I think is he's on the money about idealism separating the thinking mind from his existential context. "
So also Voegelin on scientism. (which general_re mentions, and it sounded to me like he had Hayek in mind).
I wanted to get around to this but never had the time. In the larger world of Kolmogorov Information Theory, "world-2" is fully described as a single concept in both optimal and non-optimal forms. In its optimal form, a universal Kolmogorov machine is provably the most accurate model possible of the given data being modeled. Or to put it another way, a UKM is the mathematically optimal form for world-2. As such, this form also describes the limits of knowledge about any process a particular observer can have. In fact, the most intelligent observer of some given Kolmogorov complexity is a UKM.
At its best, a world-2 will asymptotically approach world-1 and converge very quickly even when world-1 has a KC vastly larger than the observer's world-2. Of interest, there are narrow edge cases when dealing with extreme complexity differentials where a UKM will regularly exhibit "irrational" behavior, while acting extremely rationally when faced with less complex patterns.
It is worth pointing out that a tractable UKM implementation has never been published (and the mathematics really doesn't proscribe an obvious good implementation), though you can show that it will run on any boring old Turing machine. It is also worth pointing out (to take this back to the topic it originated from) that the problem of genuine AI has essentially been reduced to the problem of designing a tractable UKM; I believe you can actually find published papers regarding this particular aspect, all of them quite recent. Lots of interesting work has been happening in this area as of late. Beside the interesting fact that this describes the most accurate observer possible (in a very deeply analytical sense), of interest is that there is known to be a class of algorithms in computer science that are only tractable on such a construct, including algorithms which are essentially considered "impossible" to implement today. Some day we will look back and wonder how we missed a solution that was so "obvious".