Plato is famous for having argued that ideas are really existing things. The physical things around us are imperfect copies of these really-real—in fact more-real—things—“The Forms.” And whenever we know something, our knowledge involves our minds grasping these ideas—which nevertheless exist quite independently of our minds. These ‘ideas’ are not physical things, of course. But every physical thing exemplifies them. A triangular ‘Yield’ sign imperfectly exemplifies “triangularity.” But triangularity itself is not a physical thing and would exist even if nothing were triangular. And triangularity would exist even if none of us were thinking about it.
I think Plato was right.
Well, I guess I don’t think these ‘forms’ are more real than physical things. I think existence and reality are on-or-off affairs. Either you exist or you don’t. Either something is real or it isn’t. But I think that Plato was right that these ideas, though non-physical, are at least as real as physical things.
I also don’t think that all knowledge is actually just recollection, and is just a matter of grasping these ideas. (Plato thought that all true knowledge is seeing that certain things have to be the way they are, just because of the concepts involve. And he argued that when we come to “see” these truths, we must be recollecting what we once knew when our souls existed in the realm of the forms.)
I don’t buy that. Some of our knowledge is of conceptual truths—like mathematical truths—which have to be the way they are, for purely conceptual reason. But most of our knowledge is just knowledge of the way things, as a matter of fact, happen to be in the physical world. It isn’t conceptually necessary. And our knowledge of these contingent matters is real knowledge. I also don’t buy that our grasping of even mathematical truths is a matter of recollection; I don’t believe my soul once existed “in the realm of the forms.” I must admit, then, however, that our ability to “see” such truths really is deeply puzzling. How do we do that?! I have little idea, but I don’t buy that it’s recollection.
On the real, independent existence of ideas, however, I’m in. I’m convinced. It seems weird. But then, so? I see no good way to avoid thinking that Plato was right here.
Think about it: Is there such a thing as triangularity? I would think the sensible answer is, ‘Of course; many things have it.’
And would triangularity still exist, even if nothing “had it”—i.e., even if there were no actually triangular things in the universe? I would think the sensible answer would still be, “Of course.” Even in a world where nothing was triangular, there still could have been something triangular. In other words, even in such a world, it would still be true that there is a shape—triangularity, to be specific—which could have been exemplified; something could have had that shape. So then even in a world in which nothing is triangular, there would still be such a thing as triangularity.
In fact, do you think now that there actually are shapes which are not actually exemplified in the world? If so, there is a really existing idea (the idea of a thing being of that shape) which exists but is not exemplified.
Even simpler, is there such a thing as the idea of being a unicorn? Surely there is; we use the concept quite a lot in fairy tales. So the idea of a unicorn exists, even if there are no unicorns.
But then do these ideas exist independently of our minds? One might sensibly think that we produce these ideas; they depend upon our minds for their existence.
But run essentially the same arguments as above, altered to fit this question: If there were no triangular things, and none of us actually thought of the idea of a triangle, it would still be the case that there could have been triangular things? I.e., even in this case it still would have been the case that there is a shape—namely triangularity—which could have been exemplified but isn’t.
And surely there are shapes none of us have ever thought of. If you think there are, take that literally. There are such shapes. Obviously they weren’t produced by our minds.
So here is another aspect of reality which does not consist of physical things.
If you think that there really cannot be an idea without a mind to think it—but you believe in the whole world of mathematical objects—shapes, numbers, sets—which mathematicians talk about, and if you believe that for everything which has any characteristic, there is that characteristic, then you have a very powerful argument for the existence of God: There must be one unbelievably great mind to be thinking all these ideas.