Plato is famous for having argued that ideas that are really existing things. The physical things around us are imperfect copies of these really-real—in fact more-real—things—“The Forms.” 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, for example, imperfectly exemplifies “triangularity.” But triangularity itself is not a physical thing, and it would exist even if nothing were triangular. 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 things are more real than physical things. I think existence and reality are on-or-off affairs. Either you exist or you don’t. Either it’s real or it isn’t. But I think that Plato was right that ideas are at least as real as physical things.

I also don’t think that all knowledge is actually just recollection, and 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.

Well, I don’t buy that; though some of our knowledge is of conceptual truths—like mathematical truths—which have to be the way they are, for purely conceptual reasons, most of our knowledge is just of the way things, as a matter of fact, happen to be among physical things. It isn’t conceptually necessary. But, with due respect for Plato, our knowledge of these things is real knowledge. And I don’t believe that even our grasping of mathematical truths is a matter of recollection; I don’t believe my soul ever existed “in the realm of the forms.” But I must admit, then, that our ability to “see” such truths really is deeply puzzling. How do we do that?! But I don’t buy that it is by recollection.

On the real, independent existence of ideas, however, I’m in. I’m convinced. It seems weird. But so what? I don’t see a good way to avoid thinking Plato was right about this.

Think about this for yourself: Is there such a thing as triangularity? I would think you would answer, ‘Of course; many things have it.’

But 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 answer still would be, “Of course.” Because even in a world where nothing was triangular, there still could have been something triangular. In other worlds, 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.

In fact, do you think there actually are any shapes which are not actually exemplified in this world? If so, there is a really existing property (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, wouldn’t still be the case that there could have been triangular things? I.e., even in this case, it surely 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 an aspect of reality which does not consist of physical things.

And if you think that, really, there 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 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.

-November 2016