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Video transcript

(intro music) Hi, I'm Scott Edgar. I'm an assistant professor of philosophy at Saint Mary's University, and today I'm going to talk about an argument that the German philosopher Immanuel Kant made about the nature of space. It's an argument that comes from his book The Critique of Pure Reason, which first came out in 1781, although by that time he'd been working on it for ten years. And philosophers call the argument "The Argument from Geometry." It's an argument, as I said, about the nature of space, but as we'll see, it hints at an incredibly striking conclusion about the nature of all knowledge, in particular, the conclusion that we never have any knowledge of how things really are in themselves. I'll come back to that point later. Right now, let's start with the question "What is the nature of space?" Is it a real thing that exists independently of our minds? Or is it not a real thing that exists independently of our minds? Well, one view you might think is really natural is that space is real. And what I mean by "real" in this context is that space is a part of the mind-independent world that exists independently of our knowledge of it. So in this view, the mind-independent things that exist in the mind-independent world are arranged spatially, and space is just one more part of the world that's mind-independent. Now, the point of Kant's argument from geometry is to show that that picture is wrong, and to argue for a completely different picture of the nature of space. On the view of space that Kant argued for, space is just something that our own minds impose onto our representations of the world. More specifically, Kant thinks our minds have a capacity to sense things, and that capacity to sense things is what imposes spatial structure onto our representations of the world. This is the view that Kant calls "the transcendental ideality of space," or "transcendental idealism" for short. He loves jargon, so his way of putting the view is to say that space is merely a form of our intuition, that is, just a structure our own minds impose onto our representations, and space is not a property of things in themselves, that is, it's not a property of things as they exist independently of our minds and of our knowledge of them. So that's the conclusion of Kant's argument from geometry: that space is merely a form of intuition and not a property of things in themselves. What's really interesting about the argument is its strategy. Kant's strategy is to argue for that conclusion on the basis of certain facts about geometry. That is, he thinks certain facts about the nature of geometry and geometrical knowledge turn out to mean that space has nothing to do with mind-independent objects, and is really just something our own minds impose onto our representations. So the argument's first premise is about the nature of geometry. Here it is: "Geometrical knowledge is synthetic a priori." Now, if you don't know what synthetic a priori knowledge is, you should go back and watch the video that explains that and then come back here, because what I'm about to say will make a lot more sense if you do that. So the question is "Why does Kant think our knowledge of geometry is synthetic a priori?" Well, first, geometrical knowledge is necessary and universal. It's plausible to think that a geometrical truth, like, say, the theorem that the interior angles of a triangle sum to 180 degrees, isn't just contingently true. It can't possibly turn out to be wrong. But also, it's not the kind of truth that there are exceptions to. It's not like the theorem says that the interior angles of some triangles sum to 180 degrees. It doesn't even say "most triangles." It applies to all triangles without exceptions. But Kant learned from the Scottish philosopher David Hume that we can't get knowledge of anything necessary or universal from experience. So Kant thinks, since geometrical knowledge is necessary and universal, it can't be empirical. It has to be a priori. But our knowledge of geometry is also what Kant called "ampliative." That is, it's not just a matter of empty or trivial definitions or conceptual truths, but rather it genuinely extends our knowledge. Of course, geometry does have definitions, like any other science. So, for example, when we say that a triangle is a three-sided figure enclosed on a plane, that's true by definition and so it seems kind of trivial. But when we're talking about theorems, like the one that says "the interior angles of a triangle sum to exactly 180 degrees," it seems like we're dealing with a difference situation. That theorem actually teaches us something new about triangles that we didn't already know just from the definition of a triangle. In that sense, geometry genuinely extends our knowledge of things like triangles. And Kant thinks that means geometrical knowledge is synthetic. So that's the first premise of Kant's argument from geometry: that our knowledge of geometry is synthetic a priori. Now let's look at Kant's second premise. It's got to connect the idea that geometry is synthetic a priori to Kant's conclusion that space is just something our own minds impose onto our representations of the world and not a real part of the mind-independent world itself. The premise says that synthetic a priori knowledge is possible only if space is merely a form of our intuition and not a property of things in themselves. In other words, the second premise of Kant's argument says that synthetic a priori knowledge is possible only if his view of the nature of space is true. So why should we think that premise is true? Here's Kant's argument. The first point to make is that geometry is the mathematics of space. So when we're talking about our knowledge of geometry, we're really just talking about our knowledge of space. And so if our knowledge of geometry is synthetic a priori, our knowledge of space has to be synthetic a priori too. So far, so good. But now Kant thinks we have to ask ourselves, "What would it take for synthetic a priori knowledge "of space to be possible?" Well first, the knowledge is synthetic, so it can't just be a matter of definitional or conceptual truths, because those would be analytic. But second, the knowledge is also a priori, so it can't be based on our experience of external objects, because we can only ever know about external objects empirically, through the senses. So Kant concludes that our knowledge of geometry has to be based on nothing but our own minds. His thinking seems to be that there are external objects that exist independently of our own minds, and then there are our own minds. Since our knowledge of space can't be based on the first choice, it has to be based on the second. When we have knowledge of space, like our knowledge in geometry, all we really have knowledge of is a structure our own minds are imposing onto our representations. That's why our knowledge of space can be completely independent of experience, which is say that's why it can be a priori. But as we already know, the idea that space is nothing but a structure our own minds impose onto our representations, is just what Kant means when he says in his second premise that space is merely a form of our intuition and not a property of things themselves. So that's the second premise of Kant's argument. When we put the two premises together, we get Kant's conclusion: space is merely a form of our intuition and not a property of things in themselves. There's still a lot of questions you might have about it (whether it's a good argument or a bad argument, whether the premises are true, whether they're false), and we'll look at those next time. Subtitles by the Amara.org community