▶︎ 0:00 We were talking last time about Kant's route into the issues and problems of the Critique of Pure Reason. And we had said that Kant ends up framing the major question of what can we know in the Critique of Pure Reason in terms of what can we have synthetic a priori knowledge and of what can we not have synthetic a priori knowledge. That's his real focus in the Critique of Pure Reason.
▶︎ 0:31 And the answer that Kant gives, we noted, is that we can have synthetic a priori knowledge of objects of possible experience, but we can't have synthetic a priori knowledge for objects beyond the limits of possible experience. And what Kant has in mind when he's talking about objects of possible experience is objects given to us in space and time.
▶︎ 1:00 And so we might wonder, what is it about space and time that's special where we can have knowledge of objects, synthetic a priori knowledge of objects given to us in space and time, but allegedly not have synthetic a priori knowledge of objects beyond space and time. And the answer that we'll see in more detail going forward is that for Kant, space and time have a special status.
▶︎ 1:35 Namely, Kant maintains that space and time are ideal, that they are what he calls mere forms of intuition and that they don't count as objective features of things in themselves. So what I'm going to do is I'm going to present this aspect of Kant's philosophy, which is typically referred to as Kant's transcendental idealism, where Kant draws this distinction between appearances and things in themselves, where Kant makes the claim that appearances are spatial and temporal, whereas things in themselves are not spatial and temporal. And get this position in view and some of the reasons in view why Kant thinks people should take this position seriously.
▶︎ 2:38 And then later down the road, we'll see how exactly Kant wants to use transcendental idealism to provide an explanation for how synthetic a priori knowledge is possible for objects of possible experience, for spatial and temporal objects. But that is going to wait for a later session.
▶︎ 3:03 Remember from the last lecture that Kant gave us this very general philosophical history where Kant suggested that philosophy historically seems to have this cyclical structure where we go from dogmatism to skepticism to indifferentism, and then we return to dogmatism because indifferentism is not a really stable position for us to remain in. And things just continue like that. And I noted that one of the varieties of skepticism that Kant has in mind there seems to be the sort of skepticism that results from cases where there seem to be good arguments for contradictory conclusions, where the model for this kind of skepticism is the ancient Pyrrhonian tradition.
▶︎ 4:03 And Kant himself notes that these kinds of skeptical quandaries that result from seemingly equally good arguments in favor of contradictory conclusions was one of the things that initially drove him himself to the position in the Critique of Pure Reason. And he notes this, for example, in this late letter to one of his contemporaries, Garve, from the late seventeen nineties, where he suggests that it was a section of the Critique of Pure Reason called the antinomy of pure reason that deals with these kinds of contradictions that had played a really strong role in getting him to the position in the Critique of Pure Reason. I mentioned in the last lecture that there's some scholarly controversy about how to square this claim about the importance of this kind of skepticism with the Humean sorts of issues and Kant's intellectual development, but we'll leave all that to the side and just focus on the issues themselves.
▶︎ 5:17 Kant himself also entertained at various points the notion that it might be a good way of presenting and introducing the issues in the Critique of Pure Reason to readers by starting off with these skeptical arguments leading to different contradictions because he seemed to think this could provide a good motivation for taking one of his core positions, namely transcendental idealism, seriously, getting readers to see that there's a serious issue with traditional claims to metaphysical knowledge, seeing that transcendental idealism seems maybe like a promising route for providing some resources for dealing with those quandaries. And then taking off from there. He never ended up writing that popular work that was gonna take that structure and that exact form. But it's definitely something that he entertained and thought might be a good route into transcendental idealism and his critical philosophy more generally.
▶︎ 6:31 And so, following the suggestion from Kant, that's the route I'm gonna take here. I'm gonna look at some of these skeptical quandaries that Kant suggests a traditional metaphysics is gonna find itself in, and then illustrate how Kant thinks transcendental idealism can provide a way out of those quandaries. And then I'll talk a little bit about transcendental idealism itself, and then raise some questions at the end regarding transcendental idealism.
▶︎ 7:11 In the Critique of Pure Reason, there's a chapter called "The Antinomy of Pure Reason." And when Kant uses this term antinomy, he has in mind the notion of a conflict that results from the laws of our cognitive faculties themselves. The antinomy of pure reason is a situation where we get a conflict, that's the anti coming from the notion of two conflicting notions, where we get a conflict where there's something lawful about that conflict, namely that the conflict has arisen from our minds just following their lawful principles of reasoning. And Kant suggests that there are four conflicts that result from the different principles of our cognitive faculties, from the laws of our cognitive faculties. And he calls these four conflicts, these four antinomial conflicts.
▶︎ 8:28 And what I'm going to focus on here is the first of these four antinomial conflicts. I'm just going to call it the first antinomy. The first antinomy deals with the topic of the world taken as a whole in space and time and with the question of whether the world is spatially infinite or spatially finite. And similarly, the question whether the world is temporally infinite in the sense of not having a first beginning but having existed from eternity or temporally finite in the sense of having had a first beginning in time. Kant really isn't concerned with the question of future time, in infinitude or finitude for future time. It's a question rather about the past when he's talking about time here. But we noted in the last lecture that Kant thinks
▶︎ 9:37 Reason has this natural tendency to drive us into metaphysical speculation because reason has this sort of demand for arriving at the unconditioned. In the case of the antinomies, Kant is focused on a particular form that that demand has taken. Namely, Kant says that this demand for the unconditioned seems to drive us to the notion of the world taken as a whole, the world taken as a totality.
▶︎ 10:20 So think about the current moment of time, the world here in this current moment of time. In this current moment of time, the world in this current moment of time seems to be temporally conditioned in the sense that we take there to have been a prior moment of time, and the world had some state in that prior moment of time, and there was a prior moment of time before that, and the world had some state in that prior moment of time. And so we get this series, and reason demands that we ultimately arrive at something unconditioned.
▶︎ 11:08 It seems, Kant says, that in principle, at least at a first glance, that there's two different ways that the world could count as unconditioned, temporally speaking. One way that the world here could count as unconditioned is where we arrive at a first beginning of the world in time. That is a first beginning, and so there's no prior state of the world that conditions it. Rather, as a first beginning of the world in time, it's counting as a case of the unconditioned.
▶︎ 11:59 The other way that it might seem like the world could count as unconditioned, temporally speaking, would be if the world had literally existed since eternity. In that case, there's not a first beginning that's unconditioned in the sense of lacking some prior state of the world before it that's conditioning it. But the whole series, the whole eternal series, the whole infinite series of temporal moments counts as the full totality, counts as a case of the unconditioned.
▶︎ 12:46 So there's two structures that it seems initially like the world could have that would count as satisfying this demand for the unconditioned. First, there could be a first beginning in time, so a finite kind of structure where that first beginning is what's counting as unconditioned. Or there could be an actual infinite past series. There's no element in that series that is by itself unconditioned, but the series taken as a whole doesn't have any further condition. The series taken as a whole is what counts there as unconditioned.
▶︎ 13:32 Similarly, for space, Kant raises the question about the notion of the world as a whole in space. And so Kant notes again that there could be, it seems, a finite kind of scenario where the world has an outer boundary in space, and that outer boundary of the world is not conditioned by some further piece of the world beyond it. Rather, it's the final boundary of the world in space. Or you could have the world taking up infinite space. So you get an infinite scenario, and in that case, there's no edge of the cosmos that counts as unconditioned, but the whole totality, the whole infinite totality counts as unconditioned.
▶︎ 14:35 So Kant maintains that reason presenting us with this apparent demand for the unconditioned, when that demand is applied to the notion of the world in space and time, drives us to the notion of the world taken as a whole in space and the world taken as a whole in time, and then presents us with the question: Is the world taken as a whole in time a world with a first beginning, or is the world taken as a whole in time eternal? Is the world taken as a whole in space something that has an outer spatial boundary, or is the world taken as a whole in space something that fills infinite space?
▶︎ 15:31 What Kant aims to do is he aims to show that there are equally good philosophical arguments for the competing claims that the world has a first beginning and the world is eternal, and the world has an outer limit in space, and the world takes up infinite space. On the basis of these, what Kant takes to be equally good arguments, Kant thinks we arrive at this conflict, this contradiction, where we seem to be committed to saying that the world as a whole both is finite and infinite, temporally speaking and spatially speaking. What Kant is then going to suggest is he's going to suggest that transcendental idealism is going to provide the way out of this conflict.
▶︎ 16:32 What we want to do is we want to start by seeing the more detailed arguments Kant presents that lead to this conflict, and then once we see why Kant takes the conflict to hold, then we'll see how he takes transcendental idealism to provide a way out of the conflict. Before going into the detailed arguments, though, I should just foreshadow the following. Kant seemed to think that these arguments were really definitive. He seemed to think that he had found truly excellent arguments that any philosopher was going to need to accept, which showed that inevitably when we try to reason philosophically about the notion of the world as a whole, we find ourselves caught up in these contradictions unless we embrace transcendental idealism. But it's definitely an open question, if Kant's arguments are as solid and definitive as he himself took them to be. We'll just want to keep that in mind as we're looking at the specific arguments that he himself gives.
▶︎ 17:48 But in addition to Kant's own particular arguments, we all know that there's a ton of different philosophical paradoxes, surrounding notions like the infinite. Kant's certainly not by any means alone in the philosophical tradition in thinking that the infinite is something that ultimately philosophically is very hard to reason about or make sense of, et cetera. His arguments actually played a significant role in the intellectual history of the development of areas like set theory in contemporary mathematics that deal with notions of the infinite.
▶︎ 18:27 What are then the specific arguments that Kant gives? Let me start with the case of the world in time, and then after that, we'll look at the case of the world in space. And it's going to be easier if I draw some things on the board.
▶︎ 18:58 We're talking about the world as a whole considered in relation to time. We said there's two options. There could be a first beginning or the world could be eternal, having already existed for an infinite amount of time. The way that Kant's going to argue is he's going to assume one of these scenarios is the case, and he's going to show that assumption gets us into philosophical problems such that we should reject the assumption and accept the opposite. And he's going to do that for both scenarios.
▶︎ 19:37 In practice then, that looks like the following. Let's start off by assuming that the world is infinitely old, that the world does not have a first beginning in time, but rather exists throughout all of infinite past time. Kant understands time in a pretty standard way as something that takes place through a series of stepwise successions. So you have one second, followed by another second, followed by another second, followed by another second.
▶︎ 20:32 If the world is infinitely old, then what that entails is that the world has been going through these stepwise successions, let's say one second followed by another second. And that in doing so, the world has managed to traverse an infinite collection of these successive stepwise successions. So again, if the world's infinitely old, then the world has persisted through an infinite series of stepwise successions.
▶︎ 21:20 But Kant defines the notion of the infinite in terms of a magnitude that cannot be traversed by a successive series of finite steps. So to be infinite is to be a magnitude that's so large that it's impossible to traverse it, to get across the whole magnitude through a series of stepwise successions. So the basic intuitive idea behind Kant's claim here is just think of the natural numbers. Think one, two, three, four, five. Kant says if you're just adding one and then adding two and then adding three and then adding four, so you're moving through the collection in this stepwise way, that you're never going to complete the traversal of the entire infinite collection of natural numbers proceeding in that way.
▶︎ 22:36 This is Kant's basic definition of what it is to be an infinite magnitude. So if the world's infinitely old, then the world's age is the sort of thing that could not have been traversed through a series of stepwise succession. And now we've run ourselves into a huge conundrum. It doesn't seem like the world actually can be infinitely old, because in order to be infinitely old, it would have had to have already traversed an infinite collection of past moments. But we've defined the notion of an infinite collection of past moments as a collection that can't be traversed through a stepwise succession of different moments.
▶︎ 23:24 So Kant says it can't be the case that the world is infinitely old. It can't be the case that the world lacks a beginning in time. So the opposite must be true. It must be the case that the world has a beginning in time.
▶︎ 23:44 All right. Let's now work with the assumption that the world has a beginning in time. So this is the assumption that the world is finitely old. Kant thinks that the notion of a beginning is the notion of a certain change, a certain change of state, where something initially was not and then came to be. And so when Kant's talking about the notion of the world having a beginning in time, he's not talking about the notion of time having a beginning. He's talking about the notion of the world, the collection of entities and objects beginning in time.
▶︎ 24:46 So his picture of a beginning in time, the world having a beginning in time, is the following. We have time and the world is in time. Here's the present moment, and this is the beginning of the world in time. And so the way that Kant's understanding the question here is, could this obtain, this scenario where there's empty time and then there's a change where the world comes to be in time? And Kant says no.
▶︎ 25:38 And unfortunately, the precise reason why he says no is not entirely clear, and it's the sort of thing that's subject to different scholarly controversy. But one way that his argument is often understood is as suggesting the following: any empty moment of time seems qualitatively the same as any other empty moment of time. And so there doesn't seem to be any reason why the world would come into existence after this empty moment of time rather than after this empty moment of time or after this empty moment of time. After all, all these different empty moments of time are qualitatively the same. What explanation could there be, what rationale could there be, what reason could there be for why the world would come into existence after one of these empty moments of time rather than after one of the other empty moments of time?
▶︎ 26:57 And so, if that's the way to take Kant's argument, then Kant says we again have run into a conundrum. It's not possible for the world to have a first beginning in time because there's no way to explain it coming into existence in time after one empty moment instead of after some other empty moment. And so we're driven back to the notion of the world needing to not have a first beginning in time, but instead being infinitely old. And so we say this can't be the case. It doesn't make metaphysical sense. So the opposite must be the case. It must be that the world instead is infinitely old.
▶︎ 27:43 Now, there's some obvious questions that one can raise about these kinds of arguments, like the argument here against the world being infinitely old. One might think Kant's putting a lot of weight on his definition of infinite as the sort of thing that it's impossible to traverse through a stepwise succession. And one might wonder if that's an appropriate definition of the infinite in this case. Or here, one might wonder, Kant, why are you assuming that it's a question of if the world began at some point in empty time? Why not instead think the question should be something like, did the world and time both come into existence together?
▶︎ 28:32 And this is a point that Kant's own contemporaries recognized, and pressed him on. So again, it's not by any means clear that Kant's arguments here are as definitive as he himself would have liked them to be. Rather his own contemporaries thought that there might be other maybe potential avenues around them. I'm gonna set those potential worries for the arguments aside, because I'm gonna present the space scenario. And what I really wanna focus on is less the adequacy or inadequacy of these specific arguments and rather the larger issue of transcendental idealism that Kant himself takes these arguments to motivate. All right, so let's turn now to space.
▶︎ 29:34 So again, we have two scenarios, a finite scenario and an infinite scenario. Let's start with the infinite scenario. The assumption is that the world does not have an outer boundary in space, but rather the world is infinitely large. Kant thinks that in order for us to be able to say that the world is infinitely large, that it needs to be the case that we have a measurement of the world.
▶︎ 30:19 But the way that we measure things is, on Kant's view, through a process of stepwise succession. So let's say I wanted to measure this table and I take some kind of ruler, like this piece of chalk, and I know how long this piece of chalk is. And I say, "All right, here's one unit, here's another unit, here's another unit, here's another unit." And so by applying the unit measure successively, I arrive at a measure of how long the table is.
▶︎ 30:54 So Kant thinks that for us as human beings, this is how measurement always works. And so if we're gonna say that the world is infinitely large in this scenario, the claim is that the world has an infinitely large measure. And then for the world to have an infinitely large measure, we would need to be able to apply some unit measure over the entire expanse of the cosmos, the world here understood as the cosmos. And that application would be the sort of thing that was a successive application of the unit after the unit after the unit.
▶︎ 31:43 And now Kant says we run into the same problem we had in talking about the world as being infinitely old. Namely, in order for the world to count as being infinitely large, having this infinite measure, it needs to be the case that we could traverse that infinite measure or that infinite magnitude through this stepwise succession. But given Kant's definition of the infinite, it's by definition the case that we can't traverse that magnitude through this process of stepwise succession. And so we can't claim that the world has an infinite measure. And as such, we should reject this option and conclude the opposite, that the world is finitely large.
▶︎ 32:58 All right, so now let's work with this assumption, this different assumption that the world has a finite size and space. And again, Kant understands this scenario in a particular way. We have space. Space here should be understood as infinite, but I can't draw infinite space, so I'm drawing this rectangle instead. So here's space. And the world has a finite size in space. So the world is here. It's taking up this much space, and it has this outer edge in space.
▶︎ 33:43 So this is similar to the way that Kant was understanding the question of a first beginning in time. That the world is in time. The world is in space. And Kant says, could it be the case that this scenario obtains? And Kant says no. Kant says this scenario indicates that the world stands in relationship to space. The world is here in space. The world stands to space in a particular relationship in virtue of being here and being bordered by space here, et cetera.
▶︎ 34:30 But empty space, Kant says, is nothing. Empty space is not an object. Rather, there's nothing in empty space, and empty space itself is not an object. Indeed, there's a section of the Critique of Pure Reason called the Table of Nothing, where Kant says space is a case of nothing. It's a type of nothing.
▶︎ 35:00 And now Kant makes a further metaphysical claim. He says there can only be relations between objects. You can't have a relation between something and nothing. You can only have relations between two different objects. So for this to obtain, the world would have to be in a relation to space. But space is nothing, and so there can't be a relation between the world as an object and nothing, because there can't be a relation between something and nothing. Relations can only obtain where there's two objects and a relation between those two objects.
▶︎ 35:46 So Kant says this scenario is not possible. We should reject it. And now we should conclude the opposite, that the world size is not finite, but rather that the world is infinitely large. It fills up all of space.
▶︎ 36:07 Again, there's no doubt that these are arguments that one can raise a number of questions about. The first argument is presupposing a certain notion of what counts as a condition for something having a measure that some people very well might reject. It's also, once again, presupposing this definition of the infinite as something that can't be traversed through a stepwise succession, which some people might want to push back against. This argument is assuming that the scenario of the world having a finite size and space needs to be understood this way rather than maybe just thinking that the question is, do space and the world end together at the same place? And moreover, it's assuming that space taken by itself is nothing, whereas one could suggest that no, space isn't a standard kind of everyday object, but nevertheless, maybe it's some kind of entity or has some kind of being where it can stand in relation to things.
▶︎ 37:23 So there's no doubt that Kant's making a number of weighty assumptions in making these arguments. But he certainly thinks that these are assumptions that his contemporaries should be sharing with him. And he certainly thinks that his contemporaries should be taking these arguments as extremely strong arguments, leading us to this philosophically perilous conclusion, namely that the world is infinitely old, but also not infinitely old. The world is infinitely large, but also not infinitely large. And landing us then straight into these contradictions.
▶︎ 38:08 Let's go ahead and play along with Kant. And for the sake of considering transcendental idealism more fully, just for the sake of that, grant Kant these specific arguments leading to these contradictions. How does Kant want us to get out of these contradictions? Kant thinks that the only way that we can avoid these contradictions is by embracing his own theory of transcendental idealism, which draws a sharp distinction between the notion of appearances and the notion of things in themselves. Let me put the theory on the board, and then I'll illustrate why Kant thinks it gets us out of these contradictions.
▶︎ 39:21 Here's one way of understanding transcendental idealism. It is not the only way. This is one of Kant's best-known theories. It's also one of his most debated theories. And there's various interpretations. I'm not going to attempt to canvas all of them, but I'm just going to present what's at least one standard presentation of the view.
▶︎ 39:46 There are things in themselves understood as things the way they are independently of being observed by us. There's some kind of relation that these things in themselves have to us where we can count as being affected by things in themselves. And in being affected by things in themselves, we receive what Kant calls sensation, this kind of sensory data. Our minds have to process this sensation that's given to us by the affection, and our minds process the sensation in the following ways.
▶︎ 41:11 First, our minds present the sensation to us in a spatial way and in a temporal way, that all of our intuitions are structured by these forms of space and these forms of time. And so Kant will talk at this stage of the mental processing about there being the matter of the intuition, like the stuff that's been arranged or organized in space and time, and then space and time as the forms, the structures in which that matter is arranged.
▶︎ 41:59 He doesn't mean matter in the sense of physical matter, but just matter in the sense of the stuff that's getting an organization to it. Kant also maintains that a certain set of a priori concepts called the categories, which we'll discuss later, are involved in the general processing. And the result of the cognitive processing is spatial and temporal experience. So here's a house, here's a tree, here's a friendly dog. Everything as we experience it in space and time.
▶︎ 43:06 Now, there's a lot of questions that one can raise about transcendental idealism, in particular, about the relationship between this, which we're gonna call appearances, and things in themselves. Some people want to say that there's a way in which we can count the appearances as in some sense identical with things in themselves, like the appearances are the ways that things in themselves count as appearing to us. Other people want to say, "No, the things in themselves, the appearances should be more strictly distinguished." Let's leave that for now.
▶︎ 43:56 But let's work with this basic picture that there's sensation that's mentally processed and organized in such a way that the world appears to us in a particular way. And by itself, that's hardly a foreign idea. There's all sorts of ways in which our minds process the information that we get from the world around us, even outside of these Kantian kinds of contexts.
▶︎ 44:21 So I think one helpful example is light hits our retinas, but there's actually a lot of blood vessels in our eyes, and these blood vessels end up blocking a lot of the light that otherwise would be reaching our retinas. And so if we just represented the world purely on the basis of the information that was hitting our retinas, we would be representing the world with all sorts of dark gashes and lines where that light has been blocked out. But we obviously don't represent the world that way. We rather, in our visual experience, standardly have this kind of phenomenological continuity rather than a bunch of fissures and gaps. So our mind is obviously involved in some kind of further processing such that things appear to us in a certain way that goes beyond what was just given to us in the physical moment of sensation.
▶︎ 45:30 Kant's saying something similar, but he's not just talking about gaps from veins and blood vessels in our eyes. Rather, he's making this bolder claim that the same sort of thing is true of space and time themselves. How is this then supposed to get us out of these contradictions that Kant claimed we've been driven into by speculating on the nature of the world as a whole? Kant suggests that we have been driven into these questions of the size of the world as a whole and the age of the world as a whole because we've been making an illicit assumption. Namely, we've been illicitly assuming that the world as a spatial and temporal object is a thing in itself.
▶︎ 46:45 Kant suggests the following line of argument. If appearances are things in themselves, then the world is given as a whole. If the world is given as a whole, then it is either finite or infinite. Therefore, the world is finite or infinite. Kant thinks that this second premise is uncontroversial, that if the world is given as a whole in space and time, then it's either finite or infinite in space and time.
▶︎ 48:40 What Kant zeroes in on then is this premise, this premise that if appearances are things in themselves, then the world is given as a whole. And Kant thinks that this premise seems to be in the minds of philosophers supported by a certain position regarding things in themselves. Namely, that for things in themselves, if the conditioned is given, then the unconditioned is given. So if one accepted this principle, if one said that for things in themselves, if the condition is given, then the unconditioned is given, then if one took the world in space and time to be a thing in itself, it would be true of the world in space and time that if the conditioned is given, then the unconditioned is given. And so it would be true of the world in space and time that since there are conditioned elements like this particular moment of the world or this particular region of the world, that the world as a whole, the unconditioned would be given as well. And then it would make sense to ask if that whole is finite or infinite.
▶︎ 50:53 Let me just rehearse that line of thought one more time for everybody. Just assume this is true, that for things in themselves, if the conditioned is given, then the unconditioned is given. And now just assume that the world as a spatial and temporal object is a thing in itself or a collection of things in themselves. Then it would follow that if some aspect of the world is conditioned, if the conditioned is given, that the unconditioned is given. And what would the unconditioned be in this scenario? It would be the world taken as a totality, the world taken as a whole. And then it would make sense to ask, is that whole finite or is that whole infinite?
▶︎ 51:48 Kant's suggestion is that we need to get out of the contradictions by putting into question the very assumptions that lead us to ask, is the size of the world infinite or finite? Namely, what Kant says is we should reject this here. We should draw a distinction between the world in space and time as an appearance and things in themselves. And when we draw this distinction between the world in space and time as an appearance and things in themselves, then we don't have any reason to claim that this principle holds for the world as a spatial and temporal entity.
▶︎ 52:48 We were saying that this principle held for things in themselves, but now we're saying the world as a spatial and temporal entity is being distinguished from things in themselves. So we don't have reason to claim that this principle holds for the world as a spatial and temporal entity. And since we don't have reason to say that this principle holds for the world as a spatial and temporal entity, we don't have reason to say that the world must be given as a whole, that there must be an unconditioned world, a world whole. And since we no longer have reason to claim that the world is given as a whole, it no longer is such that we have to ask, is the size of the world infinite or is the size of the world finite? Instead, Kant's suggestion is that we can say that the size and age of the world are both indefinite.
▶︎ 54:10 If I'm talking about the age of the world, I can go back and consider the world a second before now and a second before then and a second before then. I can regress through this series of past states of the world. For any moment that I get back to in this regress, I can always consider a prior moment, but I never can complete the regress. If I'm treating the world as the spatial and temporal world in space and time as an appearance, I'm treating it in the sense of how I represent it, I'm representing it in this regress as having the structure that I can always go a step further and can always go a step further and can always go a step further.
▶︎ 55:04 So it doesn't seem right to say that the world size is finite in the sense of there being a first beginning, because I can always consider the regress further. But it also doesn't seem right to say that the age of the world is infinite because this is the world as it appears to me, the world as I represent it, and in this regress, I never complete the infinite sequence. And so it's never such that I'm saying that the world counts as an infinite appearance. So the age of the world then is taken to be indefinite, neither finite, strictly speaking, nor infinite, strictly speaking, but rather having the structure of something that we might today call a potential infinity, the sort of thing that can always be extended further and further, but it's never actually given in a totality as infinite.
▶︎ 56:04 Similarly, with the size of the world, we can always consider a certain boundary of the world, but then we recognize that that's going to need not to be bordered by empty space, but by more world stuff and more world stuff and more world stuff. And so the size of the world, spatially speaking, is also going to be seen as indefinite, not finite, strictly speaking, not an actual infinite, but rather having the structure of always being potentially extended further and further and further and further.
▶︎ 56:47 One interesting thing I'll note historically is that before Kant developed his critical philosophy, he was really interested in astronomy and cosmology and issues in cosmogony, like the origins of the solar system. And Kant's early view was such that there's an infinite space and there's stuff throughout infinite space, but that stuff is unstructured. And there's this continual process of structuring where a solar system forms here and then a larger system around it and then a larger system around it. So the stuff's all there, but you get this potential infinity structure of that stuff receiving some kind of order or structure to it, where the notion of a cosmos understood as a structured entity, already in Kant's early thought has the notion of this potential infinity.
▶︎ 58:01 But it seems like in the Critique of Pure Reason, at least on standard interpretations, that Kant's going further than he did in that earlier work. And he's no longer claiming that, "Oh yeah, there is infinite unstructured matter in infinite space." Rather, he's saying that, "No, no, even the question of the size of the matter should be taken as indefinite," the sort of thing that only can be understood in terms of a potential kind of infinity. Just leave that as an interesting historical tidbit.
▶︎ 58:43 Kant is maintaining then that if we treat the world understood as a spatial and temporal entity as an appearance, then we'll deny that the world exists as a whole and we'll deny that the size of the world is either finite or infinite. We'll say the size of the world is indefinite and we'll no longer be stuck with these contradictions that were arising from presupposing that the size of the world had to either be finite or infinite. Instead, we'll say both of those conclusions that we came to earlier are false. The size of the world instead is indefinite. The age of the world instead is indefinite.
▶︎ 59:44 Now, there's something about Kant's argument here, the way I've presented it, which raises a certain kind of question. A question about the extent to which, or the way in which Kant sees himself here as raising questions about the possibility of something that we might call metaphysical knowledge. It seems like Kant's argument, the way I had it on the board a few minutes ago, was saying that we have the following principle. For things in themselves, if the conditioned is given, then the unconditioned is given.
▶︎ 1:00:59 The argument, the motivation, the rationale that we've been presenting here for transcendental idealism as a resolution of the antinomy seems to presuppose the truth of this claim. We said, "Look, assume this claim is true, assume the world as a spatial temporal entity is a thing in itself, then you get the antinomial conflicts." And Kant says that the way to avoid the antinomial conflicts doesn't seem to be to put this principle in question. Rather, Kant says the way to avoid the antinomial conflicts is to deny that the world as a spatial and temporal entity is a thing in itself or collection of things in themselves and say, therefore, this principle doesn't pertain to the world as a spatial and temporal entity because it just pertains to things in themselves.
▶︎ 1:02:01 One way that one might obviously then question Kant's own resolution of the antinomial conflicts would be to not distinguish appearances from things in themselves, but rather to try to question this principle to say, "Kant, what reason do you really have for saying it's true of things in themselves that if the conditioned is given, then the unconditioned is given?" But let's go ahead for a second and see, if one accepts Kant's own solution of transcendental idealism and in doing so keeps this principle in place, what might follow for Kant's philosophy.
▶︎ 1:02:50 So if one keeps this principle in place, then Kant doesn't seem to, doesn't, on my interpretation, let's say, Kant does not deny that there are things in themselves. It seems perfectly reasonable to say that any given thing in itself is either conditioned or unconditioned. Those seem like good candidates for a mutually exhaustive set of options. So if a thing in itself is conditioned, then this principle holds for it, and so the unconditioned is given at the level of things in themselves. If that thing in itself that we were considering initially was not conditioned but unconditioned, then again, the unconditioned is given. It's just a quicker route to the unconditioned.
▶︎ 1:03:52 So it seems that keeping this principle in place leads us to what we might see as a relatively strong metaphysical claim, namely that the unconditioned exists. There is a metaphysically unconditioned. Some readers of Kant are going to balk at that conclusion because they're going to think to themselves, one of Kant's main claims is that we lack any kind of substantive metaphysical knowledge beyond the realm of experience. But the claim that there is some metaphysically speaking unconditioned element of reality might seem like a paradigmatically strong metaphysical sort of claim. Kant's own argument for transcendental idealism here in the context of the antinomies seems to leave this in place and as such, potentially to lead to that apparently strong metaphysical claim.
▶︎ 1:05:02 I think there's two ways to react to this. One way to react to this is to say, all right, despite the way that Kant himself writes things in the text, should he actually be maintaining this principle? Or should he maybe be open to resolving the antinomial conflicts by putting in question this principle itself, because this principle seems maybe to presuppose too much about the nature of things in themselves or grant us too much knowledge of what things in themselves are like? If Kant goes that route, fine, but then it's no longer the case that distinguishing appearances from things in themselves is the only way to avoid the antinomial conflicts.
▶︎ 1:05:53 Or one can keep this in place and one can say, "That's not really a problem for Kant," because when Kant is interested in denying knowledge, he's not interested in denying knowledge of things in themselves, of things beyond experience. He's not interested in denying knowledge wholesale. Rather, he's interested in denying specific types of knowledge. So for instance, Kant never seems interested in denying analytic knowledge of things in themselves. Kant seems perfectly happy to say that the principle of non-contradiction applies to things in themselves. And in principle, the principle of non-contradiction seems like it could be used to arrive at some kind of analytic knowledge of things in themselves. That's not a worry for Kant.
▶︎ 1:06:56 Rather, what Kant seems worried about is not potentially a trivial knowledge of things in themselves, like merely analytic claims, but substantive knowledge of things in themselves. What counts as substantive knowledge? Kant doesn't necessarily seem to think that merely asserting that something exists counts as substantive knowledge because he says things in themselves. He seems to say that things in themselves exist in many passages. There seems to be this very strong suggestion that there are things in themselves. What he insists on is that we don't know what they're like beyond merely negative claims like they're not spatial and they're not temporal. But we don't have any positive conception of what they're like. We can say a little bit about what they're not. We can say that they are, but we can't say what kinds of things they are, have knowledge that characterizes them in a positive sort of way.
▶︎ 1:08:02 Well, now let's return to this claim that the unconditioned exists. And let's say that Kant has committed himself to saying we know the unconditioned exists. Does that count by Kant's lights as substantive metaphysical knowledge? And one might at least say it's not obvious that it does because it doesn't tell us anything about what that unconditioned thing is like. That's still an incredibly indeterminate sort of notion. Is that unconditioned something like a first beginning or first cause? Is that unconditioned something like an infinite series? Is that unconditioned something that has another kind of structure? Like, I don't know, maybe like a circular or cyclical kind of thing. We don't have any real insight into a positive characterization of this. Indeed, even the claim that it's unconditioned is a kind of negative claim. It's just saying it's not conditioned. The same way that we say things in themselves are not spatial and not temporal.
▶︎ 1:09:06 So another potential way to go, but certainly a controversial way to go relative to traditional standard interpretations of Kant. But another potential way to go would be to say Kant wants to leave this in place. The way out of the antinomial conflicts then is transcendental idealism. Leaving this in place does have the commitment that we know the unconditioned exists, but that's not a problem for Kant's general prohibition on metaphysical knowledge because that prohibition is a prohibition on substantive metaphysical knowledge. And just to say that there's something I know not what that is not conditioned in some way I know not how doesn't count perhaps as substantive metaphysical knowledge. Certainly seems of a different kind than claiming something like the soul is immortal or God exists.