Kant on Space and Time – 13/06/2016

time and space

“Space is not objective and real …; instead, it is subjective and ideal, and originates from the mind’s nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally.” writes Immanuel Kant (1724 – 1804) in his Inaugural Dissertation (1770).


Yes, you read that correctly: space is not real. That is exactly what Kant is saying. But what does he mean?

When we think about space and time, it is useful to consider a couple of distinct questions:

  1. What are space and time? In what way do they exist? (an ontological question)
  2. How do we represent space and time in our mind? How do we think about space and time? (an epistemological question)

Let’s start with the first question: what are space and time? For Kant, the answers available at his time made this a multiple choice question:

  • A. Space and time are substances.
  • B. Space and time are properties of substances.
  • C. Space and time are not properties of objects, but still dependent on objects for their existence.
  • D. Space and time are not substances, but still exist independent of other objects. Or,
  • E. Space and time are not real.

Space and time can hardly be substances themselves. They do not take up space or time (as they are space and time) and they are imperceptible. They are causally inert: they do not change at all when they interact with other substances. Are they properties of substances, then? Just like red is not a substance – it does not exist on its own – but a property of substances – other, independently existing, substances such as apples and books can have red as a property -, perhaps space and time are like red in this respect: a property. Apples and books can be red, blue, big, small, round, square or… spacial and temporal. So perhaps substances exist first, and then space and time are merely properties of those substances? But that is problematic too. That would suggest that the existence of space and time is dependent on the existence of substances. Moreover, if they are properties, then they could fail to exist even when there are substances. If space and time exist, it seems that substances exist in space and time, and not the other way around.

Perhaps, then, space and time are relations between objects. There’s an apple, and a little later I place another apple about three inches next to the first apple, and space is one way in which both apples relate to each other (there is space between them) and time is another way in which they relate to each other (some time passes between the placement of each apple). But this raises a similar problem: this would imply that space and time do not exist independent of objects such as apples. This is a problem, because we would normally imagine that space is what apples are in. That is to say, each spacial object – such as an apple – takes up space, regardless of whether there is something else next or behind or above it. If there were only one object in the entire universe – say, an apple – and nothing else, then everything around it would simply be empty space, not no space.

So, if space and time cannot be dependent on the things that exist in space and time, then they must either exist, in physical reality, independently of any object, or – option E – space and time are not real, that is, not part of reality that exists independent of our knowledge of it. Kant thinks the correct answer is the latter: space and time are not real.

To explain why Kant thinks that space and time are not real, we’ll have to turn to the second question: how do we think about space and time? How do we represent them in our mind? According to Kant, space and time are pure intuitions. They are categories of the mind, which the mind imposes on our perception in order to be able to perceive anything at all. Space and time exist only in our minds.

You may find this an odd idea. Surely, space and time are real and have always been part of reality, even before there were minds. The Big Bang happened long ago in time and ever since the universe is exploding, growing bigger in space. There weren’t human minds back then, so surely, space and time are not dependent on our minds!

Indeed, that was the prevailing philosophical stance in Kant’s time too. The Empiricists believed that we get to know about space and time through experience. We see an apple, and another apple a few inches further away and that’s how we get the idea of space. Likewise, we have an apple, then we eat it, and then we are left with only its core. Experiencing a succession of events like that is how we learn about time. That, very briefly, is how the early modern Empiricists believed we acquire the concepts of space and time.

But not Kant. Kant flips this picture upside down. According to Kant, space and time are not even concepts, they are pure intuitions. Intuitions, according to Kant, are representations in our mind of singular, particular things to which we have immediate access. Concepts, on the other hand, are representations in our minds of generic classes of things, which we have acquired through learning of some kind. We can have an intuition of this particular apple in front of us, but not of apples in general. We have a concept of apples in general, and at any time, whether we have an apple in front of us or not, we can imagine this concept of apples along with the characteristics we have learned about apples. Space and time, on the other hand, don’t work like that, according to Kant, they are pure intuitions. We can only ever think about space and time as singular (space can be divided up into smaller sections, but it remains one big endless space, and the same counts for time) and we have immediate access to it: we needn’t learn anything about space and time, we always intuit them already. In fact, says Kant, we cannot imagine anything at all without imagining space and time along with it. We are simply unable to imagine spacelessness and timelessness.

Space and time, therefore, are categories of the mind, according to Kant. They are features of the mind that enable us to experience anything at all. Our mind apply space and time to our experience of reality, because otherwise we would not only fail to make sense of it, but we would fail to experience anything whatsoever.

Try it. Imagine an apple. Now imagine an apple without space. You can’t do it. Imagine a timeless apple, not an everlasting or eternal apple, but really a timeless apple. One that exists without there being any time during which it exists. Can’t be done. It’s easy to imagine things without apples, but as soon as we imagine anything, as soon as we represent anything in our mind, we must also imagine time and space at the same time.

Now, why is it impossible to imagine anything without space and time? Because space and time are always there, have always been there, and we’ve always experienced space and time, one might answer. But Kant doesn’t think so. Remember, we cannot actually perceive space and time. They are imperceptible. You don’t see space: you see things in space, but not space itself. You don’t feel time, you feel all sorts of things happening in time, but not time itself. Yet, we cannot see or feel or hear things without having an immediate intuition of space and time also.

This means, according to Kant, that our knowledge of space and time must be a priori (before experience), instead of a posteriori (after experience). Geometry, for instance, would not be able to make any progress if space were not known a priori. Geometry is not an empirical science: we don’t go around trying to find lots of triangles to test empirically whether the sum of their angles is indeed 180 degrees. Instead, geometry provides us with the knowledge that the sum of the angles of all triangles is 180 degrees purely with knowledge that is in human minds already: knowledge of space.

Therefore, according to Kant, space and time are features of the human mind, not of reality. They belong to the world of ideas rather than reality, so space and time are not real but ideal.

“But that is ridiculous,” said one of my students when I had explained this in a small group seminar, “how can space and time not exist in reality? That is just bizarre.”

“Of course!” I said, “Of course it’s bizarre. That’s exactly what Kant expects you to say, isn’t it? If space and time are how your mind enables you to experience anything at all, of course it would strike you as bizarre to suggest that space and time do not exist! That’s precisely his point.”

This view on space and time forms part of Kant’s bigger project: to show that we cannot acquire knowledge about things as they are in themselves, but only about how they appear to us. Since how things appear to us is determined by the mind – which, according to Kant, applies 12 categories in total, of which space and time are two – we can only acquire knowledge by means of reasoning. This makes Kant a rationalist as opposed to an empiricist. Kant’s view, that the mind determines what we can know by determining our perception, is called transcendental idealism. There will be more lessons on Kant to follow.


You can find Kant’s Prolegomena For Any Future Metaphysics here. It’s a short piece, difficult, but worth reading.

This video explains how Kant uses geometry to make his case that space is only in the mind:

And here’s a song about Kant:


Personal Identity: Am I the same person as that kid? – 14/03/2016

Admiral Nelson sails out with his flagship the HMS Victory. The ship takes quite a beating in battle. Upon her return, various parts have to be replaced: the masts, several cannons, some other bits and pieces, before Nelson can take her out to war again. Battle after battle, the HMS Victory sustains damage, gets the necessary parts replaced, and sails out again, until Admiral Nelson realises that each and every part of the original HMS Victory has been replaced. He scratches his head and asks himself: Is this ship really the same HMS Victory, or is it a different ship?

Now suppose that the HMS Victory had changed a lot as a result of all the work that has been done on her: higher masts, technical improvements, different layout, a more streamlined shape, different colours… would it still be the same ship? If so, in what sense? HMS Victory

The HMS Victory is not a person, she is a ship. Still, we can ask a similar question about human persons. The problem is, that when we talk about human persons, the question might get a bit more complicated.

I was born in 1983. I don’t remember anything of this period, but there are pictures to prove it, my mother says that chubby baby is me, and so says my birth certificate. I do remember going to school. I was studious, drawing and reading all the time. I also remember being a teenager, listening to teenage-anxiety-rock, like Nirvana and Alanis Morisette. I also remember being a student, trying to pass my logic and metaphysics exams, thinking that everybody was cleverer than I was. I also remember events and encounters that made me a different person in some way or other: boyfriends, breakups, deaths of loved ones, meetings with inspiring people, poems, films, books. Physically, I think nearly every cell I used to have when I was a child has by now been replaced, some of them thousands of times over. There is no doubt that I am qualitatively a different person than I used to be at various times in my personal history, but I somehow still think it’s all me. No matter how much I’ve changed, it’s me who did the changing. I am still one and the same, I’m still numerically the same person.

A lot has been said about personal identity in the qualitative sense. When can we truly make statements like “she was a different person after the divorce” or “after fighting in the war, they will never be the same again” or “He wasn’t himself at all when he was under the influence of LSD”? A question like this asks which qualities or characteristics are fundamental to our being, and which are more peripheral. It’s an ethical question, it has to do with values, or with what it means for a person to live a fulfilled or authentic life*. But in this class, we’ll discuss personal identity in the numerical sense. That, in contrast, is a metaphysical question: when do I start and stop existing? How can we tell it is one and the same person undergoing a change, or two different persons at two different times altogether? In this metaphysical sense, one cannot fail to be oneself, since everything is logically self-identical. Heraclitus confused the qualitative with the numerical question when he said “you can’t step into the same river twice”. The river changes continuously, so is never qualitatively the same as a moment ago, but it’s still numerically the same river that is changing.

So what determines my numerical identity? What makes it so that I’m still the same person as the baby in 1983?

Is it my physical continuity? This is problematic. Suppose one day I would wake up in your body, and you wake up in mine. We would still say that it is me who wakes up in your body, and not you. If you’re not convinced: suppose you wake up in my body one morning, and I in yours. However, when you (in my body) set out to look for your own body, hoping to get it back, you discover that it has been destroyed in a horrible accident – and I along with it. You now have my body and no hope of ever getting your own back. No doubt, this will mean a great qualitative change for you, but numerically, you still exist – albeit in my body – and I don’t. So physical continuity cannot determine personal identity.

How about psychological continuity? Locke thought one is the same person if one remembers being an earlier version. But this is problematic. I don’t remember large parts of my life. Most of my time asleep, for instance. It would be weird to say that I stop existing whenever I fall asleep, and that the human-shaped living and breathing and dreaming thing in the bed is not a person, let alone me. I’ve also forgotten many trivial things, like a great number of supermarket visits or dog walks. Does that mean it wasn’t me who walked the dog or bought the groceries? No, I’ve simply forgotten it. So memory can’t constitute personal identity either. But how about a more sophisticated psychological continuity view? What if we take into account not only memory, but other mental states, including unconscious or forgotten ones? Then the baby, the schoolgirl, the student and I are the same person because my current mental state, whatever that may be, is the last of an unbroken chain of mental states which began a short time before my birth. But this raises another question: how do we determine the connection between these mentalpersonal identity states? One moment I’m awake and aware, the next moment I’m asleep and unconscious. Who is to tell what connects the waking mental state with the sleeping mental state, and thus the waking me with the sleeping me? If physical continuity nor memory can offer an answer, then this is a problem of the psychological continuity view.

One possible solution is the narrative view. This view is explained, criticised, and revised in this video by Elisabeth Camp. According to the narrative view, I am the same person as the baby, the schoolgirl and the student, if these episodes are episodes in the story I tell about myself in order to make sense of myself as a person. This view has advantages. It helps explain why the numerical personal identity question is more interesting when applied to human persons than, say, to the HMS Victory. But even in the case of the HMS Victory, it explains why Nelson can still call the ship the HMS Victory and consider it the same ship, in spite of the replacement of all her parts, her qualitative changes and her lack of a mind. Since the HMS Victory was gradually fixed and amended, it forms a narrative about the ship that makes sense. If she had been destroyed completely and replaced in one go with just another ship, then that new ship would not be seen as the same ship, but a different one. However, a disadvantage of the narrative view is that it brings the qualitative personal identity question back on board. It makes it an ethical rather than metaphysical question, one about what it means to make sense of a life, rather than what it means to be someone – someONE-and-the-same – who is doing the sense-making. In addition, it seems too narrow. Who is to decide on how the narrative of myself goes? Me? Sounds lovely, but not every human person is capable of narrating anything at all. Most people have a hard time constructing a coherent narrative of themselves, but some are unable to at all: comatose patients or someone who dies aged 3 or so. Would such people not count as persons, or would we be unable to tell whether they are one and the same person?

petr Vasicek personal identity crisis
Personal Identity Crisis by Petr Vasicek

Where does this leave us? Should we follow Hume in saying that we’re looking for  something that can’t be found, because there is no such thing as a person that persists through time? So far, not a single characteristic has been formulated that can solve the puzzle. Combination theories, involving some physical and some psychological criteria, might be promising. But the exact formula is yet to be found.


An excerpt from Philosophy for AS, an A-level textbook written by my colleague Michael Lacewing, is available online here. It gives a clear overview of the various physical and psychological continuity views and some additional problems and objections (i.e. the duplication problem).

* You may think: “but this qualitative sense, that’s what I’m much more interested in!” I understand. Don’t worry. We’ll discuss this qualitative question of personal identity in another class, I promise.

Elisabeth, Princess of Bohemia and Descartes on Mind/Body Dualism – 15/02/2016

Once upon a time, Rene Descartes sat down in his armchair by the fire, closed his eyes and began to discard every belief he had that he could doubt, hoping to retain only those beliefs that could not be doubted – and that he could therefore hold with certainty.

Since we can easily doubt the senses – it is possible that we are just brains in vats, without a body, being manipulated by an evil demon – Descartes had to discard everything he had ever learned by experience. But if our senses give us only illusions, what can we know at all? Descartes concluded that the only thing we cannot doubt is our own existence. Because if we are indeed manipulated and deceived, then there must be someone that is deceived; there must exist a thinking subject. Hence, Descartes concluded: cogito ergo sum – I think, therefore I am.

Since it is possible to doubt the existence of the world, but not the existence of the thinking subject, Descartes concluded that thinking must be the essence of the mind: the mind is a thinking substance.

Initially, Descartes arrived at his mind/body dualism via a fallacy. Because he couldn’t doubt the existence of the mind as a thinking substance, but he could doubt the existence of the body (or any material thing), these things must be distinct, he thought. But he realised that this doesn’t follow. Just because he has knowledge of the mind, but not of the body, doesn’t mean they are distinct. Therefore, Descartes offered another argument: since the essence of material substances is that they are extended, and extended things cannot think, the mind must be unextended, and therefore immaterial. The body is extended, therefore material, therefore the body must be distinct from the mind. Voila: not only mind/body dualism, but also substance dualism (the view that there are two kinds of substances: material and immaterial).

But one woman wasn’t buying any of this. Descartes corresponded with Elisabeth, Princess of Bohemia, over an extended period of time. Elisabeth was well-read in philosophy, and not easily swayed by Descartes. In one of her letters, she asked an important question: how is it possible that the mind interacts with the body (and also vice versa: that the body interacts with the mind), if they are distinct substances?

Descartes admits that his answer to this question is not satisfactory, and his followers have struggled with it ever since. The aim of this lesson is to appreciate the nature and force of this interaction problem, as it is a problem one has to face if one, for instance, wants to accept an idea of a free will, or an idea of an immortal soul.