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:


Hilary Putnam’s Semantic Externalism – 11/04/2016

Philosopher Hilary Putnam (1926-2016) passed away last month. Not only did he contribute to many debates in analytical philosophy, but he was also known to exhibit a great philosophical virtue: he was his own fiercest critic. He subjected his own positions to thorough scrutiny and was never too proud to reject earlier positions, when he had exposed their flaws, and change his mind in favour of another view.

In his honour, we will discuss one of Putnam’s arguments: his argument for semantic externalism. Crudely put, semantic externalism is the view that words and sentences only have meaning when there is an external world they can refer to. Putnam’s argument in favour of this view also serves to dismiss Cartesian scepticism. I will start from this vantage point to explain Putnam’s view.

Scepticism: Are we a brain in a vat?

Imagine you are, without knowing it, no more than a brain floating around in a vat of nutrient fluids. The brain is connected to a computer which stimulates the brain in such a way that it gives you the experience of an external world – you see trees, apples, other people, you smell flowers, you feel the fur of the cat and everything else you normally experience. These computer generated experiences are, to you, indistinguishable from experiences of real trees, apples, people, flowers and cats. You have been a brain in a vat from the beginning of your existence, and you have never known that you are a brain in a vat, because the computer has generated a whole life full of experiences for you. Therefore, you think that you see apples and feel the cat, but you are mistaken, because there are no apples and cats; there are only brains, vats, and computers (of which you have no experience). A bit like in the film The Matrix. If you’ve attended the class on Descartes, you’ll recognise his idea of a mind that is deceived by an evil demon. The brain-in-vat thought experiment is based on that idea.

This thought experiment aims to show that scepticism, the view that we can’t know anything about the world, is true. The argument goes as follows: if we know something about the world, then we can thereby also know that we are not brains in vats; but there is no way of knowing whether we are brains in vats, so we don’t know that we are not brains in vats; since we don’t know that we are not brains in vats, we must conclude that we don’t know anything about the world. (The logic applied here is a modus tollens: 1. if p then q, 2. not q, therefore not p.)

Putnam’s refutation

A friend of my housemate says that his worst fear is that we are indeed brains in vats, without ever knowing it. Luckily, Putnam has good news for him: we can know that we are not brains in vats. That’s a relief! But how does Putnam know? Putnam’s argument runs as follows:

Imagine a world in which the only existing things are brains, vats with nutrient liquids, and computers that stimulate the brains. Nothing else. Quite like the scenario outlined above. In this scenario, you are a brain in a vat (henceforth BIV) who has experiences as if you see trees, apples and cats, even though there aren’t any. You think you speak English, but this too is an illusion; you don’t speak at all (because you have no mouth or vocal cords, only a brain), it’s just the computer giving you the experience as if you speak English, you don’t actually speak. Hold that image for a minute. Let’s call this world the BIV-world.

Now imagine another world where you are not a brain in a vat. You are a human being in a natural environment, exactly as you experience it. You see trees, apples and cats and they are indeed really there. There are also other people who experience these same things, and such day-to-day experiences of the environment are not illusions. In this world, you also think you speak English, but this time, that is not a mistake: you do indeed speak English. In this world, when you use the word “tree”, the meaning of that word is, according to Putnam, caused by real trees in the world. The word “tree” refers to a tree, and that’s why it is a meaningful word in the English language. Let’s call this world the natural world.

Back to the BIV-world. In your mind, you’re speaking English. You use words like “tree”, “apple” and “cat”. But what do these words mean? There are no trees, apples or cats that can give these words meaning, because there are only brains, vats and computers. What the word “tree” actually refers to, in this case, is merely a set of electrical impulses generated by the computer. So the word “tree” in the BIV-world in BIV-English means something else than the word “tree” in English in the natural world.

So in the BIV-world, the words “brain” and “vat” refer, just like “tree” and “apple” to particular sets of electrical impulses, and not to the actual brain nor the vat it’s floating in in the BIV-world. So, paradoxically, even if you were a brain in a vat, your sentence “I am a brain in a vat” would be false, since “brain” and “vat” in that sentence don’t refer to your BIV-situation, but to illusory brains and illusory vats in your illusory environment.

I understand if your brain hurts a bit after reading this. Here’s the argument again, but this time in a schematic form. Concepts, references and words referring to objects in the BIV-world are indicated with an *:

  1. Either I am a BIV (speaking vat-English*) or I am a non-BIV (speaking English).
  2. If I am a BIV (speaking vat-English*), then my utterances of ‘I am a BIV’ are true if and only if (iff) I am a brain* in a vat*.
  3. If I am a BIV (speaking vat-English*), then I am not a brain* in a vat*.
  4. If I am a BIV (speaking vat-English*), then my utterances of ‘I am a BIV*’ are false.
  5. If I am a non-BIV (speaking English), then my utterances of ‘I am a BIV’ are true iff I am a BIV.
  6. If I am a non-BIV (speaking English), then my utterances of ‘I am a BIV’ are false.
  7. My utterances of ‘I am a BIV’ are false in either case.
  8. My utterances of ‘I am not a BIV’ are true.
  9. My utterances of ‘I am not a BIV’ are true iff I am not a BIV.
  10. Conclusion: I am not a BIV

If this hurts your brain even more, I understand. It’s all very technical. That’s the thing with analytical philosophers. They tend to do that. But the bottom line of Putnam’s argument is understandable enough: the brain-in-vat hypothesis mixes two worlds of reference, which messes with the meaning of what we talk about when we say “I am a brain in a vat”. If it were true that I am a brain in a vat, it would be meaningless because the concepts I use to talk about that situation don’t take their meaning from the BIV-world, but from the world I experience. Hence, the world I experience is the only world I can talk about, and in that world I am not a brain in a vat.

The Twin Earth thought experiment

Putnam makes the same point using a different thought experiment.

Imagine that somewhere far, far away in the universe, there is a planet that is an exact copy of Earth. Let’s call it Twin Earth. On Twin Earth, there is a twin of every person on Earth. So let’s say that Tony lives on Earth, and Twin Tony lives on Twin Earth. There is only one difference between Earth and Twin Earth: there is no water on Twin Earth. Instead, there is another substance with the exact same qualities as water, except that its chemical composition is not H2O, but XYZ (elements that don’t exist on Earth) Twin Tony, who speaks Twin English, calls this substance “water”. Now let’s go back a few hundred years in time, when nobody knew about the chemical elements and the composition of water. Would we say that Tony and Twin Tony mean the same thing when they say “water”? Putnam would say “no”, because Tony means H2O when he says “water” and Twin Tony means XYZ. The stuff they refer to is different stuff, even if it has the same function and Tony and Twin Tony have the same concept in mind. It is the actual things in the world that words refer to that give those words their meaning; language on its own, isolated from a world of reference, is meaningless, according to Putnam. In his own words: “‘Meanings’ just ain’t in the head”.

Of course, Putnam wouldn’t be Putnam if he hadn’t revised his position since. He later agreed with Tyler Burge that Tony and Twin Tony wouldn’t in fact have the same mental state when they talk about “water” (Tony has the concept of H2O and Twin Tony the concept of XYZ).

Will the sun rise tomorrow? The problem of induction – 01/02/2016

In his Treatise on Human Nature (1739), the philosopher David Hume argued that it is not reasonable to believe that the sun will rise tomorrow.

I wonder if Hume was always such a gloomy character. I for one wouldn’t be inclined to invite a friend to my party if he would preach to everyone that they should give up the belief that the sun will rise tomorrow. That’d kill the party mood.

But is Hume right? Here’s why he thinks it’s not reasonable to believe the sun will rise tomorrow.

Let’s first start asking the question: why do we believe the sun will rise tomorrow? Well, you might say, it has risen every day until now. Therefore, it is reasonable to believe that the sun will rise tomorrow as well.

But Hume doesn’t think so. He argues that induction cannot lead us to this conclusion.

What is induction?
Suppose you find a raven. It is black. You look for another raven. It is also black. You go on a trip through the country, looking out for as many ravens you can find. All ravens you see are black. At the end you’ve seen many ravens and all of them are black. Based on these observations, you draw the conclusion: the next raven I’ll see will be black. Is this a valid inference?

An inference is valid if (and only if) the truth of all premises guarantees the truth of the conclusion. In this case, there are many premises:

p1. Raven no. 1 is black
p2. Raven no. 2 is black
p3. Raven no. 3 is black

pn. Raven no. n is black
conclusion: Raven no. n+1 will be black.


But do these premises guarantee the conclusion? No. Even if you’ve seen 23786 black ravens, and none of another colour, it is still possible that the next raven is an albino raven, and therefore white. So the conclusion is not valid…

…unless you add another premise. The key premise you need to add to make the inference valid is: the future resembles the past. So you get:

p1. Raven no. 1 is black
p2. Raven no. 2 is black
p3. Raven no. 3 is black

pn. Raven no. n is black
pm. The future resembles the past.
conclusion: Raven no. n+1 will be black.


But remember that the conclusion only follows if the premises are true. Is the premise ‘the future resembles the past’ true? Well, you might say, the future has so far resembled the past, because during my entire trip, the next raven was black all the time. But then you get the same problem:

p1. At t1, the future turned out to resemble the past.
p1. At t2, the future turned out to resemble the past.

pn At tn, the future turned out to resemble the past.
conclusion: The next time, the future will also resemble the past.


This is, again, an induction, so you’ll need ‘the future resembles the past’ as a premise, again. But that leads to a fallacy of circularity: one of the premises is the same as the conclusion. Circularity doesn’t prove anything, so we can’t say with certainty that it’s true that the future will resemble the past. Therefore, we can’t use it in our induction about the ravens, and therefore we can’t conclude that the next raven will be black.

albino raven

But what have these ravens to do with the sunrise?

According to Hume, the same applies to the sun. Just because it has risen every morning, doesn’t mean we can conclude that it will rise again tomorrow.

Why should I care?

Science, and indeed our daily conduct, would be impossible if we didn’t rely on inductive reasoning. So what do we do now? We have a problem!



This video explains the above in a slightly different way.

More info on Hume’s philosophy can be found in this episode of BBC’s In Our Time.