Kant on space

Much of the 17th century philosopher Immanuel Kant’s work is a response to his predecessor, the Scottish empirical philosopher David Hume. Kant’s project in The Critique of Pure Reason is to give a metaphysical account of the grounds for empiricism  (study based on observation). One of the biggest problems he faces is in reconciling doubts about claims to knowledge of the external world. How can I know that one thing really is the cause of another, if causation itself isn’t something that I perceive happening? Kant answers this question by postulating a set of necessary conditions that the observer brings to bear on what it is she is observing. Without these necessary conditions, brought by the observer, the world would fail to make sense and orientation in it would become impossible.

Like Newton and Leibniz before him, space was a problem for Kant. Newton argued that space existed as a physical substance in its own right, independent of any objects. Leibniz, on the other hand, thought that space existed only as a relational property between objects, and was constituted by the mind. For Kant, neither of these positions were satisfactory: Newton could not justify the existence of space on empirical grounds, for space as a physical substance in its own right cannot be observed; only objects can. And Leibniz could not justify the existence of space on purely rational grounds because there are certain spatial relations that cannot be derived through reason alone. A chiral object, for example, can not be superposed on to its mirror image and still look the same; but reason alone could not apprehend this.


For these reasons, Kant argues that space must be something that we bring to bear on the world; one of a set of necessary conditions that make our knowledge of the world conform to the objects in it. But how is it that these necessary conditions are more than mere subjective contingencies – if we were assembled differently would we not experience the world differently too?  This doubt holds a lot at stake, for if we cannot establish the objectivity of the necessary conditions that Kant postulates, then we cannot make any claims to knowledge about the world either.

In my previous post, An overview of Kant’s project, I briefly went over this problem, arguing that if we were not us (i.e if we were assembled differently) then we would not be able to experience anything. This might have more than a hint of circularity  about it, but Kant’s so called ‘transcendental argument’ works in this way: if p is true, then something else must be true in order for p to be true: p, therefore q. In this way, Kant works backwards from the truth of a premise (that one thing causes another, for example), to what must be necessary for that premise to be true.


If it is true that we experience the world as thus (as objects existing in space, as thoughts playing out in time, as one thing causing another thing) then something else must be true. This something else, according to Kant, is the necessary set of conditions that we, the observer, bring to bear on the world. If these were not objective, then the things we take to be true about the world could be false.

We can make some strong arguments for why the things that we take to be true about the world are in fact true. We can know, for example, that the right angles of any triangle will always add up to 180 degrees – and we can justify our knowledge by the conformity of our calculation to physical objects. Without the necessary condition of space constructing our experience of triangles, it could be false that the right angles of a triangle add up to 180 degrees. But the right angles of a triangle do add up to 180 degrees; therefore the necessary condition of space must be so.

You can see from this argument how our knowledge of the external world – the grounds for empiricism – can not be subjective. We can know certain truths about the world – but in order for us to know these things we must first be able to structure the world in such a way as to know.

*This is a written run-through of a lecture on Kant’s project given at Oxford University, which you can watch here.


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