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Kant’s attempt to refute Hume’s causal scepticism and so, too, his investigating how pure mathematics and pure natural science can exist are both intimately connected with his so-called Copernican revolution in philosophy. They are intimately connected, because he came to the conclusion that the only way to explain how mathematics and natural science can exist is by effecting a major turnabout in the way that we conceive the relationship between ourselves (the knowing mind) and the objects of our sense experience (the objects in space and time). His Copernican revolution equally has major repercussions for metaphysics and for morality. This second stage of his revolution will be touched on after I have said something about the first stage: his investigation of the possibility of mathematics and natural science.

The traditional way of conceiving the relationship between ourselves and the world that we are seeking to know by means of our senses – the world of objects existing in space and time – is to conceive of this world as existing entirely independently of the knowing mind. We, by means of our senses (in co-operation, perhaps, with our understanding), set out to discover how this mind-independent world is, both with respect to the rules governing the possible structural configurations of its objects and with respect to the laws governing their behaviour.As Kant sees it, mathematics as a science is the study of the former (the structure or form of objects), and natural science, that of the latter (the dynamical connections of objects). On the traditional way of taking the relationship between the mind and objects in space and time, it is up to our faculties of knowledge – our senses and understanding – to attune themselves, if they can, to the objects of our attempted knowledge.

Unfortunately, if this traditional picture is accepted as the correct conception of the relationship between ourselves and the objects of our hoped-for mathematical and natural scientific knowledge, then, as Kant realized, there would be no possibility of our acquiring any informative universal or necessary knowledge of these objects. At best, what we could hope to acquire would be empirical, hence only probable, knowledge. On the other hand, if we adopt the revolutionary point of view that the objects that we are seeking to learn about by means of our faculties of knowledge must themselves conform to those very faculties in order to become objects of the senses, then we might well be able to acquire some genuinely necessary and universal knowledge of objects as possible objects of the senses.For, independently of our acquiring any experience of these objects, we might be able to discover, by investigating our own faculties of knowledge, what conditions these faculties impose on the possibility of our experience and its objects.

In effect, the first major task that Kant sets himself, in the main body of the First Critique, is to show that his revolutionary way of conceiving the relationship between ourselves and the objects of our sensible knowledge – viz. that these objects must accord with our faculties of knowledge, rather than the traditional picture of trusting that our faculties of knowledge will be in accord with its sought-for objects – is, indeed, the correct one. This he seeks to accomplish by establishing two claims: first, that the dimensions in which the objects of our senses are located – namely, in space and in time – are dependent on us (are, in fact, properties of our mind); and second, that the fundamental laws governing the behaviour of the objects of our senses are dependent on concepts existing innately in us. If both of these conditions can be made out, it can be said that the whole framework by means of which objects of the senses can be known – the sensuous forms in which they are given (space and time) and the basic dynamical laws governing them – will be contributed by us. Clearly, such a picture of our relationship with the objects of our sought-after sensible knowledge is a far cry from the traditional one.

The revolutionary point of view according to which the objects of our senses should be taken to conform to our faculties for acquiring knowledge, Kant likens to Copernicus’s revolutionary hypothesis concerning the spectator of the heavens and the heavenly bodies. On the traditional conception of the latter relationship, the spectator is at rest, and the observed behaviour of the heavenly bodies is dependent on their movement alone. On the Copernican hypothesis, the observed behaviour of the heavenly bodies depends, in part, upon the movement of the spectator. This hypothesis, Kant wishes to say, was firmly established on two grounds. First, it enabled Kepler to discover the three laws governing the motion of the planets. Second, it enabled a proof to be given of Newton’s gravitational force of attraction (binding all objects together). Neither of these advances would have been possible on the pre-Copernican model.

How, though, does Kant propose to establish his Copernican revolution? It can be established, he thinks, in ways analogous to those that established Copernicus’s own hypothesis. First, on Kant’s revolutionary model of the relationship between our experience and its objects, he believes that we can explain how mathematics and natural science have provided us with universal and necessary knowledge of these objects. Second, he believes that it will enable us to provide proofs of the principles lying at the basis of natural science. Neither of these achievements is possible on the traditional model. Accordingly, just as Copernicus’s own hypothesis was established because it, and it alone, enabled us to discover the laws of planetary motion and, at the same time, to provide a proof of Newton’s force of attraction, so Kant’s Copernican revolution is to be established because it, and it alone, can explain how we are in possession of universal and necessary objective principles in mathematics and natural science, and at the same time provide proofs of the first principles of natural science. The theory that Kant constructs, on the basis of his Copernican revolution, he calls ‘transcendental idealism’.

In fact, as he sees it, there is a further ground for accepting his Copernican revolution. He argues that, on the traditional conception of the relationship between the mind and its hoped-for objects, we are bound to involve ourselves in inextricable contradictions when we attempt to prove certain judgments which entirely transcend experience (for instance, a judgment concerning freedom of the will); whereas, on his opposing, Copernican-style conception, we can show that no such contradictions arise. Now a theory can only be justified if it does not lead to contradiction. Accordingly (on the assumption that there really are only these two theories), Kant regards the consistency of his own, revolutionary theory, compared with the unavoidable inconsistencies of the traditional theory, as a further proof of the correctness of his Copernican project, and hence of transcendental idealism. Moreover (as emerges in the later Critique of Practical Reason and Critique of Judgment), there are, on the alternative theory, further contradictions in our thought – our thought about morality and beauty – which, he will argue, can be resolved only by embracing his revolution.