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For the second time proves that our first analysis of the thinking of a completely empty hours of the time before, there is a world. Such a space, here is what, in any case, there must be a time, not one time interval is differentiated from any other things which are related to the timing and things, because things and events do not exist. Now take the final interval of air time - one immediately in front of the world began. Clearly, there is a difference between this interval, from the previous all time intervals, because it is characterized by its close timing of the event in the world began, but at the same time interval should be empty, it is a contradiction of terms.           Space, Time and Kant     [Immanuel Kant, the 18th century philosopher,] was concerned with the knotty problem (which has to be faced by every cosmologist) of the finitude or infinity of the universe, with respect to both space and time. As far as space is concerned a fascinating solution has been suggested since, by Einstein, in the form of a world which is both finite and without limits. This solution cuts right through the Kantian knot, but it uses more powerful means than those available to Kant and his contemporaries. As far as time is concerned no equally promising solution of Kant's difficulties has been offered up to now.   Kant tells us that he came upon the central problem of his Critique [of Pure Reason] when considering whether the universe had a beginning in time or not. He found to his dismay that he could produce seemingly valid proofs for both these possibilities. The two proofs are interesting; it needs concentration to follow them, but they are not long, and not hard to understand.   For the first proof we start by analysing the idea of an infinite sequence of years (or days, or any other equal and finite intervals of time). Such an infinite sequence of years must be a sequence which goes on and on and never comes to an end. It can never be completed: a completed or an elapsed infinity of years is a contradiction in terms. Now in his first proof Kant simply argues that the world must have a beginning in time since otherwise, at this present moment, an infinite number of years must have elapsed, which is impossible. This concludes the first proof.   For the second proof we start by analysing the idea of a completely empty time—the time before there was a world. Such an empty time, in which there is nothing whatever, must be a time none of whose time-intervals is differentiated from any other by its temporal relation to things and events, since things and events simply do not exist at all. Now take the last interval of the empty time—the one immediately before the world begins. Clearly, this interval is differentiated from all earlier intervals since it is characterized by its close temporal relation to an event—the beginning of the world; yet the same interval is supposed to be empty, which is a contradiction in terms. Now in his second proof Kant simply argues that the world cannot have a beginning in time since otherwise there would be a time-interval—the moment immediately before the world began—which is empty and yet characterized by its immediate temporal relation to an event in the world; which is impossible.   We have here a clash between two proofs. Such a clash Kant called an 'antinomy'. I shall not trouble you with the other antinomies in which Kant found himself entangled, such as those concerning the limits of the universe in space.   What lesson did Kant draw from these bewildering antinomies? He concluded that our ideas of space and time are inapplicable to the universe as a whole. We can, of course, apply the ideas of space and time to ordinary physical things and physical events. But space and time themselves are neither things nor events, they cannot even be observed: they are more elusive. They are a kind of framework for things and events: something like a system of pigeon-holes, or a filing system, for observations. Space and time are not part of the real empirical world of things and events, but rather part of our mental outfit, our apparatus for grasping this world. Their proper use is as instruments of observation: in observing any event we locate it, as a rule, immediately and intuitively in an order of space and time. Thus space and time may be described as a frame of reference which is not based upon experience but intuitively used in experience, and properly applicable to experience. This is why we get into trouble if we misapply the ideas of space and time by using them in a field which transcends all possible experience—as we did in our two proofs about the universe as a whole.       — Karl R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, Chapter 7 - Kant's Critique and Cosmology                       Indexes/16