Kant's Antinomies
Kant points out that philosophy, or the use of reason, can seem to lead to contradictions. For instance, it can seem (and did to Descartes) that the world must have a beginning or limit in space and time. After all, doesn't everything have a beginning and/or end? But it can also seem (and did to Aristotle) that the world must be infinite in space and time. After all, what would be beyond the limit of space, or before time began?
Kant argues that his distinction between noumena and phenomena helps us to avoid such paradoxes. Space and time are not things in themselves (noumena) nor are they objects we experience (phenomena). They are forms that our experience takes or features of the way in which our minds present the world to us. To talk about the beginning or limit of space or of time is to mistakenly treat space and time as if they were objects of some kind.
Similarly, we can be led to think that there can be free will in the world, but also that there can be no such thing, since all events in the natural world are determined, i.e. caused by prior events. It is indeed a law of nature that all events are determined, Kant says, but this applies only to phenomena. In the realm of noumena it is entirely possible that there is real freedom, and indeed ethics require that we believe in such freedom of the will.
Finally, we can be led to think (as Descartes did) that there must exist a necessary being (i.e. God) that does not itself need to be caused to exist by anything else. But we can also be led to think that there are no such necessary beings in the world, that everything that exists depends for its existence on something else. Kant says it is true that there is no necessary cause in the (phenomenal) world, but we can still believe in a necessary cause of the world. This would be God.