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Click on the phrases to see them in context. The original texts by Immanuel Kant and David Hume are available from the Gutenberg Projet.

Hence I am compelled to say; "The aggregate of parts in a given phenomenon is in itself neither finite nor infinite; and these parts are given only in the regressive synthesis of decomposition--a synthesis which is never given in absolute completeness, either as finite, or as infinite." The same is the case with the series of subordinated causes, or of the conditioned up to the unconditioned and necessary existence, which can never be regarded as in itself, ind in its totality, either as finite or as infinite; because, as a series of subordinate representations, it subsists only in the dynamical regress and cannot be regarded as existing previously to this regress, or as a self-subsistent series of things.

I consequently confound the possible abstraction of my empirically determined existence with the supposed consciousness of a possible separate existence of my thinking self; and I believe that I cognize what is substantial in myself as a transcendental subject, when I have nothing more in thought than the unity of consciousness, which lies at the basis of all determination of cognition. If we admit the existence of spontaneously produced events, that is, of free agency, we are driven, in our search for sufficient reasons, on an unavoidable law of nature and are compelled to appeal to the empirical law of causality, and we find that any such totality of connection in our synthesis is too small for our necessary empirical conception. It is therefore utterly absurd to suppose any number to exist, and yet deny the existence of unites; and as extension is always a number, according to the common sentiment of metaphysicians, and never resolves itself into any unite or indivisible quantity, it follows, that extension can never at all exist.
I find in the first place, that whatever objects are considered as causes or effects, are contiguous; and that nothing can operate in a time or place, which is ever so little removed from those of its existence.
Mathematics, natural science, the common experience of men, have a high value as means, for the most part, to accidental ends--but at last also, to those which are necessary and essential to the existence of humanity. Are they real existences? Now we must admit that the doctrine of the existence of God belongs to doctrinal belief. But I am conscious, through internal experience, of my existence in time (consequently, also, of the determinability of the former in the latter), and that is more than the simple consciousness of my representation.

It follows that an infinite series already elapsed is impossible and that, consequently, a beginning of the world is a necessary condition of its existence.