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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.

That is to say, a proof in the sphere of transcendental cognition does not show that the given conception (that of an event, for example) leads directly to another conception (that of a cause)--for this would be a saltus which nothing can justify; but it shows that experience itself, and consequently the object of experience, is impossible without the connection indicated by these conceptions.

And the truth of this proposition itself rests upon the consideration that such an experience must represent to us phenomena as limited by nothing or the mere void, on which our continued regress by means of perception must abut--which is impossible.

The so-called a priori principles of these faculties he consequently held to be invalid and imaginary, and regarded them as nothing but subjective habits of thought originating in experience, and therefore purely empirical and contingent rules, to which we attribute a spurious necessity and universality.

But it is utterly impossible to go beyond our conception, without the aid of experience--which presents to the mind nothing but phenomena, or to attain by the help of mere conceptions to a conviction of the existence of new kinds of objects or supernatural beings. He who would derive from experience the conceptions of virtue, who would make (as many have really done) that, which at best can but serve as an imperfectly illustrative example, a model for or the formation of a perfectly adequate idea on the subject, would in fact transform virtue into a nonentity changeable according to time and circumstance and utterly incapable of being employed as a rule. It sounded too good to be true, but I tried everything else. The latter especially, after having derived all the conceptions and principles of the mind from experience, goes so far, in the employment of these conceptions and principles, as to maintain that we can prove the existence of God and the existence of God and the immortality of them objects lying beyond the soul--both of them of possible experience--with the same force of demonstration as any mathematical proposition. For all synthetical principles of the understanding are valid only as immanent in experience; while the cognition of a Supreme Being necessitates their being employed transcendentally, and of this the understanding is quite incapable. Nay, it may even be said that the true value of mathematics- that pride of human reason--consists in this; that she guides reason to the knowledge of nature--in her greater as well as in her less manifestations--in her beautiful order and regularity--guides her, moreover, to an insight into the wonderful unity of the moving forces in the operations of nature, far beyond the expectations of a philosophy building only on experience; and that she thus encourages philosophy to extend the province of reason beyond all experience, and at the same time provides it with the most excellent materials for supporting its investigations, in so far as their nature admits, by adequate and accordant intuitions.