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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.

This hypothesis is the philosophical, one of the double existence of perceptions and objects; which pleases our reason, in allowing, that our dependent perceptions are interrupted and different; and at the same time is agreeable to the imagination, in attributing a continued existence to something else, which we call objects.

All the paths conducting to this end begin either from determinate experience and the peculiar constitution of the world of sense, and rise, according to the laws of causality, from it to the highest cause existing apart from the world--or from a purely indeterminate experience, that is, some empirical existence--or abstraction is made of all experience, and the existence of a supreme cause is concluded from a priori conceptions alone.

Solidity, therefore, is perfectly incomprehensible alone, and without the conception of some bodies, which are solid, and maintain this separate and distinct existence.

Our present purpose is to avail ourselves of this series of states or conditions as a guide to an existence which may be the highest condition of all changeable phenomena, that is, to a necessary being. If with the intellectual consciousness of my existence, in the representation; I am, which accompanies all my judgements, and all the operations of my understanding, I could, at the same time, connect a determination of my existence by intellectual intuition, then the consciousness of a relation to something external to me would not be necessary. This cause, as the highest member in the series of the causes of cosmical changes, must originate or begin* the existence of the latter and their series. Mean while we may observe that when we talk of real distinct existences, we have commonly more in our eye their independency than external situation in place, and think an object has a sufficient reality, when its Being is uninterrupted, and independent of the incessant revolutions, which we are conscious of in ourselves. This hypothesis is the philosophical, one of the double existence of perceptions and objects; which pleases our reason, in allowing, that our dependent perceptions are interrupted and different; and at the same time is agreeable to the imagination, in attributing a continued existence to something else, which we call objects. For the conception merely enables me to cogitate an object as according with the general conditions of experience; while the existence of the object permits me to cogitate it as contained in the sphere of actual experience.
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The principle of continuity forbids any leap in the series of phenomena regarded as changes (in mundo non datur saltus); and likewise, in the complex of all empirical intuitions in space, any break or hiatus between two phenomena (non datur hiatus)- for we can so express the principle, that experience can admit nothing which proves the existence of a vacuum, or which even admits it as a part of an empirical synthesis.