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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.

It will first be proper to observe a few of those experiments, which convince us, that our perceptions are not possest of any independent existence.

That is, it is a conception without an object (ens rationis), like noumena, which cannot be considered possible in the sphere of reality, though they must not therefore be held to be impossible--or like certain new fundamental forces in matter, the existence of which is cogitable without contradiction, though, as examples from experience are not forthcoming, they must not be regarded as possible.
Not being able to reconcile these two enemies, we endeavour to set ourselves at ease as much as possible, by successively granting to each whatever it demands, and by feigning a double existence, where each may find something, that has all the conditions it desires. The absolute whole of quantity (the universe), of division, of derivation, of the condition of existence, with the question--whether it is to be produced by finite or infinite synthesis, no possible experience can instruct us concerning.

Thirdly, Account for that propensity, which this illusion gives, to unite these broken appearances by a continued existence. The process of understanding by which it represents to itself the sphere of a divided conception, is employed also when we think of a thing as divisible; and in the same manner as the members of the division in the former exclude one another, and yet are connected in one sphere, so the understanding represents to itself the parts of the latter, as having--each of them--an existence (as substances), independently of the others, and yet as united in one whole. This conception must be regarded as in some degree satisfactory, if we admit the existence of a necessary being, and consider that there exists a necessity for a definite and final answer to these questions. When I observe intelligent men disputing about the distinctive characteristics of men, animals, or plants, and even of minerals, those on the one side assuming the existence of certain national characteristics, certain well-defined and hereditary distinctions of family, race, and so on, while the other side maintain that nature has endowed all races of men with the same faculties and dispositions, and that all differences are but the result of external and accidental circumstances--I have only to consider for a moment the real nature of the subject of discussion, to arrive at the conclusion that it is a subject far too deep for us to judge of, and that there is little probability of either party being able to speak from a perfect insight into and understanding of the nature of the subject itself.