of this admission with Locke’s own doctrine of ideas as effects of a causative substance, that he modifies the theory of _physical_ certainty which he inherited. In their treatment of mathematical truths on the other hand, of propositions involving relations of distance, quantity and degree, a fundamental discrepancy appears between the two writers. The ground of certainty, which Hume admits in regard to propositions of this order, must be examined before we can appreciate his theory of probability as it affects the relations of cause and substance. [1] See above, paragraphs 45 and 97. ... and does not admit opposition of mathematical to physical certainty--here following Berkeley. 227. It has been shown [1] that Locke’s opposition of mathematical to physical certainty, with his ascription to the former of instructive generality on the ground of its bare ideality--the ‘ideal’ in this regard being opposed to what is found in sensation--strikes at the very root of his system. It implies that thought can originate, and that what it originates is in some sort real--nay, as being nothing else than the ‘primary qualities of matter,’ is the source of all other reality. Here was an alien element which ‘empiricism’ could not assimilate without changing its character. Carrying such a conception along with it, it was already charged with an influence which must ultimately work its complete transmutation by compelling, not the admission of an ideal world of guess and aspiration alongside of the empirical, but the recognition of the empirical as itself ideal The time for this transmutation, however, was not yet. Berkeley, in over-hasty zeal for God, had missed that only true way of finding God in the world which lies in the discovery that the world is Thought. Having taken fright at the ‘mathematical Atheism,’ which seemed to grow out of the current doctrines about primary qualities of matter, instead of applying Locke’s own admissions to show that these were intelligible and merely intelligible, he fancied that he had won the battle for Theism by making out that they were merely feelings or sequences of feelings. From him Hume got the text for all he had to say against the metaphysical mathematicians; but, for the reason that Hume applied it with no theological interest, its true import becomes more apparent with him than with Berkeley. [1] See above, paragraphs 117 and 125. His criticisms of the doctrine of primary qualities.