imagination, to supply this deficiency, and raise up to himself the idea of that particular shade, tho' it had never been conveyed to him by his senses? I believe there are few but will be of opinion that he can; and this may serve as a proof, that the simple ideas are not always derived from the correspondent impressions; tho' the instance is so particular and singular, that 'tis scarce worth our observing, and does not merit that for it alone we should alter our general maxim."[14] [14] Hume, _Treatise_, Bk. I, Part 1, § 1. CHAPTER XII THE ANALOGIES OF EXPERIENCE Each of the three categories of relation, i. e. those of substance and accident, of cause and effect, and of interaction between agent and patient involves, according to Kant, a special principle, and these special principles he calls 'analogies of experience'. They are stated thus:[1] (1) In all changes of phenomena the substance is permanent, and its quantity in nature is neither increased nor diminished. (2) All changes take place according to the law of the connexion of cause and effect. (3) All substances, so far as they can be perceived in space as coexistent, are in complete interaction. The justification of the term _analogy_ of experience is as follows. In mathematics an analogy is a formula which asserts the equality of two _quantitative_ relations, and is such that, if three of the terms are given, we can discover the fourth, e. g. if we know that _a_ : _b_ = _c_ : _d_, and that _a_ = 2, _b_ = 4, _c_ = 6 we can discover that _d_ = 12. But in philosophy an analogy is the assertion of the equality of two _qualitative_ relations and is such that, if three of the terms are given, we can discover, not the fourth, but only the relation of the third to the fourth, though at the same time we are furnished with a clue whereby to search for the fourth in experience. In this philosophical sense, the principles involved in the categories of relation are analogies. For instance, the principles of causality can be stated in the form 'Any known event _X_ is to _some other_ event _Y_, whatever it be, as effect to cause'; so stated, it clearly informs us not of the character of _Y_ but only of the fact that there must be a _Y_, i. e. a necessary antecedent, though at the same time this knowledge enables us to search in experience for the special character of _Y_. [1] The formulation of them in the first edition is slightly different.