But to Hume there is nothing mysterious about the association of ideas. They are combined, transposed, augmented, and diminished according to fixed rules under mechanical laws. Their relationship takes place without freedom. Impressions occur in the way they happen to occur. Ideas combine in the way they happen to combine. Relations between ideas are accidental and external. There is only one quality of ideas that does not depend on its accidental relation to other ideas. This is the quality of non-contradiction. This is the necessary property of an impression. An impression must be what it is, and cannot be conceived as having properties contrary to its own nature. The quality of identity in an impression is intrinsic and necessary. According to Hume, there are three fundamental ways in which ideas associate, called the three laws of association. (1) There is the _law of resemblance_ or contrast, by which the occurrence of a thing calls up a similar thing or its opposite. Mathematics is based upon this law of the resemblance, the contrariety, and the quantitative relations of ideas. (2) There is _the law of contiguity in time and space_, by which things happening together in time and space are recalled together. Upon this law are based the descriptive and experimental sciences. (3) There is the _law of causation_, upon which religion and the metaphysics of the world of nature are based. The question with Hume is, How is he to explain all these laws of association as derived from impressions? If they cannot be derived from impressions, then his theory that all knowledge is derived from impressions goes to the wall. The Rationalists and even his predecessors, Locke and Berkeley, had conceived mathematical propositions and causation as underived and in the nature of things. If Hume is to establish his doctrine of complete sensational empiricism, here is his test. These associations, and not isolated impressions, are the objects of human interest, inquiry, and investigation. Hume makes a further reduction of associations by his well-known classification of them as either “relations of ideas” or “matters of fact.” Associations of contiguity and associations of causation are “matters of fact,” while associations of resemblance are “relations of ideas.” Furthermore, Hume looks upon associations of contiguity as those of outer impressions, associations of resemblance as those of inner impressions, while associations of causation are not what they are alleged to be, but are derived from some inner impressions. { { 1. Contiguity Outer Descriptive { Matters { association impressions Sciences Objects of { of Fact { Knowledge { { 2. Causation Inner Metaphysics { { association[45] impressions { { Relations { 3. Resemblance Inner Mathematics { of Ideas { association impressions