This last point must be elucidated later. In the meantime we must see how this inquiry into the nature of reason crystalises itself into a seemingly abstract and trivial question: How are synthetic a priori judgments possible? It is baffling at first to find an inquiry of the scope we have indicated suddenly take such a narrow form, but a little consideration will show the importance of the question. Knowledge may be regarded as either analysis or synthesis, as a puzzling out or unravelling of what we somehow know already, or as a putting together of what had previously been known or observed separately. The rationalist school, whom we described in the last chapter, were inclined to regard all knowledge as analytical. They thought of progress in knowledge as an advance from obscure to clear apprehension, and as a thinking out or making clear of something which had always been known somehow. Mathematics, the typical form of knowledge for the rationalists, had been thought of as the analysis of what was implied or given in the definitions. The conception of analytic a priori knowledge was thus familiar and simple. On the other hand, the empiricists had thought of knowledge as primarily synthesis--or, as they called it, association--a connecting together of ideas in their nature separate. Knowledge of a thing was thought of as the observing together of several ideas. Judgments about objects were regarded as judgments about the co-existence of separate ideas, ideas which were not thought of as being bound by any logical necessity. We do not understand why a substance with the specific gravity of gold should be yellow; we only observe the co-existence of certain qualities. The judgment, then, gold is yellow, is synthetic; it is an assertion of the co-existence of separate qualities. It is also empirical; it does not express a reasoned insight into the necessary connection of gold and yellow. It seems rather a record of observation. Synthetic knowledge, then, was thought of as in its nature empirical and a posteriori. Hume, who thought of all knowledge of the world in experience as synthetic, denied to such knowledge any necessity or certainty.