not analytic: in all these propositions, no analysis of the subject will reveal the predicate. His stock instance was the proposition 7 + 5 = 12. He pointed out, quite truly, that 7 and 5 have to be put together to give 12: the idea of 12 is not contained in them, nor even in the idea of adding them together. Thus he was led to the conclusion that all pure mathematics, though a priori , is synthetic; and this conclusion raised a new problem of which he endeavoured to find the solution.