by definition I have agreed not to do so, that is all. Kant recognised that most synthetic propositions were a posteriori but these were of no interest to him; he believed that there were also synthetic propositions that were necessarily and generally true, that is to say, a priori, and he thought that the most fundamental truths of natural science and all mathematical propositions were of this kind.
He saw plainly the extreme importance of this issue (if you believe a synthetic judgment a priori you are a rationalist, although Kant did not confess to this name); if you do not, you are an empiricist, and these two philosophies are diametrically opposed to each other, and no reconcilation between them is possible. (Kant's own view does not reconcile them, as he believed it did, but is an essentially rationalistic solution.)
The results of our first two lectures make it absolutely impossible for us to accept any view except the empiristic one. Knowledge, we saw is the expression of a new fact by means of old terms, it is based on a recognition of the constituents of the fact. Without this recognition there is no knowledge, and it does not only precede knowledge, but forms the logical basis of it, it provides the ground for its validity. But this process evidently is what is commonly called "experience". What else could we mean wherever we use the the word "experience" if not this first work (and its result), of recognizing the primary material which presents itself and giving it its proper names? The material is prior to everything we can say about it — how could it be otherwise? The statement that all knowledge is empirical is itself a mere tautology — this remark will save us from being too proud of our empiricism. Rationalism, on the other hand, is not a possible point of view which just happens to be false and is discovered to be wrong after a careful examination of human reason and its relation to the world — no, it is simply self-contradictory.
A synthetic judgment a priori would be a proposition which expresses a fact without being dependent of the fact — contradictory to the essence of expression. It is well known how Kant tried to avoid this nonsense: he maintained that the facts were dependent on the propositions (at least that is what his doctrine amounts to) — a paradox which could be made to seem plausible only after the whole situation had been obscured by a great deal of confusion. It is very instructive to follow the round-about paths of Kant's
