th having established as a
fact the pure use of our faculty of knowledge.[7] And he adds that not
only in judgements, but even in conceptions, is an _a priori_ origin
manifest.[8] The second statement seems to make the _a priori_
character of a judgement consist in its origin. As this origin cannot
be experience, it must, as the first statement implies, lie in our
faculty of knowledge. Kant's point is that the existence of universal
and necessary judgements shows that we must possess a faculty of
knowledge capable of yielding knowledge without appeal to experience.
The term _a priori_, then, has some reference to the existence of this
faculty; in other words, it gives expression to a doctrine of 'innate
ideas'. Perhaps, however, it is hardly fair to press the phrase
'_test_ of _a priori_ judgements'. If so, it may be said that on the
whole, by _a priori_ judgements Kant really means judgements which are
universal and necessary, and that he regards them as implying a
faculty which gives us knowledge without appeal to experience.

[7] B. 5, M. 4.

[8] Ibid.

We may now turn to the term 'synthetic judgement'. Kant distinguishes
analytic and synthetic judgements thus. In any judgement the predicate
B either belongs to the subject A, as something contained (though
covertly) in the conception A, or lies completely outside the
conception A, although it stands in relation to it. In the former case
the judgement is called analytic, in the latter synthetic.[9] 'All
bodies are extended' is an analytic judgement; 'All bodies are heavy'
is synthetic. It immediately follows that only synthetic judgements
extend our knowledge; for in making an analytic judgement we are only
clearing up our conception of the subject. This process yields no new
knowledge, for it only gives us a clearer view of what we know
already. Further, all judgements based on experience are synthetic,
for it would be absurd to base an analytical judgement on experience,
when to make the judgement we need not go beyond our own conceptions.
On the other hand, _a priori_ judgements are sometimes analytic and
sometimes synthetic. For, besides analytical judgements, all
judgements in mathematics and certain judgements which underlie
physics are asserted independently of experience, and they are
synthetic.

[9] B. 10, M. 7.

Here Kant is obviously right in vindicating the synthetic character of
mathematical judgements. In the arithmetical judgement 7 +