It may be that there are no judgments thought with necessity at all. But Kant thought that he could produce examples of such judgments in mathematics and natural science. Since their source is not in experience, it must be in something independent of experience. And it requires a further step to establish that a source independent of experience can, for humans, only be found in the human mind itself. It is more difficult to see why a priori judgments should be necessary .
Analytic judgments are all a priori , proceeding from the analysis of concepts alone.
We can infer that they are necessarily true because their falsehood would imply a contradiction, and hence that we must think analytic judgments as necessary. For synthetic judgments, the issue is much more complicated, since no contradiction is involved in thinking a concept without the predicate which we attach to it a priori . They are necessary for those objects in that they make these objects possible. They find expression in a priori concepts to which all objects of experience necessarily conform. . . . If the objects necessarily conform to the concepts, then the judgment that they fall under the concept is thought as necessary.