[Source :] In natural science no less than in mathematics, Kant held, synthetic a priori judgments provide the necessary foundations for human knowledge. The most general laws of nature, like the truths of mathematics, cannot be justified by experience, yet must apply to it universally. In this case, the negative portion of Hume's analysis—his demonstration that matters of fact rest upon an unjustifiable belief that there is a necessary connection between causes and their effects—was entirely correct. But of course Kant's more constructive approach is to offer a transcendental argument from the fact that we do have knowledge of the natural world to the truth of synthetic a priori propositions about the structure of our experience of it.
I challenge not that natural sciences are synthetic, but only that they are a priori.
I exemplify my confusion with universal constants, whose existence (I understand) is a priori. However, how can a person's knowledge of them be a priori? Only some external experience can inform you which rational numbers describe them. For example, every human experiences atmospheric pressure, but you cannot know the unit of standard atmosphere somewhere until you experience some measure of it (eg: a barometer or a report about atmospheric pressure).
So your knowledge of natural sciences (eg: atmospheric pressure) must be a posteriori?