1.) Metaphysics = a science of God, soul, and the universe as a whole.
2.) Any science seeks to discover new information that is relatively stable and goes beyond a mere catalog of observations- i.e. it looks for universal, rational truths.
3.) Any truth is either
a1.) Necessary, universal, rational = the a priori
a2.) Contingent, non-universal, experiential/ sensed = a posteriori
b1.) Discovered by insights about the meaning of terms and the use of language = analytic “All uncles had nephews” or “all wives are married” or “algebraic cancelling is making a term equal to 1”.
b2.) Discovered by insights that go beyond the mere meaning of terms and use of language = synthetic. “A cat is on the mat” or “Water is H2O”.
4.) Logically, this gives us four propositions:
i.) The analytic a posteriori. While we can say the words it is not a real possibility. Any statement that is true simply from the meaning of the terms will also be necessary and universal.
ii.) The analytic a priori. As just indicated, these are given. That said, they cannot give us science since we can’t develop new knowledge about the world from them. The statements are true only in the sense that they tell us how the language must be used.
iii.) The synthetic a posteriori. These are the normal truths of experience. As such, however, they don’t give us science since they don’t take a step beyond the merely observational.
iv.) The synthetic a priori = By elimination, if science exists at all it must exist here. So does it?
5.) Mathematics is clearly synthetic and a priori since the stable and universal knowledge it gives us can’t be gathered merely from an understanding of how terms are used.
We can also extend this certitude to nature by noticing mathematical relations in it, but doing this requires that we observe a thing that has a repeatable, predictable behavior exercised in a controlled setting.
6.) But what would it mean to have synthetic a priori knowledge of God, the soul, or the cosmos? If we wanted a universal law of God or soul we would need to observe repeated, predictable behaviors of God or the soul in controlled settings. But we can only treat either of these as beings with free choice, and so we cannot understand them in a way that would give us universal and necessary laws. Metaphysics degrades God and soul, which is why rational investigation into either tends to lead to skepticism and atheism.
7.) We can only have synthetic a priori knowledge of what is repeatable, and therefore only of what is homogenous or one-of-many. By this criterion, we not only rule out knowledge of God and of the human person (for personality is irreducibly unique, even where we notice patterns in it) but also any knowledge of the universe. The universe cannot be one of many. Any claim to a knowledge of the universe as a whole (as is claimed by materialism, idealism, Naturalism, panpsychism, creationism) is ruled out by the uniqueness and totality of the supposed object of study.