Verified answer

To paraphrase Yogi Berra, "When you come to Hume's fork in the phenomenal road, take it...as there ain't no third."

Hume's synthetic is physical evidence data; as your other answerer wrote, the non-physical cannot be known by the physical.

Hume's analytic is not as likely an argument, b/c Hume's analytic is ideation. For Hume, thinking is valid only when mathematical/logical--i.e., tautologic. This is equivalent to Wittgenstein's notion that all thought-problems (philosophy) are reducible to clear tautologies and statements (e.g., "This is a brick"). This is close to Leibniz' notion of certitude, Francis Bacon's scientific induction, and so on. The problem with this type of reasoning: it assumes that all minds are at the level of, or less so, than the particular philosopher. Thus, when a Kant encounters a Swedenborg (who is able to falsify the notion of only 5 sense phenomenal awareness by reporting in real time on a unique event some miles distant), Kant's analytic cannot account for it. A good faith effort at raising self-awareness, e.g. via Saint Teresa of Avila's "Interior Castle" protocols, parallels and exceeds Plato's Diotima ladder--i.e., essentially Saint Teresa is teaching "Jacob's Ladder," Kierkegaard's third sphere of "God is in this place and I knew it not."

So too is Hume's synthetic argument in question, in that "contingency" is falsified by the occasional miracle transecting laws of physics--e.g., the "Host of Light" at Garabandal--a predicted Host of Light, filmed up close by several skeptics, coalescing out of thin air.

So, basically, Hume is dogmatically asserting "God is not discernable" via either materialist or reductionist scientism or logic--scarcely surprising, if God is termed Spirit, in the debased matter, but not of it. This latter is Plotinus' teaching.

It doesn't "show" some thing. First, it is flawed, so it can be no longer even a legitimate logical argument. 2nd, a legitimate logical argument might only show that a distinct claimed god concept used to be logically valid -- not that the god existed. To show that, you'll nonetheless need evidence that the claimed god truely exists, no longer just that it can be logically viable for it to. Peace.

The finite cannot grasp the infinite.