The learned have subtypes, the ones who have been existentially embedded in Dasein, and those who have evolved to the level as to be able to calculate a schema whereby they can free themselves from embededness. So actually there are two types , and one more-subtype.
Leibnitz was the forerunner who was able to ground the third by the calculus of the middle ground. Both You and Peter hold to the synthetic Kantian middle which was already recalculated , so as to enable Kant to qualify it
The run down is very expansive , but feel that it is a way out from the pro lens posed.It was solved by Brower, an intuitionist , to support Hilbert. I’m adding the reference so as to avoid appearing presumptive.
I think many of most of these problems could be looked at, from this point , by calibration unto the balance needed to identify what’s at hand, and to reduce some of the clutter dealing with 'existential contraptions.
That’s the best I can do, Lamiguous, because this matter would take a very expansive /extensive work, but there is no harm in trying.