Philosophy has a prime number problem. This is not making a claim about any kind of mathematical ontology; it’s merely intended to be an analogy.
Why prime numbers? It’s the incessant remainders. When giving an account of something, we can just reduplicate that thing and have truth necessarily on our side, at the cost of saying precisely nothing. Or, alternatively, say something that can be said of anything, 1, ‘being is’, a is a, -(p&-p), and establish only the thinnest of truths. Philosophy is very good at finding these truths, and showing their vacuity. In its own way, these discoveries do the eternal good work of closing avenues and streets in front of the stampede of dangerous forms of imbecility— exposing when general or ordinary points are being presented as special or particular.
The remainders emerge when thought tries to step off the two pillars of sterile reproduction and tautological law. Suddenly, from that position of clarity and stillness, indivisibility begins to multiply. One crunches it over here, organizes the reproductions down fixed laws, only to have this gritty surplus emerge over there, whack-a-mole like. There’s always something left over, some haunting, something opaque and disobedient, which from the perspective of the stable mapping appears as a nomadic, undocumented, distribution, causing the numbers to forever just be approximations.
Witness this (admittedly, comical) game enough, and one then develops a sense for it: there’s either a remainder, something being passed over in the silence, a sensitive and raw protrusion, or nothing is being said at all, a bland reproduction. This is not always immediately apparent, but one can stick to even this principle of the limit of principles: “It all fits” — “It either doesn’t, or it’s meaningless”.
There’s nothing special about philosophy as a domain of knowledge and this problem — all knowledge perpetuates itself through the endless crunching of an irreverent and errant remainder; paradigm shifts and breakthroughs redistribute new problems, fortunately. But philosophy is most uniquely driven by it, insofar as it is the most disturbed by it. In the flow of these endless remainders, philosophy has few riverside picnics.