There's no such thing as first principles.
Russell and Whitehead tried this, they attempted to find a set of building blocks, rooted in set theory, from which one could construct a proof for any true theorem in mathematics. It was not long before critical holes were found in their would be magnum opus. They attempted a couple of revisions, but the project was proven futile upon the publication of Godel's Incompleteness Theorems, in which it was shown that syntactic entailment could not do the job alone of, in a logically consistent fashion, either proving or disproving any possible proposition such a syntax could generate. Whatever your "first principles", those same axioms will inevitably generate questions that they themselves can't answer.
Contrary to what the positivists of the early 20th century believed, mathematics, let alone the whole of knowledge, was never a monolith fabricated from atomic building blocks, but a mesh of indefinitely deepening roots. At times these channels make contact with bedrock, concepts solid enough to serve as a foundation for our endeavors: Euclidean geometry, Newtonian mechanics, Turing machines, Peano arithmetic; all kernels of stability indubitably capable of running software epistemological and civilizational alike. Yet however sturdy, they're never static; the movement of their tectonic plates inevitably create fissures. Whether it's the inability of a set of axioms to account for all the things they could say, or the incongruence of a scientific paradigm with its own experiments, an inevitable gap between language and reality reveals a space of semantics that lies outside of an otherwise endless regress of signs. Newton gives way to Einstein, and Euclid's straight lines are erased by hyperbolic curvature, all as if, as Kant noted, one doesn't merely keep walking around the world and ending up in the same place but eventually infers that they stand atop the surface of a sphere.
In the midst of these earthquakes, through the jagged crevices of tectonic shifts, flows the magma that will fit any shape and possibly burn away a few things in the process before cooling down into a solid layer. Where science bores its way towards bedrock, philosophy is the magma that finds its way into any crevice it can find. Einstein therefore may have had the last word on the concept of time when talking about inert bodies, but Bergson could still speak of what else such a concept could encompass when one takes into account more than the arbitrary starting positions and speeds of otherwise identical objects. Science always generalizes, and in doing so must shave off the innumerable details of any specific repetition; philosophy's job is the interminable and thankless task of cleaning up whatever inevitable mess of blood and limbs that Procrustes leaves all over the place and fashioning materials he'll inevitably appropriate to assemble yet another bed.
But that's okay, because it's only with a little help from this intractable tango of obstinate geological turbulence and megalomaniacal searing heat that life can flourish.