Arcane Sciences
In the past, humanity considered the study and practice of the arcane to be an art. Practitioners generally learned as apprentices at the feet of masters and the knowledge was primarily passed down orally. The written record was paltry, incomplete, and inconsistent. Each author used his own terminology and the result was often worse than useless. The arcane is hardly unique in this regard. Astronomy, chemistry, and medicine were once taught the same way and were trapped in the amber of their pasts.
The Scientific Revolution changed all of that.
The great philosopher Lord Francis Bacon laid forth the fundamentals of the scientific method: the idea that knowledge can and must be gained by gathering the particulars of nature, organizing them into a formal structure, and identifying tests that can be used to determine the truth of the underlying hypotheses. Men such as Isaac Newton, William Harvey, and Robert Boyle built upon this to create a scaffold for the physical sciences that remains in place to this day.
Arcane knowledge seemed immune from this revolution for more than a century. Until the Witchcraft Act of 1735, conjuration, witchcraft, and enchantments were illegal, with severe punishments. This tended to suppress inquiries into these topics, at least publicly. When the Service was organized, and more particularly, the Arcana and Occultism section, this changed. There was now an organization dedicated to the scientific study of the arcane and occult. It was reasonably believed that before long, the nature of these topics would be laid down in a Philosophiæ Unnaturalis Principia.
While that lofty and noble goal remains unfulfilled, a great deal more is now known and documented for future generations to build upon.
Axiomata Arcanorum
Several axioms about the nature of the arcane have been found. This knowledge has been hard-won, but it is far from representing a true and complete model of the arcane. An analogy might be that we are now at the point of Copernicus's heliocentric theory — we can show that the worlds circle the sun, but we are still several steps from understanding why.