Analysis of A Certain Magical Index.
As You Know, Aleister Crowley, the founder of Academy City is based off a real person. What you might not know is that not just Crowley himself, but the Liber Al Vel Legis (Book of the Law), the angelic being, Aiwass who dictated it and the concepts of the Aeon of Osiris and Aeon of Horus all originate from the religion, Thelema, a real-world religious philosophy founded by the real-life Aleister. This goes far beyond being a mere Genius Bonus within the Index series and actually resides at the root of the themes that drive the series as a whole. Keep in mind my understanding of real-life Thelema is limited to a perusal of the relevant Wikipedia pages and most of my conjectures come from interpretations of the text of the novel series itself.
In the series, several characters are referenced as being from or possessing the Aeon of Osiris, which is defined (in as simplified manner) as having their worldview defined by the God of Christianity. However, even this definition is too narrow, as some non-Christian characters, in particular Accelerator, are also described as being in the Aeon of Osiris. Therefore, from what I can determine, characters in the Aeon of Osiris have their worldview limited not specifically by the God of Christianity, but rather by an existential belief in outside objective systems of good and evil or right and wrong that are imposed on the character from without. Accelerator may not be a Christian, but up to a certain point, he is controlled by his belief in the notions of "heroism" and "villainy" as they are defined from an outside standpoint. It is because of these systems that he believes he is locked into his role of being a "villain," which leaves him unable to remain with Last Order. This manifests in Accelerator's initial "awakenings" with his wings being black as a sign of him being imprisoned by outside moral structures. When he is defeated by Touma in Russia, Accelerator's ideas of heroism and villainy are shattered and he abandons them in order to ultimately embrace his desire to be with Last Order in Volume 22, which not coincidentally is the time when he truly awakens with his wings turning white, signifying that he has abandoned limiting structures created from without and embraced his True Will.
True Will is a central concept within Thelema and a hallmark of the Aeon of Horus. True Will originates from within the individual and could be referred to as their "true calling." In essence it is the idea that a fully actualized person will act in accordance with their personal drive to act according to what they truly need to do. This is differentiated from a person merely doing what they want to and is not simply a call to hedonism. Instead, True Will appears to be similar in concept to Friedrich Nietzche's concept of the Übermensch, a person who surpasses the limitations of normal people by abandoning ideas of "right" and "wrong" as imposed by social norms and instead creating their own concept of morality that is true to themselves...a Personal Reality if you will.
We already see examples of True Will in the Index series even if it hasn't been referred to as such (but I wouldn't be surprised if Kamachi-sensei brings it up as concrete concept in a later novel). Accelerator in Volume 22 is one such example, but another even more telling example is that of Kamijou Touma himself. Touma could be seen as a perfect example of someone existing within the Aeon of Horus and embracing his True Will from the very beginning of the series. He is not limited by ideals and outside structures such as religion or duty. His heroic nature is not derived from some outside preconceived notion of what a hero is "supposed" to do. Throughout the novels, he fights pitched battles against various enemies only turn around and extend his hand to them in their time of need. A perfect example is his relationship with Agnese and is illuminated in his conversation with Kaori at the end of the Orsola Aquinas arc. In spite of having been severely injured and put into the hospital by Agnese's attacks and witnessing her horrid treatment of Orsola, Touma points out to Kaori that he's perfectly willing to go to Agnese's rescue if she ends up in trouble, a promise that he follows through on a few story arcs later. After defeating Fiamma of the Right, Touma turns right around and saves his life even though Fiamma had been trying to kill him moments before. Even after losing his memories in the first volume, Touma's desire to save people in need is so powerful that his behavior afterwards is enough that almost nobody realizes he has lost his memories, indicating that this tendency of his is something that originates from within his self rather than as something that is expected of him because of some external systematic belief (which would have been erased along with his memories). Thus, the concept of True Will could be considered the driving force of the Index series as a whole.