Pure World

The Pure World (まっさらな世界) is a term used to refer to the world beyond all filters and Phases, a world of science unaffected by religion.

Principles
The world, which in this context refers to the universe or reality itself, as it is normally perceived is not pure and untouched - various layers known as Phases exist over it which act like filters, affecting how it appears. The various religions which have arisen throughout human history have had the effect of creating layers over the world.

Beyond these Phases is the Pure World, which is described as a 'World of Science' (科学世界), untouched and unaffected by religion.

Aiwass, not originating from any religious category and subsequently the phases of magic, is described as the angel of the bottommost layer, closest to the world of pure physical laws, and as such, is at the core of Aleister Crowley's plan to eliminate the phases by establishing a means of controlling him and using his power to destroy the other filters above him, leaving only a magicless world.

Background
At some point in the past, Aleister Crowley began attempts to directly interfere with the Pure World.

Magic God Othinus Arc
While explaining the concept of Phases to Kamijou Touma, Othinus mentions how the man known as the Silver Star has been attempting to interfere with the Pure World beyond the filters.

Coronzon Arc
While Aleister's plan was to destroy all other phases while preserving the Pure World, Coronzon had the opposite intent. By performing the Ceremony of Mo Athair, she was looking to descend to the very bottom of the Sephiroth and destroy the foundational layer which would subsequently destroy all of the phases overlaid 'above' it since they cannot exist entirely independently.