According to Kenneth Grant:
“The one place in Crowley’s writings where he gives the meaning of the initials A∴A∴ is in his magical record (Cefalu, 1921) where it appears as ACTHP APLOC. This is a corrupt Graeco-Coptic form of Argenteum Astrum (the Silver Star) yet it is the true occult key to the nature of the order, which is not expressed by the correct Latin version of the name. Argos derives from arg or arca, the female generative power symbolized by the moon, the womb-shaped argha used in the mysteries, synonymous with the queen of heaven. Arghya (Sanskrit) is the libation cup; Aster Argos is the lunar or “silver” star.
“The lunar component is represented by the eye of Isis, and her star is Sirius, the dog-star (Set). The order of the Silver Star is thus the order of the eye of Set, “the Son behind the Sun,” represented astronomically by the star of Isis, which is Sothis (Sirius).
“The constellation of which Sirius was the chief star was once named the Phoenix (this constellation probably corresponded to the complex of stars now known as Cygnus and Aquila). This was the secret name of Baphomet (Crowley) as the supreme head of the O.T.O. (the Ordo Templi Orientis or Order of the Temple of the East), so called because the east is the place of sunrise. The reference is not, however, to the physical sun, but to the eye of Set, astronomically imaged by Sirius.] He assumed the god-form of this bird (an emblem of the sothic year or cycle) because it reached the meridian (i.e. attained supremacy) at the moment of the rising of Sirius, or Set.
“The Silver Star (A∴A∴) is Sirius. As Hoor-paar-Kraat, whose formula is silence and strength, he is the undying god, beyond our solar system. Horus is the “son” of this god and the sun (or father) of our solar system. Horus is thus Hrumachis (son of) the star, Sirius. Sirius, Sothis or Set-An, thus represents the supreme, the eternal light. The star is therefore the key to the present aeon of Horus, for it represents the energy of Satan that will permeate the earth during the present cycle.”
Aleister Crowley & the Hidden God, p. 59-60
1973 by Kenneth Grant, Skoob, London, ISBN 1-871438-36-5