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The Philosopher's Stone: What does Adam Halistan believe?

 (p.46) "He's a Hermetic philosopher – though he has a great admiration for the Neo-Platonists as well."

Hermeticism was a mixture of intellectualised paganism, mysticism, and practical pre-scientific experiment. Members of the "order" would be referred to as Magi or Alchemists.
We can see the variety of sources of his ideas in the texts Kathleen has him quote:

(p.11) "…the Love that moves the Sun and the other stars." from Dante's Paradiso (Canto XXX111) – a Christian text.

(p.11) "The Dragon dieth not …"  This text accompanies Emblem 25 in Atalanta Fugiens Michael Maier (1617) The idea is expressed earlier in the Rosarium Philosophorum (1550) –a treatise on Alchemy.

(p.13 and other crucial points in the story) "I am a child of earth and starry heaven…"  translation of gold plates found in Petelia, Italy (4th Cent. B.C.) and Eleuthernae, Crete (2nd Cent B.C.)  - Orphic texts.

(pp 67/8) "As above so below…"  Rosamund recognises Simon as a "brother of your order" when he recites  "the Hermetic creed", quoting from the Emerald Tablet (ascribed to Hermes Trismegistus) an ancient key text for Hermetic philosophy which divided the "wisdom of the universe" into three parts: Alchemy, Astrology and Theurgy. Sir Isaac Newton published his own translation and notes on the text.

(p.230) "To know, to dare, to will, to keep silent." Simon quotes a Rosicrucian maxim.

(p.86 and passim) Rosamund's necklet is a Rosicrucian symbol of the rose (the soul) and the cross (the body of 4 elements). In other words, the human soul crucified on the cross of the material plane. Rosicrucianism is a Hermetic/Christian movement dating back to the 15th century.