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==Theology and philosophy== As a theologian Alain de Lille shared in the mystic reaction of the second half of the 12th century against the [[Scholasticism|scholastic philosophy]]. His [[mysticism]], however, is far from being as absolute as that of the [[Victorines]]. In the ''Anticlaudianus'' he sums up as follows: Reason, guided by prudence, can unaided discover most of the truths of the physical order; for the apprehension of religious truths it must trust to faith. This rule is completed in his treatise, ''Ars catholicae fidei'', as follows: Theology itself may be demonstrated by reason. Alain even ventures an immediate application of this principle, and tries to prove geometrically the dogmas defined in the Christian [[creed]]. This bold attempt is entirely factitious and verbal, and it is only his employment of various terms not generally used in such a connection ([[axiom]], [[theorem]], [[corollary]], etc.) that gives his treatise its apparent originality.{{sfn|Alphandéry|1911}} Alan's philosophy was a sort of mixture of [[Aristotelian logic]] and [[Neoplatonic]] philosophy. The Platonist seemed to outweigh the Aristotelian in Alan, but he felt strongly that the divine is all intelligibility and argued this notion through much Aristotelian logic combined with [[Pythagoras|Pythagorean]] mathematics.<ref name="auto1" />
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