Is there evidence that Plotinus and the Neoplatonists got their philosophy of their 'trinity' from the Bible or from Christian sources? Or the other way round, was Augustine influenced by Plotinus when he developed the doctrine of the Trinity?
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Merely believing in the Father, Son and Holy Spirit leaves open too many possibilities, most of which were long ago ruled out as heresies. The Trinity is a label for the concept of a God who is a complex unity. If you say you are Trinitarian then you are saying you believe all three persons are divine, that all three are uncreated, that all three are equally eternal, that all three are distinct, that all three are united together, etc. You could still have the Father, Son and Holy Spirit while rejecting the trinity by believing any of the classical heresies. The Trinity may be hard to understand, but the heresies and the problems they lead to are often fairly straightforward.