If each Person is fully divine yet really distinct from the others, at least two beings are identical to the same divine essence, making them identical to each other—contradicting their distinction.

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Trinity (implied context)(this statement is addressing the classic logical puzzle of the Trinity): The Christian theological doctrine that God exists as three distinct Persons (Father, Son, Holy Spirit) who share one divine essence or nature.
contradiction(Relevant to distinguishing contradictions from false contingent statements in the logic student variant of the preface paradox.): A statement that is necessarily false in all interpretations; in this context, specifically the negation of a tautology or any falsehood drawn from a list containing only tautologies and contradictions.
distinct(in formal systems): Different from each other; not the same thing.
divine(Cross 2009: 453): Having the properties of being necessary, necessarily omniscient, omnipotent, eternal, immutable, impassible, and impeccable

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