Synonyms for Divinatory (same or very similar meaning)
WordNet sense 1 (resembling or characteristic of a prophet or prophecy):
sibylline, mantic, sibyllic, vatic, vatical
WordNet sense 2 (foretelling events as if by supernatural intervention):
prophetic, prophetical
WordNet sense 3 (based primarily on surmise rather than adequate evidence):
conjectural, hypothetical, supposed, hypothetic, suppositional, suppositious, supposititious
WordNet sense 4 (concerned primarily with theories or hypotheses rather than practical considerations):
theoretic, theoretical
From the ODE community, based on WordNet
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