This is the first of a two-volume collection of studies in inconsistencies in Greek and Roman religion. Their common aim is to argue for the historical relevance of various types of ambiguity and dissonance. The first volume focuses on the central paradoxes in ancient henotheism. The term 'henotheism' -- a modern formation after the stereotyped acclamation: #EIS O QEOS# ("one is the god"), common to early Christianity and contemporaneous paganism -- denotes the specific devotion to one particular god without denying the existence of, or even cultic attention to, other gods. After its prime in the twenties and thirties of this century the term fell into disuse. Nonetheless, the notion of henotheism represents one of the most remarkable and significant shifts in Graeco-Roman religion and hence deserves fresh reconsideration.