A difficult question, that would require much reading and thinking!
Mattingly in
BMC V (1950), pp.cli-ii:
'Providentia' unquestionably suggests the
Πpovoiα which could be used as an epithet of
Minerva (
Athena). The
wise goddess becomes the 'wisdom', the virtue that inspires her all-wise father. But the two
types - the large
head with wings and the smaller
head on
aegis - have not as yet been fully explained. Both
types are very
rare and the winged
head recurs on the coinage of
Victorinus.
