Which preposition to use with doubleness

of Occurrences 2%

I recalled the queer doubleness of my memories overnight.

towards Occurrences 1%

He expects no appointment or other appreciable gain through Tulpian's favour; he has no doubleness towards Felicia; there is no sneering or backbiting obverse to his ecstatic admiration.

Which preposition to use with  doubleness