The letter ℘: name and origin? (2017)

It could be motivated by the fact that Russell and Whitehead needed a symbol for printing that the printer had in his type case but could not be confused with anything else. Taking a iota and simply turning it upside down would then be a rather ingenious idea. But that is just my speculation ...

https://math.stackexchange.com/questions/1885938/whats-meani... says 'in the article Frege, Peano and Russell on Descriptions: a Comparison, Francisco A. Rodríguez-Consuegra tracks down the source to Peano's Studii di logica matematica (1897) as where the operator first appears'

That page in 'Studii di logica matematica' appears to be https://archive.org/details/peano-studii-di-logica-matematic... .

It also uses an upside-down C and upside-down E.

And the Lambda looks like an upside-down V. The bases of all these upside-down letters do not match the baseline of the text. Obviously there were no special upside-down moveable types available of freshly cast for this book. Peano had to creatively repurpose what types were available.

There are loads of examples of this, e.g. ∀ and ∃, but iota is a really poor choice.