Genitive with assigno

Question

In Ethics, De Dei, Proposition 11, Second demonstration we read:

Cujuscunque rei assignari debet causa seu ratio tam cur existit quam cur non existit

cujuscunque rei is genitive, but because of assignari I expect it to be dative. What's the point?

Answer 1

The difference is not great between "The cause and reason ought to be assigned to each thing why or why not..." and "The cause and reason of each thing why or why not... ought to be assigned..." Though the Genitive after causa is more literal.
I think the most significant reason for choosing the Genitive rather than the dative is continuity. The formula "each one of the...ought" helps the reader to see how the argument develops:

PROPOSITIO X: Unumquodque unius substantiæ attributum...debet.
'each several attribute of a single substance...ought.'

This is followed (in the middle of Proposition XI) with

... infinitis attributis quorum unumquodque...necessario...
'with infinite attributes each one of which...by necessity...'

So, in the first horn of the dilemma

ALITER: Cujuscunque rei assignari debet causa seu ratio
'IN THE ONE CASE: The causa or ratio of each res ought to be attributed...

Answer 2

I would take cujuscunque rei causa to be a single noun phrase: "a cause for/of every individual thing". That is, assignari has a subject, but the object is left implied; if it were made explicit, it would be something like illi "…to that thing".

A cause of every individual thing must be assigned [to that thing]: either a reason why it exists, or a reason why it doesn't exist.