George Boole proposed something similar in The Laws of Thought: he considered a definition of c = a/b where a = c AND b (even if he didn't write it like that).

Thus, 0/0 was an indeterminate value, and 1/0 was seen as an impossibility.

Boole's example: if m means "is mortal" and h means "is human", then saying "there is no immortal humans" is h AND NOT m = 0, and Boole explains that from it you could deduce: m = h + 0/0 and not h meaning "mortals are humans and something indeterminate which is not human"

here it's still George Boole trying to cram normal arithmetics into logic, but still.