I recall that I read---in a book by Constance Reid---of a named principle that guided the arithmetic conventions that applied to operations on newly discovered mathematical objects.
For example, when negative numbers were finally admitted into the fold of arithmetic, the product of two negative numbers was defined to be positive (even if it appeared on face value to be counter intuitive) to maintain logical consistency with all that went before it.
I thought this idea was called the "Principle of Arithmetic Consistency" or something like that, but I have not been able to Google successfully for any such candidate expression.
I do not believe my recollection to be false.
Could someone please tell is if such a principle does indeed exist and is recognized, and if so, what its formal name and definition are.