Difference between zero apples and zero oranges.

Question

There are two plates, one with an apple and another with orange. Yes, they are different now, but what if I take both the fruits out?

Answer 1

It depends on what formalism you're working in.

If you're in some kind of type theory, where plates have types, then you've probably got left a plate with zero apples and a plate with zero oranges. These plates are not comparable to each other, because they have different types; and you can't put an orange onto the empty apples plate (just as you can't put an orange onto a plate with three apples), because the apples plate can only hold apples. But you might be able to turn the apples plate into a fruit plate, and then put an orange onto it.

If you're in some untyped setting like set theory, you have two identical and indistinguishable empty plates. You could add an apple and an orange to each plate without any problems.