At this point I hold one object that we agree to label "apple". Note that even seeing it as a single object is a layer of abstraction. In reality it's a clump of fundamental particles temporarily banding together
> and then handed you another apple,
What's "another apple"? What does it have in common with the thing I'm already holding? We label this thing to be also an apple, but it's a totally different set of atoms, from a different tree, perhaps from the other side of the planet. Perhaps the atoms formed in stellar processes light years away from that of the other apple.
Calling both of these things "apple" is a required first step to having two of them, but that is an of abstraction, a mental trick we use to simplify the world so we can represent it in our minds.
I'm not a particle physicist but I hear electrons *can* be counted without any unwitting help from our lower-level neural circuitry.
The numbers themselves aren't a problem, I'm just pointing out that our cognition involves many overlapping layers of abstraction, and we're doing mathematics and every other mental activity in one or more of those layers.
That this seems to correlate strongly to real-world phenomena speaks well of the types of abstraction that nature has equipped us with.
However, what about virtual things, e.g. apples in a computer game.
Addition is abstract phenomena based on math which itself is abstract, so it can only function in abstract setup.
You are differentiating, classifying, etc.