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It's a matter of language and logic. "another" is a contraction of "one other", and "other" means "distinct".

So, given you have "one (element) and one different (element)", at that point, you have, ipso facto, 2 elements.

It's not ipso facto 2 elements. You need to define what it means for there to be 2 elements, or 2 apples. Which goes back to question: "At what point does one apple and another one apple become two apples?"

I can simply say there's only one's of apples. The existence of the number two is optional in this case. Its existence is completely up to my own mind (Distance? Likeness? Etc.). Prove to me in this case that the number two exists outside our own minds.

Natural numbers are objective, observable relations between collections of things (and also between a collection and its sub-collections). They can only be understood by observing differences and similarities between collections. (Similar to how the color red would not exist if everything was red.)

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