[jonnybgood]

At what point does one apple and another one apple become two apples? Is a matter of distance? Likeness? Practicality doesn’t say there must be two apples, just one apple and another one apple. Two (apples) is just an abstraction in my mind.

[templeosenjoyer]

>At what point does one apple and another one apple become two apples? Is a matter of distance? Likeness?

Perhaps I am misinterpreting, but it seems to me like this would occur whenever you formed a coherent question. "How many apples are there?" would be insoluble, whilst "how many apples are there in this room?" or "how many red apples are there resting on that table?" would result in an answer belonging to the set of naturals.

[Koshkin]

You are right in that one apple and another apple do not make two apples. You need a matching pair of happy horses for the number two to emerge.

[talaketu]

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.

[jonnybgood]

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.

[Koshkin]

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.)