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Or we just start counting with 1, since 1 is the first number we start with. Do small kids start with a concept of zero and then adding one to it, or do they just start at one?


If you start at 1, how do you answer the question "how many apples are in the basket", when the basket is empty?

Or do you believe that the answer "none" or "zero" is then given without the activity of counting having taken place?

What do we call the meta-activity then: the procedure that results either in the "empty" answer or "one", "two"? Whatever that activity is called, it starts with a concept of zero. Let's call that activity "quanting". Quanting starts with a motivation to enumerate items, and an initially empty result. When no items are present, quanting terminates, reporting that zero/nothing/none result. Otherwise quanting branches into a subprocedure called counting, and that begins at 1.


Humans could do basic counting prior to the concept of zero. Obviously kids or anyone prior to zero would say there are no apples in the basket, but if you were to ask an ancient Greek philosopher if that meant "no apples" is something worthy of being denoted, they might think you're doing sophistry and trying to elevate nothing to something.

A smart ass kid might reply there are zero oranges in the basket, or zero miniature unicorns. Since the basket is empty, it could have potentially had anything if we're just going to imagine things in baskets. But we don't enumerate over all possible zero items in the basket. And anyway, the basket isn't really empty since it has N air molecules, N fibers or whatever.

The pedantic point I'm making is that counting at zero is a convention we developed for mathematical reasoning when appropriate, but not a starting place for counting things in everyday language.


If an ancient Greek philosopher had three apples in his basket, and I took them away while he wasn't looking, oh, he would definitely find "no apples" something worthy of being denoted.




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