Does anyone know if there is there a name for the idea that new concepts (such as negative numbers, complex numbers or type constructors in a type system) are only ever introduced into a preexisting "system" so that they can be eliminated later, after helping make some progress?
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I'm a little bit confused about your example - negative numbers aren't eliminated, are they? They're still around? Sometimes after I eliminate everything else, I'm left with a negative number, right?
If the problem is stated in terms of positive numbers (e.g. anything in the material world), any problem stated in those terms ultimately needs to get back to them. If an "answer" is negative, then I'd contest that it will still ultimately be reconciled to make a positive answer.
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e.g. if I promise you ten apples, and I give you three, then I still owe you seven, which I might think of as -7. But something feels ephemeral about that, in that I don't really "have" -7 apples, and ultimately we need to resolve everything to nonnegative numbers of apples.
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