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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But... isn't most mathematics approachable as such "bridges" or "scaffold"? Integers, to complex, limits, definite integration, to differential equations, to Fourier/Laplace transforms, algebraic structures (groups/vector spaces), categories, generating functions...
Yes, it's everywhere... And I think it's become so natural for us to apply these bridges that as a "phenomenon" or "method" it doesn't even really have a name...
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I considered answering "maths", but "completion" and "closure" come to mind. Complex numbers are IIRC the algebraic closure of reals; the Yoneda embedding injects any category into a category with more limits. "Freely generated" structures are also relevant...
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But indeed, it seems all the names are for specific ways to complete a structure... Except maybe "embedding"?
End of conversation
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