The Hidden Identity Crisis of Numbers

We define numbers as sets, yet there is no logical reason to choose one set over another. This means our basic math definitions are arbitrary and based on mere conventions.

Paul Benacerraf pointed out that while we define the number two as a specific set, there are endless other sets that could serve the same purpose equally well. Since no single definition is mathematically superior, the objects we call numbers remain strangely undefined. This realization forced philosophers to move away from Platonism and toward structuralism. It suggests that math is less about specific objects and more about the relationships between them.