more from Kit Fine

Single Idea 12211

[catalogued under 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism]

Full Idea

It is not implausible that before the 'introduction' of complex numbers, it would have been incorrect for mathematicians to claim that there was a solution to the equation 'x^2 = -1' under a completely unrestricted understanding of 'there are'.

Gist of Idea

It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced'


Kit Fine (The Question of Ontology [2009])

Book Reference

'Metametaphysics', ed/tr. Chalmers/Manley/Wasserman [OUP 2009], p.163

A Reaction

I have adopted this as the crucial test question for anyone's attitude to platonism in mathematics. I take it as obvious that complex numbers were simply invented so that such equations could be dealt with. They weren't 'discovered'!