I just came across a reference to the work of the philosopher of mathematics Hartry Field. This is what Wikipedia has to say:
Fictionalism was introduced in 1980 when Hartry Field published Science Without Numbers, which rejected and in fact reversed Quine’s indispensability argument. Where Quine suggested that mathematics was indispensable for our best scientific theories, and therefore should be accepted as true, Field suggested that mathematics was dispensable, and therefore should be rejected as false. He did this by giving a complete axiomatization of Newtonian mechanics that didn’t reference numbers or functions at all. He started with the “betweenness” axioms of Hilbert geometry to characterize space without coordinatizing it, and then added extra relations between points to do the work formerly done by vector fields.
Does anyone know if that is an accurate summary of Field’s argument? It seems obviously wrong to me.
Via Crooked Timber.