Heavy Duty Platonism

Heavy duty platonism (HDP) is of great dialectical importance in the philosophy of mathematics. It is the view that physical magnitudes, such as mass and temperature, are cases of physical objects being related to numbers. Many theorists have assumed HDP’s falsity in order to reach their own conclusions, but they are only justified in doing so if there are good arguments against HDP. In this paper, I present all five arguments against HDP alluded to in the literature and show that they all fail. In doing so, I establish two related truths: HDP has been unfairly ignored, and the arguments which take its falsity as a key premise should be re-assessed.