 There is direct evidence that Poincaré thought that mathematics must be in place before we can do any empirical science. For example, in the opening of Chapter 12 of Science and Hypothesis, he remarks that: “The purpose of mathematical theories is not to reveal the true nature of things. Such a claim would be unreasonable. Their only goal is to coordinate the physical laws that experiment reveals to us, but that we could not even state without the help of mathematics” (Poincaré 1902, 2017, 143). Dunlop, by contrast, seems to have something much stronger in mind with the idea of the hierarchy, which is perhaps why she calls the thesis the dependency hierarchy interpretation. She seems to take the interpretation to be a thesis of reductionism, that geometry reduces to arithmetic, or at least, the intuitive reasoning used in arithmetic is all that we need in geometry.