Mathematics and Empiricism

In a recent LessWrong post titled 'Mathematics and Empiricism', the writer 'Ape in the coat' takes on philosopher Lorenzo Elijah's argument that the 'unreasonable effectiveness of mathematics' poses a problem for empiricism and physicalism. Elijah, in his piece 'Does the Universe Speak a Language We Just Made Up?', suggests that if math is just a human invention, its ability to describe and predict natural phenomena—from quantum mechanics to general relativity—seems almost magical. But the author, a mathematician by training, disagrees entirely. They argue that there's nothing weird about math being the backbone of science; instead, confusion arises from how we define 'real'.

The author defends a view close to mathematical fictionalism, treating math as an extremely precise and general language, not a repository of independently existing abstract objects. They challenge the notion that the number '4' must refer to some non-physical entity. Instead, they propose three possible meanings: 1) there are at least four physical objects in the universe (true), 2) humans have a mental concept of 'fourness' (true), or 3) 'fourness' exists in a separate Platonic realm (which fictionalists reject). The post argues that conflating these meanings leads to false philosophical puzzles. Ultimately, the author suggests that math's effectiveness is a byproduct of its logical structure and our ability to model reality with it, not evidence for mathematical Platonism.