When compared to scientific progress as well as other kinds of inquiry, the nature of philosophical progress is different because of a lacking structural methodological process. Williamson argues that in order to make philosophical progress, we should make clear our philosophical intuitions by adopting a methodology that largely depends on mathematics, “one that prizes clarity, rigor, and open-eyed reflection on the sorts of constraints – including logical constraints – that should be held to fix the contours of the debate.”

A plethora of problems arises when relating mathematics to the natural world; imperfect models, observational noise, false negatives and positives, uncertainty of the initial condition, etc. All those problems allow for uncertainty and an exponential growth of that uncertainty over time, debilitating any predictive power. However, the most important problem is not one regarding prediction but one about representing reality.