The conditions involved in the applicability of mathematics in science are the subject of ongoing debates. One of the best‐received approaches is the inferential account, which involves structural mappings and pragmatic considerations in a three‐step model. According to the inferential account, these pragmatic considerations happen in the immersion and interpretation stages, but not during derivation (symbol‐pushing in a mathematical formalism). In this work, I draw inspiration from the later Wittgenstein and make the case that the applicability of mathematics also rests (...) on pragmatic considerations at the mathematical derivation level. I make the further case that pragmatic considerations at the mathematical derivation level may substitute pragmatic considerations in the other two stages, thus showing how they are holistically interrelated. I illustrate these two points with the solution of a simple geometrical problem. (shrink)

This paper has two aims. First, we argue that Wittgenstein’s notion of petrification can be used to explain phenomena in advanced mathematics, sometimes better than more popular views on mathematics, such as formalism, even though petrification usually suffers from a diet of examples of a very basic nature (in particular a focus on addition of small numbers). Second, we analyse current disagreements on the absolute undecidability of CH under the notion of petrification and hinge epistemology. We argue that in contemporary (...) set theory the usage of construction techniques for set-theoretic models in which the Continuum Hypothesis holds and those in which it fails have petrified into the normative demand that CH remain undecidable. That is, the continuous and successful practices involving the construction of various set-theoretic models now act as a normative hinge shared among practitioners, i.e., have normative force in the discipline. However, not all hinges are universal, which is why we find disagreements in set theory. We will show that this is a refinement of, and partially conflicts with, the arguments presented by set theorist Joel David Hamkins. (shrink)