The Application of Mathematics

Why is abstract mathematics applicable within science? Jeffrey Ketland describes the metatheory of the application of mathematics in science and highlights the 'entanglement' of physical systems with mathematical objects and structures. Applied Mathematics inferences are regimented into 'canonical form', involving an ambient foundational base theory and the specific physical premises and conclusions. These latter are formulated using concepts called 'entanglers', which relate physical objects and systems to mathematical objects. The simplest example is the membership predicate, 'x is an element of y', and other examples are coordinate functions, quantity functions (such as mass, length, or temporal duration), and fields (on space or spacetime). Mathematical terms denoting these, as well as impure sets, relations, and structures, are called 'entanglement constants'. Ketland shows that such inferences satisfy a form of topic neutrality called Hilbert's Beermug Principle, and all such inferences can be seen to be instantiations of general mathematical theorems with such constants.