TY - JOUR
AU - Marshall, Douglas Bertrand
AB - Just as mathematics helps us to represent and reason about the natural world, in its internal applications one branch of mathematics helps us to represent and reason about the subject matter of another. Recognition of the close analogy between internal and external applications of mathematics can help resolve two persistent philosophical puzzles concerning its applicability: a platonist puzzle arising from the abstractness of mathematical objects; and an empiricist puzzle arising from mathematical propositions’ lack of empirical factual content. In order to see how this is the case, we will examine what it is to apply mathematics internally and describe examples.
TI - Internal Applications and Puzzles of the Applicability of Mathematics
JF - Philosophia Mathematica
DO - 10.1093/philmat/nkad019
DA - 2023-10-25
UR - https://www.deepdyve.com/lp/oxford-university-press/internal-applications-and-puzzles-of-the-applicability-of-mathematics-HTk8BjhBgs
SP - 1
EP - 20
VL - 32
IS - 1
DP - DeepDyve
ER -