Volume 12, Issue 1, 2010
Toward a Realist Modal Structuralism
A Christian Philosophy of Mathematics
The aim of this paper is to propose a philosophy of mathematics that takes structures to be basic. It distinguishes between mathematical structures and real structures. Mathematical structures are the propositional content either of consistent axiom systems or (algebraic or differential) equations. Thus, mathematical structures are logically possible structures. Real structures—and the mathematical structures that represent them—are related essentially to God’s plan in Christ and ultimately grounded in God’s awareness of his ability. However, not every mathematical structure has a correlative real structure. Mathematical structures are either true or fictional, yet all are possible.