Philosophia Christi: How Should We Think About a Philosophy of Mathematical Structures?

June 11, 2010
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Labels: 12:1, philosophia christi, philosophy of mathematics, realist modal structuralism, structuralism, walter schultz
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The Summer 2010 issue of Philosophia Christi features an interesting proposal for a philosophy of mathematics. Subscribe today to the journal!

Walter J. Schultz (Northwestern College), “Toward a Realist Modal Structuralism: A Christian Philosophy of Mathematics.”

Abstract: 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.

We recently published a helpful background piece to what Schultz argues in the Summer 2010 issue. See his “Dispositions, Capacities, and Powers: A Christian Account” from Winter 2009 issue, which can be purchased here.