by Jonathan Witt
(Dr. Witt is a Fellow of Discovery Institute and of Acton Institute)
Summary:Derek Abbott's "Is Mathematics Invented or Discovered?" asks why mathematics is so effective in describing our universe, and ultimately reduces the debate to a simplistic binary of mathematics as wholly created (Abbott's position) versus the neo-Platonic idea that mathematical models can perfectly and exhaustively describe nature. Abbott overlooks the view that drove the founders of modern science: the cosmos is the product of an extraordinary mathematician but one not restricted to the mathematical. Moreover, because the founders of modern science had theological reasons for emphasizing not only the cosmic designer's surpassing intellect and freedom but also human fallibility, they emphasized the need to test their ideas empirically. In these and other ways, Judeo-Christian theism matured Platonism and, in the process, sparked the scientific revolution.
Derek Abbott's recent piece in The Huffington Post, "Is Mathematics Invented or Discovered?", offers a thoughtful taxonomy of views on an issue with important metaphysical implications, but a crucial alternative possibility goes unexplored in the essay. Since Ben Wiker and I explore these issues in our book, A Meaningful World: How the Arts and Sciences Reveal the Genius of Nature, I'd like to summarize what I find useful in Abbott's piece and what I find incomplete.
The Abbott essay boils down to an effort to answer a question that thinkers have wrestled with for centuries and that was nicely expressed by Albert Einstein in this way: "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" Abbott says there is no consensus among mathematicians and scientists, but highlights four common answers: