For Everything There Is a Season

Mathematics, Hierarchy, and the Puzzle of Hartman's Shining Vision

Abstract

This paper is a response to C. Stephen Byrum’s article, “A Bushel and a Peck: Robert S. Hartman’s Axiology and Transfinite Mathematics.” It examines two of Byrum’s assertions. Regarding Byrum’s first assertion that transfinite mathe- matics is not necessary to Hartman’s axiology, though it provides a good metaphor for “talking about” values, this paper responds that math was Hartman’s hope for turning the philosophy of axiology into a science, and then suggests that the math component may be reassuring to intuitive/thinking personalities. Regarding Byrum’s second assertion that the domains of value may relate better to each other as a gestalt than in their current hierarchical arrangement, this paper agrees that the current hierarchy bears continued questioning, and then asserts that it may be best to maintain both the analytical and synthetic processes which are alive in the Institute today. The paper continues by asking whether Byrum’s work will bring the Institute closer to, or farther from, achieving Hartman’s vision, and briefly entertains two different views of what that vision may be. It further questions whether science — or any other system — is capable of fulfilling Hartman’s highest vision. The paper concludes with a short discussion of attention density and how the current tensions in formal axiology, and indeed in Byrum’s paper, may enhance the fulfillment of Hartman’s vision of a better and safer world.