The Baby or the Bath Water? The Role of Transfinite Mathematics in the Nascent Hartman Science

Authors

  • Gary G. Gallopin

DOI:

https://doi.org/10.67945/jfa.v5i.104

Keywords:

transfinite mathematics, formal axiology, philosophy of science

Abstract

I take up the issue of the relationship between formal axiology and transfinite math- ematics. I note the call from some important members of the R. S. Hartman Institute to do away with the use of transfinite mathematics in formal axiology; then I discuss the reasons why I believe that it is not a good idea to do this. The issue is complex, has a long history, reaches into many corners of formal axiology, and extends be- yond it into the realm of the philosophy of science, so this article is only a begin- ning. I discuss narrow parts of the issue, including questions arising out of trans- finite mathematics’ use in transpositions, Hartman’s own ordering of the Hartman Value Profile (HVP) using transfinite math, and questions regarding Hartman’s use of à1 to denote the value of a human being. I also discuss various errors that have been made in the critiques of transfinite mathematics, including violating the rules of transfinite mathematics and of science in general. This issue is an important one because not only does it determine whether Rob- ert S. Hartman founded a real science of axiology, or merely extended axiological philosophy, but it also determines whether or not we truly understand formal axiol- ogy at its roots—set theory. If we ever hope to add new and equally powerful instru- ments to our current inventory of a single technical product, the HVP and its vari- ants, we need to understand how the HVP was created using transfinite mathematics.

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Published

2012-07-01

How to Cite

Gallopin, G. G. (2012). The Baby or the Bath Water? The Role of Transfinite Mathematics in the Nascent Hartman Science. Journal of Formal Axiology: Theory and Practice, 5, 131–156. https://doi.org/10.67945/jfa.v5i.104

Issue

Vol. 5 (2012)

Section

Discussions

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