Review of Gary Gallopin's Article

Abstract

I find Gary Gallopin’s article to be very illuminating about the role of transfinite mathematics in Hartman foundations for a scientific axiology. Gallopin’s views in this article support the use of transfinite mathematics as one of necessity when following the logical consequences of Hartman’s axiom of value. From my perspec- tive as a practicing axiologist, Gallopin’s article provides a compelling explanation, and it is fairly easy to understand with the examples he used. The main comment I want to make concerns a quote from Gallopin’s article expressing the necessity of using set-theory or transfinite mathematics. Gallopin writes, “The point is, Hartman had no choice in the matter. Once he started down the road of the axiom of value, he had to follow logic” (Gallopin, 2012, 138, italics added). I want to examine further in what sense this is true. Gallopin concludes that the best path for developing a scientific axiology is to follow formal set theory. I agree, and I will discuss the inner structure of large sets to resolve some of the issues brought forward by critics.