Transfinite Mathematics, and Axiology as a Future Science
DOI:
https://doi.org/10.67945/jfa.v2i.23Keywords:
transfinite mathematics, philosophy of science, formal axiologyAbstract
This article explains that and why Robert S. Hartman associated his three dimensions of value—systemic, extrinsic, and intrinsic—with three types of concepts and with transfinite mathematics. It argues that his philosophical justification for using transfinite math was unsuccessful, based as it was on his indefensible philosophical "proofs for the infinite value of man," and that if axiology is to become a "real science" in the future, a new and better mathematics for it is needed, one that will provide for a workable axiological calculus of value. It explores and accepts the defining characteristics of axiology as science, but not one of the natural sciences, as Hartman understood them. As explained, he thought that real sciences must have 1) a subject matter, a "set of objects," 2) mathematical formalities, or a formal "frame of reference," and 3) isomorphous patterning between 1) and 2). This article explains in depth that applying transfinite math to the three dimensions of value fail to meet criterion 3). Some alternatives to transfinite math are briefly explored toward the end.
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