von John Henry Ryskamp
Paradox, natural mathematics, relativity and twentieth-century ideas
In: General science journal, 2005
New historical research shows that twentieth-century thought was expressed in terms of the “natural” mathematics developed at the turn of the century in order to cope with
the supposed “paradoxes” generated by Cantorian set theory.
Economics, physics, biology – apparently no area of inquiry has escaped being made part of the “natural” mathematics project. This mathematics asserts that mathematical formulations are inherently anomalous; the evidence of this is that they generate paradoxes. Therefore, the idea that mathematics is an aspect of human perception, must be made a part of mathematical formulations even though it plays no internally consistent role in any “natural” mathematical formulation.
The role of “natural” mathematics has gone unremarked for the very reason it was influential in the first place. Whether the researcher was the physicist Albert Einstein, the economist Piero Sraffa, the logician Kurt Gödel, the philosopher Ludwig Wittgenstein, or the biologist Motoo Kimura, scientists in non-mathematics disciplines felt they were unable to express their ideas mathematically. This is the chief revelation of the new historical research, and a remarkable and unexpected (given the exalted reputations of these figures) unifying feature of twentieth-century intellectual history.
These thinkers had to search for appropriate mathematical terms in the latest mathematics of their day. They were unprepared to cope with the idea that flaws in the mathematics lodged errors in their theories. The current reexamination of the mathematics of the disciplines began with the revelation of the faulty approach taken to set theory by some of the chief proponents of “natural” mathematics.
- 18. April 2013