In a recent Guardian article, Bonnie Greer suggests that Kurt Gödel “had shown the world years before that nothing can be 100% proven” (“Me and Sister Carmela”, 20th September). In fact, what he showed was the subtly different notion that not 100% of true statements (of a particular, broad class of mathematical statements) can be proven.
This is not just a pedantic factual correction. Frequently, mathematicians (and practitioners of other rigorous reasoning systems) are attacked in the media for their arrogance. This is often characterised as an assumption that “everything” can be shown to be true or false with 100% certainty. By contrast, only specific types of statements are amenable to mathematical methods; furthermore, even within that domain, not everything will be provable!
In particular, the elision of words used in some specific technical way (“proven”, “statement”) to imply that these narrow technical results magically mean something about the day-to-day meaning of these words is ubiquitous. It is not the mathematicians who are at fault in such situations, as they are precise about the narrowness of the applicability of their results.
It could be argued that it is the practitioners of the literary arts that are guilty of the arrogant over-reach that mathematicians are frequently blamed for: consider the slapdash use of metaphor to extend the reach of statements, overinterpretation of the meaning of technical notions based on mere co-incidence of words, and drawn out discussions that amount to little more than extended puns. This is ultimately destructive to both the understanding of science and literature and to attempts to create a meaningful dialogue between the disciplines.