Friday, September 4, 2009

Truth, untruth, and probability

Truth and untruth are opposites. Where does probability fit in? As we talk about the probability that a proposition is true, we often suggest we have an idea of the provability of the proposition's truth. At the root of the noun probability (and also the noun probe) and the adjective probable is the Latin verb probare, meaning to try or to test. The English noun proof and the verb prove have the same Latin roots. Therefore, the words probability and provability do not just look alike, they have the same meaning from an etymological viewpoint. This has recently been illustrated by Chandler Davis in a discourse on mathematical reasoning [1]:
There is no doubt that the idea of probability was close to the idea of truth at the early stage [16th century]—etymologically, “probable” is “provable”, and even today, “probity” means utter reliability—and the emerging notion of something having positive probability had to be disentangled from the different notion of appearing credible. This fascinating story has been closely studied in recent years, especially by Ian Hacking and Lorraine Daston, and I have nothing to add to their work.

Keywords: etymology, mathematics, logic, philosophy, Latin

[1] Chandler David: The Role of the Untrue in Mathematics. The Mathematical Intelligencer Summer 2009, Volume 31, Number 3, pp. 4-8.

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