When Can Finite Testing Ensure Infinite Trustworthiness?

In this paper we contribute to the general philosophical‎ ‎question as to whether empirical testing can ever prove a physical law.‎ ‎Problems that lead to this question arise under several contexts‎, ‎and the ‎matter has been addressed by the likes of Bayes and Laplace‎. ‎After pointing‎ ‎out that a Bayesian approach is the proper way to address this problem‎, ‎we‎ ‎show that the answer depends on what we start with‎. ‎Namely‎, ‎under certain‎ ‎prior assumptions‎, ‎a finite amount of testing can lead to the conclusion of‎ ‎total trustworthiness‎, ‎though such priors could be unrealistic‎. ‎However‎, ‎we ‎do produce a new class of priors under which a finite amount of testing can‎ ‎lead to a high degree of trustworthiness‎, ‎at a relatively fast pace‎. ‎We use ‎the scenario of software testing as a way to motivate and discuss our‎ ‎development.