Consider the likelihood ratio test of Neyman and Pearson. As indicated, the significance or p-value of a test is an error rate that will manifest if data collection and testing is repeated, assuming that the null hypothesis is in fact true.  Notably, the p-value does not tell us anything about how probable the truth of the null hypothesis is. However, many scientists do use hypothesis testing in this manner, and there is much debate over what can and cannot be derived from a p-value (cf. Berger and Sellke 1987, Casella and Berger 1987, Cohen 1994, Harlow et al 1997, Wagenmakers 2007, Ziliak and McCloskey 2008, Spanos 2007, Greco 2011, Sprenger forthcoming-a). After all, the test leads to the advice to either reject the hypothesis or accept it, and this seems conceptually very close to giving a verdict of truth or falsity.