Carl G Hempel - Collected Quotes

"All the theories and hypotheses of empirical science share this provisional character of being established and accepted ‘until further notice’, whereas a mathematical theorem, once proved, is established once and for all; it holds with that particular certainty which no subsequent empirical discoveries, however unexpected and extraordinary, can ever affect to the slightest extent." (Carl G Hempel, "Geometry and Empirical Science", 1935)

"The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results." (Carl G Hempel, "Geometry and Empirical Science", 1945)

"Theories are usually introduced when previous study of a class of phenomena has revealed a system of uniformities. […] Theories then seek to explain those regularities and, generally, to afford a deeper and more accurate understanding of the phenomena in question. To this end, a theory construes those phenomena as manifestations of entities and processes that lie behind or beneath them, as it were." (Carl G Hempel, "Philosophy of Natural Science", 1966)

"A geometrical theory in physical interpretation can never be validated with mathematical certainty […] like any other theory of empirical science, it can acquire only a more or less high degree of confirmation." (Carl G Hempel)

"The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter." (Carl G Hempel)