For English speakers, epistemology is a study of knowledge (scientific or unscientfic); for French speakers, it specifically consists in a study of scientific knowledge.
Epistemology puts questions on nature and value of principles, conceptions, methods, and results of sciences. It is a reflexive and critical view (it is not just a description of sciences without judgment).
Formal sciences / Empirical sciences
Formal sciences leave aside of content and focus on form. Hypothetico-deductive reasoning constitutes demonstration methods in formal sciences (proofs). It consists in puting hypothesis and, thank to this formal logic, deducing conclusions. Empirical sciences are interested in specific sides of tangible experiences. They presuppose knowledge of contingent fact and describe the real world.
- Lena Soler (2000). Introduction à l'épistémologie. Coll. Philo, Eds Ellipses.