This course is a general survey of the following three lines of contemporary Anglo-American philosophical development. It is said that contemporary Anglo-American philosophy first took the "linguistic turn" (including the development of contemporary logics) and then the "cognitive turn" in the twentieth century. The linguistic turn began with the three major figures, Frege, Russell, and Wittgenstein, and with the rise of logical positivism (and later, logical empiricism). Frege and Russell set up the beginning stage of analytic philosophy by initiating studies in the foundations of mathematics logic and philosophy of language. In its heyday there came Quine, Kripke, and Putnam who make great contributions in logics, semantics, and ontology. The cognitive turn began with the computational/representational theory of mind and cognition, and initiated the rise the new interdisciplinary "cognitive sciences". The third development began with the rise of logical positivism (logical empiricism) deeply influenced by Wittgenstein. Logical positivism (logical empiricism) then dominated studies in the philosophy of science concerning issues such as the demarcation of science, the nature of scientific explanation and theory, and theoretical reduction and unity. Theories of scientific explanation have occupied contemporary philosophical studies of sciences ever since Carl Hempel. We will introduce the development from his Covering Law models to Salmon's SR approach.