This course is an introduction to philosophy, logic, and conceptual issues underlying the foundations of the natural and social sciences. We will examine and analyze a range of patterns of reasoning that lead to surprising, even alarming, conclusions. These go from fallacious arguments whose mistakes can be clearly pinpointed, to conceptual puzzles whose resolution leads to insights about reasoning, to four genuine paradoxes for which there are no clear solutions at all. Most of these paradoxes have been known since antiquity: Zeno's Paradox, about the concepts of space, time, and motion; the Liar Paradox, about the notions of truth and reference; the Sorites Paradox, about the notion of vagueness; and a surprise paradox to be announced in class. The analysis of fallacies and puzzles leads to the study of deductive logic. On the basis of a working knowledge of logic, we will be in a position to see how the paradoxes challenge both the fundamental assumptions that we make in thinking about the world and the very assumptions that underlie rational thought itself.