Fundamentals for Political Scientists: Preliminaries & Review Will H. Moore ∗ August 31, 2005 The goal of a science of politics is to identify general patterns among abstract concepts. That is, political scientists think about politics and invent abstract concepts that help us describe the political world. But a science of politics requires more than inventive description. It in- volves the specification of expected causal relationships among the concepts and, ultimately, the determination of whether those expected relationships comport with evidence. Mathematics is an abstract discipline. All of its concepts have been invented. It is nothing more than a formal language, a set of definitions and rules, a syntax. However, since we are not studying mathematics for the purpose of contributing to its development, we need not concern ourselves with that. Instead, we are interested in mathematics to help us discipline our conceptualization, our specification of hypotheses, and our testing of hypotheses. In other words, we are interested in mathematics to help us develop rigorous theories of politics and rigorous tests of the implications of those theories. This chapter provides some preliminaries. I discuss concepts and the labels one can use to identify some relevant properties. I also review some arithmetic and algebra that you studied in elementary and middle school that we will use throughout this course. Finally, I introduce notation. 1 Constants, Variables & Levels of Measurement Political scientists are interested in concepts such as participation, voting, democracy, party discipline, alliance commitment, war, etc. If scholars are to communicate meaningfully then they must be able to understand what one another are arguing. In other words, they must be specific about their theories and their tests. * Joseph K. Young wrote the initial draft of section 3. 1