Logic Tutorial

Author: Hu Longbiao
Publisher:
Publish Date: 2006-06-01
Features: Logic is both an ancient and a young discipline. It is ancient because its history is long-standing; it is young because it still brims with vitality today, playing an irreplaceable role in people's practical thinking and communication, which no other discipline can fulfill. Based on the theoretical construction principle of "ascending from the abstract to the concrete," we have organized the teaching system of this book into nine chapters. The first chapter introduces the object, function, and history of logic, aiming to provide a general outline of logic and give readers a preliminary understanding of it. The second and third chapters of this book discuss issues within the scope of propositional logic. In propositional logic, the simplest and basic elements are propositional connectives, so the second chapter begins with connectives. The third chapter discusses propositional calculus, which is the formalization and systematization of propositional logic. Propositional calculus includes both axiomatic systems and natural deduction systems, and this chapter provides concise introductions to both. Chapters four, five, and six discuss predicate logic. Predicate logic serves as the "cell" of modern logic systems built upon propositional logic. Following this analytical approach, propositional logic reveals valid reasoning, i.e., the patterns of inference based on propositional connectives. However, there is another type of valid reasoning that cannot be explained by the theory of propositional logic, as its validity is rooted in the internal structure of propositions. Therefore, it is necessary to delve into the internal structure of propositions; examine the subject terms, predicate terms, and individual terms as components of propositional structure, thereby explaining the validity of this type of reasoning—this is the task of predicate logic. The seventh chapter discusses modal logic, which is an extension of both propositional logic and predicate logic. The discussion of the coherence and validity of propositional logic and predicate logic is based on the real world, whereas the validity of modal reasoning involves possible worlds. Thus, compared to propositional logic and predicate logic, modal logic offers a broader logical perspective. The main content of this chapter includes informal modal propositional logic, concepts, and other related ideas. The eighth chapter discusses inductive logic, encompassing both traditional and modern inductive logic. The first three sections primarily deal with "traditional" content, while the last two sections have a more "modern" flavor. Inductive logic, which differs from the deductive logic discussed in the previous chapters two to seven, is equally indispensable for cultivating people's logical analysis and reasoning abilities. Therefore, we provide a brief introduction to it here. The ninth chapter discusses pragmatic logic. The focus of pragmatic logic is the communicative nature of human speech activities; it attempts to explore the specific meaning of statements by combining the subject and context, making it highly complex and concrete. Although the logic community has engaged in much discussion about the nature, classification, and core concepts of pragmatic logic, the system and content of pragmatic logic have yet to take shape. The reason we introduce these immature theories at the end is simply to broaden readers' perspective on logic and to spark interest and attention to new logical fields on a broader scale.