Logic In The Wild

Logic in the Wild

Is logic a good tool for making decisions? Can it make us better listeners and help us find coherence in views that we disagree with? Is Sherlock Holmes actually good at logic? Patrick Girard addresses these and other questions by presenting logic as the guardian of coherence. Logic, Girard argues, finds coherence in the patterns of reasoning across science, religion, and everyday decision making. It helps communities engage safely by replacing contentious debates with shared, constructive reasoning – logic provides neutral ground for the healthy pursuit of common goals and interests. Logic in the Wild employs common sense language, eschewing technical jargon, symbols, and equations. Girard’s attention focuses on logic’s power to find what unites the complex and the simple, the abstract and the concrete, the theoretical and the practical. In treating logic not as a passive subject to learn but as an active discipline to engage with, Logic in the Wild teaches us to identify patterns in our own reasoning, which inevitably helps us better confront questions central to everyday life.

Mathematical Logic

This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are usedto study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

Principles of logic