The Art of Logic in an Illogical World

At the heart of mathematics is the proof—a logical argument from an agreed-upon set of axioms to reach some conclusion. In the real world few things are that simple. In her latest work, mathematician Cheng (Beyond Infinity), using current areas of disagreement from political to social, explains how logical arguments should be constructed and why they frequently fail. These include some cases in which a statement does not necessarily follow logically from the one before but still manages to fail in a different way. For example, people may have similar yet different or unspoken sets of basic assumptions. Other disagreements may arise from unclear generalizations, false equivalencies, or faulty analogies. In clear and easy-to-read prose, Cheng walks readers through simple logic, the limitations of the law of the excluded middle, handling gray areas, and even a little about logical paradoxes.