THE ART OF LOGIC IN AN ILLOGICAL WORLD

Logic helps people build bridges to understanding. But what if people don’t want those bridges? Aha, says this entertaining guide: There’s a meta-problem for you….

In our current landscape of the postfactual, the loudest bellower is king. Enter Cheng (Beyond Infinity: An Expedition to the Outer Limits of Mathematics, 2017, etc.), the scientist in residence at the Art Institute of Chicago—now there’s a good idea—and possessor of a formidable, mathematically inclined mind. Though the author aims to teach math, science, and formal logic as she progresses, she really means to help readers construct better arguments, which may turn out to be a world-saving proposition. There is a built-in advantage to using logic, she writes, in that it provides a framework for discovering what is true, and “one of the main reasons to have a clear framework for accessing truth is to be able to agree about things.” The notion of agreement will come into play late in the book, when Cheng analyzes the best kinds of arguments, which allow us to understand another person’s point of view. Until that point, there are theorems, axioms, and proofs to go through, for mathematically based logic hinges on such things as the union of sets (the place where two circles meet in a Venn diagram) and the proper application of analogy to any particular problem. The author isn’t exactly playful, but she pitches a few paradoxes as she moves along—one of them being the fact that, since logic doesn’t actually correspond to what we know as the real world, we have to “forget the pesky details that prevent things from behaving logically.” In other words, we have to think abstractly, which poses plenty of other challenges.

Though full of pauses, second glances, and head-scratches, this is a very welcome primer in logical thinking.