The Art of Logic

Chalkdust

6 February 2020

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Eugenia Cheng is a mathematician who is currently Scientist-in-Residence at the School of the Art Institute of Chicago. You can read more about her in our interview with her that was printed in issue 08. The third book on the Chalkdust Magazine Book of the Year 2019 shortlist is The Art of Logic: How to Make Sense of a World that Doesn’t (Amazon UK, Waterstones), Eugenia’s effort to drag formal logic down from its ivory tower and modern political discourse up from the gutter, and sit them round a conference table for a long overdue reconciliation.

Style, control, damage and aggression

Eugenia has grand ambitions in her latest book. When I first picked it up I confess I assumed that it wasn’t really aimed at me, a mathematician, and someone who is already reasonably well versed in formal logic. To some extent this is true of the first of three parts of the book, which surveys the essentials of propositional and quantifier logic. It does this however through the lenses of some of the hottest points of contention in modern social and political discourse: gone are the dreary predicates and facile conclusions of other treatise on logic, instead we learn implication by interrogating white privilege; negation by negotiating Brexit; and quantifiers by questioning sexism.

In a book which is ostensibly advocating for the broader use of abstract logic across all modes of discourse, part two comes as a refreshing riposte to that particular brand of mathematician who holds their subject as not merely superior to all others, but also claim its logical basis as an unimpeachable ziggurat. Cheng is not only forthcoming about the limits of logic, but actively embraces them as the way in to productively unifying the logical and emotional approaches to argument, discussion, and consensus.

This sets the stage for part three, where the promise of the subtitle is repaid. It provides a practical guide for how normal people (and indeed mathematicians) can actually apply ideas from formal logic to every day situations, as well as to interrogate their own beliefs and justifications for those beliefs. It is also an opportunity for Cheng to lay down her vision of the ideal format of interpersonal arguments and political discourse, and what it means to be an intelligently rational person. Contrary to the perhaps widely held belief that logic and emotion are antithetical – that the only things emotion can bring to an argument are fallacies – Cheng argues that logic and emotions not only can coexist in a rational debate, but must coexist. She writes “I think we can use this superpower [intelligent rationalism] to help the world bridge divides, foster a more nuanced and less divisive dialogue, and work towards a community that operates as one connected whole.”

Overall then I think the book succeeds in being approachable for someone with no training in formal logic, while still being engaging enough to sustain the interest of a professional mathematician throughout. From the start with an apparent oxymoronic title, at every stage Cheng manages to subvert the expectations of the reader as to the scope, applicability, and practicality of logic. The core message of the book, which if it can be reduced to a single word would be empathy, is hardly a novel one; the novelty comes from the framework with which Cheng approaches the topic, and this really makes this book stand out.