Skip to main content

The Art of Logic - Eugenia Cheng ***

This is an important book, though I'm not sure Eugenia Cheng would agree with my logic in saying so. 

Going on the marketing, what we have here is a counter to fake news and dodgy argumentation in the form of mathematical logic. The back cover tells us 'Newspaper headlines and social media use emotions to warp the facts. Politicians and companies master rhetoric to mislead us. What one book could help us make sense of it all?' Admittedly they don't answer their rhetorical question, but I assume the answer is intended to be The Art of Logic. (Did the company behind this book realise it was using rhetoric, though presumably not to mislead us?) 

What we actually have is a combination of a lucid and interesting explanation of the basics of logic with the mathematical equivalent of those books such as Algorithms to Live By that were so popular a couple of years ago. They used the logic of algorithms (differently worded, and, to me, easier to understand), the heart of computer programs, to look at everyday problems. Here, Cheng is using the purer mathematical form of logic to the same end.

Cheng does a good job at explaining logic from a mathematical viewpoint and gives a useful brief dip into her own field of category theory. Her illustrations of concepts like the lost middle are effective, and though it sometimes feels points are being laboured, this can be an alien area to many, and a slow and steady approach is undoubtedly best.

There were a few small content issues. We are told that scientists pick their confidence limits based on the seriousness of the situation - but this seems at odds with the way that physicists use vastly higher confidence limits when dealing with the fascinating, but hardly life-changing Higgs boson than psychologists do when trying to understand and improve human behaviour. There's quite a lot in the book about blame, some of which doesn't sit well with the meaning of the word. We are told that both dropping a glass and a hard floor are 'to blame' for a glass breaking. But where both are causal, blame can't be ascribed to a passive object. And there's a total misunderstanding of the origins of airline overbooking. However, these are small points - overall, the book is engaging and effective in putting across its message.

So far, so good. The problem - and the reason I think this is an important book - comes in two ways when Cheng attempts to apply logic to everyday life. Mathematics works by starting with axioms and building up a logical structure piece by piece. As Cheng says, this is part of its wonderful appeal if you can get past the fear of maths. But what is not emphasised enough is how axioms can cause difficulties. Mathematical axioms seem extremely straightforward statements such as 'A straight line segment can be drawn joining any two points,' or 'two sets are equal if and only if they have the same elements.' But Cheng's axioms are all about what she feels is right. I'm not saying I disagree with her ethics, but rather that value judgements are a poor basis for logical axioms.

The other aspect of the problem is that, as Cheng examines, in applying logic you can select different levels of abstraction from, say, the experience of an individual person up to all people. In her examples, she makes the choice of which level to render that abstraction: yet that choice itself has a major influence on the outcome that isn't recognised in her logical structure. As a mathematician, she should know from the history of set theory that when choice enters the game, even mathematics has problems.

By ignoring these two issues, Cheng gets to a position where, for example, she is prepared to argue that justice should not be blind, but rather the scales of justice should be weighted in favour of those she decides are disadvantaged (as opposed to privileged). Unfortunately, history shows that when society decides to weight justice to favour a particular viewpoint - however apparently worthy - that society is on the road to totalitarianism. 

Of course, there is no suggestion that this is Cheng's intention. But this brings me back to back to why I think this book is important. Unlike the algorithms books, which generally concentrate on trying to use logic to deal with everyday practical tasks, Cheng applies logic to societal structures and relationships. In doing so, she demonstrates why taking a mathematical logic approach to life is not only impractical, but quite possibly dangerous.

Hardback:  

Kindle:  
Using these links earns us commission at no cost to you


Review by Brian Clegg

Comments

Popular posts from this blog

How to Drive a Nuclear Reactor - Colin Tucker ****

How To Drive A Nuclear Reactor does exactly what it says on the tin. The book is a general overview of nuclear reactors. From the basic principles that make them work through to what buttons to press in what order (and of course how and why they can go wrong).Nuclear power could be a good step on the path to a greener energy future, but there is a lot of understandable fear. This book can give some idea of what an incredible feat of both science and engineering one of these machines is and, hopefully, make anyone reading it feel far more comfortable about them.The book presents information about everything, almost down to the literal nuts and bolts, giving you a near complete understanding of how a nuclear works. From putting in the fuel to getting out the power and down from the control panel to the construction material. Everything you could ever want to know is here. By the end you'll likely feel ready to walk into a control room and get started (do not try doing this, nuclear …

Meteorite - Tim Gregory ****

There have been many books on astronomy, ranging from exploring individual aspects of the solar system, such as the Sun or Mars, through to studies of the most distant depths of the universe, but there has been relatively little on the only astronomical objects that we're able to touch (other than the Earth itself) - meteorites.

In Meteorite, Tim Gregory fills in many details of the nature of these rocks from outer space, from how they formed in the first place to the range of types and origins that are possible. Most come from the debris of the forming solar system left in the asteroid belt, but some were smashed off the Moon or Mars by an incoming impactor.

Although the main focus is the meteorites themselves (if there's any doubt, we are talking about the solid remains that fall to Earth when a meteor - a shooting star - in part survives the journey through the atmosphere), Gregory also fills us in on the contribution that meteorites have made to the Earth, whether it be brin…

Being Mortal - Atul Gawande ****

I heard recently that the local geriatric ward puts a photograph of the patient in his or her prime by each bed. The aim is to help staff to treat their patients as individuals, but it makes me uneasy. Do these people only matter because of what they were, not what they are? Because once they stood proud and handsome in their uniform, or looked lovely on their wedding day?

Professor Atul Gawande has the problem surgically excised and laid out for inspection in one of his unflinching but compassionate case studies:

‘What bothered Shelley was how little curiosity the staff members seemed to have about what Lou cared about in his life and what he had been forced to forfeit... They might have called the service they provided assisted living, but no-one seemed to think it was their job to actually assist him with living – to figure out how to sustain the connection and joys that most mattered to him.’

Gawande is an eminent surgeon. As a young resident he displayed little overt emotion when hi…