The Art of Logic in an Illogical World

by Eugenia Cheng

How both logical and emotional reasoning can help us live better in our post-truth world

In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic--for example, emotion--is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.

Genres: Nonfiction, Philosophy, Science, Psychology, Mathematics, Logic, Self Help

320 pages, Hardcover

First published July 5, 2018

About the author

Eugenia Cheng is a mathematician, pianist, and lecturer. She is passionate about ridding the world of math-phobia. Eugenia’s first book, How to Bake Pi, has been an international success. Molly’s Mathematical Adventure is her first children's book.

Reviews

[Brian Clegg · Rating 3 out of 5]

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 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.

[Jonathan Donihue · Rating 1 out of 5]

Wow! I have rarely seen such a flagrant display of unnecessary narcissism in a supposed STEM book. If you're expecting a book about the uses and benefits of logic in everyday life, you'll be terribly disappointed.

Let me cut to the chase.

This book is little more than a platform for Ms Cheng to proselytize her readers with her social and political views. Only about half of the book is spent explaining the rules and uses of logic, and that half isn't very illuminating. The other half of the book is spent breaking many of those same rules as she tries to convince her readers - and, I suspect, herself - of the validity of her ardently held beliefs.

Although her skill in written communication demonstrates her high level of education, her inability to step outside of herself and consider the needs of her readers makes her book virtually useless as an instructional guide.
________________

If I could give a bit of advice to Ms Cheng, it would be this: Write with the needs of your readers in mind. If your writing starts becoming about you, stop writing. Narcissists give nothing of value to the world.

As an example, I didn't comment at all about whether or not I agree with your sociopolitical views. That would not have served my readers (few though they may be). It would only have gratified my ego. Instead, I commented on what your book purports to deliver and whether or not it delivers on its promises.

It's rare that I give a one star review. Had you been an average person, I probably would have cut you some slack but, as you so proudly proclaim in your book, you are a Cambridge graduate . Such credentials carry quite a bit of power and, you see, I'm very concerned with how people use their power.

Next time, Ms Cheng, use your power more responsibly! A book like this should teach people how to think, not tell them what to think!

[Stuart · Rating 2 out of 5]

Although I began the book excited, I was soon and repeatedly disappointed. The error is this: Cheng became too conversational and focused too much on her beliefs, while the logic took a back seat, and for it, the book suffers. To expand, the logic is not rigorously expounded or treated at any depth; analogies are employed endlessly, even when they are contextually inappropriate; and for each brief description of a piece of logic, we are treated to lengthy parables attempting to illustrate points (often political in nature) which are not expository of the logical concept up for explanation.

If the book was not meant to teach logic, perhaps it could be redeemed for it's secondary purpose, applying logic to everyday life. But there are two problems with this. First, Cheng's applications of logic to the everyday are poor, often missing details or misinterpreting real world examples. I give her credit for repeatedly acknowledging what a messy affair it is to apply logic to everyday life, but this is not redeeming.

The second problem is the most fatal, Cheng alienates any reader who does not agree with her politics, which are progressive/liberal. The vast majority of the examples throughout the book are political in nature, or devolve into politics. Even when Cheng is not walking through a necessarily political topic, this does not stop her from driving barbs at the political other, to no great effect. I myself agree with every political stance put forward by Cheng, yet I barely made it past her divisive language. Without having read this, I could not have imagined that it would have been written from any place other than perched on the limb of an olive tree, with a branch extended out towards the reader, but this is not how it was written.

I want to draw attention to one passage that struck me. Cheng made a point along the lines that she often makes decisions and judgements based on her emotions or flash assessments, and that she is glad that logic can back them up. I will credit her that I don't know what specific judgements she had in mind, and it may have made perfect sense to her as she wrote it, but certainly, any belief can be rationalized by logic when our framework is broad, and to do the logical arithmetic ex post facto admits our biases into the process. And the personal axioms which Cheng permits are problematic. By following her own process, we should boil down our thoughts and beliefs until we have some basic beliefs from which everything else follows logically, and this system must lead to no contradictions. In general, I don't think Cheng boiled down her axioms far enough, otherwise I would have expected the conversation to turn towards deontology, teleology, or the like. You can imagine someone reducing their beliefs into a strain of utilitarianism.

The personal axiom that Cheng highlights, which is her own, is that she cares "more about false negatives than false positives". This is problematic, because the false positive/negative dichotomy is relative to what is being measured -- what defines a positive result. Meaning, it could be framed in reverse, which leads to a contradiction. Certainly it would have been more interesting to explore personal axioms philosophically.

I will not pass judgement on Eugenia Cheng's talent as a mathematician, and I will not claim that she is necessarily a poor writer, but there were mistakes in the approach and execution of The Art of Logic in an Illogical World that leave it feeling like fodder which I cannot recommend. It is too simple for the sophisticated reader, and not explanatory enough for the ordinary reader. A certain reader may find this enjoyable, but there are better books on logic, philosophy, and politics which cover the entire gamut of audiences, whereas this fits none. I applaud her for writing so vulnerably, but in my opinion it is simply not worth reading. I would recommend reading Bertrand Russell instead.

[Harry · Rating 1 out of 5]

I eventually gave up on this book and it went in the bin. Why? Well, here's an extract from the introduction to logic under the heading LOGIC AND DISCOVERY:

With [the statement] "If you have white privilege then you have privilege" the conclusion is rather obvious, but the power of logic builds up when you string together a series of logical conclusions one after the other, gradually getting somewhere further from when [sic] you started. For example, we could string these implications together:

1. If you are white then you have white privilege.

2. If you have white privilege then you have privilege.

Now we have the implication "If you are white then you have privilege".

Sometimes the revelation happens suddenly, like unearthing spadefuls of dirt until suddenly hitting treasure. Sometimes it happens gradually, like in the wonderful example of a guy who swapped a paperclip for a house.

It seems the author wants you to take the following from this passage (based also on the broader context of the introduction): logic (which the author assures us elsewhere leads to unquestionable truth when correctly applied - a statement with which I agree wholeheartedly) allows us to see a buried truth, namely that, if you're white, then you are privileged.

However, one thing I learned about logic in school is that no conclusions can be drawn from a false premise. Hence, if statement 1 is false, nothing can be deduced about the truth or otherwise of statement 2. Furthermore, statement 1 could be true and statement 2 could still be false. The reason for this is that for statement 2 to be true then it would have to be self-evident that 'white privilege' and 'privilege' are the same thing (for instance, if 'white privilege' is a type of privilege).

Statement 1 is acknowledged by the author to be false (actually, she doesn't say so, she merely says that white privilege is not enjoyed by all white people, just by those in Europe and the US). Even if you agree with this, the statement is still not universally true.

However, is the term 'white privilege' synonymous with 'privilege'? The term 'privilege' concerns an actual advantage enjoyed by one person over another. The term 'white privilege' concerns a hypothetical advantage that you have on the basis of your race even if you have no advantage whatsoever. Hence an uneducated, penniless, homeless, disabled white American man with failing health has white privilege despite enjoying no advantages at all (if not, then I would welcome Eugenia Cheng approaching such a man and telling him at length what privileges he enjoys). Therefore despite the terms 'privilege' and 'white privilege' including the word 'privilege', they describe very different ideas and should not be confused as synonyms.

I therefore contend that both statements 1 and 2 are false or highly questionable.

The example I quoted above doesn't show how logic leads from 'a spadeful of dirt to treasure'. It shows the misuse of logic. Soon after this passage I decided that there is little point in reading a book about logic from someone who clearly misuses it (and ought to know better).

[Pete Harris · Rating 3 out of 5]

It is probably a tribute to this book that I feel the need to apply its methods, or at least reflect its language in attempting to review it. I have a degree in hard sums (pure hard sums in fact), and my world outlook is, and has always been a liberal one. (with a definite small l). This is a book about logic and is relentlessly liberal. One would therefore seem to think it logical that I would be a real enthusiast for it. Except I'm not, begging the question, why not.

My description of it as relentlessly liberal, bringing some emotion into play, is an indication of my first difficulty. All the way through author Eugenia Cheng uses examples to illustrate logical concepts and techniques, and these are without fail examples addressing issues of liberal interest - race, gender, sexuality - from a liberal standpoint. So again the question, why do I, favouring the technique and and the point of view, struggle with that. I think I need to go back to my own axioms, which would include a belief in a sense of balance. I would expect Cheng to counter that (from a number of arguments deployed in the book) by saying that such balance is only really justifiable where there is a power balance as well. Fair enough, so let's examine another angle.

I came to this book expecting to be a book about logic which fell into the set of popular science books, making logic accessible to a wider audience, helping a wider audience to develop a logical approach to life. If that were to be its purpose, I would expect it to fail, simply because it would immediately exclude itself from a significant proportion of that wider audience. My belief is that anyone who doesn't hold similar views to Cheng's would tire of it very quickly.

Again, I will challenge my axiom about the book's purpose. I think it is actually pretty clear that its purpose is not the one I have stated. My conclusion is that its purpose is either to help those who agree with the author to use logic to reinforce their own views, or to enable them to enter into persuasive debate with those who disagree with them. The first would seem a little pointless, preaching to the converted. If I then take the second, I get to what I conclude to be my main disappointment with the Art of Logic. Probably 95% of the book is spent describing the tools using liberally skewed examples, only the last chapter or so is concerned with their use. My conclusion would be that if my assumption about the purpose of the book is correct and if I add an assumption that the average reader needs more guidance in their deployment, then I conclude that the book will not succeed in achieving its goal. Of course, to challenge my own assumptions again, I may have totally missed the point. It may well be that Cheng's objective is to get people to use the tools for themselves, and to give too much guidance would be to defeat the object. We could then have a reasonable debate about what constitutes effective education. To bring debate onto a rational plane is one of the author's stated intentions so perhaps, at the end she has succeeded.

Schadenfreude is a dangerously seductive concept, particularly when reading a book about logic. It is satisfying to try to find flaws in a logicians logic. One area where I think Cheng's logic isn't as rigorous as it could be is also an illustration, in the interest of my axiom of balance, of where her techniques are useful in challenging one's own assumptions. To step on once more, it also points to an area into which I believe she could usefully have extended her book. She talks extensively of false positives and false negatives. Roughly speaking some who cares about false negatives believe that it is better that someone undeserving benefits than someone deserving misses out (Guardian reader). Some who cares more about false positives would prefer to see someone deserving suffer, than see someone undeserving benefit (Daily Mail reader). Cheng makes the statement that her focus on false negatives implies that she would rather see untrue allegations of sexual harassment believed than true ones disbelieved. This shocked me, as having the same starting axiom would lead me to conclude that it is wrong for an innocent man to be wrongly convicted. I would suggest that the author doesn't quite follow her own methodology in that she misses a level from her chain of logic. That level would be a care for false negatives in a world where there is a gender power imbalance. Now having identified that extra step, I am enabled to challenge my own assumption in a rational way. That I am still uncomfortable with the original conclusion steers me towards understanding I am a man, Cheng's conclusion would lead to more men being wrongly convicted, I am afraid I would be wrongly convicted. That points to where I would have liked to have seen more,or perhaps to the next volume - using logic to address fears.

As an aside, I would suggest that the cover and blurb are slightly misleading. They do nothing to suggest the strong, if to my eyes laudable, liberal agenda.

In summary, I strongly believe in both of this book's central themes. I am disappointed by it as it will only find an audience with the already converted and spends too much time preaching to them, and not enough on using the tools she provides.

[Graeme Roberts · Rating 5 out of 5]

Eugenia Cheng is a great teacher. I never expected to rip through a book on logic and its applications in the real world, but she writes beautifully and very personally. I like stories about people, so applying logic to her excessive love of ice cream (impossible) and her battles with weight gain seems interesting and reasonable.

She chooses to use examples of sexism and racism, particularly in the United States, as fodder for her logical arguments. Despite her kind heart and goodwill, she demonstrates the normal academic contempt for anyone who does not fight for "social justice" or questions political correctness. At first, it made me a little angry, but she is so likable that I couldn't sustain it. Eugenia Cheng is extremely talented and a worthy leader. I hope that many follow her commitment to education and human betterment.

[Ginny · Rating 1 out of 5]

This is one bad book. It reads like a thesis paper written by a grad student. The beginning 20+ pages of the book explained what the book was going to explain. Each chapter ended with literally repeating what the chapter had just explained. Then the next chapter literally spells out what we had just read.

Its supposed hook is that the author analyzes current events so that we can better cope with the current horrible state of political life. At least, that is what the NYT book review promised. The reviewer didn’t read the same book I did. There are periodic quips referring to current politics. But, this book does not focus on current politics, let alone provide useable guidance to intellectually work our way through it.

Bad writing like this infuriates me. My only revenge is that I didn’t waste money on this stupidity. I rented it from the library.

[Algirdas · Rating 2 out of 5]

Tokia kažkokia. Lyg ir kažkas, lyg ir nieko. Patiko apie logikos ribas, apie logikos ir emocijų santykį. Perskaičius liko jausmas, kad knyga buvo ne tiek apie logiką, kiek apie autorės asmeninius įsitikinimus, užpiltus logikos padažu? Perspaudė rašydama apie lytinį priekabiavimą, skaitydamas vis labiau ėmiau jaustis tuo vyru-blogiuku.

[Moh. Nasiri · Rating 3 out of 5]

How to find truth and clarity within chaos.

As a species, we’re an irrational bunch. We make snap decisions based on instinct, stubbornly argue a position we haven’t deeply investigated, and let our emotions control us in ways we can’t fully explain. And this is just what’s happening inside each of us.

On the outside, we’re constantly bombarded with other people’s agendas. They use rhetoric, fear, and bullying to try to win us over. Fake news, clickbait, flimsy reporting: How can we possibly cut through all of this to arrive at truth? And if we can’t identify what’s true, how are we ever going to fully understand the world we live in, or decide how to act?

There is a way – a surprising tool we can all learn to use, once we know how it works. This tool helps us step back and explore the complex issues that hound our lives. It provides us with a methodology that can unearth a range of possibilities in any scenario, so that we can find a pathway that resonates with us. What is this powerful tool that can create clarity in the face of chaos?

The answer is logic. 

In this book , you’ll discover

why logic won’t determine what you eat for dinner;
what expiration dates reveal about logic and reality; and
the connection between handwriting and social injustice.

ref: blibkist.com

[Junior Marquez · Rating 1 out of 5]

The writer just wants to stand out her political view by trying to explain the logic behind her view. You will only get 10% of what you expect and the other 90% is the writer being insanely political correct.

The title of the book is misleading and that should be illegal 🤣

[Andrea McDowell · Rating 4 out of 5]

This was probably closer to a 3.5 for me, but I rounded up.

Her explanations of logic were fantastic and I enjoyed her use of logic and logical arguments to defend progressive positions and ideas very much. And I should add, before I go further, that I listened to the audiobook from the library, and I think this is one case where reading it in print is a much better idea; there were many many parts of the book where the narrator said something like "to see the illustration, please see the pdf accompanying this audiobook"--which of course I didn't get with the library version--or, "the graph is a rectangle representing people. One circle in the rectangle, shaded grey, represents black people; one circle in the rectangle, shaded grey, represents women; where they overlap represents black women. Outside of the circles and within the rectangles are non-black non-women," which is clear enough, but the effort of visualizing it took away from the pleasure of following the argument, if you see what I mean.

The downside for me was those times when Cheng didn't follow her own argument back to its own fundamental principles. There were several examples, so I'll focus on what I found the most egregious: her description of the conflict between BLM and the police. Now: overall her argument was fantastic and in full support of BLM; I don't want to exaggerate. But where she is describing police violence towards black people as a matter of what came first, the violence or the distrust of the police, my jaw actually dropped open: obviously what came first was SLAVERY and centuries of institutional racism and a state that built police forces in its early days to track down fugitive slaves. This can't be ignored in favour of some well-intentioned both-sides wishy-washy false equivalencies.

Or, hell, one more: where she complains that people criticize her for fat-shaming and misogyny when she says she watches what she eats so she won't get fat, saying that her desire not to get fat herself is not a judgement on other fat people or whether or not others should watch what they eat. This is at best a half-argument. A personal desire to avoid fatness doesn't come out of nowhere; it is shaped by society, in this case a society that is deeply fat-phobic. Of course anyone can choose what they will or won't put in their mouths, with very very few exceptions, for any reason whatsoever, and that's a fundamental human right (i.e. don't eat people, and don't kill the neighbour's cat for dinner, but other than that, I don't care). The personal desire to avoid fatness is unavoidably rooted in a society that treats fat people terribly, deprives them of advancement and respect and dignity and income. The statement hardly makes sense outside of that context. And, like every personal lifestyle preference that reflects and reinforces societal prejudices, that needs to be acknowledged.

I don't want to make too much of these; I found them frustrating and they clearly stuck, but overall, the book was a great description of logic, its values, how to structure an argument, and a lovely refutation of the common idea that "logic" is a property of the right and the soft-hearted lefties are operating on something called "emotion" alone. If you've ever been frustrated by someone attacking an argument in favour of feminism, lgbt rights, climate change, etc., by charging that you're just not being "logical" or "reasonable," you'll enjoy this book.

[Eleanor · Rating 3 out of 5]

A good book for an easy Maths related read, and enlightens you on certain political/controversial topics. The only thing is that’s it’s slightly repetitive so it sometimes feels like it’s dragging on. I would still recommend this book.

[Johnathan Nazarian · Rating 1 out of 5]

This was, by far, more about pushing Cheng's progressive political viewpoints and agenda and a lot less about logic. While Cheng provides a cursory overview of primary logic features, she describes copious examples of the most controversial liberal positions and attempts to force them into those logical precepts. Instead of using the sound logic she purports to use, she brings in many assumptions and presuppositions as her starting point, effectively negating subsequent logical steps.

I came to this book with hopes of learning logical steps. Instead, I was disappointed by diatribe and arrogance.

Admittedly I am a fairly middle of the road conservative. However, it is telling when even Cheng's self-proclaimed liberal readers can recognize this book for what it is. Much respect to them for being true to logic.

If you are looking for scientific and sociological explanations and explorations of logic, move on. If you are looking to reinforce your liberal group think, move on as well. Because you won't find any arguments to logically support your stances. Cheng becomes the media that her blurb criticizes. If that's what you're looking for you'll probably love another source of political agenda masqueraded in false humility.

[John Fredrickson · Rating 3 out of 5]

This book is an extraordinarily lucid description of the thought processes that we engage in during our engagement with current issues. The author discusses logic in many forms, starting from an informal basis, then including more formal systems (propositional and prepositional), which are touched on at a very high level. Having done this, she then explores areas where logic fails us, and also how the intelligent use of analogies and emotions fits in. She also discusses how we endeavor to use logic to protect fear-induced positions, or in the service of manipulation or deceit.

As indicated above, the book is extremely well written, and presents its material very clearly. Having said this, this is not a book I will keep, but this is because it is a "basic" book that does not go deep enough in its subject to make it more valuable to me. Some of the material was great, including her presentation of paradoxes, and also the section on Category Theory, which was a refreshing way to look at how to visually depict the dynamics of relationships. Much of the book, however, felt like a refresher course for material we should all already know.

[Fotis Koutoulakis · Rating 1 out of 5]

The **worst** book that I have ever read.

It's supposedly a book on Logic, and while it does contain a good chunk of information on introductory propositional logic (and a little bit of first order, for good measure), it just gets drowned into the constant moral lecturing by the author. (Getting told that you have asymmetric privileges by an author who is a Cambridge-educated mathematician grows old quite fast).

While the writing is reasonable (not bad - but nothing to write home about either), the author constantly comes across as having multiple chips on her shoulder (as an example, she mentions interpreting someone asking a question about Russel's paradox and its meaning for mathematics as a personal attack. I don't know about you, but if someone told me "Gee, I heard that Turing machines are dogshit, lololol" or something, I would just think that the poor bugger doesn't know about computers and not take it as a personal attack on my knowledge or capacity as a computer scientist).

It's a pity, because this book could have been so much more. It's also a pity for me personally, because I was really looking forward to the author's new book on Category Theory. Not anymore.

[Hao · Rating 1 out of 5]

I rarely give books an one star rating, if you are reading this, I think you’ll save money and time by looking else where.

I picked up this book wanting to dive deeper into the world of mathematic logic. I am disappointed to say that it was not helpful on the slightest, it covered some of the logic knowledge I learned at University but added in a lot of unnecessary examples and did a poor job at that. I think my lecture’s slides would teach someone logic better than this book.

Other reviewers say she is trying to push her own agenda and believes into this book, I actually thought she wanted to use those controversial believes/topics to “shock” and get the reader “hooked”, and then failed miserably.

I think the idea for the book is excellent, I picked up this book thinking it would merge maths logic into everyday argument. Unfortunately, the delivery is terrible and I had to put the book down after reading several chapters. I don’t mind a boring book but with this book I don’t feel like the author herself knows what she is going on about.

[Lee Slater · Rating 2 out of 5]

Unfortunately what might have been a good book (and is certainly a good premise) is undone by the author’s strong axiomatic take on modern societal issues which is peppered throughout the book. These examples are quite distracting and highly charged, but, where you might expect a book about logic to be wielded equally against all views, the author comes down hard on her side. Frustrating because I hoped this book would be a precursor to “better debate” but it’s more likely to inflame those who don’t share her view, or preaching to the converted for those that share her views. It felt in the end that all the logic she presented was pointless as it is applied post hoc to the axiomatic lens in which you view the world.

[Scott · Rating 2 out of 5]

I have read many books on logic and this is one of them.

[Robert Case · Rating 4 out of 5]

The art of rhetoric flourishes in the virtual world of social media. It's powerful reach was conclusively demonstrated in the results of the USA's 2016 election. This latest book by Eugenia Cheng offers a logical construct for considering and even countering the most tiresome of rhetorical tirades.

Her book is a discussion about the efficacy of applying the principles of logic to the memes that seem to dominate the current political and cultural landscape of the USA and the UK. Her wit and sense of humor give the book an even flow, even as she courageously considers a wealth of thorny issues including Brexit, weight gain and obesity, Black Lives Matter, gender based inequality, and white privilege.

It reads like the work of a college professor that has compiled her lecture notes into a book. There's a lot of repetition, and, it's generally worth the effort. I recommend it to anyone with an interest in the politics of current events, modern history, or philosophy.

[Marenka · Rating 4 out of 5]

I was very sceptical when I started this book in fear that it will be some sort of pythagorean style glorification of maths, however it wasn't anything like that!
Author describes everything that can be solved using mathematical logic and points out flaws of this approach and this all is done in a friendly, conscise and clear manner. She walks through different methods of looking at things when applying both logic and emotions and explains how both are crucial when leading a discussion.
Loved the examples that author was using in the book as well.

[Rafsan · Rating 3 out of 5]

(Review is on the way)

[Stone · Rating 3 out of 5]

Emotion (instinctive feeling or opinion)
Axioms(groundwork/starting point)
Abstraction (level of analogies, logic & meta-logic)
Converse (A->B & B->A, B(False)->A(False) & A(False)->B(False))
Negation ("not" - Grey Area )
Opposite ( Dichotomy )
Privilege (animosity)
Contrapositive (A->B & B(False)->A(False))
Equivalent (A->B & B<-A, B->A & A<-B, A->B & B(False)->A(False))
Pivot (?)
Paradoxes
Faulty Argument (?)
Problems with logics
False Negative
False Positive
Vacuous truth
Causation

Study notes:

If you give a child a cookie and another cookie, how many cookies will they have? Possibly none, as they will have eaten them.

Logic is a process of constructing arguments by careful deduction. We can try to do this in normal life with varying results, because things in normal life are logical to different extents. I would argue that nothing in normal life is truly entirely logical

in one sense (the process) they are different but in another sense (the answer) they are the same.
All equations that we study in mathematics are like this. They show us two things that can be regarded as the same in some way even though they are different in other ways. This is how equations help us. If there was really nothing different about the two sides, the equation would be true but unilluminating.

Logical explanations come from the deep and unchanging meanings of things, rather than from sequences of events or personal decisions and tastes. (inherentness)

crucially it is possible to reach a different conclusion from me by applying logic perfectly soundly but starting from different basic beliefs. So two people can both be logical but still disagree about things.

All this doesn’t necessarily mean that I am being illogical, it just means that we have different axioms

I will judge you to be unreasonable if I think your fundamental beliefs are not reasonable. But this might not mean you’re contradicting logic, it just means we have some fundamental disagreements. If two mathematical systems have different axioms they do not disagree – they are just different systems, and the best we can do is discuss which system is a better model of the situation in question

This happens when you tell students that they have to work hard in order to do well, and then they think that if they work hard they should automatically do well. Working hard is a necessary but not sufficient condition for doing well. It is not sufficient because you also have to work hard in the right sort of way, and if you think otherwise you are making a converse error.

the converse of a statement is logically independent of the old statement, which means that there is no logical connection between the two. That is to say just because one of them is true, it does not necessarily mean the other one is true, nor does it necessarily mean the other one is false.

the negation is a broader statement than the opposite. The opposite is the exact opposite extreme, or, as we might say for emphasis, the “polar opposite”.

In reality, most people do some good things and some bad things. In fact, most things are themselves partly good and partly bad.

if you don’t condemn every single thing a person did then it can sound to some (less logical) people that you are supporting them. This is the trouble with black and white thinking.

If we’re thinking about the concept of “good”, then the grey (mediocre) is included in “not good”, so it gets lumped in with “bad”. If we’re thinking about whether or not the EU is terrible, then the grey (so-so) is included with “not terrible”, so it gets lumped in with “fantastic”.

just one drop of “black blood” was considered to be black

Allowing for some uncertainty can seem unsettling, but it can avoid both the extremes and the anomalies of drawing a line.

Grey areas are an important part of the human experience, but are not very well dealt with by logic. Logic is about getting rid of ambiguity. The law of the excluded middle forces us to put the whole grey area in with black or in with white. That is better than the sort of black and white thinking that pretends the whole grey area doesn’t exist, but it can have the same effect as it can push people to think only the black or the white if they try to pursue logic to its rigid conclusion.

So, if I want to be rational, what can I do about grey areas? I might have to let go of the most obvious logical approach and learn to deal with something more complex.

The person who believes in social services probably doesn’t believe in simply giving out large amounts of money to everyone who asks for it, without question. The person who believes that everyone should take responsiblity for themselves might be able to acknowledge that some particularly “worthy” people need help, perhaps members of the military who have been injured during active service.

If this is so, then we have established that the question is not whether or not we should help people, but to what extent we should, and under what circumstances. It is now a question of where we place people in the grey area and how we treat the grey area.

The purpose of pushing something to extremes is to show that many (or even most or all) general principles have limits to their scope, and the difficult part is not in establishing the principle but in establishing the scope. It is a key to understanding disagreements, as the source of the disagreement is often exactly where to draw the line, rather than the principle itself. It’s a way we can use grey areas, to show that the difference between opposing positions might not be black and white, but in shades of grey.


All analogies break down somewhere. That is the whole point of an analogy: it is not the same as the original thing; it is similar in some way but therefore it is also different in some way. Pointing out that an analogy breaks down does not mean the analogy is bad. But if the analogy breaks down in some way that is relevant to what we’re discussing, that could be more important.


Erroneously equating one statement with another one is a devious tactic, and is not logical. It is often invoked to twist someone’s words and turn their reasonable position into a much worse one, and then attack them for it. It often drives arguments into further and further extremes. It involves an incorrect piece of logic, claiming two things are logically equivalent when they are not, so is a form of logical fallacy.
Sometimes it’s a flawed analogy as described in the previous chapter, where someone goes to too high an abstract level and claims your statement is analogous to something absurd. In all cases this creates divisions instead of finding common ground.

everything is the same if we go up to a high enough level of abstraction

A simpler case is if you say to someone “I wouldn’t call you skinny” and they burst into tears wailing “You think I’m fat!” They are jumping to this false dichotomy: A: I am skinny. B: I am fat. possibly out of fears that come from society’s pressure on women to be thin. It’s a false dichotomy because it’s possible for neither A nor B to be true.

Here is how that faulty argument tries to proceed, in more detail: 1. Some black people are better off than me even though I am white. 2. If some black people are better off than you then you don’t have white privilege. 3. Therefore I do not have white privilege.

White privilege doesn’t mean that every white person is better off than every non-white person; it means that if any given non-white person were in exactly the same circumstances but white, they would be better placed in society and life.

the logic of causing an outcome is not the same as the logic of preventing an outcome. If two things are needed to cause an outcome, only one needs to change to prevent the outcome.

So, instead of arguing about trying to attribute blame individually, it is more productive to understand how the system makes all those factors interact with each other to cause that outcome.

In normal life, outside some specialised situations, there isn’t a clearly defined panel acting as peer review on our logical arguments. In a court of law it’s the jury, and their decisions might be based less in the logic of the arguments and more in their emotional response to witness testimony. Either way, jury is not generally required to justify its decision. For politicians, the “peer review” is the election – it doesn’t matter if they’re right or not, and it doesn’t matter if their arguments are sound or not, it just matters if people vote for them or not. Voters do not have to justify their vote either. You might hope that the votes will depend on the soundness of the politicians’ arguments, but probably not if you’ve ever experienced an election. For corporations, the “peer review” is the money: they just need to persuade people to buy their product, and it doesn’t necessarily matter if their methods are sound or logical (although if they’re outright fraudulent they might get into legal trouble).

We need to find ways to attribute one type of privilege to someone without invalidating their feeling of disadvantage with respect to another type, as that invalidation causes anger, animosity, divisiveness and resistance to change.

the first version is more about what you need to do in order to travel whereas the second is more about what you can’t do without a passport. These are two slightly different points in human terms although they’re logically equivalent.

the contrapositive is not to be confused with the negation: which does not fit into the above picture anywhere.

difference between knowing something intellectually and knowing something emotionally

If we hold it close, the light will be bright but will illuminate only a small spot. If we move it further up, we illuminate a wider area but the light will be less bright. Eventually if we hold it too far out the light will become so diffuse that we won’t see anything at all. But if we put it right on top of the things we’re studying, we also won’t see much. Logic and abstraction are like shining a light at things.

Many scientists are disparaging about religion because it consists of people believing things without scientific evidence, because of something written in a book or told to them by a religious leader. However, science is asking people to believe in it in a somewhat similar way: there may well be evidence to back up scientific findings, but non-scientists are not expected to read all the research data and check all the research for themselves. Scientists seem to be asking non-scientists to believe them, or believe what is written in books and journals, in an analogous way to religious leaders asking people to believe what they preach, or what is written in the Bible or another holy book. There may well be something crucially different about those situations, but if so we should admit that at this level of abstraction the two appear somewhat similar, and thus, the argument that you “shouldn’t just believe what someone says” is not a very convincing argument in favour of science.

This is supposed to encourage us that it’s better to do things we perhaps shouldn’t have done (false positive) than not do something we should have done (false negative).

There is a difference between loyalty and blind support, and a difference between healthy scepticism and science denial. I think it’s an example of fuzzy logic. Loyalty means not changing your support over minor issues. Blind support means not changing your support over major issues, or any issues at all. Of course, a question remains over what counts as “major” and “minor” issues.

One aspect of growing up is developing the ability to comprehend longer chains of causation and logic. One concrete way this manifests itself is in the ability to make long-term plans, or make short-term sacrifices for long-term gains, rather than just living for instant gratification in the moment. At least, this is one of my personal axioms; at the other extreme there are some people who strongly believe in only living in the moment, or living entirely emotionally. When adults live strongly in the emotional world it doesn’t necessarily mean they are neglecting the logical world. I believe I live very strongly in both. I respect and trust my emotions, but always look for logical explanations of them so that they’re not “just” emotions. The two are not mutually exclusive.


Hmm

to push it to a greater extreme, that men sexually harassing women is worse than women sexually harassing men. Others argue that this is the same. There is no right or wrong answer to this, but there is a sense in which the two are the same and a sense in which they are different. The sense in which they are the same is that both consist of “people mistreating other people”. At this level of abstraction we have an equivalence. However, this has forgotten very many details about the situation. We could instead retain the information about power in society, and only abstract as far as “people with power mistreating people without power”. At this level, men mistreating women is equivalent to white people mistreating black people, but not equivalent to women mistreating men, or black people mistreating white people:

The internal approach to thinking about axioms is where we pick some axioms and see what system this generates, logically.
The external approach is to start with a world that you are trying to understand, say numbers or shapes or relationships or surfaces, or the world we actually do live in.

If you say “all women experience sexism” someone (usually a man) is likely to protest that men experience sexism too. This may or may not be true, but in any case it is not logically related to the first question. The first implication says that if you are a woman then you have experienced sexism; it does not claim anything if you are a man.

draw the line somewhere where you definitely feel safe, before things start being at all questionable

We can unify everyone, ignore race, and declare that we’re “all humans”, as some people do when they call themselves “colour-blind”. But this discounts people’s real experiences of racial discrimination. I think that above all we should acknowledge that there are grey areas and become more comfortable with accepting them.

The purpose of pushing something to extremes is to show that many (or even most or all) general principles have limits to their scope, and the difficult part is not in establishing the principle but in establishing the scope. It is a key to understanding disagreements, as the source of the disagreement is often exactly where to draw the line, rather than the principle itself. It’s a way we can use grey areas, to show that the difference between opposing positions might not be black and white, but in shades of grey.

All analogies break down somewhere. That is the whole point of an analogy: it is not the same as the original thing; it is similar in some way but therefore it is also different in some way.

people do often get upset when I say I don’t want to be fat, and they are rarely placated by my explanation of the logic. In the next chapter we are going to talk more about attempting to override emotional responses, but I think it’s worth noting here that uncovering the false equivalence gives us the logic behind their feeling of offence: they are equating me not wanting to be fat with me criticising people who are fat. A more compassionate thing to do with this piece of logic is to admit that human language is not the same as logic, because it can carry connotations in a way that logic doesn’t.

1. Some black people are better off than me even though I am white. 2. If some black people are better off than you then you don’t have white privilege. 3. Therefore I do not have white privilege.

White privilege doesn’t mean that every white person is better off than every non-white person; it means that if any given non-white person were in exactly the same circumstances but white, they would be better placed in society and life.

“If some black people are better off than a white person then that person does not have white privilege.” is equivalent to believing this: “If you have white privilege then you are better off than all black people.”

It just means that if those sports stars had all the same success but were also white, we’d expect them to have even higher status in society.
("White Privilege" as a slogan?)

If you feel something you are definitely feeling it. If someone tells you that you are not justified in feeling it, that doesn’t help. Nor does it help if they tell you that they feel completely differently. There is still always a reason you are feeling it, and in this sense there is always some sort of logic to emotions. Instead of denying or suppressing emotions we should understand and explain them. I will go one step further and say we should even use them: it is important to remember that emotions can, and probably should, play a role even when we’re being logical.
(but the problem is how do you prove your emotions)

we could decide that we are going to be tolerant of people’s ideas, but not necessarily of their meta-ideas.

In the case of Rocky promising all his eggs to the rats, the “for all” clause was fulfilled because “all” happened to be zero. This can often seem like a bit of a cheat although the logic strictly holds. This is called vacuous truth, or a condition being vacuously satisfied. Consider this statement: All the elephants in the room have two heads. This sounds (and is) a ridiculous statement, but it is certainly true of the room I’m in at the moment.

Mathematics makes a steady advance, while philosophy continues to flounder in unending bafflement at the problems it confronted at the outset.

[Domhnall · Rating 5 out of 5]

The quality of political and social education and debate in the US and the UK is deplorably poor. Eugenia Cheng, who is an honorary fellow in pure mathematics in Sheffield, UK, and also teaches in Chicago, suggests that a lot would be gained by applying her academic discipline of mathematical logic to real life decisions, and to this end she considers a helpful array of logical principles and techniques, explains them well and with a light touch, and illustrates them with topics that interest her, personally.

Cheng does not say this is an erudite account of mathematical logic; she does say that this is a range of ideas about logic that can be easily explained and which the ordinary reader might find helpful. So it is some logic, a selection from logic, and it is her personal selection. To illustrate the use of her techniques, she picks arbitrary but topical issues that reflect her own particular interests, from weight loss (a common preoccupation) to feminism (she is a female academic in a male dominated field) to racial discrimination (she belongs to an ethnic group that is often disadvantaged in the UK and USA). This gives a real sense of her warm, agreeable personality and coats the presentation of potentially dry academic material with a style that is accessible and supportive.

Cheng has the pleasing attitude that the purpose of logical argument is not always to prove who is right or wrong but rather to help people reach agreement. She suggests various techniques that might help close the gap between incompatible, diametrically opposed points of view, perhaps by revealing some higher level principle that both can agree upon, while retaining their divergent opinions, perhaps by demonstrating that there are intermediate positions, grey areas, that might enable them to build a bridge. Cheng also makes the point quite often that logic is not always the only or the best tool in the box; sometimes being excessively logical is a mistake.

For what it sets out to do, this is an excellent and highly readable book. I am quite sure it will assist many people to enter discussion more effectively and more agreeably, especially around social media. I was initially dubious about some of the more technical ideas presented, but by the end of the book I appreciated the value of what Cheng was offering and she has given me some new ways of tackling certain types of argument. I would like to debate some of her claims but I do not think this introduction is intended to be a definitive statement about the more demanding aspects of logic and real arguments.

Incidentally, I was deterred from buying this book by negative reviews, but received it as a gift all the same and I am glad to have read it now. I am quite confident that the negative reviews make two serious errors. One is to assert that Cheng advocates a far greater role for logic than she actually does; she shows how to use logic but also emphasises its limits and advocates keeping logic in its place. I would personally like to explore some of her claims more fully, because of the problems they bring to mind from my experience, but I think that would go too far beyond this book's actual scope and intentions: it is an introduction, not an exhaustive manual. The other type of error is to claim that she is pursuing a political agenda with her choice of illustrative topics; this is nonsense: she uses examples from her own world and it is up to others to apply the lessons to their different worlds, bearing in mind that not all opinions will survive logical scrutiny and perhaps those with reactionary minsdsets would be better off reading something less challenging. It seems to me reasonable to expect readers to understand her examples, which are very orthodox, without needing to agree with all or any of them. but unreasonable to expect her to anticipate and incorporate the diverse political opinions of her many readers.

Quotes

One of the main reasons to have a clear framework is to be able to agree about things. [p5]

The rules of scientific discovery involve experiments, evidence and replicability. The rules of mathematical discovery do not involve any of those things; they involve logical proof. Mathematical truth is established by constructing logical arguments, and that is all. [p8]

In some uses, a “theory” is just a proposed explanation for something. In science, a “theory” is an explanation that is rigorously tested according to a clear framework and deemed to be statistically highly likely to be correct... In mathematics, though, a “theory” is a set of results that have been proved to be true according to logic. There is no probability involved, no evidence required, and no doubt. [p11]

Some of the disagreements around arguments in real life is unavoidable, as it stems from genuine uncertainty about the world. But some of the disagreement is avoidable, and we can avoid it by using logic. [p12]

Logical arguments mostly come down to unpacking what things really mean, and in order to do that you have to understand what things mean very deeply .... We can try to use logic to construct arguments about the real world, but ... if we start with concepts that are ambiguous, there will be ambiguity in the result. [p17]

Logic and abstraction are like shining a light at things. As we get more abstract, it’s like raising the light off the ground. We see a broader context, but with less fierce detail. .. In all cases the aim should be illumination of some kind. First we need some light, and then we can decide where and how to shine it. [p21]

The primary use of normal language is communication, whereas the primary aim of logical language is to eliminate ambiguity. [p24]

We can build up huge arguments from logical implications and the argument will still have this feature: the concluding statement is only known to be true when the opening conditions are fulfilled. But the argument itself tells us that if the opening conditions are fulfilled then the concluding statement is true, and this argument is always correct. This sort of argument, in mathematics, is proof. I am gradually going to argue that stringing together long chains of implications gives us logical power. It is what enables us ... to start from something obvious and work our way to something complex and unobvious. Being able to construct and follow such complex arguments is hard but is a critical part of making good use of our human brains. .. Long chains of implications often require us to package many connected ideas into a single unit so that we can build on them more easily, like vacuum packing our clothes. What we gain in the process is new insights and deeper understanding. [p34]

We can work out that Y is implied by X, which is implied by W, which is implied by V, and so on, but at some point we need to stop ... We need a starting point in logic, because we can only deduce things from other things – we can’t deduce something from nothing. ... Looking for axioms, or starting points, in my own system of beliefs has led me to a much clearer understanding of my own thinking. It has enabled me to identify basic beliefs that some other people don’t hold... crucially it is possible to reach a different conclusion from me by applying logic perfectly soundly but starting from different basic beliefs. So two people can be both logical but still disagree about things. Working out what the basic starting points in an argument are is an important part of analysing it logically. [p40, 41]

The region of overlap in the middle is where both things are true. In the language of sets and Venn diagrams this is called the intersection ... [p86]

You might meet someone who very implausibly claims to be a billionaire, and you might exclaim: “If you’re a billionaire then I’m the Queen of Sheba!”... If a falsehood is true then truth and falsehood have become the same things, which means everything is true, but also everything is false. It’s not a very useful situation to be in. [p120]

I believe that a useful way to be a rational person is to look for the sense in which things are true rather than simply deciding if they are true or false. Someone might say something that is untrue in strictly logical terms, but perhaps they were really trying to say something else, perhaps something with strong emotional content that we should listen to if we are intelligent humans rather than intelligent emotionless robots. [p125]

We don't learn to speak our native language logically, we do it by immersion, by copying, by emotional connections, and by desire. [p167]

Logic cannot explain and decide everything in the world, so we are going to have to do something when it runs out. We should not pretend that those non-logical things are logical, but we should also not assume that those non-logical things are bad. [p179] [says earlier – some things are just not governed by logic.]

One way to axiomatise a system of beliefs is to take every single belief as an axiom. This certainly means all your beliefs can be derived from the axioms using logic, but it has not achieved anything. It wold be a bit like a recipe for lasagne where the only ingredient is “lasagne”. Rather, the point of axiomatisation is to understand the roots of a system and what holds it together. ... We do meet people who are unable to justify certain beliefs of theirs vey much at all – they take quite complex beliefs as fundamental, without justification. ... Our fundamental beliefs are rooted in something beyond logic. However, sometimes abstraction can help us find something more fundamental inside what we believe... [p189]

...the idea of compulsory voting in general elections, as in Australia. ... it’s not about forcing people to vote. It’s about forcing the government to make it possible for everyone to vote, to reduce voter suppression and disenfranchisement. [p217]

...human language is not the same as logic, because it can carry connotations in a way that logic doesn’t... [p243]

[Jimi'O · Rating 1 out of 5]

She panders to the masses with this book,
covering the most cliche and trendy of the
Internet's worst discussion - definitely not
laying off the toxicity with her SJW(Social Justice Warrior) tongue.

I knew I would not like this book, after reading 15 pages in,
but I like the challenge of reading books I don't agree with.
Much to my dismay This book, unlike many philosophical
books have read has offered nothing at all to brandish from
the occasion; and I am glad I have finished it!

This is sort of like watching the recent film 'Joker',
when you see him do bad-bad things
over and over : but instead here -she- is telling you
these toxic, backwater opinions - brewed freshly
from the big bad world, getting dumped and the
fallout from Cosmopolitan ideals; And man... It's Toxic!
Leave it well alone !
don't give em-air – Let alone a waste of 300 pages!(And more a waste of your time!)

About what it covers: It discusses and analyses structure of logical arguments and compares argument structure. It also discusses some paradoxes SHALLOWLY,( so you know what your not meant to do I suppose... very little mention of fallacies though) a bit of popular maths and using that argument structure to determine various attributes. Oh, I wont forget - a lot of talking about herself. Half the time, this talking acts to prove her points, sometimes these points are WAY too shallow to do the job right – most the time it just sounds too cliché. i.e. Hey I'm a girl, I love chocolate!

It also contains ALOT of discussion, fresh from the internet, about infamous political problems, 90% of which is concluded as shallowly as an intimate argument over a bottle of Lambrini where she shows her SJW tendencies obnoxiously. The girl's conclusions are quite immature and she seems glad to become the protagonist.

Finally she discusses her plans for humanity when she has perfected her newly found 'intelligence' - right off a Hebrew Sephirot tree, which includes brain washing the stupid into doing what she thinks 'is best for humanity' (through the help of her logic and some 'EMOTION'); I'm not joking unfortunately. At least she is sweet as a 'rose' in the last 30 pages... Hail Shakespeare!

[Ashley Lambert-Maberly · Rating 2 out of 5]

I don't think I'm the target market for this book (which is "ironic" because prior to reading it I was certain that I was the ideal customer for it).

It's okay, but I was expecting to learn something, and it's very, very basic--at least to me. I didn't think I was a logic expert, but you learn something new every day. It's like reading a cookbook that starts out by explaining how you can mix various ingredients together in different ways, and sometimes heat them, and it will make all this interesting food, and kind of does that for 100 pages or so, to begin with. That's how I felt reading this book. There were no new concepts for me, so halfway through the book I stopped.

There's one very good joke in the first half ... I actually laughed out loud when I read it. Sadly, no one I know (so far) has gotten it, they just stare at me like I'm a crazy person, forcing me to explain the joke (which kills it. Humor never survives explanation). So I appreciate that, at least.

Too simple, no new information, apparently written for 4th graders. Sadly, not for me (and I loved her book on Infinity and found some of it, gasp, beyond my ken, so this is a surprising turn of events.)

(Note: 5 stars = amazing, wonderful, 4 = very good book, 3 = decent read, 2 = disappointing, 1 = awful, just awful. I'm fairly good at picking for myself so end up with a lot of 4s).

[Ted Morgan · Rating 5 out of 5]

This is a gentle introduction for general readers to logic. It is not a substitute for a textbook or more advanced presentations but it does explain fundamental notions of logic that a general reader ought to know.

[Andy · Rating 4 out of 5]

I usually hem and haw over books in a bookstore, afraid I'll buy it and regret the purchase, but this book grabbed me and I knew I'd like it. Cheng brings mathematics and logic alive and relevant. It has made me think about current political arguments, internet arguments, and situations in my own life from a more objective—even compassionate—perspective. I feel like the author could go on a bit in over-explaining concepts and repeating more than necessary, but I appreciated her effort. Basic understanding of the logical foundation of arguments and the fallacies we can fall into is so necessary in this "post-truth" world.

[Jing Xu · Rating 4 out of 5]

As a reader, you need to work hard to extract the bits and pieces that are useful to you. This is not exactly a book where the author tries to meet where you are, so it depends on whether you are willing to meet where the author is. I would give the first half 3 stars and second half 4+ as the second half is significantly more useful to me.

[Rolf W. · Rating 1 out of 5]

Pedantic

[Jeff · Rating 3 out of 5]

Never thought I'd say this but, I wish there'd been more math and less psychology.