# The Art of Logic in an Illogical World Epub Þ Art of

How both logical and emotional reasoning can help us live better in our post truth worldIn a world where fake news stories change election outcomes, has rationality become futile InThe 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 cookies than she should If a mathematician can t be logical, what are we to do Inthis 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, thisessential book is for anyone who wants to think clearly [PDF / Epub] ☉ Book Lover Author Jennifer Kaufman – Ralphslaurensoutlet.co.uk has rationality become futile InThe Art of Logic in an Illogical World ★ Secret Delivery / Her 24-Hour Protector PDF / Epub ✪ Author Delores Fossen – Ralphslaurensoutlet.co.uk Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life Cheng is a mathematician ➥ [Epub] ➟ Kholodovs Last Mistress By Kate Hewitt ➯ – Ralphslaurensoutlet.co.uk so she knows how to make an airtight argument But even for her ❮Télécharger❯ ➺ Wicked Sinner (Regency Sinners 7) ✤ Auteur Carole Mortimer – Ralphslaurensoutlet.co.uk logic sometimes falls prey to emotion [KINDLE] ❃ If the Stiletto Fits... ❧ Wendy Etherington – Ralphslaurensoutlet.co.uk which is why she still fears flying and eats cookies than she should If a mathematician can t be logical [Download] ➺ What Phoebe Wants (Harlequin Flipside, By Cindi Myers – Ralphslaurensoutlet.co.uk what are we to do Inthis book ❮Download❯ ➻ Ruthlessly Royal (Self-Made Millionaires Author Robyn Donald – Ralphslaurensoutlet.co.uk Cheng reveals the inner workings and limitations of logic [Epub] ❧ An Amish Family Christmas By Marta Perry – Ralphslaurensoutlet.co.uk and explains why alogic for example [PDF / Epub] ☃ Interrupted Lullaby ✑ Dana R. Lynn – Ralphslaurensoutlet.co.uk 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 ☃ [PDF / Epub] ☂ Gift-Wrapped Governess By Sophia James ✑ – Ralphslaurensoutlet.co.uk mansplaining ❰Epub❯ ➛ Vows of Revenge Author Dani Collins – Ralphslaurensoutlet.co.uk and manipulative memes Insightful [Download] ➹ Not a Fairy Tale By Romy Sommer – Ralphslaurensoutlet.co.uk useful [EPUB] ✹ The Midwife and the Single Dad Author Gill Sanderson – Ralphslaurensoutlet.co.uk and funny [Epub] ❧ Small-Town Billionaire Author Renee Andrews – Ralphslaurensoutlet.co.uk thisessential book is for anyone who wants to think clearly 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 he 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 discussioneffectively andagreeably, especially around social media I was initially dubious about some of thetechnical 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 thedemanding 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 claimsfully, 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 getabstract, 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 themeasily, 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 somethingfundamental 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 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 t 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 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 littlethan 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 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 littlethan 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 powerresponsibly A book like this should teach people how to think, not tell them what to think I think this is a very valuable book and I will recommend it to any and everyone Now, some of the points made may seem intuitive enough depending on how logically prone you are , but Eugenia Cheng presents her ideas and points in such a way that even highly technical concepts become accessible to everyoneI enjoyed reading and learning from this book