Cheng, Eugenia. _The Art of Logic: How to Make Sense in a World That Doesn’t_. London: Profile Books, 2018. # Progressive Summary # Key Points ## Why Logic? Mathematics is a theory of justification. Higher maths (not the kind taught in secondary school) is about how to think, and is applicable to the entire human world. Most arguments, including mathematical ones, are not about right and wrong, but about the *sense* in which something is right and wrong. If people disagree, it's because they have different world views. Key definition: Maths is the logical study of how logical things work. Logic helps us understand the world by simplifying it in two ways: - Abstraction - forgetting parts of it. It helps us find similarities between otherwise different things. Mathematics as a whole may be thought of as a theory of analogies. - By helping us become cleverer so we understand more parts of it. One disadvantage of the logical world is that you don't get to win arguments by shouting the loudest or using force. > The idea of logic is to have clear rules so that conclusions can be drawn unambiguously and consistently by different people. The robustness of logic means that mathematicians are able to reach agreement on what is true, and these things remain true thousands of years later. In contrast, not much from science 2000 years ago is still being taught. In science, a "theory" is a hypothesis that has to be rigorously tested and shown to be statistically likely to be correct. In mathematics, a "theory" is a set of results proven to be true. There is no probability involved. # Resonances # Oppositions # Questions / Comments # Quotes > Maths isn't just about numbers and equations: it's a theory of justification. > Logic makes our arguments rigorous but emotions make them convincing ... Emotions and logic do not have to be enemies. Logic works perfectly in the abstract mathematical world, but life is more complicated than that. Life involves humans, and humans have emotions. Here in this beautiful and messy world of ours we should use emotions to back up logic, and logic to understand emotions. I firmly believe that when we use emotions and logic together, each working to their own strengths and not beyond them, we can think more clearly, communicate more effectively, and achieve a deeper and more compassionate understanding of our fellow human beings. That is the true art of logic. > There has been an alarming gradual increase in non-experts dismissing expert consensus as elite conspiracy, as with climate science and vaccinations. Just because a lot of people agree about something doesn't mean there is a conspiracy. Many people agree that Roger Federer won Wimbledon in 2017. In fact, probably everyone who is aware of it agrees. This doesn't mean it's a conspiracy: it means there are very clear rules for how to win Wimbledon, and many, many people could all watch him do it and verify that he did in fact win, according to the rules. > > The touble with science and mathematics in this regard is that the rules are harder to understand, so it is more difficult for non-experts to verify that the rules have been followed.