For thousands of years, mathematicians have used the timeless art of logic to see the world more clearly. In The Art of Logic, Royal Society Science Book Prize nominee Eugenia Cheng shows how anyone can think like a mathematician - and see, argue and think better.

Learn how to simplify complex decisions without over-simplifying them. Discover the power of analogies and the dangers of false equivalences. Find out how people construct misleading arguments, and how we can argue back.

Eugenia Cheng teaches us how to find clarity without losing nuance, taking a careful scalpel to the complexities of politics, privilege, sexism and dozens of other real-world situations. Her Art of Logic is a practical and inspiring guide to decoding the modern world.

This book tells the story of human civilisation as a series of historical periods, from Prehistory to the present day, describing the way each evolved into the next. In so doing, it explains the reasons behind what happened in each period, in terms of their contribution to the whole. It describes the way the ideas process evolves along with society, and explains the myths, religions and philosophical ideas which developed in the Ancient world, and the way its great empires appeared. Then, according to new technology and principles, how the events of the Middle Ages led to the rediscovery of the Americas and took us into the Modern periods, where the industrial revolution gave rise to the Middle Classes, and a new type of politics featured more representative forms of government. However, after two world wars which redefined the era, Postmodernity emerged as a term for the structure of Cold War society, which gave rise to the success of digital technology, but also led to the new problem of terrorism. Hence, many questions have arisen over the direction of human society, how it has evolved out of history, and how we address its issues. What type of problems can we solve at each stage? Perhaps with computers we are now able to analyse data in a way which was not possible before and this will lead to the next era.

The Legacy of Aristotelian Enthymeme provides a historical-logical analysis of Aristotle's rhetorical syllogism, the enthymeme, through its Medieval and Renaissance interpretations. Bringing together notions of credibility and proof, an international team of scholars highlight the fierce debates around this form of argumentation during two key periods for Aristotle's beliefs. Reflecting on medieval and humanist thinkers, philosophers, poets and theologians, this volume joins up dialectical and rhetorical argumentation as key to the enthymeme's interpretation and shows how the enthymeme was the source of a major interpretive conflict. As a method for achieving the standards for proof and credibility that persist across diverse fields of study today including the law, politics, medicine and morality, this book takes in Latin and Persian interpretations of the enthymeme and casts contemporary argumentation in a new historical light.

Logics of Worlds stands as one of the most important texts in contemporary thought. Conceived as the sequel to Alan Badiou's Being and Event, the book expands upon and elucidates the questions that were posed in the first book. As a complex theory of worlds, the text has, for the most part, been misunderstood, but in William Watkin's diligent and critical close reading of the book, he makes the case for Logics of Worlds being the essential Badiou book for anyone interested in existence, meaning and the potential for radical change. For Watkin, this recasting of ontology is followed by a transformation of logic, which is not only a theory of being, but of appearing and allows Badiou to give new meaning to the object, body and relation. To do this, he explores these concepts through architecture, astronomy and renowned thinkers such as Kant, Hegel and Kierkegaard. For students of French Continental philosophy, ontology and Badiou himself, Watkin's commentary on the philosopher's text provides a brilliant and incisive new interpretation of this underrated work by the leading Continental philosopher of our time.

The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist.The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference.

The philosopher Abu Nasr al-Farabi (c. 870-c. 950 CE) is a key Arabic intermediary figure. He knew Aristotle, and in particular Aristotle's logic, through Greek Neoplatonist interpretations translated into Arabic via Syriac and possibly Persian. For example, he revised a general description of Aristotle's logic by the 6th century Paul the Persian, and further influenced famous later philosophers and theologians writing in Arabic in the 11th to 12th centuries: Avicenna, Al-Ghazali, Avempace and Averroes. Averroes' reports on Farabi were subsequently transmitted to the West in Latin translation. This book is an abridgement of Aristotle's Prior Analytics, rather than a commentary on successive passages. In it Farabi discusses Aristotle's invention, the syllogism, and aims to codify the deductively valid arguments in all disciplines. He describes Aristotle's categorical syllogisms in detail; these are syllogisms with premises such as 'Every A is a B' and 'No A is a B'. He adds a discussion of how categorical syllogisms can codify arguments by induction from known examples or by analogy, and also some kinds of theological argument from perceived facts to conclusions lying beyond perception. He also describes post-Aristotelian hypothetical syllogisms, which draw conclusions from premises such as 'If P then Q' and 'Either P or Q'. His treatment of categorical syllogisms is one of the first to recognise logically productive pairs of premises by using 'conditions of productivity', a device that had appeared in the Greek Philoponus in 6th century Alexandria.

As the foundation of our rationality, logic has traditionally been considered fixed, stable and constant. This conception of the discipline has been challenged recently by the plurality of logics and in this book, Pavel Arazim extends the debate to offer a new view of logic as dynamic and without a definite, specific shape. The Problem of Plurality of Logics examines the origins of our standard view of logic alongside Kant's theories, the holistic view, the issue of logic's pragmatic significance and Robert Brandom's logical expressivism. Arazim then draws on proof-theoretical approaches to present a convincing argument for a dynamic version of logical inferentialism, which opens space for a new freedom to modify our own logic. He explores the scope, possibilities and limits of this freedom in order to highlight the future paths logic could take, as a motivation for further research. Marking a departure from logical monism and also from the recent doctrine of logical pluralism in its various forms, this book addresses current debates concerning the expressive role of logic and contributes to a lively area of discussion in analytic philosophy.

Aristotle's Topics is a handbook for dialectic, i.e. the exercise for philosophical debates between a questioner and a respondent. Alexander takes the Topics as a sort of handbook teaching how to defend and how attack any philosophical claim against philosophical adversaries. In book 3, Aristotle develops strategies for arguing about comparative claims, in which properties are said to belong to subjects to a greater, lesser, or equal degree. Aristotle illustrates the different argumentative patterns that can be used to establish or refute a comparative claim through one single example: whether something is more or less or equally to be chosen or to be avoided than something else. In his commentary on Topics 3, here translated for the first time into English, Alexander of Aphrodisias spells out Aristotle's text by referring to issues and examples from debates with other philosophical school (especially: the Stoics) of his time. The commentary provides new evidence for Alexander's views on the logic of comparison and is a relatively neglected source for Peripatetic ethics in late antiquity. This volume will be valuable reading for students of Aristotle and of the developments of Peripatetic logic and ethics in late antiquity.