Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy. In this new edition Graham Priest expands his discussion to cover the subjects of algorithms and axioms, and proofs in mathematics.
About the Series: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis,...
From the philosophy of Aristotle and Confucius, to Thomas Aquinas' Summa Theologiae, to the paintings of Raphael, Botticelli and many more, fascination with the virtues has endured and evolved to fit a wide range of cultural, religious, and philosophical contexts through the centuries. This Very Short Introduction introduces readers to the various virtues: the moral virtues, the intellectual virtues, and the theological virtues, as well as the capital vices. It explores the role of the virtues in moral life, their cultivation, and how they offer ways of thinking and acting that are alternatives to mere rule-following. It also considers the relationship of the virtues to our own emotions, desires, and rational capacities. ABOUT THE SERIES:The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts,...
How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries.
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How much faith should we place in what scientists tell us? Is it possible for scientific knowledge to be fully 'objective'? What, really, can be defined as science? In the second edition of this Very Short Introduction, Samir Okasha explores the main themes and theories of contemporary philosophy of science, and investigates fascinating, challenging questions such as these. Starting at the very beginning, with a concise overview of the history of science, Okasha examines the nature of fundamental practices such as reasoning, causation, and explanation. Looking at scientific revolutions and the issue of scientific change, he asks whether there is a discernible pattern to the way scientific ideas change over time, and discusses realist versus anti-realist attitudes towards science. He finishes by considering science today, and the social and ethical philosophical questions surrounding modern science.
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What is knowledge? How does it differ from mere belief? Do you need to be able to justify a claim in order to count as knowing it? How can we know that the outer world is real and not a dream? Questions like these are ancient ones, and the branch of philosophy dedicated to answering them—epistemology—has been active for thousands of years. In this thought-provoking Very Short Introduction, Jennifer Nagel considers these classic questions alongside new puzzles arising from recent discoveries about humanity, language, and the mind. Nagel explains the formation of major historical theories of knowledge, and shows how contemporary philosophers have developed new ways of understanding knowledge, using ideas from logic, linguistics, and psychology. Covering topics ranging from relativism and the problem of scepticism to the trustworthiness of internet sources, Nagel examines how progress has been made in understanding knowledge, using everyday examples to explain the key...
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The concept of law lies at the heart of our social and political life. Legal philosophy, or jurisprudence, explores the notion of law and its role in society, illuminating its meaning and its relation to the universal questions of justice, rights, and morality. In this Very Short Introduction Raymond Wacks analyses the nature and purpose of the legal system, and the practice by courts, lawyers, and judges. Wacks reveals the intriguing and challenging nature of legal philosophy with clarity and enthusiasm, providing an enlightening guide to the central questions of legal theory. In this revised edition Wacks makes a number of updates including new material on legal realism, changes to the approach to the analysis of law and legal theory, and updates to historical and anthropological jurisprudence.
About the Series: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the...
What is time? What does it mean for time to pass? Is it possible to travel in time? What is the difference between the past and future? Until the work of Newton, these questions were purely topics of philosophical speculation. Since then we've learned a great deal about time, and its study has moved from a subject of philosophical reflection to instead became part of the subject matter of physics. This Very Short Introduction introduces readers to the current physical understanding of the direction of time, from the Second Law of Thermodynamics to the emergence of complexity and life. Jenann Ismael charts the line of development in physical theory from Newton, via Einstein's Theory of Relativity, to the current day. Einstein's innovations led to a vision of time very different from the familiar time of everyday sense. In this new vision, time is one of the dimensions in whichthe universe is extended alongside the spatial dimensions. The universe appears as a static block of...
Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals. In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of...
Stoicism is two things: a long past philosophical school of ancient Greece and Rome, and an enduring philosophical movement that still inspires people in the twenty-first century to re-think and re-organize their lives in order to achieve personal satisfaction. What is the connection between them? This Very Short Introduction provides an introductory account of Stoic philosophy, and tells the story of how ancient Stoicism survived and evolved into the movement we see today. Exploring the roots of the school in the philosophy of fourth century BCE Greece, Brad Inwood examines its basic history and doctrines and its relationship to the thought of Plato, Aristotle and his successors, and the Epicureans. Sketching the history of the school's reception in the western tradition, he argues that, despite the differences between ancient and contemporary Stoics, there is a common core of philosophical insight that unites the modern version not just to Seneca, Epictetus, and Marcus...
Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them. But number theory has also recently become of great practical importance—in the area of cryptography, where the security of your credit card, and indeed of the nation's defence, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed other spectacular developments, such as Andrew Wiles's proof of 'Fermat's last theorem' (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction Robin...
The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?")
About the Series: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new...
Numbers are integral to our everyday lives and feature in everything we do. In this Very Short Introduction Peter M. Higgins, the renowned mathematics writer, unravels the world of numbers; demonstrating its richness, and providing a comprehensive view of the idea of the number. Higgins paints a picture of the number world, considering how the modern number system matured over centuries. Explaining the various number types and showing how they behave, he introduces key concepts such as integers, fractions, real numbers, and imaginary numbers. By approaching the topic in a non-technical way and emphasising the basic principles and interactions of numbers with mathematics and science, Higgins also demonstrates the practical interactions and modern applications, such as encryption of confidential data on the internet.
About the Series: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These...
Throughout history scepticism and the urge to question accepted truths has been a powerful force for change and growth. Today, as we are bombarded by adverts, scientific studies praising the latest superfoods, and political rhetoric, a healthy amount of scepticism is widely encouraged. But when is such scepticism legitimate - for example, as a driver of new ideas - and when is it problematic? And what role might adopting a sceptical outlook play in leading an intellectually virtuous life? In this Very Short Introduction Duncan Pritchard explores both the advantages of scepticism, in challenging outdated notions, and also how it can have unhelpful social consequences, in generating distrust. He considers the role of scepticism at the source of contemporary social and political movements such as climate change denial, post-truth politics, and fake news. Pritchard also examines the philosophical arguments for a radical form of scepticism which maintains that knowledge is...
Is the neurophysiology of pain all there is to pain? How do words and mental pictures come to represent things in the world? Do computers think, and if so, are their thought processes significantly similar to our thought processes? Or is there something distinctive about human thought that precludes replication in a computer? These are some of the puzzles that motivate the philosophical discipline called "philosophy of mind," a central area of philosophy. This Very Short Introduction introduces the philosophy of mind, and looks at some of the most interesting and important topics in this fascinating field, including the mind-body problem and dualism. Barbara Montero also discusses minds other than our own, and the problems associated with defining consciousness in animals, aliens and machines. Considering these and other such thorny issues such as physicalism and intentionality, she demonstrates how questions of the philosophy of mindalso infiltrate disciplines outside of...
Metaphysics is one of the traditional four main branches of philosophy, alongside ethics, logic and epistemology. It is also an area that continues to attract and hold a fascination for many people yet it is associated with being complex and abstract. For some it is associated with the mystical or religious. For others it is known through the metaphysical poets who talk of love and spirituality. This Very Short Introduction goes right to the heart of the matter, getting to the basic and most important questions of metaphysical thought in order to understand the theory: What are objects? Do colours and shapes have some form of existence? What is it for one thing to cause another rather than just being associated with it? What is possible? Does time pass? By using these questions to initiate thought about the basic issues around substance, properties, changes, causes, possibilities, time, personal identity, nothingness and emergentism, Stephen Mumford provides a clear and simple...
In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory.
About the Series: The Very Short Introductions series from Oxford University Press contains hundreds of...
Objectivity is both an essential and elusive philosophical concept. An account is generally considered to be objective if it attempts to capture the nature of the object studied without judgement of a conscious entity or subject. Objectivity stands in contrast to subjectivity: an objective account is impartial, one which could ideally be accepted by any subject, because it does not draw on any assumptions, prejudices, or values of particular subjects. Stephen Gaukroger shows that it is far from clear that we can resolve moral or aesthetic disputes in this way and it has often been argued that such an approach is not always appropriate for disciplines that deal with human, rather than natural, phenomena. Moreover, even in those...
Causation is the most fundamental connection in the universe. Without it, there would be no science or technology. There would be no moral responsibility either, as none of our thoughts would be connected with our actions and none of our actions with any consequences. Nor would we have a system of law because blame resides only in someone having caused injury or damage. Any intervention we make in the world around us is premised on there being causal connections that are, to a degree, predictable. It is causation that is at the basis of prediction and also explanation. This Very Short Introduction introduces the key theories of causation and also the surrounding debates and controversies. Do causes produce their effects by guaranteeing them? Do causes have to precede their effects? Can causation be reduced to the forces of physics? And are we right to think of causation as one single thing at all?
How ought we to live? What really exists? How do we know? This Very Short Introduction discusses some of the key questions philosophy engages with. Edward Craig explores important themes in ethics, and the nature of knowledge and the self, through readings from Plato, Hume, Descartes, Hegel, Darwin, and Buddhist writers. Throughout, he emphasizes why we do phiilosophy, explains how different areas of philosophy are related, and explores the contexts in which philosophy was and is done. This new edition includes a new chapter on free will, discussing determinism and indeterminism in the context of Descartes and Hegel's work. Craig also covers the Problem of Evil, and Kant's argument on the source of moral obligation.
ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts,...
What are philosophers trying to achieve? How can they succeed? Does philosophy make progress? Is it in competition with science, or doing something completely different, or neither? Timothy Williamson tackles some of the key questions surrounding philosophy in new and provocative ways, showing how philosophy begins in common sense curiosity, and develops through our capacity to dispute rationally with each other. Discussing philosophy's ability to clarify our thoughts, he explains why such clarification depends on the development of philosophical theories, and how those theories can be tested by imaginative thought experiments, and compared against each other by standards similar to those used in the natural and social sciences. He also shows how logical rigour can be understood as a way of enhancing the explanatory power of philosophical theories. Drawing on the history of philosophy to provide a track record of philosophical thinking's successes and failures, Williams...
Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics.
About the Series: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine...
The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof - deductive reasoning from a set of axioms - first arose. To this day geometry remains a very active area of research in mathematics. This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Starting from the basics, Maciej Dunajski proceeds from concrete examples (of mathematical objects like Platonic solids, or theorems like the Pythagorean theorem) to general principles. Throughout, he outlines the rolegeometry plays in the broader context of science and art. Very Short Introductions: Brilliant, Sharp, Inspiring ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every...
Very Short Introductions: Brilliant, Sharp, Inspiring Our self-image as moral, well-behaved creatures is dogged by scepticism, relativism, hypocrisy, and nihilism, and by the fear that in a Godless world science has unmasked us as creatures fated by our genes to be selfish and tribalistic, or competitive and aggressive. Here, Simon Blackburn tackles the major moral questions surrounding birth, death, happiness, desire, and freedom, showing us how we should think about the meaning of life, and why we should mistrust the soundbite-sized absolutesthat often dominate moral debates. This second edition of the Very Short Introduction on Ethics has revised and updated aspects of the original to reflect changing times and mores. It highlights the importance of an understanding of approaches to ethics and its foundations, confronted as we are with a fluid and uncertain world of eroding trust, swirling conspiracy theories, and a dismaying loss of respect in public discourse. ABOUT THE...
Epicureanism is commonly associated with a carefree view of life and the pursuit of pleasures, particularly the pleasures of the table. However it was a complex and distinctive system of philosophy that emphasized simplicity and moderation, and considered nature to consist of atoms and the void. Epicureanism is a school of thought whose legacy continues to reverberate today. In this Very Short Introduction, Catherine Wilson explains the key ideas of the School, comparing them with those of the rival Stoics and with Kantian ethics, and tracing their influence on the development of scientific and political thought from Locke, Newton, and Galileo to Rousseau, Marx, Bentham, and Mill. She discusses the adoption and adaptation of Epicurean motifs in science, morality, and politics from the 17th Century onwards and contextualises the significance of Epicureanism in modern life.
About the Series: The Very Short Introductions series from Oxford University Press contains...
What is agnosticism? Is it just the 'don't know' position on God, or is there more to it than this? Is it a belief, or merely the absence of belief? Who were the first to call themselves 'agnostics'? These are just some of the questions that Robin Le Poidevin considers in this Very Short Introduction. He sets the philosophical case for agnosticism and explores it as a historical and cultural phenomenon. What emerges is a much more sophisticated, and much more interesting, attitude than a simple failure to either commit to, or reject, religious belief. Le Poidevin challenges some preconceptions and assumptions among both believers and non-atheists, and invites the reader to rethink their own position on the issues.
About the Series: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts,...
Born of the desire to understand the workings of motions of the heavenly bodies, trigonometry gave the ancient Greeks the ability to predict their futures. Most of what we see of the subject in school comes from these heavenly origins; 15th century astronomer Regiomontanus called it "the foot of the ladder to the stars". In this Very Short Introduction Glen Van Brummelen shows how trigonometry connects mathematics to science, and has today become an indispensable tool in predicting cyclic patterns like animal populations and ocean tides. Its historical journey through major cultures such as medieval India and the Islamic World has taken it through disciplines such as geography and even religious practice. Trigonometry has also been a major player in the most startling mathematical developments of the modern world. Its interactions with the concept of infinity led to Taylor and Fourier series, some of the most practical tools of modern science. The birth of complex numbers led...
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Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy. In this new edition Graham Priest expands his discussion to cover the subjects of algorithms and axioms, and proofs in mathematics.
About the Series: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis,...