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Why is abstract mathematics applicable within science? Jeffrey Ketland describes the metatheory of the application of mathematics in science and highlights the 'entanglement' of physical systems with mathematical objects and structures. Applied Mathematics inferences are regimented into 'canonical form', involving an ambient foundational base theory and the specific physical premises and conclusions. These latter are formulated using concepts called 'entanglers', which relate physical objects and systems to mathematical objects. The simplest example is the membership predicate, 'x is an element of y', and other examples are coordinate functions, quantity functions (such as mass, length, or temporal duration), and fields (on space or spacetime). Mathematical terms denoting these, as well as impure sets, relations, and structures, are called 'entanglement constants'. Ketland shows that such inferences satisfy a form of topic neutrality called Hilbert's Beermug Principle, and all such inferences can be seen to be instantiations of general mathematical theorems with such constants.
This book explores how language shapes our engagement with fiction, from understanding characters to discussing stories. It delves into the unique ways we communicate about fictional worlds, showing how fiction-related talk is used in a variety of situations. Andreas Stokke explores the semantics and pragmatics of fiction-related language, focusing on how we use language to create and discuss fictional stories and characters. He argues that the linguistic tools used for fiction are the same as those for reality, yet fictional communication is distinct as it is unconstrained by real-world reference and allows for saying things without incurring factual commitments. He also shows how fictional names retain their meaning across many ways of using them. He then analyses the various ways in which we talk about fiction, including metafictional, interfictional, and counterfictional discourse.
This is a comprehensive introduction to one of philosophy's deepest and most fascinating puzzles, the Liar Paradox. It introduces key theories of truth and paradox, and combines accessibility with depth, tracing the paradox from its simplest formulations to the most sophisticated contemporary theories. Chapters by leading philosophers and logicians present both classical and non-classical approaches - supervaluationist, paracomplete, paraconsistent, and substructural - and examine broader families of paradoxes alongside general theories of paradoxicality. The volume also explores the paradox's connections to meta-mathematics, modality, vagueness, quantifiers, context-dependence, and natural language semantics, demonstrating its far-reaching significance and its central role in logic, philosophy of language, and theoretical linguistics. Structured for clarity, each chapter introduces key ideas and develops advanced arguments, making the book an essential resource for students, researchers, and professionals seeking a comprehensive understanding of semantic paradoxes and theories of truth.
Representationalists view thought and language as mirrors of a mind-independent world. On this view, knowing is about accurately representing reality, and meaning lies in representational content. This book offers a pragmatist alternative: it argues that our practices are not just relevant but fundamental to both knowing and meaning—and that knowing-how should be seen as the primary form of knowledge. Building on neopragmatist tradition and engaging with classical pragmatism as well as recent work in epistemology, the philosophy of language, and the philosophy of science, the book develops and defends methodologism. This novel framework reorients questions of knowledge and meaning around rule-guided rational practices. The book will appeal to students and scholars in these fields, as well as readers across the humanities and social sciences interested in language, rationality, and their role in communities.
The Early German Romantics elaborated a highly original philosophical-political framework where subjectivity is not construed as essentially the property of an isolated individual having control over other people and over nature. Rather, each subject can exist and flourish only within a web of harmonious relations of mutual dependency which connects it with history, with other people, and with the natural world. The implications of such a conception for our notion of individual and collective autonomy and for political life are radical. This book explains and analyses this novel way of thinking, places it in its historical context, and brings out some of the major consequences it has for our social life, and in particular for a number of issues of special contemporary relevance such as gender and ecology.
Philosophical problems fundamentally infuse the theory and practice of astronomy. Bringing together fifteen historians, eleven philosophers, and four pioneering scientists, this volume provides a rigorous yet largely accessible examination of the conceptual and methodological challenges that lie at the intersection of philosophy and astronomy – broadly construed to include astrophysics, cosmology, space science, and astrobiology. Drawing largely on interdisciplinary advances from the past two centuries, the book's chapters tackle metaphysical inquiries into the fundamental nature of reality, the limits of reasoning, the problematic nature of observation and inference, the role of technology, and the epistemology of concepts such as space, time, life, and intelligence. Discussions are anchored to fascinating theories and examples from the 'canals' of Mars to exoplanets, black holes, dark matter, and the multiverse. Written primarily for practicing scientists, this volume will also serve historians and philosophers of science, as well as the curious general reader.
Combining historical insight with contemporary theory, this book demonstrates that Kant's aesthetics can ground a robust theory of art criticism. It challenges the widespread view that Kant's rejection of aesthetic testimony – the idea that we cannot simply adopt someone else's judgment without first-hand experience - and his dismissal of general rules such as 'symmetry guarantees beauty' or 'a tragic ending ensures depth' leaves critics powerless. If testimony and rules are excluded, evaluations such as 'Blade Runner is a masterpiece' lose authority, while descriptions like 'most of the story takes place in perpetual rain and darkness' seems irrelevant to the critic's evaluation. This book locates the solution in Kant's overlooked judgments of perfection such as 'the film innovates within the neo-noir genre.' It reimagines what critical communication can be by positioning these judgments as mediators. They guide aesthetic evaluations and draw support from descriptions of a work's non-aesthetic features.
Consumed by thoughts of a mysterious flower, Heinrich leaves his cold homeland and travels south until he meets Mathilde, who opens his eyes to the world's mysteries. Then a tragic event reveals the secret power of poetry… Heinrich von Ofterdingen, left unfinished at the time of the author's death, is a masterpiece of philosophical fiction and a classic of German literature. This highly detailed and original interpretation is the most detailed, comprehensive, and systematic study of the novel ever written. Developing fresh insights into the philosophical ideas of the novel while also attending to its symbolic, literary, and creative qualities, Owen Ware explores how Novalis probes the core problem of modern life – fragmentation and our sense of alienation from the world. Ultimately, he shows us, this novel is a timeless expression of the Romantics' idea that only the imagination, guided by love, can bring us back to our spiritual home.
This Element traces the development of Wittgenstein's views on belief formation throughout the different phases of his philosophy. Section 1 concentrates on the Tractarian period, where the sparse references to belief consist primarily of reactions to Russell. The logical purism of the early Wittgenstein led him to reject psychological stances such as those found in Russell's epistemological works. Section 2 explores Wittgenstein's 'middle' period, focusing on his evolving views on belief formation, influenced by his shift to viewing language as a social practice. It addresses key texts, including The Big Typescript and 'Cause and Effect', and links the psychological mechanisms of belief to Wittgenstein's later grammatical investigations in an analysis that extends to his reflections on mathematics and religion. Section 3 reconstructs the intellectual trajectory that would culminate in On Certainty, tracing the influence of Moore and Newman on the range of belief-forming processes Wittgenstein examines in his final writings.
In recent writings on popular science, there has been much handwringing about the apparently deterministic picture of human decision making suggested by the latest scientific research. Robert Sapolsky's bestselling Determined boldly argues that morality must be reformed because free will has been effectively refuted. But the question of whether free will and morality can be reconciled with a causally determined world is nothing new, nor is it the sort of question that can be answered by scientists. This Element examines how these questions were answered by Spinoza, history's most forceful defender of the claim that all things are necessarily determined, who also was keenly interested in the prospects for morality in a determined world. The Element aims to show that this figure from the past offers a timely and insightful explanation of how we can be free and responsible even if our actions are inevitable.
This Element is about Wittgenstein's engagement with skepticism. Two forms of skepticism will be at the center of this Element: skepticism concerning our knowledge of the 'external world,' and skepticism concerning our knowledge of 'other minds.' It will be shown that Wittgenstein is neither a skeptic nor an anti-skeptic. Rather, Wittgenstein thinks of the skeptic's doubt as a form of denial: a denial of knowledge that one cannot but have. The aim of this Element is to bring out what it means to think of the skeptic's doubt in a Wittgensteinian way, that is, as a doubt that manifests a denial of knowledge that one cannot but have, rather than a philosophical position about the possibility of knowledge that is either true or false and hence an object either of justification or refutation. Wittgenstein's relation to skepticism is therefore unique and highly original.
This element is a study on Hegel's dialectic. One motivation for turning to dialectic is the idea that in order to understand the complex and dynamic structure of reality and of our thinking itself, we need a different way of thinking from that provided by standard logic and by traditional philosophy. The aim of the book is to present Hegel's basic idea of dialectic and to explain it through an interpretation of the text, an account of its reception, and a survey of themes in the secondary literature. The main theses discussed are that Hegel's dialectic is primarily a method of thinking and that he develops a unified theory of dialectic in his various writings.
This Element focuses on contemporary forms of nativism (belief in innateness), which mostly concern the existence of domain-specific learning mechanisms with innate structure and content. After sketching some innate capacities that are widely believed to be shared with other animals, the Element thereafter discusses a number of (alleged) distinctively-human ones. One concerns a faculty of language, another our capacity for representing the mental states of others (and derivatively, ourselves). It then turns to discuss some proposed innate adaptations that support culture. These include a number of learning biases, as well as affective learning mechanisms that enable swift acquisition of cultural values. The final two sections then discuss 'tribal psychology.' This may include an innate disposition to stereotype social groups as well as innate 'tribal' motivations (both positive and negative). The over-arching thesis of the Element is that human nature might best be thought of as culture-enabling nature.
Traditionally, Christians have viewed unbelief as resulting from moral and/or cognitive shortcomings. However, a recent proposal such as John Schellenberg's 'divine hiddenness argument' for atheism has supported the idea that there is no-fault unbelief. In this Element, the author draws on important insights from medieval Christian thought to argue that both believers and non-believers should stop blaming each other based on mere evidence. Believers may recognise that no-fault unbelief can, in a sense, apply to them, too. They may find it perplexing that they neither believe nor achieve communion with God as much as they would like. Proponents of no-fault unbelief might focus on achieving communion with God rather than solely worrying about absolving themselves of blame. Ultimately, believers and non-believers alike might promote spiritual progress by setting aside the primacy of evidence and committing themselves to God and the good.
In this book, Mikael Stenmark identifies and explores several prominent religious and secular worldviews that people in contemporary society hold. Three nonreligious worldviews are highlighted: scientism, secular humanism, and transhumanism. These are contrasted with four religious worldviews: Abrahamic theism, Buddhism, the new spirituality (the so-called 'spiritual but not religious' individuals, SBNR), and religious naturalism. Some challenges facing each of these worldviews are discussed toward the end of each chapter. The book offers a unique study of several key secular outlooks on life that go far beyond previous studies of atheism, nonreligion, and religious 'nones.' It also provides a rare insight into the beliefs, values, and attitudes that secular and religious thinkers consider essential to our identity and place in the world, as well as what we should deeply care about in life.
Bad lawyering has come under increasing focus though NDAs, SLAPPs, the banking crisis, and latterly the UK's Post Office Scandal, an extraordinary legal scandal spanning more than 20 years that ruined thousands of lives. This book examines the commercial, cultural, legal, and psychological drivers of ethical failure weaving them together with case studies in a compelling account of what is wrong with lawyers' ethics. Rather than concentrating on a few bad apples, it shows how deep-seated traditions, psychological frailties, the complacency and aggression of well-paid lawyers, and the pragmatism, cynicism, and hubris of organisations combines to pollute decision-making and weaken the rule of law. Be it through awful orthodoxies or legality illusions, it shows how a lawyer's naturally uncomfortable relationship with truth and justice can become improper or even criminal. This title is also available as open access on Cambridge Core.
The central ideas of Isaiah Berlin (1909–1997) remain as alive for our century as they did for his, and his enduring importance as a thinker is matched by his reputation as an essayist of the first rank. This in-depth exploration of a selection of Berlin's most important essays, by a rich variety of distinguished scholars, offers a critical appraisal of Berlin's wide-ranging intellectual preoccupations and their relation to the deep, persistent questions of human life. Each of the contributors examines Berlin's understanding of humanity through one of his essays, including 'The Hedgehog and the Fox', 'Two Concepts of Liberty' and 'Winston Churchill in 1940', together with less famous ones such as 'The Divorce between the Sciences and the Humanities' and 'The Purpose of Philosophy'. The result is a fresh, insightful portrait of a fascinating mind.
Aristotle's account of justice has inspired thinkers as diverse as Thomas Aquinas and Martha Nussbaum. Concepts such as distributive justice, equity, the common good, and the distinction between just and unjust political organizations find articulations in his writings. But although Aristotle's account of justice remains philosophically relevant, its intellectual, social, and political origins in the Mediterranean world of the fourth century BCE have often been overlooked. This book places Aristotle's account of justice in dialogue with his fourth-century intellectual colleagues such as Plato, Xenophon, and Isocrates, and allows it to be understood within the framework of fourth-century institutions as they were experienced by citizens of ancient Greek political communities. It thus provides the modern reader with the framework which Aristotle presupposed for his original work in antiquity, including the intellectual debates which formed its context.
Computer programs are often factored into pure components - simple, total functions from inputs to outputs - and components that may have side effects - errors, changes to memory, parallel threads, abortion of the current loop, and so on. In this Element, the authors make the case that human languages are similarly organized around the give and pull of pure values and impure processes, and show how denotational techniques from computer science can be leveraged to support elegant and illuminating analyses of semantic composition in natural language.