If numbers were objects, how could there be human knowledge of number? Numbers are not physical objects: must we conclude that we have a mysterious power of perceiving the abstract realm? Or should we instead conclude that numbers are fictions? This book argues that numbers are not objects: they are magnitude properties. Properties are not fictions and we certainly have scientific knowledge of them. Much is already known about magnitude properties such as inertial mass and electric charge, and much continues to be discovered. The book says the same is true of numbers. In the theory of magnitudes, the categorial distinction between quantity and individual is of central importance, for magnitudes are properties of quantities, not properties of individuals. Quantity entails divisibility, so the logic of quantity needs mereology, the a priori logic of part and whole. The three species of quantity are pluralities, continua and series, and the book presents three variants of mereology, one for each species of quantity. Given Euclid's axioms of equality, it is possible without the use of set theory to deduce the axioms of the natural, real and ordinal numbers from the respective mereologies of pluralities, continua and series. Knowledge and the Philosophy of Number carries out these deductions, arriving at a metaphysics of number that makes room for our a priori knowledge of mathematical reality.

Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes.

This book discusses how scientific and other types of cognition make use of models, abduction, and explanatory reasoning in order to produce important or creative changes in theories and concepts. It includes revised contributions presented during the international conference on Model-Based Reasoning (MBR'015), held on June 25-27 in Sestri Levante, Italy. The book is divided into three main parts, the first of which focuses on models, reasoning and representation. It highlights key theoretical concepts from an applied perspective, addressing issues concerning information visualization, experimental methods and design. The second part goes a step further, examining abduction, problem solving and reasoning. The respective contributions analyze different types of reasoning, discussing various concepts of inference and creativity and their relationship with experimental data. In turn, the third part reports on a number of historical, epistemological and technological issues. By analyzing possible contradictions in modern research and describing representative case studies in experimental research, this part aims at fostering new discussions and stimulating new ideas. All in all, the book provides researchers and graduate students in the field of applied philosophy, epistemology, cognitive science and artificial intelligence alike with an authoritative snapshot of current theories and applications of model-based reasoning.

This Handbook offers students and more advanced readers a valuable resource for understanding linguistic reference; the relation between an expression (word, phrase, sentence) and what that expression is about. The volume's forty-one original chapters, written by many of today's leading philosophers of language, are organized into ten parts: I Early Descriptive Theories II Causal Theories of Reference III Causal Theories and Cognitive Significance IV Alternate Theories V Two-Dimensional Semantics VI Natural Kind Terms and Rigidity VII The Empty Case VIII Singular (De Re) Thoughts IX Indexicals X Epistemology of Reference Contributions consider what kinds of expressions actually refer (names, general terms, indexicals, empty terms, sentences), what referring expressions refer to, what makes an expression refer to whatever it does, connections between meaning and reference, and how we know facts about reference. Many contributions also develop connections between linguistic reference and issues in metaphysics, epistemology, philosophy of mind, and philosophy of science.

This book introduces a new form of argumentative analysis: rhetorical heuremes. The method applies the concepts of heuristic thinking, probability, and contingency in order to develop a better understanding of complex arguments in classical oratory. A new theory is required because Greek and Roman rhetoric cannot provide detailed answers to problems of strategic argumentation in the analysis of speeches. Building on scholarship in Ciceronian oratory, this book moves beyond the extant terminology and employs a concept of heuristic reasoning derived from the psychology of decision making and mathematical problem solving. The author analyses selected passages from Cicero's forensic speeches where arguments of probability are deployed, and shows that the Sophistic concept of probability can link ancient rhetoric and modern theories of argumentation. Six groups of heuremes are identified, each of which represents a form of probabilistic reasoning by which the orator plays upon the perception of the jurors.

The Topics is Aristotle's treatise on dialectical argument, a practice perhaps as old as human language, systemized for the first time by Aristotle. This seminal text offers many important insights into his conception of logic, his development of the notion of the predicables (the Five Terms), and his ideas on the method of philosophical inquiry itself. This volume contains a clear and accurate translation of Books I and VIII of Aristotle's Topics together with a philosophical commentary on these books and additional selections from Books II and III, and from the Sophistical Refutations . These books and selections best give a general view of the main ideas, arguments, and techniques expounded in the Topics . The volume is well suited to the requirements of students, including those who do not know Greek.

We all engage in the process of reasoning, but we don't always pay attention to whether we are doing it well. This book offers the opportunity to practise reasoning in a clear-headed and critical way, with the aims of developing an awareness of the importance of reasoning well and of improving the reader's skill in analyzing and evaluating arguments. In this third edition, Anne Thomson has updated and revised the book to include fresh and topical examples which will guide students through the processes of critical reasoning in a clear and engaging way. In addition, two new chapters on evaluating the credibility of evidence and decision making and dilemmas will fully equip students to reason well. By the end of the book students should be able to: identify flaws in arguments analyze the reasoning in newspaper articles, books and speeches assess the credibilty of evidence and authorities make sound decisions and solve dilemmas approach any topic with the ability to reason and think critically.

Other Logics: Alternatives to Formal Logic in the History of Thought and Contemporary Philosophy challenges the widespread idea of formal logic as inherently monolithic, universal, and ahistorical. Written by both leading and up-and-coming scholars, and edited by Admir Skodo, Other Logics offers a wide variety of historical and philosophical alternatives to this idea, all arguing that logic is a historical, concrete, and multi-dimensional phenomenon. To name a few examples, Frank Ankersmit lays down a representationalist logic, Alessandra Tanesini forcefully argues for the possibility of logical aliens, Christopher Watkin analyzes how leading contemporary French philosophers view the idea of logic, and Aaron Wendland unearths Heidegger's critique of formal logic. In Other Logics readers will find provocative interventions in a highly contested field in contemporary philosophy. Contributors include: Frank Ankersmit, Christopher Watkin, Giuseppina D'Oro, Alessandra Tanesini, Admir Skodo, Aaron Wendland, Ervik Cejvan, Anders Kraal, Christopher Fear, Karim Dharamsi, Johan Modee, and Thord Svensson.

Superb insight into the development of Russell's thinking by the master himself Clearly and engaging written, charting his intellectual development from young idealist to celebrated sceptic This Routledge Classics edition includes a new foreword by Nicholas Griffin Ideal companion to Russell's own Autobiography, which is concerned with his incredibly colourful life rather than philosophy

This volume contains 12 papers addressed to researchers and advanced students in informal logic and related fields, such as argumentation, formal logic, and communications. Among the issues discussed are attempts to rethink the nature of argument and of inference, the role of dialectical context, and the standards for evaluating inferences, and to shed light on the interfaces between informal logic and argumentation theory, rhetoric, formal logic and cognitive psychology.

The aim of the present book is to give a comprehensive account of the 'state of the art' of substructural logics, focusing both on their proof theory (especially on sequent calculi and their generalizations) and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.

The Routledge Companion to Pragmatism offers 44 cutting-edge chapters-written specifically for this volume by an international team of distinguished researchers-that assess the past, present, and future of pragmatism. Going beyond the exposition of canonical texts and figures, the collection presents pragmatism as a living philosophical idiom that continues to devise promising theses in contemporary debates. The chapters are organized into four major parts: Pragmatism's history and figures Pragmatism and plural traditions Pragmatism's reach Pragmatism's relevance Each chapter provides up-to-date research tools for philosophers, students, and others who wish to locate pragmatist options in their contemporary research fields. As a whole, the volume demonstrates that the vitality of pragmatism lies in its ability to build upon, and transcend, the ideas and arguments of its founders. When seen in its full diversity, pragmatism emerges as one of the most successful and influential philosophical movements in Western philosophy.

This book focuses on the game-theoretical semantics and epistemic logic of Jaakko Hintikka. Hintikka was a prodigious and esteemed philosopher and logician, and his death in August 2015 was a huge loss to the philosophical community. This book, whose chapters have been in preparation for several years, is dedicated to the work of Jaako Hintikka, and to his memory. This edited volume consists of 23 contributions from leading logicians and philosophers, who discuss themes that span across the entire range of Hintikka's career. Semantic Representationalism, Logical Dialogues, Knowledge and Epistemic logic are among some of the topics covered in this book's chapters. The book should appeal to students, scholars and teachers who wish to explore the philosophy of Jaako Hintikka.

The book analyses the concept of discoverability, and some current epistemological problems related to it, with a special attention to science. It shows that discoverability is closely related to the sustainability of human creativity in an "eco-cognitive" perspective. Advocating the need of an integral ecology and leveraging the important concept of abduction, it demonstrates that an ecology of human creativity should have priority over other needs, i.e that the first ecological duty is to protect and sustain discoverability. Enhancing discoverability will protect human creativity, and it is exactly human creativity, a form of innovative abductive cognition, that can promote the implementation of the other kinds of ecology. The author guides readers through a comprehensive discussion on the concept of discoverability, eco-cognitive situatedness, and eco-cognitive openness and closure alike. By describing some key real-world examples, he highlights the main challenges that are currently posed to human creativity and epistemic integrity. He also describes future eco-cognitive settings, discussing the problem of overcomputationalism and suggesting a reinterpretation of the role of human knowledge. Overall, this book fills an important gap in the literature on the nexus abduction - creativity - discovery, offering a source of inspiration to philosophers, epistemologists, and cognitive scientists. Yet, it also addresses researchers in other disciplines interested in the problems of scientific discovery and epistemic integrity of research.

A system of philosophy of the sort presented in this and the following volumes begins with logic. Philosophy properly speaking is characterized by the kind oflogic it employs, for what it employs it assumes, however silently; and what it assumes it presupposes. The logic stands behind the ontology and is, so to speak, metaphysically prior. One word of caution. The philosophical aspects of logic have lagged behind the mathematical aspects in point of view of interest and develop ment. The work of N. Rescher and others have gone a long way to correct this. However, their work on philosophical logic has been more concerned with the logical than with the philosophical aspects. I have in mind another approach, one that would call attention to the ontological (systematic meta physics) or metaphysical (critical ontology) aspects, whichever term you prefer. It is this approach which I have pursued in the following chapters. Since together they stand at the head of a system of philosophy which has been developed in some seventeen books, a system which ranges over all of the topics of philosophy, the chosen approach can be seen as the necessary one. But I have not written any logic, I have merely indicated the sort of logic that has to be written."

The history of interwar Polish logic, including philosophical logic, is still a relatively little known area, especially if compared with the movement's well-documented contemporaries - the Vienna Circle or the Berlin Circle, for instance. The book aims to address this lacuna, by presenting the state of the art of research into this part of the history of analytic philosophy. It comprises thirteen essays, written by outstanding philosophers and exemplifying different approaches to the history of philosophy. One approach focuses on some little known aspects of Polish philosophy (e.g., Lesniewski's arithmetic, Tarski's geometry, philosophy of mathematics in interwar Krakow), analyzing it in great detail, sometimes by using current formal techniques. Another group of papers looks at the inspiration the Poles got from the founding fathers of analytic philosophy (Frege, Husserl, Wittgenstein), and locates Polish philosophy in the larger landscape of European analytic philosophy. Finally, some contributors pick a topic from the Polish school (sometimes only mentioned, but not developed by the Poles), and construct an alternative account which is then compared with the earlier account. Most of the papers were presented at a symposium celebrating the 70th birthday of Jan Wolenski, whose book "Logic and Philosophy of the Lvov-Warsaw School" has played a substantial role in sparking contemporary interest in Polish analytic philosophy.

This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories. The author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce's own favorite themes. The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking.

This book argues that there is a common cognitive mechanism underlying all indexical thoughts, in spite of their seeming diversity. Indexical thoughts are mental representations, such as beliefs and desires. They represent items from a thinker's point of view or her cognitive perspective. We typically express them by means of sentences containing linguistic expressions such as 'this (F)' or 'that (F)', adverbs like 'here', 'now', and 'today', and the personal pronoun 'I'. While generally agreeing that representing the world from a thinker's cognitive perspective is a key feature of indexical thoughts, philosophers disagree as to whether a thinker's cognitive perspective can be captured and rationalized by semantic content and, if so, what kind of content this is. This book surveys competing views and then advances its own positive account. Ultimately, it argues that a thinker's cognitive perspective - or her indexical point of view - is to be explained in terms of the content that is believed and asserted as the only kind of content that there is which thereby serves as the bearer of cognitive significance. The Indexical Point of View will be of interest to philosophers of mind and language, linguists, and cognitive scientists.

The Rational Shakespeare: Peter Ramus, Edward de Vere, and the Question of Authorship examines William Shakespeare's rationality from a Ramist perspective, linking that examination to the leading intellectuals of late humanism, and extending those links to the life of Edward de Vere, Seventeenth Earl of Oxford. The application to Shakespeare's plays and sonnets of a game-theoretic hermeneutic, an interpretive approach that Ramism suggests but ultimately evades, strengthens these connections in further supporting the Oxfordian answer to the question of Shakespearean authorship.

This book explores a large variety of topics involved in Arabic philosophy. It examines concepts and issues relating to logic and mathematics, as well as metaphysics, ethics and aesthetics. These topics are all studied by different Arabic philosophers and scientists from different periods ranging from the 9th century to the 20th century, and are representative of the Arabic tradition. This is the first book dealing with the Arabic thought and philosophy and written only by women. The book brings together the work and contributions of an international group of female scholars and researchers specialized in the history of Arabic logic, philosophy and mathematics. Although all authors are women, the book does not enter into any kind of feminist trend. It simply highlights the contributions of female scholars in order to make them available to the large community of researchers interested in Arabic philosophy and to bring to the fore the presence and representativeness of female scholars in the field.

This volume collects fifteen original essays on E. J. Lowe's work on metaphysics and ontology. The essays connect Lowe's insights with contemporary issues in metaphysics. E. J. Lowe (1950-2014) was one of the most influential analytical philosophers of the twentieth and early twenty-first century. Drawing inspiration from Aristotle's thought, E. J. Lowe treated metaphysics as an autonomous discipline concerned with the fundamental structure of reality. The chapters in this volume reflect on his path-breaking work. They deal with a wide range of metaphysical issues including four-category ontology, the causal and non-causal aspects of agency, categorial fundamentality and non-fundamentality, the existence of relations, property dualism, powers and abilities, personal identity, predication, and topological ontology. Taken together, the chapters reflect the liveliness of contemporary debates in metaphysics and the enduring impact of Lowe's thought on them. E. J. Lowe and Ontology will be of interest to researchers and advanced students working in metaphysics and philosophy of mind.

Interest in the metaphysics and logic of possible worlds goes back at least as far as Aristotle, but few books address the history of these important concepts. This volume offers new essays on the theories about the logical modalities (necessity and possibility) held by leading philosophers from Aristotle in ancient Greece to Rudolf Carnap in the twentieth century. The story begins with an illuminating discussion of Aristotle's views on the connection between logic and metaphysics, continues through the Stoic and mediaeval (including Arabic) traditions, and then moves to the early modern period with particular attention to Locke and Leibniz. The views of Kant, Peirce, C. I. Lewis and Carnap complete the volume. Many of the essays illuminate the connection between the historical figures studied, and recent or current work in the philosophy of modality. The result is a rich and wide-ranging picture of the history of the logical modalities.

People tend to rank values of all kinds linearly from good to bad, but there is little reason to think that this is reasonable or correct. This book argues, to the contrary, that values are often partially ordered and hence frequently incomparable. Proceeding logically from a small set of axioms, John Nolt examines the great variety of partially ordered value structures, exposing fallacies that arise from overlooking them. He reveals various ways in which incomparability is obscured: using linear indices to summarize partially ordered data, relying on an inadequately defined concept of parity, or conflating incomparability with vagueness. Incomparability can enrich and clarify a range of topics including the paradoxes of Derek Parfit, rational decision theory, and the infinite values of theology. Finally, Nolt shows how to generalize many of the concepts introduced earlier, explores the intricate depths of certain noteworthy partially ordered value structures, and argues for the finitude of value. Incomparable Values will be of interest to scholars and advanced students working in ethics, value theory, rational decision theory, and logic.

This book is about the idea that some true statements would have been true no matter how the world had turned out, while others could have been false. It develops and defends a version of the idea that we tell the difference between these two types of truths in part by reflecting on the meanings of words. It has often been thought that modal issues-issues about possibility and necessity-are related to issues about meaning. In this book, the author defends the view that the analysis of meaning is not just a preliminary to answering modal questions in philosophy; it is not merely that before we can find out whether something is possible, we need to get clear on what we are talking about. Rather, clarity about meaning often brings with it answers to modal questions. In service of this view, the author analyzes the notion of necessity and develops ideas about linguistic meaning, applying them to several puzzles and problems in philosophy of language. Meaning and Metaphysical Necessity will be of interest to scholars and advanced students working in metaphysics, philosophy of language, and philosophical logic.