Bernard Bolzano (1781-1850) is increasingly recognized as one of the greatest nineteenth-century philosophers. A philosopher and mathematician of rare talent, he made ground-breaking contributions to logic, the foundations and philosophy of mathematics, metaphysics, and the philosophy of religion. Many of the larger features of later analytic philosophy (but also many of the details) first appear in his work: for example, the separation of logic from psychology, his sophisticated understanding of mathematical proof, his definition of logical consequence, his work on the semantics of natural kind terms, or his anticipations of Cantor's set theory, to name but a few. To his contemporaries, however, he was best known as an intelligent and determined advocate for reform of Church and State. Based in large part on a carefully argued utilitarian practical philosophy, he developed a program for the non-violent reform of the authoritarian institutions of the Hapsburg Empire, a program which he himself helped to set in motion through his teaching and other activities. Rarely has a philosopher had such a great impact on the political culture of his homeland. Persecuted in his lifetime by secular and ecclesiastical authorities, long ignored or misunderstood by philosophers, Bolzano's reputation has nevertheless steadily increased over the past century and a half. Much discussed and respected in Central Europe for over a century, he is finally beginning to receive the recognition he deserves in the English-speaking world. This book provides a comprehensive and detailed critical introduction to Bolzano, covering both his life and works.

Bertrand Russell, (1872 - 1970) was a British philosopher, logician, mathematician, historian, and social critic. Russell's books are excellent for those who have no experience of reading philosophy. This volume contains many of his most notable works: The Problems with Philosophy, The Analysis of the Mind, Mysticism and Logic and other Essays, Political Ideals, The Problem of China, The Practice and Theory of Bolshevism, Proposed Roads to Freedom, Our Knowledge of the External World as a Field for Scientific Method in Philosophy

The first critical work to attempt the mammoth undertaking of reading Badiou's Being and Event as part of a sequence has often surprising, occasionally controversial results. Looking back on its publication Badiou declared: "I had inscribed my name in the history of philosophy". Later he was brave enough to admit that this inscription needed correction. The central elements of Badiou's philosophy only make sense when Being and Event is read through the corrective prism of its sequel, Logics of Worlds, published nearly twenty years later. At the same time as presenting the only complete overview of Badiou's philosophical project, this book is also the first to draw out the central component of Badiou's ontology: indifference. Concentrating on its use across the core elements Being and Event-the void, the multiple, the set and the event-Watkin demonstrates that no account of Badiou's ontology is complete unless it accepts that Badiou's philosophy is primarily a presentation of indifferent being. Badiou and Indifferent Being provides a detailed and lively section by section reading of Badiou's foundational work. It is a seminal source text for all Badiou readers.

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration
Serves as a singular contribution to the intellectual history of the 20th centuryContains the latest scholarly discoveries and interpretative insights

Material objects persist through time and survive change. How do they manage to do so? What are the underlying facts of persistence? Do objects persist by being "wholly present" at all moments of time at which they exist? Or do they persist by having distinct "temporal segments" confined to the corresponding times? Are objects three-dimensional entities extended in space, but not in time? Or are they four-dimensional spacetime "worms"? These are matters of intense debate, which is now driven by concerns about two major issues in fundamental ontology: parthood and location. It is in this context that broadly empirical considerations are increasingly brought to bear on the debate about persistence.
Persistence and Spacetime pursues this empirically based approach to the questions. Yuri Balashov begins by setting out major rival views of persistence -- endurance, perdurance, and exdurance -- in a spacetime framework and proceeds to investigate the implications of Einstein's theory of relativity for the debate about persistence. His overall conclusion -- that relativistic considerations favour four-dimensionalism over three-dimensionalism -- is hardly surprising. It is, however, anything but trivial. Contrary to a common misconception, there is no straightforward argument from relativity to four-dimensionalism. The issues involved are complex, and the debate is closely entangled with a number of other philosophical disputes, including those about the nature and ontology of time, parts and wholes, material constitution, causation and properties, and vagueness.

To clarify and facilitate our inquiries we need to define a disquotational truth predicate that we are directly licensed to apply not only to our own sentences as we use them now, but also to other speakers' sentences and our own sentences as we used them in the past. The conventional wisdom is that there can be no such truth predicate. For it appears that the only instances of the disquotational pattern that we are directly licensed to accept are those that define "is true" for our own sentences as we use them now. Gary Ebbs shows that this appearance is illusory. He constructs an account of words that licenses us to rely not only on formal (spelling-based) identifications of our own words, but also on our non-deliberative practical identifications of other speakers' words and of our own words as we used them in the past. To overturn the conventional wisdom about disquotational truth, Ebbs argues, we need only combine this account of words with our disquotational definitions of truth for sentences as we use them now. The result radically transforms our understanding of truth and related topics, including anti-individualism, self-knowledge, and the intersubjectivity of logic.

'You shouldn't drink too much. The Earth is round. Milk is good for your bones.' Are any of these claims true? How can you tell? Can you ever be certain you are right? For anyone tackling philosophical logic and critical thinking for the first time, Critical Thinking: An Introduction to Reasoning Well provides a practical guide to the skills required to think critically. From the basics of good reasoning to the difference between claims, evidence and arguments, Robert Arp and Jamie Carlin Watson cover the topics found in an introductory course. Now revised and fully updated, this Second Edition features a glossary, chapter summaries, more student-friendly exercises, study questions, diagrams, and suggestions for further reading. Topics include: the structure, formation, analysis and recognition of arguments deductive validity and soundness inductive strength and cogency inference to the best explanation truth tables tools for argument assessment informal and formal fallacies With real life examples, advice on graduate school entrance exams and an expanded companion website packed with additional exercises, an answer key and help with real life examples, this easy-to-follow introduction is a complete beginner's tool set to good reasoning, analyzing and arguing. Ideal for students in basic reasoning courses and students preparing for graduate school.

The book is a collection of the author's selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields.

This volume of newly written chapters on the history and interpretation of Wittgenstein's Tractatus represents a significant step beyond the polemical debate between broad interpretive approaches that has recently characterized the field. Some of the contributors might count their approach as 'new' or 'resolute', while others are more 'traditional', but all are here concerned primarily with understanding in detail the structure of argument that Wittgenstein presents within the Tractatus, rather than with its final self-renunciation, or with the character of the understanding that renunciation might leave behind. The volume makes a strong case that close investigation, both biographical and textual, into the composition of the Tractatus, and into the various influences on it, still has much to yield in revealing the complexity and fertility of Wittgenstein's early thought. Amongst these influences Kant and Kierkegaard are considered alongside Wittgenstein's immediate predecessors in the analytic tradition. The themes explored range across the breadth of Wittgenstein's book, and include his accounts of ethics and aesthetics, as well as issues in metaphysics and the philosophy of mind, and aspects of the logical framework of his account of representation. The contrast of saying and showing, and Wittgenstein's attitude to the inexpressible, is of central importance to many of the contributions. By approaching this concern through the various first-level issues that give rise to it, rather than from entrenched schematic positions, the contributors demonstrate the possibility of a more inclusive, constructive and fruitful mode of engagement with Wittgenstein's text and with each other.