Kurt Gödel (1906-1978) was the most outstanding logician of the twentieth century. This second volume of a comprehensive edition of Gödel's works collects the remainder of his published work, covering the period 1938-1974. (Volume I included all of his publications from 1929-1936). Each article or closely related group of articles is preceded by an introductory note that elucidates it and places it in historical context. The aim is to make the full body of Gödel's work as accessible and useful to as wide an audience as possible, without in any way sacrificing the requirements of historical and scientific accuracy.

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

Newton's bucket, Einstein's elevator, SchrAdinger's cat a " these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking?

In this revised and updated new edition of his classic text The Laboratory of the Mind, James Robert Brown continues to defend apriorism in the physical world. This edition features two new chapters, one on a oecounter thought experimentsa and another on the development of inertial motion. With plenty of illustrations and updated coverage of the debate between Platonic rationalism and classic empiricism, this is a lively and engaging contribution to the field of philosophy of science.

Newton's bucket, Einstein's elevator, SchrAdinger's cat a " these are some of the best-known examples of thought experiments in the natural sciences. But what function do these experiments perform? Are they really experiments at all? Can they help us gain a greater understanding of the natural world? How is it possible that we can learn new things just by thinking?

In this revised and updated new edition of his classic text The Laboratory of the Mind, James Robert Brown continues to defend apriorism in the physical world. This edition features two new chapters, one on a oecounter thought experimentsa and another on the development of inertial motion. With plenty of illustrations and updated coverage of the debate between Platonic rationalism and classic empiricism, this is a lively and engaging contribution to the field of philosophy of science.

The A to Z of Logic introduces the central concepts of the field in a series of brief, non-technical, cross-referenced dictionary entries. The 352 alphabetically arranged entries give a clear, basic introduction to a very broad range of logical topics. Entries can be found on deductive systems, such as propositional logic, modal logic, deontic logic, temporal logic, set theory, many-valued logic, mereology, and paraconsistent logic. Similarly, there are entries on topics relating to those previously mentioned such as negation, conditionals, truth tables, and proofs. Historical periods and figures are also covered, including ancient logic, medieval logic, Buddhist logic, Aristotle, Ockham, Boole, Frege, Russell, Goedel, and Quine. There are even entries relating logic to other areas and topics, like biology, computers, ethics, gender, God, psychology, metaphysics, abstract entities, algorithms, the ad hominem fallacy, inductive logic, informal logic, the liar paradox, metalogic, philosophy of logic, and software for learning logic. In addition to the dictionary, there is a substantial chronology listing the main events in the history of logic, an introduction that sketches the central ideas of logic and how it has evolved into what it is today, and an extensive bibliography of related readings. This book is not only useful for specialists but also understandable to students and other beginners in the field.

Timothy Smiley has made ground-breaking contributions to modal logic, free logic, multiple-conclusion logic, and plural logic. He has illuminated Aristotlea (TM)s syllogistic, the ideas of logical form and consequence, and the distinction between assertion and rejection, and has worked to debunk the theory of descriptions. This volume brings together new articles by an international roster of leading logicians and philosophers in order to honour Smileya (TM)s work. Their essays will be of significant interest to those working across the logical spectruma "in philosophy of language, philosophical and mathematical logic, and philosophy of mathematics.

First Published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

Reading Wittgenstein's Philosophical Investigations: A Beginners Guide is written for anyone who faces the challenge of reading Philosophical Investigations. John J. Ross guides the reader slowly through each relevant section of text, explaining and elaborating key ideas, and providing the philosophical and biographical background that illuminates the problems Wittgenstein is addressing. Reading Wittgenstein's Philosophical Investigations is designed to be used in the examination of the Investigations as a whole or in part; the reader can focus solely on Mathematics or Psychology, if needed. While Ross does address some of the philosophical controversies surrounding Wittgenstein's ideas, the discussions are appropriate for an undergraduate, so the book can be used fruitfully by anyone with that level of education who has an interest in Wittgenstein's seminal work.

Reading Wittgenstein's Philosophical Investigations: A Beginners Guide is written for anyone who faces the challenge of reading Philosophical Investigations. John J. Ross guides the reader slowly through each relevant section of text, explaining and elaborating key ideas, and providing the philosophical and biographical background that illuminates the problems Wittgenstein is addressing. Reading Wittgenstein's Philosophical Investigations is designed to be used in the examination of the Investigations as a whole or in part; the reader can focus solely on Mathematics or Psychology, if needed. While Ross does address some of the philosophical controversies surrounding Wittgenstein's ideas, the discussions are appropriate for an undergraduate, so the book can be used fruitfully by anyone with that level of education who has an interest in Wittgenstein's seminal work.

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission.

The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission.

From alcohol and drug addiction to rage on national highways and in airports, many human beings have kept themselves in perpetual turmoil and despair. From encroachment on individual rights and liberties to wars of attrition and mass genocide, human history has continually repeated itself due to a failure to see the light. Containing numerous skill-building exercises, Critical Thinking Unleashed seeks to cultivate the reasoning skills required to overcome such destructive human tendencies and to live meaningful and productive lives in a democratic society. In contrast to other treatments of practical reasoning, Elliot D. Cohen not only teaches students how to identify and refute irrational premises he also teaches them how to construct rational antidotes to combat the personal, social, and political obstacles they confront in everyday life. Moreover, Cohen encourages students to use the theories and ideas embodied in the history of philosophy in order to construct these rational guides, drawing examples from many contemporary sources. Demonstrating the practical relevance and import of many historically significant philosophers (e.g. Socrates, Aristotle, Epictetus, Hume, Kant, Mill, Sartre, and Nietzsche), the book presents a practical, non-technical, and comprehensive approach to critical thinking."

From alcohol and drug addiction to rage on national highways and in airports, many human beings have kept themselves in perpetual turmoil and despair. From encroachment on individual rights and liberties to wars of attrition and mass genocide, human history has continually repeated itself due to a failure to see the light. Containing numerous skill-building exercises, Critical Thinking Unleashed seeks to cultivate the reasoning skills required to overcome such destructive human tendencies and to live meaningful and productive lives in a democratic society. In contrast to other treatments of practical reasoning, Elliot D. Cohen not only teaches students how to identify and refute irrational premises_he also teaches them how to construct rational antidotes to combat the personal, social, and political obstacles they confront in everyday life. Moreover, Cohen encourages students to use the theories and ideas embodied in the history of philosophy in order to construct these rational guides, drawing examples from many contemporary sources. Demonstrating the practical relevance and import of many historically significant philosophers (e.g. Socrates, Aristotle, Epictetus, Hume, Kant, Mill, Sartre, and Nietzsche), the book presents a practical, non-technical, and comprehensive approach to critical thinking.

In her innovative take on G.W. F. Hegel's The Encyclopaedia Logic, Julie E. Maybee uses pictures and diagrams to cut through the philosopher's dense, difficult writing. Picturing Hegel: An Illustrated Guide to Hegel's Encyclopaedia Logic utilizes diagrams in order to rehabilitate Hegel's logic for serious consideration by showing how each stage develops step-by-step from earlier stages according to definite, logical patterns. This interpretation makes Hegel's work accessible and understandable for new and experienced readers alike. Because Hegel uses the same logic in all of his works, Maybee's analysis and defense of the logic will capture the attention of those readers interested in Hegel's ethics, politics, history, philosophy of religion, and phenomenology. Through the included diagrams, Maybee is able to define central Hegelian concepts such as "being-in-itself," and "being-in-and-for-itself" with a new level of precision. Maybee argues that Hegel's logic does not include the one logistical pattern most often attributed to him; namely, the pattern "thesis-antithesis-synthesis." Rather, Hegel's model of logic was more scientific than formalistic in nature, as the philosopher himself pointed out. Hegel considered himself an encyclopedic culmination of Western philosophy in some ways, and indeed his work summarizes many of the presuppositions of Western philosophy. By picturing Hegel's logic, we can gain a greater understanding of ourselves.

In her innovative take on G.W. F. Hegel's The Encyclopaedia Logic, Julie E. Maybee uses pictures and diagrams to cut through the philosopher's dense, difficult writing. Picturing Hegel: An Illustrated Guide to Hegel's Encyclopaedia Logic utilizes diagrams in order to rehabilitate Hegel's logic for serious consideration by showing how each stage develops step-by-step from earlier stages according to definite, logical patterns. This interpretation makes Hegel's work accessible and understandable for new and experienced readers alike. Because Hegel uses the same logic in all of his works, Maybee's analysis and defense of the logic will capture the attention of those readers interested in Hegel's ethics, politics, history, philosophy of religion, and phenomenology. Through the included diagrams, Maybee is able to define central Hegelian concepts such as 'being-in-itself, ' and 'being-in-and-for-itself' with a new level of precision. Maybee argues that Hegel's logic does not include the one logistical pattern most often attributed to him; namely, the pattern 'thesis-antithesis-synthesis.' Rather, Hegel's model of logic was more scientific than formalistic in nature, as the philosopher himself pointed out. Hegel considered himself an encyclopedic culmination of Western philosophy in some ways, and indeed his work summarizes many of the presuppositions of Western philosophy. By picturing Hegel's logic, we can gain a greater understanding of ourselves.

We see the face of the Virgin Mary staring up at us from a grilled cheese sandwich and sell the uneaten portion of our meal for $37,000 on eBay. While science offers a wealth of rational explanations for natural phenomena, we often prefer to embrace the fantasies that reassured our distant ancestors. And we'll even go to war to protect our delusions against those who do not share them.
These are examples of what evolutionary psychologist Hank Davis calls "Caveman Logic." Although some examples are funny, the condition itself is no laughing matter. In this engagingly written book, Davis encourages us to transcend the mental default settings and tribal loyalties that worked well for our ancestors back in the Pleistocene age. Davis laments a modern world in which more people believe in ESP, ghosts, and angels than in evolution. Superstition and religion get particularly critical treatment, although Davis argues that religion, itself, is not the problem but "an inevitable by-product of how our minds misperform."
Davis argues, "It's time to move beyond the one-size-fits-all, safety and comfort-oriented settings that got our ancestors through the terrifying Pleistocene night." In contrast, Davis advocates a world in which "spirituality" is viewed as a dangerous rather than an admirable quality, and suggests ways in which we can overcome our innate predisposition toward irrationality. He concludes by pointing out that "biology is not destiny." Just as some of us succeed in watching our diets, resisting violent impulses, and engaging in unselfish behavior, we can learn to use critical thinking and the insights of science to guide individual effort and social action in the service of our whole species.

"Oh, no, not another philosophy book " After twenty-six centuries of reflecting and writing, what can be said about philosophy that hasn't already been said? This book is different because it is written for students who are not interested in philosophy or who are struggling to understand it. Professor Malikow makes it easy to understand the sophisticated ideas and profound truths of philosophy by his use of everyday language, analogies, examples, and stories mixed with a bit of humor.

Sword of Philosophy attempts to address some of the fundamental questions in philosophy. Beginning with the problem of our conceptions of the outside world and reality itself, it moves into an application of these issues to our experiences of the world and the consequential scientific systems we create. The problem of the nature of values and ethics are considered, and the applications of these problems to society are delineated. The nature of logic and mathematics are considered, with a focus on the incompleteness, model theory, and the differing approaches of formalism and realism. The nature of God is also considered.

This work is an introduction to informal and formal logic. It covers what is usually taught in the first term of a two-term sequence in logic at community colleges and at four-year colleges and universities. Following treatment of the nature of argument, this book distinguishes induction from deduction. The book then covers how to fill out argument fragments (or enthymemes) and how to recognize, as well as how to avoid constructing, deceptive or mistaken arguments (informal fallacies). Aristotle's class logic is canvassed, specifying rules for constructing valid arguments, and identifying formal fallacies committed when these rules are broken. Boole's modifications of class logic and the formal system are also introduced. Under the heading of the formal system, truth trees, the truth table method for determining validity, and finally, proof construction are all covered. The section on proof construction walks students through the process of building a demonstration in logic.

After Plato's Forms, and Aristotle's substances, the Stoics posited the fundamental reality of lekta - the meanings of sentences, distinct from the sentences themselves. This is the first time in the tradition of Western philosophy that what is signified is properly distinguished from signs and signifiers. The Stoics on Lekta offers a synoptic treatment of the many implications of this distinction, which grants an existential autonomy to lekta: language can only ever express meanings, but what happens to meanings which are there, ready to be said, but which are never actually expressed? It analyses the deep shift in ontological paradigm required by the presence of lekta in reality, and reveals a truly unique, complex, and consistent cosmic view in which lekta are the keystones of the structure of reality. According to this view, we cannot not speak or think in terms of lekta, and for this reason, they are in fact all there is to say. The Stoics' position ignited many fiery debates in antiquity and continues to do so in the modern era: they were the first to be concerned with questions about language and grammar, and the first to put the relation of language to reality at the heart of the enquiry into human understanding and the place of man in the cosmos. Such questions remain central to life and philosophy to this day, and by explicitly comparing and contrasting the themes and topics discussed to twentieth-century treatments of the status of the proposition, propositional structure, speech act theory, and the relation of attribution of the predicate to a subject-term, this volume seeks to demonstrate the enduring value of a direct Stoic contribution to the contemporary debate.

Naturalism, Reference, and Ontology is a collection of twelve original essays honoring Roger F. Gibson, who has been a leading proponent and defender of W. V. Quine's philosophy for nearly thirty years. The essays address a wide range of topics, including normativity and naturalized epistemology, holism, consciousness, the philosophy of logic, perception, value theory, and the arts. The contributors are an international group of prominent philosophers as well as rising scholars including: Robert Barrett, Lars Bergstrom, Richard Creath, David Henderson, Terence Horgan, Ernest Lepore, Pete Mandik, Alex Orenstein, Kenneth Shockley, J. Robert Thompson, Josefa Toribio, Joseph Ullian, Josh Weisberg, and Chase B. Wrenn.

The topic of vagueness re-emerged in the twentieth century from relative obscurity. It deals with the phenomenon in natural language that manifests itself in apparent semantic indeterminacy - the indeterminacy, for example, that arises when asked to draw the line between the tall and non-tall, or the drunk and the sober. An associated paradox emphasises the challenging nature of the phenomenon, presenting one of the most resilient paradoxes of logic. The apparent threat posed for orthodox theories of the semantics and logic of natural language has become the focus of intense philosophical scrutiny amongst philosophers and non-philosophers alike. Vagueness, Logic and Ontology explores various responses to the philosophical problems generated by vagueness and its associated paradox - the sorites paradox. Hyde argues that the theoretical space in which vagueness is sometimes ontologically grounded and modelled by a truth-functional logic affords a coherent response to the problems posed by vagueness. Showing how the concept of vagueness can be applied to the world, Hyde's ontological account proposes a substantial revision of orthodox semantics, metaphysics and logic. This book will be of particular interest to readers in philosophy, linguistics, cognitive science and geographic information systems.

First published in 1998, Loughlin examines the conception of rationality through the gazes of science, philosophy and political philosophy to further explain the concept of rational reasoning, the effects it has on the development on natural and social science and its implications on how we think about morals and politics.

Just as The Elements of Style provides a quick and authoritative reference for writers, The Rowman & Littlefield Handbook for Critical Thinking provides a quick and authoritative reference for issues regarding reasoning. The Handbook provides clear and succinct discussions of the following issues: * Issues germane to clarifying sentences: ambiguity, vagueness, and propositional attitudes * General discussions of descriptions, explanations, and arguments * Criteria for evaluating observational statements and testimony * Categorical syllogisms, including issues germane to both the Boolean and Aristotelian interpretations * A complete system of propositional logic and a brief discussion of the use of truth tables * Induction: generalization and particularization arguments, analogies, arguments to the best explanation, Mill's Methods, counterfactual reasoning, and making decisions under risk and uncertainty * A brief discussion of the principle formulas involved in calculating probabilities * An extended discussion of informal fallacies * An essay on the relationship between critical thinking and writing