Aristotle's Topics is a handbook for dialectic, which can be understood as a philosophical debate between a questioner and a respondent. In book 2, Aristotle mainly develops strategies for making deductions about 'accidents', which are properties that might or might not belong to a subject (for instance, Socrates has five fingers, but might have had six), and about properties that simply belong to a subject without further specification. In the present commentary, here translated into English for the first time, Alexander develops a careful study of Aristotle's text. He preserves objections and replies from other philosophers whose work is now lost, such as the Stoics. He also offers an invaluable picture of the tradition of Aristotelian logic down to his time, including innovative attempts to unify Aristotle's guidance for dialectic with his general theory of deductive argument (the syllogism), found in the Analytics. The work will be of interest not only for its perspective on ancient logic, rhetoric, and debate, but also for its continuing influence on argument in the Middle Ages and later.

Alain Badiou's Being and Event continues to impact philosophical investigations into the question of Being. By exploring the central role set theory plays in this influential work, Burhanuddin Baki presents the first extended study of Badiou's use of mathematics in Being and Event. Adopting a clear, straightforward approach, Baki gathers together and explains the technical details of the relevant high-level mathematics in Being and Event. He examines Badiou's philosophical framework in close detail, showing exactly how it is 'conditioned' by the technical mathematics. Clarifying the relevant details of Badiou's mathematics, Baki looks at the four core topics Badiou employs from set theory: the formal axiomatic system of ZFC; cardinal and ordinal numbers; Kurt Goedel's concept of constructability; and Cohen's technique of forcing. Baki then rebuilds Badiou's philosophical meditations in relation to their conditioning by the mathematics, paying particular attention to Cohen's forcing, which informs Badiou's analysis of the event. Providing valuable insights into Badiou's philosophy of mathematics, Badiou's Being and Event and the Mathematics of Set Theory offers an excellent commentary and a new reading of Badiou's most complex and important work.

This volume is a result of the international symposium "The Tradition of the Lvov-Warsaw School in European Culture," which took place in Warsaw, Poland, September 2015. It collects almost all the papers presented at the symposium as well as some additional ones. The contributors include scholars from Austria, the Netherlands, Ireland, and Poland. The papers are devoted to the history and reception of the Lvov-Warsaw School, a Polish branch of analytic philosophy. They present the School's achievements as well as its connections to other analytic groups. The contributors also show how the tradition of the School is developed contemporarily. The title will appeal to historians of analytic philosophy as well as historians of philosophy in Central Europe.

Saul Kripke's Naming and Necessity was one of the most influential philosophical works of the twentieth century. In this collection of essays leading specialists explore issues arising from this and other works of Kripke's.

This book explores what it means to be 'critical' in different disciplines in higher education and how students can be taught to be effective critical thinkers. This book clarifies the idea of critical thinking by investigating the 'critical' practices of academics across a range of disciplines. Drawing on key theorists - Wittgenstein, Geertz, Williams, Halliday - and using a 'textographic' approach, the book explores how the concept of critical thinking is understood by academics and also how it is constructed discursively in the texts and practices they employ in their teaching. Critical thinking is one of the most widely discussed concepts in debates on university learning. For many, the idea of teaching students to be critical thinkers characterizes more than anything else the overriding purpose of 'higher education'. But whilst there is general agreement about its importance as an educational ideal, there is surprisingly little agreement about what the concept means exactly. Also at issue is how and what students need to be taught in order to be properly critical in their field. This searching monograph seeks answers to these important questions.

Despite the resurgence of interest in the philosophy of John Dewey, his work on logical theory has received relatively little attention. Ironically, Dewey's logic was his "first and last love." The essays in this collection pay tribute to that love by addressing Dewey's philosophy of logic, from his work at the beginning of the twentieth century to the culmination of his logical thought in the 1938 volume, "Logic: The Theory of Inquiry." All the essays are original to this volume and are written by leading Dewey scholars. Ranging from discussions of propositional theory to logic's social and ethical implications, these essays clarify often misunderstood or misrepresented aspects of Dewey's work, while emphasizing the seminal role of logic to Dewey's philosophical endeavors.

This collection breaks new ground in its relevance to contemporary philosophy of logic and epistemology and pays special attention to applications in ethics and moral philosophy.

Since the middle of the 20th century Ludwig Wittgenstein has been an exceptionally influential and controversial figure wherever philosophy is studied. This is the most comprehensive volume ever published on Wittgenstein: thirty-five leading scholars explore the whole range of his thought, offering critical engagement and original interpretation, and tracing his philosophical development. Topics discussed include logic and mathematics, language and mind, epistemology, philosophical methodology, religion, ethics, and aesthetics. Wittgenstein's relation to other founders of analytic philosophy such as Gottlob Frege, Bertrand Russell, and G. E. Moore is explored. This Handbook is the place to look for a full understanding of Wittgenstein's special importance to modern philosophy.

Writing on the justification of certain inductive inferences, the author proposes that sometimes induction is justified and that arguments to prove otherwise are not cogent. In the first part he examines the problem of justifying induction, looks at some attempts to prove that it is justified, and responds to criticisms of these proofs. In the second part he deals with such topics as formal logic, deductive logic, the theory of logical probability, and probability and truth.

This book presents adaptive logics as an intuitive and powerful framework for modeling defeasible reasoning. It examines various contexts in which defeasible reasoning is useful and offers a compact introduction into adaptive logics. The author first familiarizes readers with defeasible reasoning, the adaptive logics framework, combinations of adaptive logics, and a range of useful meta-theoretic properties. He then offers a systematic study of adaptive logics based on various applications. The book presents formal models for defeasible reasoning stemming from different contexts, such as default reasoning, argumentation, and normative reasoning. It highlights various meta-theoretic advantages of adaptive logics over other logics or logical frameworks that model defeasible reasoning. In this way the book substantiates the status of adaptive logics as a generic formal framework for defeasible reasoning.

This volume provides a comprehensive collection of classic and contemporary readings in the philosophy of logic. The selections include some of the most important, technically exact, yet lucid and readable expositions of central concepts and controversies in philosophical logic. Areas of coverage include classical logic, truth, propositions and meaning, quantifiers and quantificational theory, validity, inference and entailment, and modality, intensionality and propositional attitude.

Since the articles are written from a variety of perspectives, the reader is able to critically assess the background and current trends in philosophical applications of symbolic logic. The volume also examines the limitations of classical and nonstandard logics.

The book complements "Philosophy of Mathematics: An Anthology" and "A Companion to Philosophical Logic, "also edited by Dale Jacquette.

This new digital edition of The Trial and Death of Socrates: Euthyphro, Apology, Crito and Phaedo presents Benjamin Jowett's classic translations, as revised by Enhanced Media Publishing. A number of new or expanded annotations are also included.

This is an important collection of new essays on various topics relating to realism and its rivals in metaphysics, logic, metaethics, and epistemology. The contributors include some of the leading authors in these fields and in several cases their essays constitute definitive statements of their views. Although not primarily historical this volume includes discussion of philosophers from the Middle Ages to the present day, from Aquinas to Wittgenstein. No one seriously interested in questions about realism can afford to be without this collection.

Is critical argumentation an effective way to overcome disagreement? And does the exchange of arguments bring opponents in a controversy closer to the truth? This study provides a new perspective on these pivotal questions. By means of multi-agent simulations, it investigates the truth and consensus-conduciveness of controversial debates. The book brings together research in formal epistemology and argumentation theory. Aside from its consequences for discursive practice, the work may have important implications for philosophy of science and the way we construe scientific rationality as well.

This monograph examines truth in fiction by applying the techniques of a naturalized logic of human cognitive practices. The author structures his project around two focal questions. What would it take to write a book about truth in literary discourse with reasonable promise of getting it right? What would it take to write a book about truth in fiction as true to the facts of lived literary experience as objectivity allows? It is argued that the most semantically distinctive feature of the sentences of fiction is that they areunambiguously true and false together. It is true that Sherlock Holmes lived at 221B Baker Street and also concurrently false that he did. A second distinctive feature of fiction is that the reader at large knows of this inconsistency and isn't in the least cognitively molested by it. Why, it is asked, would this be so? What would explain it? Two answers are developed. According to the no-contradiction thesis, the semantically tangled sentences of fiction are indeed logically inconsistent but not logically contradictory. According to the no-bother thesis, if the inconsistencies of fiction were contradictory, a properly contrived logic for the rational management of inconsistency would explain why readers at large are not thrown off cognitive stride by their embrace of those contradictions. As developed here, the account of fiction suggests the presence of an underlying three - or four-valued dialethic logic. The author shows this to be a mistaken impression. There are only two truth-values in his logic of fiction. The naturalized logic of Truth in Fiction jettisons some of the standard assumptions and analytical tools of contemporary philosophy, chiefly because the neurotypical linguistic and cognitive behaviour of humanity at large is at variance with them. Using the resources of a causal response epistemology in tandem with the naturalized logic, the theory produced here is data-driven, empirically sensitive, and open to a circumspect collaboration with the empirical sciences of language and cognition.

How science can convey a profound sense of wonder, connectedness, and optimism about the human condition.
This book makes a compelling case that now more than ever the public at large needs to appreciate the critical-thinking tools that science has to offer and be educated in basic science literacy. The author emphasizes that the methods and facts of science are accessible to everyone, and that, contrary to popular belief, understanding science does not require extraordinary intelligence. He also notes that scientific rationality and critical thinking are not only good for our physical well-being but also are fully in sync with our highest moral codes. He illustrates the many ways in which the scientific worldview offers a profound sense of wonder, connectedness, and optimism about the human condition, an inspiring perspective that satisfies age-old spiritual aspirations.
At a time of daunting environmental challenges and rampant misinformation, this book provides a welcome corrective and reason to hope for the future.

One hundred years ago, Russell and Whitehead published their epoch-making Principia Mathematica (PM), which was initially conceived as the second volume of Russell's Principles of Mathematics (PoM) that had appeared ten years before. No other works can be credited to have had such an impact on the development of logic and on philosophy in the twentieth century. However, until now, scholars only focused on the first parts of the books - that is, on Russell's and Whitehead's theory of logic, set-theory and arithmetic.
Sebastien Gandon aims at reversing the perspective. His goal is to give a picture of Russell's logicism based on a detailed reading of the developments dealing with advanced mathematics - namely projective geometry and the theory of quantity. This book is not only the first study ever made of the 'later' portions of PoM and PM, it also shows how this shift of perspective compels us to change our view of the logicist program taken as a whole.

Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance. This framework allows for sentences whose truth-conditions are not representational, which are made true or false by conditions residing in the circumstances of utterances but not transparently in the sense.
Applications to projectivism and fiction pave the way for the claim that mathematical utterances are made true or false by the existence of concrete proofs or refutations, though these truth-making conditions form no part of their sense or informational content.
The position is compared with rivals, an account of the applicability of mathematics developed, and a new account of the nature of idealisation proffered in which it is argued that the finitistic limitations Godel placed on proofs are without rational justification. Finally a non-classical logical system is provided in which excluded middle fails, yet enough logical power remains to recapture the results of standard mathematics.

This book presents the current state of the art regarding the application of logical tools to the problems of theory and practice of lawmaking. It shows how contemporary logic may be useful in the analysis of legislation, legislative drafting and legal reasoning concerning different contexts of law making. Elaborations of the process of law making have variously emphasised its political, social or economic aspects. Yet despite strong interest in logical analyses of law, questions remains about the role of logical tools in law making. This volume attempts to bridge that gap, or at least to narrow it, drawing together some important research problems-and some possible solutions-as seen through the work of leading contemporary academics. The volume encompasses 20 chapters written by authors from 16 countries and it presents diversified views on the understanding of logic (from strict mathematical approaches to the informal, argumentative ones) and differentiated choices concerning the aspects of law making taken into account. The book presents a broad set of perspectives, insights and results into the emerging field of research devoted to the logical analysis of the area of creation of law. How does logic inform lawmaking? Are legal systems consistent and complete? How can legal rules be represented by means of formal calculi and visualization techniques? Does the structure of statutes or of legal systems resemble the structure of deductive systems? What are the logical relations between the basic concepts of jurisprudence that constitute the system of law? How are theories of legal interpretation relevant to the process of legislation? How might the statutory text be analysed by means of contemporary computer programs? These and other questions, ranging from the theoretical to the immediately practical, are addressed in this definitive collection.

In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes "the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined"; in another fragment he takes the mathesis to be "the science of all things that are conceivable." Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between "arbitrary objects" ("objets quelconques"). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the "reasons" ("Grunde") of others, and the latter are "consequences" ("Folgen") of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.