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.

There is, first of all, the distinction between that part of our belief which is rational and that part which is not. If a man believes something for a reason which is preposterous or for no reason at all, and what he believes turns out to be true for some reason not known to him, he cannot be said to believe it rationally, although he believes it and it is in fact true. On the other hand, a man may rationally believe a proposition to be probable, when it is in fact false. -from Chapter II: Probability in Relation to the Theory of Knowledge" His fame as an economist aside, John Maynard Keynes may be best remembered for saying, "In the long run, we are all dead." That phrase may well be the most succinct expression of the theory of probability every uttered. For a longer explanation of the premise that underlies much of modern mathematics and science, Keynes's A Treatise on Probability is essential reading. First published in 1920, this is the foundational work of probability theory, which helped establish the author's enormous influence on modern economic and even political theories. Exploring aspects of randomness and chance, inductive reasoning and logical statistics, this is a work that belongs in the library of any interested in numbers and their application in the real world. AUTHOR BIO: British economist JOHN MAYNARD KEYNES (1883-1946) also wrote The Economic Consequences of the Peace (1919), The End of Laissez-Faire (1926), The Means to Prosperity (1933), and General Theory of Employment, Interest and Money (1936).

Taking students beyond classical mathematical logic, Philosophical Logic is a wide-ranging introduction to more advanced topics in the study of philosophical logic.

Starting by contrasting familiar classical logic with constructivist or intuitionist logic, the book goes on to offer concise but easy-to-read introductions to such subjects as quantificational and syllogistic logic, modal logic and set theory.

Chapters include:

- Sentential Logic- Quantificational Logic- Sentential Modal Logic- Quantification and Modality- Set Theory- Incompleteness- An Introduction to Term Logic- Modal Term Logic

In addition, the book includes a list of symbols and a glossary of terms for ease of reference and exercises throughout help students master the topics covered in the book. Philosophical Logic is an essential, student-friendly guide for anyone studying these difficult topics as part of their Logic course.

'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.

This edited book focuses on concepts and their applications using the theory of conceptual spaces, one of today's most central tracks of cognitive science discourse. It features 15 papers based on topics presented at the Conceptual Spaces @ Work 2016 conference. The contributors interweave both theory and applications in their papers. Among the first mentioned are studies on metatheories, logical and systemic implications of the theory, as well as relations between concepts and language. Examples of the latter include explanatory models of paradigm shifts and evolution in science as well as dilemmas and issues of health, ethics, and education. The theory of conceptual spaces overcomes many translational issues between academic theoretization and practical applications. The paradigm is mainly associated with structural explanations, such as categorization and meronomy. However, the community has also been relating it to relations, functions, and systems. The book presents work that provides a geometric model for the representation of human conceptual knowledge that bridges the symbolic and the sub-conceptual levels of representation. The model has already proven to have a broad range of applicability beyond cognitive science and even across a number of disciplines related to concepts and representation.

The Logic Manual is a clear and concise introduction to logic for beginning philosophy students. It offers a complete introductory course, guiding the reader carefully through the topics in logic that are most important for the study of philosophy. It covers propositional and predicate logic with and without identity. It includes an account of the semantics of these languages including definitions of truth and satisfaction. Natural deduction is used as a proof system. Volker Halbach introduces the essential concepts through examples and informal explanations as well as through abstract definitions.
The Logic Manual provides the best entry to the general abstract way of thinking about language, logic, and semantics which is characteristic of contemporary philosophy. Exercises, examples, and sample examination papers are provided on an accompanying website.

Our experience of objects (and consequently our theorizing about them) is very rich. We perceive objects as possessing individuation conditions. They appear to have boundaries in space and time, for example, and they appear to move independently of a background of other objects or a landscape. In Ontology Without Boundaries Jody Azzouni undertakes an analysis of our concept of object, and shows what about that notion is truly due to the world and what about it is a projection onto the world of our senses and thinking. Location and individuation conditions are our product: there is no echo of them in the world. Features, the ways that objects seem to be, aren't projections. Azzouni shows how the resulting austere metaphysics tames a host of ancient philosophical problems about constitution ("Ship of Theseus," "Sorities"), as well as contemporary puzzles about reductionism. In addition, it's shown that the same sorts of individuation conditions for properties, which philosophers use to distinguish between various kinds of odd abstracta-universals, tropes, and so on, are also projections. Accompanying our notion of an object is a background logic that makes cogent ontological debate about anything from Platonic objects to Bigfoot. Contemporary views about this background logic ("quantifier variance") make ontological debate incoherent. Azzouni shows how a neutral interpretation of quantifiers and quantifier domains makes sense of both philosophical and pre-philosophical ontological debates. Azzouni also shows how the same apparatus makes sense of our speaking about a host of items-Mickey Mouse, unicorns, Martians-that nearly all of us deny exist. It's allowed by what Azzouni shows about the background logic of our ontological debates, as well as the semantics of the language of those debates that we can disagree over the existence of things, like unicorns, without that background logic and semantics forcing ontological commitments onto speakers that they don't have.

Ascriptions of mental states to oneself and others give rise to many interesting logical and semantic problems. Attitude Problems presents an original account of mental state ascriptions that are made using intensional transitive verbs such as "want," "seek," "imagine," and "worship." Forbes offers a theory of how such verbs work that draws on ideas from natural language semantics, philosophy of language, and aesthetics.

Subtle Implications is a defining clarification of the human experience as presented in the story of the author's life, and expressed in his 'Theories of Everything. Through his unrelenting quest to understand and come to terms with life's wide variety of apparently random events, he developed a methodology we can use to analyze and understand the madness. At the very least, the author offers the opportunity to gain the insight and strength needed to cope with even the worst of life's emotionally crippling crises. What are the true natures of our physical and spiritual realities? How did our Universe begin? Why are we here? Why do bad things happen in our lives? What happens when we die? Do we live again? Life is not that complicated. Pertinent information and the proper perspective can help you see life as your own creation. You alone are responsible for the present state of every facet of your life. Together we are responsible for every aspect of the world that greets us every morning. Together we can create a world where a comfortable life is the rule and not the exception. It is all up to us

This book investigates a number of central problems in the philosophy of Charles Peirce grouped around the realism of his semiotics: the issue of how sign systems are developed and used in the investigation of reality. Thus, it deals with the precise character of Peirce's realism; with Peirce's special notion of propositions as signs which, at the same time, denote and describe the same object. It deals with diagrams as signs which depict more or less abstract states-of-affairs, facilitating reasoning about them; with assertions as public claims about the truth of propositions. It deals with iconicity in logic, the issue of self-control in reasoning, dependences between phenomena in their realist descriptions. A number of chapters deal with applied semiotics: with biosemiotic sign use among pre-human organisms: the multimedia combination of pictorial and linguistic information in human semiotic genres like cartoons, posters, poetry, monuments. All in all, the book makes a strong case for the actual relevance of Peirce's realist semiotics.

Between Saying and Doing aims to reconcile pragmatism (in both its classical American and its Wittgensteinian forms) with analytic philosophy. It investigates the relations between the meaning of linguistic expressions and their use. Giving due weight both to what one has to do in order to count as saying various things and to what one needs to say in order to specify those doings, makes it possible to shed new light on the relations between semantics (the theory of the meanings of utterances and the contents of thoughts) and pragmatics (the theory of the functional relations among meaningful or contentful items). Among the vocabularies whose interrelated use and meaning are considered are: logical, indexical, modal, normative, and intentional vocabulary. As the argument proceeds, new ways of thinking about the classic analytic core programs of empiricism, naturalism, and functionalism are offered, as well as novel insights about the ideas of artificial intelligence, the nature of logic, and intentional relations between subjects and objects.

The philosophy of modality investigates necessity and possibility, and related notions--are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This volume presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the papers address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal logic and its relations to necessary existence and to counterfactual reasoning. The general introduction locates the individual contributions in the wider context of the contemporary discussion of the metaphysics and epistemology of modality.

Wittgenstein's philosophical career began in 1911 when he went to Cambridge to work with Russell. He compiled the Notes on Logic two years later as a kind of summary of the work he had done so far. Russell thought that they were "as good as anything that has ever been done in logic," but he had Wittgenstein himself to explain them to him. Without the benefit of Wittgenstein's explanations, most later scholars have preferred to treat the Notes solely as an interpretative aid in understanding the Tractatus (which draws on them for material), rather than as a philosophical work in their own right.
Michael Potter unequivocally demonstrates the philosophical and historical importance of the Notes for the first time. By teasing out the meaning of key passages, he shows how many of the most important insights in the Tractatus they contain. He discusses in detail how Wittgenstein arrived at these insights by thinking through ideas he obtained from Russell and Frege. And he uses a challenging blend of biography and philosophy to illuminate the methods Wittgenstein used in his work.
The book features the complete text of the Notesi in a critical edition, with a detailed discussion of the circumstances in which they were compiled, leading to a new understanding of how they should be read.

This monograph proposes a new (dialogical) way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyas. According to the authors' view, qiyas represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general (including legal reasoning in Common and Civil Law) but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical reasoning studied in contemporary philosophy of science and argumentation theory. After an overview of the emergence of qiyas and of the work of al-Shirazi penned by Soufi Youcef, the authors discuss al-Shirazi's classification of correlational inferences of the occasioning factor (qiyas al-'illa). The second part of the volume deliberates on the system of correlational inferences by indication and resemblance (qiyas al-dalala, qiyas al-shabah). The third part develops the main theoretical background of the authors' work, namely, the dialogical approach to Martin-Loef's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general.

Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy. Part I of Reading Frege's Grundgesetze develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses his notorious 'Basic Law V' and attempts to secure its status as a law of logic. Part II examines the mathematical basis of Frege's logicism, explaining and exploring Frege's formal arguments. Heck argues that Frege himself knew that his proofs could be reconstructed so as to avoid Russell's Paradox, and presents Frege's arguments in a way that makes them available to a wide audience. He shows, by example, that careful attention to the structure of Frege's arguments, to what he proved, to how he proved it, and even to what he tried to prove but could not, has much to teach us about Frege's philosophy.

Syllogism is a form of logical argument allowing one to deduce a consistent conclusion based on a pair of premises having a common term. Although Aristotle was the first to conceive and develop this way of reasoning, he left open a lot of conceptual space for further modifications, improvements and systematizations with regards to his original syllogistic theory. From its creation until modern times, syllogism has remained a powerful and compelling device of deduction and argument, used by a variety of figures and assuming a variety of forms throughout history. The Aftermath of Syllogism investigates the key developments in the history of this peculiar pattern of inference, from Avicenna to Hegel. Taking as its focus the longue duree of development between the Middle Ages and the nineteenth century, this book looks at the huge reworking scientific syllogism underwent over the centuries, as some of the finest philosophical minds brought it to an unprecedented height of logical sharpness and sophistication. Bringing together a group of major international experts in the Aristotelian tradition, The Aftermath of Syllogism provides a detailed, up to date and critical evaluation of the history of syllogistic deduction.