This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance." The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, such as out-of-the-box regression, cannot help in discovering cause. This new way of looking at uncertainty ties together disparate fields - probability, physics, biology, the "soft" sciences, computer science - because each aims at discovering cause (of effects). It broadens the understanding beyond frequentist and Bayesian methods to propose a Third Way of modeling.

This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth's notion of implicit definition and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap. The volume further examines what it means that a quantifier can have multiple meanings and addresses how existential vagueness can induce vagueness in our modal notions. Finally, the book explores the role played by quantifiers with respect to various kinds of semantic paradoxes, the logicality issue, ontological commitment, and the behavior of quantifiers in intensional contexts.

Lambda Calculi: A Guide Interpolation and Definability Discourse Representation Theory

Instance ontology, or particularism - the doctrine that asserts the individuality of properties and relations - has been a persistent topic in Western philosophy, discussed in works by Plato and Aristotle, by Muslim and Christian scholastics, and by philosophers of both realist and nominalist positions. This book by D. W. Mertz is the first sustained analysis that applies the rules and systems of mathematics and logic to instance ontology in order to argue for its validity and for its problem-solving capacities and to associate it with a version of the realist position that Mertz calls "moderate realism". Mertz surveys the history of instance ontology in writings from Plato and Aristotle through Leibniz, followed by modern philosophers such as Bertrand Russell and D. M. Armstrong, among others. He also includes a thorough critique of the recent work of Keith Campbell and other contemporary nominalists. Building on the insights gained through this historical overview, he delves deeper into the logic of instance ontology and uncovers some of its extraordinary problem-solving features: distinguishing legitimate from illegitimate impredicative reasoning; uniformly diagnosing the self-referential paradoxes; being free from the limitation theorems of Godel and Tarski; providing a basis for the derivation of arithmetic construed intensionally; and formally distinguishing identity and indiscernibility.

This volume opens up stimulating new perspectives on a broad variety of Barcan Marcus's concerns ranging from the systematic foundation and interpretation of quantified modal logic, nature of extensionality, necessity of identity, direct reference theory for proper names, notions of essentialism, second-order modal logic, modal metaphysics, properties and classes, substitutional and objectual quantification, actualism, the Barcan formula, possibilia and possible-world semantics to epistemic and deontic modalities, non-language-centered theories of belief, accounts of rationality, consistency of a moral code, moral dilemmas, and much more. The contributions demonstrate that Barcan Marcus's original and clear ideas have had a formative influence on the direction in which certain themes central to today's philosophical debate have developed. Furthermore, the volume includes an illuminating intellectual autobiography from Barcan Marcus herself as well as an informal interview containing her unfiltered, frank answers. The book brings together contributions by Ruth Barcan Marcus, Timothy Williamson, Dagfinn Follesdal, Joelle Proust, Pascal Engel, Edgar Morscher, Erik J. Olsson, and Michael Frauchiger.

The book offers a reflection on the nature, scope, and limits of knowledge that have been at the focus of the author's work over decades. The essays collected in this volume expound and extend these efforts in exploring the outer fringes of understanding: the outer boundaries of conceivability, the limits of cognition, and the ramifications of ineffability and paradox. They join in exploring the lay of the land at the boundaries of knowledge. The first chapters address basic facts regarding the conceptualization of knowledge. This is followed by a study on how to deal with problems relating to the affirmation and considerations of truth. The final chapters scrutinize the limits of demonstration and the inherent impossibility of realizing an ideal systematization of our knowledge of totalities. The book affords novel perspectives regarding the thought of a widely appreciated philosopher. It is an original work aimed for readers interested in the theory of knowledge and philosophy of cognition.

Since 1970-ties in the theory of syntax of natural language quite a number of competing, incommensurable theoretic frameworks have emerged. Today the lack of a leading paradigm and kaleidoscope of perspectives deprives our general understanding of syntax and its relation to semantics and pragmatics. The present book is an attempt to reestablish the most fundamental ideas and intuitions of syntactic well-formedness within a new general account. The account is not supposed to compete with any of today 's syntactic frameworks, but to provide a deeper understanding of why these frameworks succeed or fail when they do and to show a new way for cooperation between logicians and linguists which may lead in future to a unified, yet more specific account.

This book aims to lay bare the logical foundations of tractable reasoning. It draws on Marvin Minsky's seminal work on frames, which has been highly influential in computer science and, to a lesser extent, in cognitive science. Only very few people have explored ideas about frames in logic, which is why the investigation in this book breaks new ground. The apparent intractability of dynamic, inferential reasoning is an unsolved problem in both cognitive science and logic-oriented artificial intelligence. By means of a logical investigation of frames and frame concepts, Andreas devises a novel logic of tractable reasoning, called frame logic. Moreover, he devises a novel belief revision scheme, which is tractable for frame logic. These tractability results shed new light on our logical and cognitive means to carry out dynamic, inferential reasoning. Modularity remains central for tractability, and so the author sets forth a logical variant of the massive modularity hypothesis in cognitive science. This book conducts a sustained and detailed examination of the structure of tractable and intelligible reasoning in cognitive science and artificial intelligence. Working from the perspective of formal epistemology and cognitive science, Andreas uses structuralist notions from Bourbaki and Sneed to provide new foundational analyses of frames, object-oriented programming, belief revision, and truth maintenance. Andreas then builds on these analyses to construct a novel logic of tractable reasoning he calls frame logic, together with a novel belief revision scheme that is tractable for frame logic. Put together, these logical analyses and tractability results provide new understandings of dynamic and inferential reasoning. Jon Doyle, North Carolina State University

This collection of essays explores the philosophy of human knowledge from a multitude of perspectives, with a particular emphasis upon the justification component of the classical analysis of knowledge and with an excursion along the way to explore the role of knowledge in Texas Hold 'Em poker. An important theme of the collection is the role of knowledge in religion, including a detailed argument for agnosticism. A number of the essays touch upon issues in philosophical logic, among them a fascinating new counter-example to Modus Ponens. The collection is rounded out with essays on causality and the philosophy of mind. The author's perspective on the philosophy of human knowledge is fresh and challenging, as evidenced by essays entitled "On Epistemic Preferability;" "On Being Unjustified;" "The Logic of 'Unless'" and "Is 'This sentence is true.' True?" An interesting feature of The Logic of Philosophy: Pesky Essays is the inclusion of responses to several of its key essays, contributed by such prominent contemporary philosophers as Roderick Chisholm, Ted Sider and Tomas Kapitan.

This contribution to Palgrave's 'Advances' series addresses a wide range of issues that have arisen in post-Gricean pragmatic theory, in chapters by distinguished authors. Among the specific topics covered are scalar implicatures, lexical semantics and pragmatics, indexicality, procedural meaning, the semantics and pragmatics of negation. The volume includes both defences and critiques of Relevance Theory and of Neo-Gricean Pragmatics.

This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

This book is a companion to logical thought and logical thinking in China with a comparative and interdisciplinary perspective. It introduces the basic ideas and theories of Chinese thought in a comprehensive and analytical way. It covers thoughts in ancient, pre-modern and modern China from a historical point of view. It deals with topics in logical (including logico-philosophical) concepts and theories rooted in China, Indian and Western Logic transplanted to China, and the development of logical studies in contemporary China and other Chinese communities. The term "philosophy of logic" or "logico-philosophical thought" is used in this book to represent "logical thought" in a broad sense which includes thinking on logical concepts, modes of reasoning, and linguistic ideas related to logic and philosophical logic. Unique in its approach, the book uses Western logical theories and philosophy of language, Chinese philology, and history of ideas to deal with the basic ideas and major problems in logical thought and logical thinking in China. In doing so, it advances the understanding of the lost tradition in Chinese philosophical studies.

Philosophical logic has been, and continues to be, a driving force behind much progress and development in philosophy more broadly. This collection by up-and-coming philosophical logicians deals with a broad range of topics, including, for example, proof-theory, probability, context-sensitivity, dialetheism and dynamic semantics.

In informal terms, abductive reasoning involves inferring the best or most plausible explanation from a given set of facts or data. This volume presents new ideas about inferential and information-processing foundations for knowledge and certainty. The authors argue that knowledge arises from experience by processes of abductive inference, in contrast to the view that it arises noninferentially, or that deduction and inductive generalization are enough to account for knowledge. The book tells the story of six generations of increasingly sophisticated generic abduction machines and the discovery of reasoning strategies that make it computationally feasible to form well-justified composite explanatory hypotheses, despite the threat of combinatorial explosion. This book will be of great interest to researchers in AI, cognitive science, and philosophy of science.

In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic, supposingthat someone were capable to compile it, would ?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers, historians of philosophy, linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic (there are a lot of excellent textbooks on the market, and the expert reader will realize how much we bene?ted from manyofthem)buttoo?ertoeveryreader, evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal opera

In this volume, the author investigates and argues for, a particular answer to the question: What is the right way to logically analyze modalities from natural language within formal languages? The answer is: by formalizing modal expressions in terms of predicates. But, as in the case of truth, the most intuitive modal principles lead to paradox once the modal notions are conceived as predicates. The book discusses the philosophical interpretation of these modal paradoxes and argues that any satisfactory approach to modality will have to face the paradoxes independently of the grammatical category of the modal notion. By systematizing modal principles with respect to their joint consistency and inconsistency, Stern provides an overview of the options and limitations of the predicate approach to modality that may serve as a useful starting point for future work on predicate approaches to modality. Stern also develops a general strategy for constructing philosophically attractive theories of modal notions conceived as predicates. The idea is to characterize the modal predicate by appeal to its interaction with the truth predicate. This strategy is put to use by developing the modal theories Modal Friedman-Sheard and Modal Kripke-Feferman.

A new approach to reading Frege's notations that adheres to the modern view that terms and well-formed formulas are any disjoint syntactic categories. On this new approach, we can at last read Frege's notations in their original form revealing striking new solutions to many of the outstanding problems of interpreting his philosophy.

Penetrating and practical, Logic Made Easy is filled with anecdotal histories detailing the often muddy relationship between language and logic. Complete with puzzles you can try yourself and questions you can use to raise your test scores, Logic Made Easy invites readers to identify and ultimately remedy logical slips in everyday life. Even experienced logicians will be surprised by Deborah Bennett's ability to identify the illogical in everything from maddening street signs to tax forms that make April the cruelest month. Designed with dozens of visual examples, the book guides readers through those hair-raising times when logic is at odds with common sense. Logic Made Easy is indeed one of those rare books that will actually make you a more logical human being.

The present collection represents an attempt to bring together several contributions to the ongoing debate pertaining to supervenience of the normative in law and morals and strives to be the first work that addresses the topic comprehensively. It addresses the controversies surrounding the idea of normative supervenience and the philosophical conceptions they generated, deserve a recapitulation, as well as a new impulse for further development. Recently, there has been renewed interest in the concepts of normativity and supervenience. The research on normativity - a term introduced to the philosophical jargon by Edmund Husserl almost one hundred years ago - gained impetus in the 1990s through the works of such philosophers as Robert Audi, Christine Korsgaard, Robert Brandom, Paul Boghossian or Joseph Raz. The problem of the nature and sources of normativity has been investigated not only in morals and in relation to language, but also in other domains, e.g. in law or in the c ontext of the theories of rationality. Supervenience, understood as a special kind of relation between properties and weaker than entailment, has become analytic philosophers' favorite formal tool since 1980s. It features in the theories pertaining to mental properties, but also in aesthetics or the law. In recent years, the 'marriage' of normativity and supervenience has become an object of many philosophical theories as well as heated debates. It seems that the conceptual apparatus of the supervenience theory makes it possible to state precisely some claims pertaining to normativity, as well as illuminate the problems surrounding it.

Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.

We do not perceive the present as it is and in totality, nor do we infer the future from the present with any high degree of dependability, nor yet do we accurately know the consequences of our own actions. In addition, there is a fourth source of error to be taken into account, for we do not execute actions in the precise form in which they are imaged and willed. Frank H. Knight [R4.34, p. 202] The "degree" of certainty of confidence felt in the conclusion after it is reached cannot be ignored, for it is of the greatest practical signi- cance. The action which follows upon an opinion depends as much upon the amount of confidence in that opinion as it does upon fav- ableness of the opinion itself. The ultimate logic, or psychology, of these deliberations is obscure, a part of the scientifically unfathomable mystery of life and mind. Frank H. Knight [R4.34, p. 226-227] With some inaccuracy, description of uncertain consequences can be classified into two categories, those which use exclusively the language of probability distributions and those which call for some other principle, either to replace or supplement.

Arguing that our attachment to Aristotelian modes of discourse makes a revision of their conceptual foundations long overdue, the author proposes the consideration of unacknowledged factors that play a central role in argument itself. These are in particular the subjective imprint and the dynamics of argumentation. Their inclusion in a four-dimensional framework (subjective-objective, structural-procedural) and the focus on thesis validity allow for a more realistic view of our discourse practice. Exhaustive analyses of fascinating historical and contemporary arguments are provided. These range from Columbus s advocacy of the Western Passage to India, over the trial of King Louis XVI during the French Revolution, to today s highly charged controversies surrounding euthanasia and embryo research.

Excavating foundational issues such as the purpose of argument itself (assent of an audience or critical examination of validity claims) and the contested role of argument as a generator of knowledge, the book culminates in a discussion of the relationship between rationality and reasonableness and criticizes the restrictions of rational argument relying on fixed logical, economic or cultural criteria that in reality are mutable. Here, a true, open argument requires the infusion of Paul Lorenzen s principle of transsubjectivity, which recognizes but transcends the partiality of the individual and which can be seen in the pragmatic and expanding consensus that humanity can control itself to safeguard the future of a fragile, damaged world."

The rise of scientific (analytic) philosophy since the turn of the twentieth century is linked to the philosophical interaction between, on the one hand, Ernst Mach, the Vienna Circle around Moritz Schlick and Otto Neurath, the Berlin Group (Hans Reichenbach, Carl G. Hempel), and the Prague Group (Rudolf Carnap, Philipp Frank), and, on the other, philosophers and scientists in Denmark (Niels Bohr, Joergen Joergensen), Finland (Eino Kaila, Georg Henrik von Wright and their disciples), Norway (Arne Naess and his students), and Sweden (Ake Petzall, the journal Theoria and a younger generation of philosophers in Uppsala). In addition, the pure theory of law of Hans Kelsen achieved wide dissemination in the Nordic countries (through, for example, Alf Ross). One of the key events in the relations between the Central European philosophers and those of the Nordic countries was the Second International Congress for the Unity of Science which was arranged in Copenhagen in 1936.

Besides considering the interactions of these groups, the book also pays special attention to their interactions, in the context of the Cold War period following the Second World War, with the so-called Third Vienna Circle and with the Forum Alpbach/Austrian College around Viktor Kraft and Bela Juhos (along with Ludwig Wittgenstein and Paul Feyerabend), where the issues of (philosophical and scientific) realism and "psychologism"-the relationship between psychology and philosophy-were matters of controversy.

By comparison with the more extensively investigated and better known transatlantic transfer and transformation of "positivism" and logical empiricism, the developments outlined above remain

neglected and marginalized topics in historiography. The symposium aims to reveal the remarkable continuity of the philosophical enlightened "Nordic Connection." We intend to shed light on this forgotten communication and to reconstruct these hidden scholarly networks from an historical and logical point of view, thereby evaluating their significance for today's research."

Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general 'malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundation of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates.

This book, provides a critical approach to all major logical paradoxes: from ancient to contemporary ones. There are four key aims of the book: 1. Providing systematic and historical survey of different approaches - solutions of the most prominent paradoxes discussed in the logical and philosophical literature. 2. Introducing original solutions of major paradoxes like: Liar paradox, Protagoras paradox, an unexpected examination paradox, stone paradox, crocodile, Newcomb paradox. 3. Explaining the far-reaching significance of paradoxes of vagueness and change for philosophy and ontology. 4. Proposing a novel, well justified and, as it seems, natural classification of paradoxes. "