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Experience and the Ultimate Structure of Reality, Husserl's Pursuit of Truth follows the evolution of Edmund Husserl's thought through those crucial years at the end of the nineteenth century and the beginning of the twentieth century when reason compelled the young doctor of mathematics to forsake empirical psychology and to strive to find the theories respecting the central traits of reality necessary to buttress the ultimate knowledge of reality he was seeking. Those theories about, to borrow Willard Quine's expression, "limning the true and ultimate structure of reality", were to be the spine he needed to back up his nascent phenomenology, which would put flesh on the purely logical skeleton he was uncovering and give it a brain and a heart. The book's chapters chronicle Husserl's anguished search for answers to the spiny questions at the intersection of what he called the "strange" worlds of actual consciousness and the purely logical that unnerved him as he worked on logic and the foundations of arithmetic. They explore discoveries that he made about those worlds during those many years of mental travels in them as he struggled to come to clarity regarding the underlying objective structure of reality.

This book is intended for the formal argumentation community and for the sex offender therapist community.Both communities use logic.The message of this book is that the argumentation logic models are applicable for modelling and improving the practices of the sex offender therapist community and in parallel stimulate new logic models of argumentationDov Gabbay is a Professor at King's College London, University of Luxembourg and Bar-Ilan University.Dr Gadi Rozenberg is a lecturer at Ashkelon Academic College and Merhavim - Medical Center for Treatment of Brain and Mind (Maba'n)Lydia Rivlin is an author and broadcaster

Hilbert and Bernays' 'Grundlagen der Mathematik' appeared in two volumes in 1934 and 1939, a second edition in 1968 and 1970. It offers a foundation for proof theory and it is a major source on David Hilbert's formalist programme, Paul Bernays' philosophy, the epsilon operator, and much more. It has had a profound influence on mathematics, logic, and philosophy, and it covers formal ground and philosophical perspectives beyond the scope of Whitehead and Russell's 'Principia Mathematica' and Frege's 'Grundlagen der Arithmetik'. This book is not only essential to any scholar of the history and philosophy of modern mathematics, but it also contains formal research - on the epsilon and iota operators - of contemporary relevance to logicians, mathematicians and computer science. For us, it is one of the most fascinating books ever written. This a bilingual German-English, commented edition of the 'Grundlagen'. It is the first English publication of these texts and shows the facsimile of the German original text on the left-hand side of a double page, and its English translation on the right-hand side. In addition to extensive comments on the history and the interpretation of the text's mathematical and philosophical content, there are also careful annotations regarding the differences between the two German editions (1934/39,1968/1970) of this two volume monograph.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.

This book is an introduction to the logic of partitions on a set as well as the (quantum) logic of partitions (direct-sum decompositions or DSDs) on a vector space. Partitions of a set are categorically dual to subsets of a set. Thus the logic of partitions is, in that sense, the dual to the Boolean logic of subsets (usually presented as the special case of propositional logic).Since partitions can be seen as the inverse image partitions of random variables or numerical attributes, partition logic is the logic of random variables or numerical attributes (abstracted from the actual values). On the lattice of partitions of an arbitrary unstructured set, there is a rich algebraic structure of dual operations of implication and co-implication - resembling a non-distributive version of Heyting and co-Heyting algebras.

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2022, Teplá, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.

Lógica Dialógica. Reglas y ejercicios para hacer lógica con diálogos constituye la primera introducción a la Lógica dialógica en castellano dirigida a la práctica de la dialógica y que contiene comentarios precisos sobre ejercicios y soluciones tanto de lógica proposicional como de lógica clásica de primer orden, intuicionista y elementos de lógica modal proposicional. Es la primera parte de la obra Los Diálogos de la Lógica, concebida en dos textos autónomos separados sobre lógica dialógica. Los dos textos deberían ofrecer conjuntamente una visión técnica y filosófica completa del enfoque dialógico de la lógica

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.

Fertile rather than sterile, what makes constructive debate possible? How to reason together at tackling such a vital issue as drinking water management? Claire Polo here presents textbook case diving into the argumentative mechanisms of discussions among teenagers from Mexican, US and French schools. Challenges are huge on this socio-scientific global problem, and no preexisting correct answer is to be found. Through a deep linguistic approach, this study reveals how associating knowledge with other cognitive resources is necessary to explore a controversy, recognizing the importance of values and emotions. Beyond the student, the person; beyond a task, a group: whenever identity and relational dynamics are favorable, collective reasoning may occur, producing cognitive advancement for each participant. Anyone searching how to better apprehend a complex issue or to share and imagine alternatives through social interaction might draw lessons from this research. Paying attention to the construction of young people's speech and opinions, this book offers great food for thought about learning and teaching nothing less than democracy. Claire Polo is a permanent teacher and researcher at the Institute of Educational Sciences and Practices (ISPEF) at Lyon 2 University, in France. At the crossroads of the linguistic sciences and the learning sciences, she develops research on argumentation and the socioaffective dimensions of educational interactions.

This book studies 1-D and 2-D solutions of discrete and continuous analogue dynamical systems and identifies their intrinsic differences. It starts by introducing discrete dynamical systems before comparing them to continuous analogue ones. It studies in some depth periodic and chaotic-type solutions of quadratic and cubic equations and the harvesting/fishing effect on non-periodic and periodic solutions of populations models based on them. Considerations about the stability of the solutions are critical in their study. It contains examples of applications to accounting, pharmacology, harvesting/fishing strategies, economic and population models and historical battles.

This book is a different approach to teaching the foundations of mathematical analysis and of computation. The main idea is to delay the use of "formal definitions", which are definitions that nobody can understand without working with them. The approach of this book is to employ the history of mathematics to first develop fundamental concepts of mathematical analysis and the theory of computation and to only introduce formal definitions after the concepts are understood by the students.The historical order clarifies what analysis is really about and also why the theory of computation came about. The book provides students with a broader background involving for instance glimpses of cardinal arithmetic, predicate logic background, as well as the importance of a sound theory of the infinitesimal (which is in essence the foundations of mathematics and computation).There is a wealth of exercises and numerous graphical illustrations which give an experienced instructor lots of possibilities to select a stimulating course with a broader background. Even for just browsing by general readers, this book presents stories, insights and mathematical theories, covering a window of ancient times to the present.The book is self explanatory and self sufficient, so any staff member in the departments of mathematics or computer science can teach this course.This book will give the students the right techniques and skills to work with mathematical analysis and the theory of computation and to go on further to study more advanced courses on the subject.

In this book Dr. Amelia Spivak uncovers a type of tannaitic argument that was lost: neither traditional nor academic scholars seem to have known of its existence. The author finds examples scattered across the range of tannaitic literature - including in well-trodden passages - suggesting that such argumentation was widely practiced. Spivak identifies a signaling Hebrew phrase, o'kheiluf, along with accompanying expressions as uniquely tannaitic logical terminology. The author lays bare how this precise tannaitic logic - none of which appears to be of Greek or Roman origin - operates and how it relates to the contrapositive. The o'kheiluf argument is shown to betray blanket ignorance of both Aristotelian and Stoic logic. The author offers reasons for why this form of argument died out in amoraic times.This book also serves as a persuasive argument for the use of modern logic as a tool for historical and literary investigations of rabbinic texts. Spivak identifies logical differences in the o'kheiluf arguments in the Midrash Halakhah of the R. Ishmael and R. Akiva schools and uses those as markers for attributing school affiliation to particular passages where authorship is contested. Using her study of the o'kheiluf the author is able to clarify a famously puzzling Mishnah, one that mystified the Bavli and Yerushalmi and even later commentaries on the Talmuds. Spivak also unravels what a popular passage in the Yerushalmi is really busy with when it tries to prove, contrary to the Torah, that a reptile is pure. She shows that this passage and its analog in the Bavli have been incorrectly understood and require the logic she exposes in the o'kheiluf argument for a proper rendering.

This is the first book-length study of the fallacy of composition. It focuses on arguments from parts to whole, from micro to macro, and from some to all; and it discusses both their structures and the conditions of their correctness. The topic is approached through a series of critical reviews, conceptual analyses, and case studies.The critical reviews elaborate interpretations and evaluations of works by such distinguished scholars as: philosophers John Woods and Trudy Govier; economists Paul Samuelson, William Nordhaus, and Paul Krugman; and political sociologists Robert Michels, Robert Dahl, and Seymour Martin Lipset. The conceptual analyses involve the clarification of notions such as: argument vs. fallacy of composition, composition vs. division, hasty generalization, flawed argumentfrom analogy, fallaciousness vs. incorrectness, and meta-argumentation. The case studies explain issues such as: the geocentric-geostatic argument from natural motion, the design argument for the existence of God, the iron law of oligarchy, the paradox of thrift, the argument from private to public debt, bank creation of money, the paradox of the bumper harvest, and current arguments for global warming.Because of this content and this approach, the book is aimed at both scholars and students of philosophy, economics, and political sociology.

This book marks the inauguration of the Historia Logicae book series, which seeks to publish high-quality monographs, dissertations, textbooks, proceedings, and anthologies on the history of logic in either German or English. Serving as the inaugural volume in this series, the book explores the contemporary interpretation of logic across many centuries and cultures. The first section of the volume comprises a compilation of papers dedicated to ancient and medieval logic, examining prominent thinkers such as Plato, Aristotle, Seneca, Porphyry, Proclus, Boethius, Buridan, andKilwardby. The second section shifts focus towards early-modern and contemporary logics, including the works of Caramuel, Kant, Drobisch, Husserl, and Jakowski.Topics of discussion encompass the relationship between mathematics and logic, natural deduction, intuitionism, graph theory, categorical judgments, theories of truth, modal logic, opposition relations, logic diagrams, definitions of formal logic, many-sorted logic, model theory, and paraconsistent logic.

This comprehensive volume features the proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, held in Hangzhou, China on September 8-9 and 11-12, 2023. The collection offers a diverse range of papers that explore the intersection of logic, artificial intelligence, and law. With contributions from some of the leading experts in the field, this volume provides insights into the latest research and developments in the applications of logic in these areas. It is an essential resource for researchers, practitioners, and students interested in the latest advancements in logic and its applications to artificial intelligence and law.

In 1922, Curry started reading Principia Mathematica and was intrigued by the complications of its substitution rule. As a result of trying to analyze substitution, Curry conceived the combinators in 1926. This collection is dedicated to Jonathan Seldin's 80th anniversary. Seldin is the penultimate PhD student of Curry and the guardian of Curry's paradigm.The search at the beginning of the 20th century for powerful systems that combine computations and deductions (functions and logic) and that are able to formalise mathematics has led to the birth of the mighty ¿-calculus of Church, Combinatory Logic of Curry and Category Theory of Eilenberg and Mac Lane, all of which are well represented in this collection. The struggle for internalising as much as possible while keeping the system consistent is clear in the evolution of the ¿-calculus and combinatory logic and can be felt again in the articles in this volume. Similarly, the struggle for elegant theories that minimise the number of basic concepts while remaining as close as possible to the language's structure is clear. Generalising concepts, connecting areas that may seem far apart and applying useful techniques from one area to the other is also represented well in this volume where for example notions like coherence, confluence, commuting diagrams, are extended between ¿-calculus, rewriting systems and category theory, and where embedding relations are given to allow a lot of disciplines from logic to mathematics to computer science to meet.

This book explores the major historical phenomenon of the algebraization of mathematics in the second half of the 17th and 18th centuries, offering a broader understanding of the consolidation of analytic geometry and infinitesimal calculus as disciplines. The authors examine the external (intellectual, geographical, and political) factors that influenced these transformations and shed light on the process of acquisition and integration of analytical mathematics into traditional curricula. Drawing on new trends in historiography of science, this book emphasizes the importance of "dwarfs", that is mathematicians but also technicians, artisans, military personnel, engineers, and architects, often ignored or marginalized in traditional histories, in the circulation of original mathematical knowledge, and of peripheral countries such as Italy and Spain as important sites for the appropriation and production of such knowledge.

Transparent Intensional Logic (TIL) is a fi ne-grained framework with considerable expressive power for a systematic, non-reductionist semantic and logical analysis of (natural) languages. It does not subscribe to model-theoretic semantics, but to an interpreted realist version of procedural semantics. TIL has covered a lot of ground since the publication of the book Procedural Semantics for Hyperintensional Logic by Springer in 2010. The areas that have been covered over the last decade include not least the following topics: existential quantification into various kinds of hyperintensional contexts, property modification, topic and focus articulation, inferences with hyperpropositions, varying degrees of hyperintensional individuation, various rules of the lambda calculus, fictional and religious discourse, and impossibility. This volume contains 27 papers that have been published across a wide range of venues since 2010. The papers are organised into six thematically organized chapters: hyperintensional logic; cohyperintensionality, synonymy and propositional unity; deduction and substitution; logic of intensions: (a) presuppositions, requisites and prerequisites, (b) property modifiers; questions, answers, obligations and norms; fiction, religion, and impossibility. This volume thus provides a detailed survey of the state-of-the-art of the foundations of TIL and its most recent applications.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.

This textbook combines methodologies of vehicle dynamics with modeling, analysis, and optimization of suspension systems, power train, and aerodynamics. Chapter topics provide the reader with a broad range of design concepts. The book begins with an introduction of the design process and an overview of basic suspension systems. Subsequent chapters focus on fundamental mathematical modeling of vehicle dynamics and vehicle interaction with a road surface. The book strives to combine a hands-on approach to the mechanical design of suspension componentsalong with the related theoretical concepts. The material presents these concepts at a fairly deep level, providing understanding and insight into the application of vehicle dynamics theory.The textbook is addressed primarily to senior level engineering students; however, the book is written in a self-study style. The book can be particularly useful for undergraduate senior design projects in which students are pursuing automotive specialization.

Stages of Theater: The Dramatic Criticism of Stanley Kauffmann, 1951-2006 is a collection of 100 pieces of dramatic criticism by the late Stanley Kauffmann (1916-2013). Kauffmann's creative life spanned seven decades: starting in 1951 and continuing until 2013, he was a drama (and film) critic for the New Republic, the New York Times, and Saturday Review. He was also an actor, stage manager, playwright, novelist, professor, and editor. Along with John Simon, Robert Brustein, and Richard Gilman, Kauffmann was one of the most potent, influential critics included in the New York school of twentieth-century American theater criticism.With style and erudition Kauffmann discusses plays and productions from the following countries in Stages of Theater: England, the United States, France, Spain, Russia, Ireland, Germany, Sweden, Greece, South Africa, Norway, and Spain. Among the many works discussed are Phaedra, by Jean Racine; The Caucasian Chalk Circle, by Bertolt Brecht; The Dance of Death, by August Strindberg; All's Well That Ends Well, by William Shakespeare; The Three Sisters, by Anton Chekhov; Old Times, by Harold Pinter; The Master Builder, by Henrik Ibsen; The Misanthrope, by Molière; The Bacchae, by Euripides; and Strange Interlude, by Eugene O'Neill.Also included in Stages of Theater are essays and articles on the following subjects: theater versus film; the idea of repertory; recorded drama; Shakespeare and the cinema; Broadway and Off-Broadway; the genre of comedy; and bio-criticism concerning such figures as Edmund Kean, Jean-Paul Sartre, and Bernard Shaw. Once again, the precision, wit, and wisdom of Kauffmann's writing chime in Stages of Theater, as he reveals his sense of cultural mission-and love of all the arts-by applying to theater and drama the same high standards he applied during his long career to fiction, poetry, music, and film.

This book is for readers who have learned about first order logic; Gödel's completeness theorem; the Löwenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories T; mainly countable. That is, properties dividing them in some sense between understandable and complicated ones.The main test problem is the number of models of T of the infinite cardinal l as a function of l. This culminates in the so-called main gap theorem saying the number is either maximal or quite small in suitable sense. Toward this, other properties are introduced and investigated, such as being stable or being super stable, where can we define dimension and weight, particularly for super stable theories.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.

Paradoxes seized the attention of logicians in the middle ages, and were used both as tests for the viability of theories of logic, language, epistemology, and possibly every philosophical issue, and also in the specific genre of insolubles as needing a theoretical solution, usually involving issues about signification, truth, knowledge and modality. Numerous theories were developed, not only in the Latin West, but also in the Islamic world and in the Byzantine tradition. Some of these theories are well known, others barely investigated, if at all. The papers in this volume discuss and contrast a range of these theories and consider their advantages and drawbacks, and their relation to more recent theories of paradox and antinomy. Several of the papers were presented at a workshop organised at the University of St Andrews, Scotland, as part of the Leverhulme-funded project 'Theories of Paradox in Fourteenth-Century Logic: Edition and Translation of Key Texts'.

Oiva Ketonen (1913--2000) was the closest to a student the creator of modern proof theory Gerhard Gentzen ever had. Their encounter took place in 1938--39 in Göttingen, with Ketonen hoping to receive a suitable topic for a doctoral dissertation and Gentzen instead deeply immersed in attempts at proving the consistency of analysis. Ketonen's thesis of 1944, his only work in logic, introduced what is today called the G3-sequent calculus. It is his best-known discovery, a sequent calculus for classical propositional logic the logical rules of which are all invertible. Few read his thesis, the results of which were instead made available through a long review by Paul Bernays. Ketonen's calculus is the basis of Evert Beth's tableau method and of the sequent calculi in Stephen Kleene's influential {\it Introduction to Metamathematics}. A second result was a sharpening of the midsequent theorem, by which the number of quantifier inferences with eigenvariables could be minimized. The existence of a weakest possible midsequent followed, in the sense that if any midsequent is derivable, a weakest one is. Turning this into a contrapositive, Ketonen found a purely syntactic method for proofs of underivability that he applied to affine plane geometry. His result, in modern terms, was a positive solution to the word problem for the universal fragment of plane affine geometry, with a syntactic proof of underivability of the parallel postulate from the rest of the affine axioms as a corollary.

The idea of a knowledge base lies at the heart of symbolic or "good old-fashioned" artificial intelligence (GOFAI). A knowledge-based systemdecides how to act by running formal reasoning procedures over a body of explicitly represented knowledge, its knowledge base. The system isnot programmed for specific tasks; rather, it is told what it needs to know, and expected to infer the rest.This book is about the logic of such knowledge bases. It describes in detail the relationship between symbolic representations of knowledge and abstract states of knowledge, exploring along the way, the foundations of knowledge, knowledge bases, knowledge-based systems, and knowledge representation and reasoning. Assuming some familiarity with first-order predicate logic, the book offers a rigorous mathematical model of knowledge that is general and expressive, yet more workable in practice than previous models.The first edition of the book appeared in the year 2000, and since then its model of knowledge has been applied and extended in a number of ways.This second edition incorporates a number of new results about the logic of knowledge bases, including default reasoning, reasoning about actionand change, and tractable reasoning.Hector Levesque is Professor Emeritus in the Department of Computer Science, University of Toronto. Gerhard Lakemeyer is Professor and Chair of the Department of Computer Science, RWTH Aachen University, and Professor (status only) in the Department of Computer Science, University of Toronto.