Mathematical logic Books
Springer International Publishing AG Logical Foundations of Mathematics and
Book SynopsisThe two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability.Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs.Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.Trade Review“This monograph by the outstanding Czech logician Pavel Pudlák provides a broad but also deep survey of work in logic and computer science relevant to foundational issues, interpreted in a wide sense. … This is a fine overview of logic and complexity theory that can be confidently recommended to anybody who would like to orient themselves in an increasingly intricate and difficult field.” (Alasdair Urquhart, Philosophia Mathematica, Vol. 23 (3), October, 2015)“For the non-expert it offers indeed a ‘gentle introduction’ to logic that is well selected and excellently explained. And for the logician it certainly offers some of the best introductions to those topics outside their area of direct expertise. … it contains plenty of informal explanations, intuition and motivation. … It is truly a gift to the logic and wider communities … . This book is very enjoyable to read and I wish it all success.” (Olaf Beyersdorff, Mathematical Reviews, August, 2014)“It spans the historical, logical, and at times philosophical underpinnings of the theory of computational complexity. Students of mathematics seeking a transition to higher mathematics will find it helpful, as will mathematicians with expertise in other areas. … an excellent choice for a first text in studying complexity, or as a clarifying adjunct to any assigned text in this area. … a compact guide for graduate students with a need for or interest in computational complexity and its foundations.” (Tom Schulte, MAA Reviews, July, 2014)“This book, exactly as indicated by its title, deals with the main philosophical, historical, logical and mathematical aspects … in a quite approachable and attractive way. … the prospective readers of this book are mathematicians with an interest in the foundations, philosophers with a good background in mathematics, and also philosophically minded scientists. Due to the author’s nice style, the book will be a very good choice for the first text in studying this subject.” (Branislav Boričić, zbMATH, Vol. 1270, 2013)Table of ContentsMathematician’s world.- Language, logic and computations.- Set theory.- Proofs of impossibility.- The complexity of computations.- Proof complexity.- Consistency, Truth and Existence.- References.
£142.49
Springer International Publishing AG Saved from the Cellar: Gerhard Gentzen’s
Book SynopsisGerhard Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today. Another noteworthy achievement is his resolution of the embarrassing situation created by Gödel's incompleteness results, especially the second one about the unprovability of consistency of elementary arithmetic. After these successes, Gentzen dedicated the rest of his short life to the main problem of Hilbert's proof theory, the question of the consistency of analysis. He was arrested in the summer of 1945 with other professors of the German University of Prague and died soon afterward of starvation in a prison cell. Attempts at locating his lost manuscripts failed at the time, but several decades later, two slim folders of shorthand notes were found. In this volume, Jan von Plato gives an overview of Gentzen's life and scientific achievements, based on detailed archival and systematic studies, and essential for placing the translations of shorthand manuscripts that follow in the right setting. The materials in this book are singular in the way they show the birth and development of Gentzen's central ideas and results, sometimes in a well-developed form, and other times as flashes into the anatomy of the workings of a unique mind.Trade Review“This book is obviously indispensable to historians of logic in the immediate wake of Gödel’s 1931 incompleteness theorems. … Saved from the Cellar is also valuable for less specialist readers (like myself ) who wish to understand the broader outlines of what proof theory has meant to several of its leading creators.” (Colin McLarty, Isis, Vol. 111 (1), 2020)“The book contains translations of shorthand notes which survived in the Nachlass of the mathematical logician Gerhard Gentzen. ... The book is valuable source for the history of modern logic; the editor did an excellent work in getting the shorthand notes, first transcribed in normal German text, and then translating it to English.” (Reinhard Kahle, zbMath 1414.03002, 2019)“Every general reader interested in modern logic and its history, … may find a source of inspiration in Genzen’s unpublished notes of the thirties, as well as for the philosopher concerned with epistemological aspects of modern logic.” (Adrian Rezus, Studia Logica, Vol. 107, 2019)“This is an account and transcription of two slim folders of stenographic material in Gerhard Gentzen's handwriting that were found in 1984. … this book is a valuable contribution to the history of the development of mathematical logic in the first half of the twentieth century.” (Henry Africk, Mathematical Reviews, December, 2017)Table of ContentsPart I: A Sketch of Gentzen's Life and Work.- 1. Overture.- 2. Gentzen's years of study.- Dr. Gentzen's arduous years in Nazi Germany.- 4. The scientific accomplishments.- 5. Loose ends.- 6. Gentzen's genuis.- Part II: Overview of the Shorthand Notes.- 1. Gentzen's series of stenographic manuscripts.- 2. The items in this collection.- Practical remarks on the manuscripts.- Manuscript illustrations.- The German alphabet in Latin, Sutterlin, and Fraktur Type.- Bibliography for parts I and II.- Index of names for Parts I and II.- Part III: The Original Writings.- 1. Reduction of number-theoretic problems to predicate logic.- 2. Replacement of functions by predicates.- 3. The formation of abstract concepts.- 4. Five different forms of natural calculi.- 5. Formal conception of correctness in arithmetic I.- 6. Investigations into logical inferences.- 7. Reduction of classical to intuitionistic logic.- 8. CV of the candidate Gerhard Gentzen.-0 9. Letters to Heyting.- 10. Formal conception of correctness in arithmetic II.- 11. Proof theory of number theory.- 12. Consistency of artihmetic, for publication.- 13. Correspondence with Paul Bernays.- 14. Forms of type theory.- 15. Predicate logic.- 16. Propositional logic.- 17. Foundational research in mathematics.- Table of cross-references in the Gentzen papers.- Index of names in the Gentzen papers.- Index of subjects in the Gentzen papers.
£113.99
Springer Fachmedien Wiesbaden Einführung in die klassische und intensionale
Book SynopsisDas Buch setzt sich zum Ziel, auch mathematisch wenig vorgebildete Leser in die klassische zweiwertige Logik und ihre intensionalen Erweiterungen wie Modal-Logik, Zeit-Logik und dynamische Logik einzuführen. Die hier näher betrachteten intensionalen Systeme hängen zusammen mit Fragen aus der Beweistheorie der Peano-Arithmetik, Korrektheitsfragen in der Theorie der Programmiersprachen und mit Problemen, die die Semantik natürlicher Sprachen betreffen.Table of ContentsAussagenlogik - modale Aussagenlogik und Varianten - Grundbegriffe der Prädikatenlogik - Herbrandscher Satz - Gödelscher Vollständigkeitssatz - modale Aspekte der Gödelschen Unvollständigkeitssätze - modelltheoretische Begriffe - modale und dynamische Prädikatenlogik - höherstufige Prädikatenlogik und Typentheorie.
£49.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Cambridge Summer School in Mathematical Logic: Held in Cambridge /U. K., August 1-21, 1971
Book SynopsisLectures on intuitionism.- Realizability: A retrospective survey.- Some applications of Kleene's methods for intuitionistic systems.- Notes on intuitionistic second order arithmetic.- Some properties of intuitionistic zermelo-frankel set theory.- Ouelques Resultats sur les Interpretations Fonctionnelles.- Combinator realizability of constructive finite type analysis.- The arithmetic theory of constructions.- The priority method for the construction of recursively enumerable sets.- Admissible ordinals and priority arguments.- Abstract computability versus analog-generability (a survey).- Infinitary combinatorics.- The maximum sum of a family of ordinals.- Effective implications between the "finite" choice axioms.- On descendingly complete ultrafilters.- XVI. A model for the negation of the axiom of choice.- Filters closed under MAHLO's and GAIFMAN's operation.- On chromatic number of graphs and set systems.- Countable models of set theories.- Errata.- Descriptive set theory in .- Modal model theory.- A preservation theorem for interpretations.- Vaught sentences and Lindström's regular relations.Table of ContentsLectures on intuitionism.- Realizability: A retrospective survey.- Some applications of Kleene's methods for intuitionistic systems.- Notes on intuitionistic second order arithmetic.- Some properties of intuitionistic zermelo-frankel set theory.- Ouelques Resultats sur les Interpretations Fonctionnelles.- Combinator realizability of constructive finite type analysis.- The arithmetic theory of constructions.- The priority method for the construction of recursively enumerable sets.- Admissible ordinals and priority arguments.- Abstract computability versus analog-generability (a survey).- Infinitary combinatorics.- The maximum sum of a family of ordinals.- Effective implications between the "finite" choice axioms.- On descendingly complete ultrafilters.- XVI. A model for the negation of the axiom of choice.- Filters closed under MAHLO's and GAIFMAN's operation.- On chromatic number of graphs and set systems.- Countable models of set theories.- Errata.- Descriptive set theory in .- Modal model theory.- A preservation theorem for interpretations.- Vaught sentences and Lindström's regular relations.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces
Book SynopsisThe territory of preserver problems has grown continuously within linear analysis. This book presents a cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is placed on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. In addition, local automorphisms and local isometries of operator algebras and function algebras are discussed in detail.Trade ReviewFrom the reviews: "Preserver problems deal with maps on subsets of algebras that preserve certain sets, relations, functions, etc. … The book is very well organized. … One of its remarkable features is that it links several areas, particularly operator theory and mathematical physics. The audience of this book is therefore potentially wide: operator algebraists, mathematical physicists, linear algebraists, ring theorists, etc. I warmly recommend this book to anyone interested in preserver problems." (Matej Brešar, Mathematical Reviews, Issue, 2007 g) "The monograph under review collects many important and highly nontrivial results and efforts. It is important to recall that the basic material is based on the research done by the author, who belongs to the eminent researchers in this field. The style is very fresh … . I recommend to book for students and experts interested in operator algebra, noncommutative measure theory and mathematical foundations of quantum physics. The monograph is welcome in the quantum structures realm." (Anatolij Dvurecenskij, Zentralblatt MATH, Vol. 1119 (21), 2007)Table of ContentsSome Linear and Multiplicative Preserver Problems on Operator Algebras and Function Algebras.- Preservers on Quantum Structures.- Local Automorphisms and Local Isometries of Operator Algebras and Function Algebras.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings
Book SynopsisOver the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.Table of ContentsPreliminaries.- Beginnings.- Partition Properties.- Forcing and Sets of Reals.- Aspects of Measurability.- Strong Hypotheses.- Determinacy.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Felix Hausdorff - Gesammelte Werke Band IA:
Book SynopsisDer Band 1A beginnt mit einem Vorwort zur Gesamtedition. Den Hauptteil des Bandes bilden Hausdorffs Arbeiten über geordnete Mengen aus den Jahren 1901-1909. Diese haben der Entwicklung der Mengenlehre nachhaltige Impulse verliehen. Sie enthalten zahlreiche für die Untersuchung geordneter Mengen grundlegende neue Begriffe sowie tiefliegendere Resultate. Alle diese Arbeiten sind sorgfältig kommentiert. Die Kommentare zeigen, dass einige von Hausdorff's Ideen und Resultaten für die moderne Grundlagenforschung hochaktuell sind. Ferner enthält der Band Hausdorff's kritische Besprechung von Russells "The Principles of Mathematics", aus dem Nachlass seine Vorlesung "Mengenlehre" von 1901 (eine der ersten Vorlesungen über dieses Gebiet überhaupt) sowie einen Essay "Hausdorff als akademischer Lehrer". Table of ContentsTeil I. Arbeiten über geordnete Mengen.– Über eine gewisse Art geordneter Mengen.- Kommentar.- Der Potenzbegriff in der Mengenlehre.- Kommentar.- Untersuchungen über Ordnungstypen I, II, III.- Untersuchungen über Ordnungstypen IV, V.- Kommentar.- Über dichte Ordnungstypen.- Kommentar.- Grundzüge einer Theorie der geordneten Mengen.- Kommentar.- Die Graduierung nach dem Endverlauf.- Comments.- Summe von N1 Mengen.- Comments.- Gaps in partially ordered sets and related problems.- Teil II. Aus dem Nachlaß zur Mengenlehre.- Mengenlehre. Vorlesung der Universität Leipzig, Sommersemester 1901.- Kommentar.- Alefsätze.- Anhänge.- Bertrand Russell, The Principles of Mathematics (Besprechung).- Kommentar.- Hausdorff als akademischer Lehrer.- Entstehung der Hausdorff-Edition.- Personenregister.- Sachregister.
£125.99
Springer Fachmedien Wiesbaden Die Gödel'schen Unvollständigkeitssätze: Eine geführte Reise durch Kurt Gödels historischen Beweis
Book SynopsisIm Jahr 1931 erschien im Monatsheft für Mathematik und Physik ein Artikel mit dem geheimnisvoll klingenden Titel Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. In dieser Arbeit hat Kurt Gödel zwei Unvollständigkeitssätze bewiesen, die unseren Blick auf die Mathematik von Grund auf verändert haben. Gödels Sätze manifestieren, dass zwischen dem Begriff der Wahrheit und dem Begriff der Beweisbarkeit eine Kluft besteht, die wir nicht überwinden können. Die Mathematik fügt sich in kein formales Korsett.Seit ihrer Entdeckung sind die Unvollständigkeitssätze in aller Munde und eine Flut an Büchern widmet sich ihrem fulminanten Inhalt. Doch kaum ein Werk behandelt die Gödel‘sche Arbeit in ihrer ursprünglichen Form − und dies hat triftige Gründe: Seine komplexen, in akribischer Präzision beschriebenen Argumentationsketten, die vielen Definitionen und Sätze und die heute weitgehend überholte Notation machen Gödels historisches Meisterwerk zu einer schwer zu lesenden Arbeit.In diesem Buch wird Gödels Beweis aus dem Jahr 1931 detailliert aufgearbeitet. Alle Einzelschritte werden erläutert und anhand zahlreicher Beispiele verständlich erklärt. Doch dieses Buch ist mehr als eine kommentierte Fassung der historischen Arbeit. Die Beweise der Unvollständigkeitssätze in vollem Umfang zu verstehen, bedingt, die Geschichte zu verstehen, und so versetzen zahlreiche Exkurse den Leser in die Zeit zu Beginn des zwanzigsten Jahrhunderts zurück. Es ist die Zeit, in der die Mathematik die größte Krise ihrer Geschichte durchlebte, die Typentheorie und die axiomatische Mengenlehre Gestalt annahmen und sich Hilberts formalistische Logik und Brouwers intuitionistische Mathematik mit offenem Visier gegenüber standen.Die 2. Auflage ist vollständig durchgesehen.Stimme zur ersten Auflage: „...eine didaktisch sehr gut gemachte Darstellung.“ Prof. Dr. Matthias Homeister, FH BrandenburgTable of ContentsEinleitung.- Die formalen Grundlagen der Mathematik.- Beweisskizze.- Das System P.- Primitiv-rekursive Funktionen.- Die Grenzen der Mathematik.- Epilog.
£36.09
Springer Fachmedien Wiesbaden Einführung in die Mathematische Logik: Ein
Book SynopsisDieses umfassende Lehrbuch wurde geschrieben für Studenten und Dozenten der Mathematik und Informatik, und wegen der ausführlichen Darstellung der Gödelschen Unvollständigkeitssätze auch für Fachstudenten der Philosophischen Logik. Für diese Neuauflage wurde der Text sachlich und stilistisch vollständig überarbeitet, er enthält verbesserte Beweise und Übungen mit Lösungshinweisen sowie eine historisch orientierte Einleitung. Das Buch kann ganz unabhängig von Vorlesungen aber auch zum Selbststudium genutzt werden. Table of ContentsAussagenlogik - Prädikatenlogik - Syntax und Semantik - Der Gödelsche Vollständigkeitssatz - Nichtstandardmodelle - Logikprogammierung - Resolution und Unifikation - Elemente der Modelltheorie - Ehrenfeucht-Spiele und Ultraprodukte - Entscheidbarkeit, Unentscheidbarkeit und Unvollständigkeit - Lösungshinweise zu den Übungen
£27.99
Springer Verlag Logica: Volume 1 - Dimostrazioni e modelli al
Book SynopsisGli autori, basandosi sulla loro esperienza di ricerca, propongono in due volumi un testo di riferimento per acquisire una solida formazione specialistica nella logica.Nei due volumi vengono presentati in maniera innovativa e rigorosa temi di logica tradizionalmente affrontati nei corsi universitari di secondo livello.Questo primo volume è dedicato ai teoremi fondamentali sulla logica del primo ordine e alle loro principali conseguenze.Il testo è rivolto in particolare agli studenti dei corsi di laurea magistrale.Table of Contents1 Introduzione.- 2 Alcune nozioni preliminari.- 3 Dimostrabilità e soddisfacibilità.- 4 Verso la teoria della dimostrazione: il teorema del taglio per LK.- 5 Verso la teoria dei modelli: alcune conseguenze del teorema di compattezza.
£18.99
Springer Verlag, Singapore Advances in Mathematical Logic: Dedicated to the
Book SynopsisGaisi Takeuti was one of the most brilliant, genius, and influential logicians of the 20th century. He was a long-time professor and professor emeritus of mathematics at the University of Illinois at Urbana-Champaign, USA, before he passed away on May 10, 2017, at the age of 91. Takeuti was one of the founders of Proof Theory, a branch of mathematical logic that originated from Hilbert's program about the consistency of mathematics. Based on Gentzen's pioneering works of proof theory in the 1930s, he proposed a conjecture in 1953 concerning the essential nature of formal proofs of higher-order logic now known as Takeuti's fundamental conjecture and of which he gave a partial positive solution. His arguments on the conjecture and proof theory in general have had great influence on the later developments of mathematical logic, philosophy of mathematics, and applications of mathematical logic to theoretical computer science. Takeuti's work ranged over the whole spectrum of mathematical logic, including set theory, computability theory, Boolean valued analysis, fuzzy logic, bounded arithmetic, and theoretical computer science. He wrote many monographs and textbooks both in English and in Japanese, and his monumental monograph Proof Theory, published in 1975, has long been a standard reference of proof theory. He had a wide range of interests covering virtually all areas of mathematics and extending to physics. His publications include many Japanese books for students and general readers about mathematical logic, mathematics in general, and connections between mathematics and physics, as well as many essays for Japanese science magazines. This volume is a collection of papers based on the Symposium on Advances in Mathematical Logic 2018. The symposium was held September 18–20, 2018, at Kobe University, Japan, and was dedicated to the memory of Professor Gaisi Takeuti. Table of ContentsS. Fuchino and A. Ottenbreit Ottenbreit Maschio Rodrigues, Reflection principles, generic large cardinals, and the Continuum Problem.- D. Ikegami and N. Trang, On supercompactness of ω1.- S. Iwata, Interpolation properties for Sacchetti’s logics.- T. Kurahashi, Rosser provability and the second incompleteness theorem.- H. Kurokawa, On Takeuti’s early view of the concept of set.- Yo Matsubara and T. Usuba, On Countable Stationary Towers.- M. Ozawa, Reforming Takeuti’s Quantum Set Theory to Satisfy De Morgan’s Laws.- T. Usuba, Choiceless Lowenheim-Skolem property and uniform definability of grounds.- M. Yasugi, Y. Tsujii, T. Mori, Irrational-based computability of functions.- M. Yasugi, “Gaisi Takeuti’s finitist standpoint” and its mathematical embodiment.- Y. Yoshinobu, Properness under closed forcing.
£123.49
Clarendon Press Features and Fluents
Book SynopsisTechniques for reasoning about actions an change in the physical world is one of the classical research topics in artificial intelligence. It is motivated by the needs of autonomous robots which must be able to anticipate their immediate future, to plan their future actions, and to figure out what went wrong in case of problems. It is also motivated by the needs of common-sense reasoning for example in the understanding of natural language texts, where processes and change over time is an ever-present phenomenon. The same set of problems arises in several other areas of computing such as in conceptual modelling for data bases, and in the rapidly growing area of intelligent control.The present research monograph presents and uses a novel methodology for reasoning about actions and change. Traditional research contributions have proposed new logic variants which were only supported by episodical examples. THe work described here uses a systematic methodology for identifying the exact ranTrade ReviewThe book presents deep and serious insight into inert and inhabited dynamical systems (IDS). * Zentralblatt fur Mathematik *Those working in nonmonotonic reasoning, planning, temporal logic, reasoning about actions and change, and related areas will find this book worth reading. * Computing Reviews *Table of ContentsInert and inhabited dynamical systems ; Inference operations on scenario descriptions ; Underlying semantics for IDS worlds ; Elementary feature logic and meta-logical concepts ; Lexical-domain object-feature logic ; Temporal feature logic for discrete time domains ; Chronicle completion in k-IA ; Intended models for chronicles in k-IA ; Entailment methods for k-IA using DFL-1 ; Duration constraints ; Entailment methods for k-OA using occlusion ; Composite actions ; Upper applicability bounds and assessment of soundness ; Future directions ; Terms index ; Notation ; References to related work
£93.72
Oxford University Press The Reasons Proper Study
Book SynopsisBob Hale and Crispin Wright draw together here the key writings in which they have worked out their distinctive neo-Fregean approach to the philosophy of mathematics. The two main components in Frege''s mathematical philosophy were his platonism and his logicism -- the claims, respectively, that mathematics is a body of knowledge about independently existing objects, and that this knowledge may be acquired on the basis of general logical laws and suitable definitions. The central thesis of this collection is that Frege was -- his own eventual recantation notwithstanding -- substantially right in both claims. Where neo-Fregeanism principally differs from Frege is in taking a more optimistic view of the kind of contextual explanation (proceeding via what are now commonly called abstraction principles) of the fundamental concepts of arithmetic and analysis which Frege considered and rejected. On this basis, neo-Fregeanism promises defensible and attractive answers to some of the most impoTable of ContentsI. ONTOLOGY AND ABSTRACTION PRINCIPLES ; II. RESPONSES TO CRITICS ; III. HUME'S PRINCIPLE ; IV. ON THE DIFFERENTIATION OF ABSTRACTA ; V. BEYOND NUMBER-THEORY
£55.10
Taylor & Francis Ltd Hex
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Taylor & Francis Ltd Beyond First Order Model Theory Volume II
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Taylor & Francis Time Logic
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Taylor & Francis Ltd Algorithms and Theory of Computation Handbook Volume 2 Special Topics and Techniques Chapman HallCRC Applied Algorithms and Data Structures series
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Taylor & Francis Nondeductive Inference 2 Routledge Library
Book SynopsisOriginally published in 1966. An introduction to current studies of kinds of inference in which validity cannot be determined by ordinary deductive models. In particular, inductive inference, predictive inference, statistical inference, and decision making are examined in some detail. The last chapter discusses the relationship of these forms of inference to philosophical notions of rationality. Special features of the monograph include a discussion of the legitimacy of various criteria for successful predictive inference, the development of an intuitive model which exhibits the difficulties of choosing probability measures over infinite sets, and a comparison of rival views on the foundations of probability in terms of the amount of information which the members of these schools believe suitable for fruitful formalization. The bibliographies include articles by statisticians accessible to students of symbolic logic. Table of Contents1. Inductive and Predictive Inference 2. Hypothesis and Predictive Inference 3. Probability and Predictive Inference 4. Statistical Inference 5. Bayesian Statistical Inference 6. Statistical Decision and Utility 7. Theories and Rationality 8. Bibliography
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Taylor & Francis Quantification Theory 7 Routledge Library Editions Logic
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Taylor & Francis Ltd The Equation of Knowledge
Book SynopsisThe Equation of Knowledge: From Bayes'' Rule to a Unified Philosophy of Science introduces readers to the Bayesian approach to science: teasing out the link between probability and knowledge. The author strives to make this book accessible to a very broad audience, suitable for professionals, students, and academics, as well as the enthusiastic amateur scientist/mathematician. This book also shows how Bayesianism sheds new light on nearly all areas of knowledge, from philosophy to mathematics, science and engineering, but also law, politics and everyday decision-making.Bayesian thinking is an important topic for research, which has seen dramatic progress in the recent years, and has a significant role to play in the understanding and development of AI and Machine Learning, among many other things. This book seeks to act as a tool for proselytising the benefits and limits of Bayesianism to a wider public. Features Trade ReviewLê Nguyên Hoang takes us on a fascinating intellectual journey into Bayesianism, cutting across many social and natural sciences. The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science is a real page turner.—George Zaccour, HEC Montréal and co-author of Handbook of Dynamic Game Theory"Each chapter is opened with a fascinating epigraph quoting famous persons, and is completed by the most recent references. There are multiple illustrations, and the Bayes’ formulae are many times presented via various funny symbols of emoji kind. The book is addressed to a wide audience of students, professionals, and actually any reader interested to be better acquainted with modern ideas in various sciences and philosophy of science, and their Bayesian statistical description and interpretation."— Stan Lipovetsky, Technometrics (Volume 63, 2021 - Issue 1)"[. . . ] Trained in the hard school of online videos, Le Nguyen Hoang has found a new tone to talk about science, a tone that is both rigorous and narrative, where examples illuminate the most abstract questions."— From the Foreword by Gilles Dowek, Professor at École Polytechnique and researcher at the Laboratoire d'Informatique de l'École Polytechnique and the Institut National de Recherche en Informatique et en Automatique (INRIA).Lê Nguyên Hoang takes us on a fascinating intellectual journey into Bayesianism, cutting across many social and natural sciences. The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science is a real page turner.— George Zaccour, HEC Montréal and co-author of Handbook of Dynamic Game Theory"Making math accessible to everyone, showing its connections with dozens of different domains, narrating scientific discovery as a personal human adventure, and sharing impressive enthusiasm: there is definitely something of Greg Chaitin's Meta Math! in Lê Nguyên Hoang's book!" — Rémi Peyre, École des Mines de Nancy"A remarkable piece of work, broad and insightful at the same time. This book is unique in that it gives an accessible journey from subtle probabilistic puzzles to the most advanced concepts at the heart of the machine learning revolution; with unrivalled clarity, it exposes deep ideas that have remained very confidential outside of specialized circles, and that yet are becoming fundamental in the way we understand our world."— Clément Hongler, Associate Professor and Chair of Statistical Field Theory, EPFL "As someone who practices research and publishes academic papers, it is frustrating to note how little we, scientists, are trained in epistemology. ‘How do we know that we know?’ This question is often neglected or taken for granted. The recent controversies about reproducibility of scientific publishing might be one of the tips of a larger iceberg. This book will, in my opinion, be remembered as one of those that helped melt the iceberg." — El Mahdi El Mhamdi, École Polytechnique Fédérale de Lausanne."The book has a lively writing style, rather like you are listening to an inspiring lecturer. Indeed the author has a French YouTube channel and is clearly enthusiastic about exposition. It is overtly an account of what the author personally finds interesting. [. . .] In teaching a basic college course, focused on the mathematical setup and on the analysis of data, I often find there is one student who comes to office hours and is interested in seeing connections with broad scientific fields, or in conceptual issues of the philosophy of science. I could certainly recommend this book to such a student. Similarly, for the MAA community it could be an innovative basis for an undergraduate seminar course, in which students would choose a topic from the book and delve deeper into it."— David Aldous, Mathematical Association of AmericaTable of ContentsSction I. Pure Bayesianism. 1. On A Transformative Journey. 2. Bayes Theorem. 3. Logically Speaking... 4. Let’s Generalize! 5. All Hail Prejudices. 6. The Bayesian Prophets. 7. Solomonoff’s Demon. Section II. Applied Bayesianism. 8. Can You Keep A Secret? 9. Game, Set and Math. 10. Will Darwin Select Bayes? 11. Exponentially Counter-Intuitive. 12. Ockham Cuts to the Chase. 13. Facts Are Misleading. Section III. Pragmatic Bayesianism. 14. Quick And Not Too Dirty. 15. Wish Me Luck. 16. Down Memory Lane. 17. Let’s Sleep On It. 18. The Unreasonable Effectiveness of Abstraction. 19. The Bayesian Brain. Section IV. Beyond Bayesianism. 20. It’s All Fiction. 21. Exploring The Origins Of Beliefs. 22. Beyond Bayesianism.
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