Inconsistent Mathematics

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Inconsistent Mathematics

C.E. Mortensen
Inconsistent Mathematics Book PDF

Author : C.E. Mortensen
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 46,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401584531

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Inconsistent Mathematics by C.E. Mortensen Pdf

without a properly developed inconsistent calculus based on infinitesimals, then in consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories.

Paradoxes and Inconsistent Mathematics

Zach Weber
Paradoxes and Inconsistent Mathematics Book PDF

Author : Zach Weber
Publisher : Cambridge University Press
Page : 339 pages
File Size : 41,5 Mb
Release : 2021-10-21
Category : Mathematics
ISBN : 9781108834414

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Paradoxes and Inconsistent Mathematics by Zach Weber Pdf

Why are there paradoxes? This book uses paraconsistent logic to develop the mathematics to find out.

50 Visions of Mathematics

Sam Parc
50 Visions of Mathematics Book PDF

Author : Sam Parc
Publisher : Oxford University Press
Page : 225 pages
File Size : 51,8 Mb
Release : 2014-05
Category : Mathematics
ISBN : 9780198701811

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50 Visions of Mathematics by Sam Parc Pdf

"To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain"--Provided by publisher.

Applying Mathematics

Otávio Bueno,Steven French
Applying Mathematics Book PDF

Author : Otávio Bueno,Steven French
Publisher : Oxford University Press
Page : 288 pages
File Size : 54,8 Mb
Release : 2018-05-24
Category : Science
ISBN : 9780192546654

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Applying Mathematics by Otávio Bueno,Steven French Pdf

How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? What has been called 'the unreasonable effectiveness of mathematics' sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character, whereas others have pointed to the range of structures that mathematics offers. Otávio Bueno and Steven French offer a middle way, which focuses on the moves that have to be made in both the mathematics and the relevant physics in order to bring the two into appropriate relation. This relation can be captured via the inferential conception of the applicability of mathematics, which is formulated in terms of immersion, inference, and interpretation. In particular, the roles of idealisations and of surplus structure in science and mathematics respectively are brought to the fore and captured via an approach to models and theories that emphasize the partiality of the available information: the partial structures approach. The discussion as a whole is grounded in a number of case studies drawn from the history of quantum physics, and extended to contest recent claims that the explanatory role of certain mathematical structures in scientific practice supports a realist attitude towards them. The overall conclusion is that the effectiveness of mathematics does not seem unreasonable at all once close attention is paid to how it is actually applied in practice.

Encyclopaedia of Mathematics

Michiel Hazewinkel
Encyclopaedia of Mathematics Book PDF

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512886

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Inconsistent Geometry

Chris Mortensen
Inconsistent Geometry Book PDF

Author : Chris Mortensen
Publisher : Unknown
Page : 174 pages
File Size : 50,7 Mb
Release : 2010
Category : Mathematics
ISBN : 1848900228

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Inconsistent Geometry by Chris Mortensen Pdf

The Theory of Inconsistency has a long lineage, stretching back to Herakleitos, Hegel and Marx. In the late twentieth-century, it was placed on a rigorous footing with the discovery of paraconsistent logic and inconsistent mathematics. Paraconsistent logics, many of which are now known, are "inconsistency tolerant," that is, they lack the rule of Boolean logic that a contradiction implies every proposition. When this constricting rule was seen to be arbitrary, inconsistent mathematical structures were free to be described. This book continues the development of inconsistent mathematics by taking up inconsistent geometry, hitherto largely undeveloped. It has two main goals. First, various geometrical structures are shown to deliver models for paraconsistent logics. Second, the "impossible pictures" of Reutersvaard, Escher, the Penroses and others are addressed. The idea is to derive inconsistent mathematical descriptions of the content of impossible pictures, so as to explain rigorously how they can be impossible and yet classifiable into several basic types. The book will be of interest to logicians, mathematicians, philosophers, psychologists, cognitive scientists, and artists interested in impossible images. It contains a gallery of previously-unseen coloured images, which illustrates the possibilities available in representing impossible geometrical shapes. Chris Mortensen is Emeritus Professor of Philosophy at the University of Adelaide. He is the author of Inconsistent Mathrmatics (Kluwer 1995), and many articles in the Theory of Inconsistency.

Time-Inconsistent Control Theory with Finance Applications

Tomas Björk,Mariana Khapko,Agatha Murgoci
Time Inconsistent Control Theory with Finance Applications Book PDF

Author : Tomas Björk,Mariana Khapko,Agatha Murgoci
Publisher : Springer Nature
Page : 328 pages
File Size : 52,7 Mb
Release : 2021-11-02
Category : Mathematics
ISBN : 9783030818432

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Time-Inconsistent Control Theory with Finance Applications by Tomas Björk,Mariana Khapko,Agatha Murgoci Pdf

This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications. In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker’s preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent’s current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.

Understanding Inconsistent Science

Peter Vickers
Understanding Inconsistent Science Book PDF

Author : Peter Vickers
Publisher : Oxford University Press
Page : 286 pages
File Size : 55,8 Mb
Release : 2013-08-22
Category : Philosophy
ISBN : 9780199692026

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Understanding Inconsistent Science by Peter Vickers Pdf

Peter Vickers examines 'inconsistent theories' in the history of science—theories which, though contradictory, are held to be extremely useful. He argues that these 'theories' are actually significantly different entities, and warns that the traditional goal of philosophy to make substantial, general claims about how science works is misguided.

Doubt Truth to be a Liar

Graham Priest
Doubt Truth to be a Liar Book PDF

Author : Graham Priest
Publisher : Clarendon Press
Page : 240 pages
File Size : 40,9 Mb
Release : 2005-12-15
Category : Philosophy
ISBN : 9780191532474

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Doubt Truth to be a Liar by Graham Priest Pdf

Dialetheism is the view that some contradictions are true. This is a view which runs against orthodoxy in logic and metaphysics since Aristotle, and has implications for many of the core notions of philosophy. Doubt Truth to Be a Liar explores these implications for truth, rationality, negation, and the nature of logic, and develops further the defence of dialetheism first mounted in Priest's In Contradiction, a second edition of which is also available.

Oral Storytelling and Teaching Mathematics

Michael Schiro
Oral Storytelling and Teaching Mathematics Book PDF

Author : Michael Schiro
Publisher : SAGE
Page : 284 pages
File Size : 43,6 Mb
Release : 2004-03-19
Category : Education
ISBN : 0761930108

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Oral Storytelling and Teaching Mathematics by Michael Schiro Pdf

Oral Story Telling And Teaching Mathematics provides the first serious exploration of the role that oral storytelling can play in helping children learn mathematics. It should be of interest to those concerned with providing children with powerful mathematical and literary experiences and those concerned with multicultural education. An accompanying CD-ROM contains the full text of two epic stories plus addition worksheets and handouts.

Shadows of Syntax

Jared Warren
Shadows of Syntax Book PDF

Author : Jared Warren
Publisher : Oxford University Press, USA
Page : 409 pages
File Size : 46,6 Mb
Release : 2020
Category : Mathematics
ISBN : 9780190086152

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Shadows of Syntax by Jared Warren Pdf

What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. In Shadows of Syntax, Jared Warren offers the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. He argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims. In Part I, Warren explains exactly what conventionalism amounts to and what linguistic conventions are. Part II develops an unrestricted inferentialist theory of the meanings of logical constants that leads to logical conventionalism. This conventionalist theory is elaborated in discussions of logical pluralism, the epistemology of logic, and of the influential objections that led to the historical demise of conventionalism. Part III aims to extend conventionalism from logic to mathematics. Unlike logic, mathematics involves both ontological commitments and a rich notion of truth that cannot be generated by any algorithmic process. To address these issues Warren develops conventionalist-friendly but independently plausible theories of both metaontology and mathematical truth. Finally, Part IV steps back to address big picture worries and meta-worries about conventionalism. This book develops and defends a unified theory of logic and mathematics according to which logical and mathematical truths are reflections of our linguistic rules, mere shadows of syntax.

An Historical Introduction to the Philosophy of Mathematics: A Reader

Russell Marcus,Mark McEvoy
An Historical Introduction to the Philosophy of Mathematics A Reader Book PDF

Author : Russell Marcus,Mark McEvoy
Publisher : Bloomsbury Publishing
Page : 896 pages
File Size : 49,9 Mb
Release : 2016-02-11
Category : Philosophy
ISBN : 9781472532916

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An Historical Introduction to the Philosophy of Mathematics: A Reader by Russell Marcus,Mark McEvoy Pdf

A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.

Principia Mathematica

Alfred North Whitehead,Bertrand Russell
Principia Mathematica Book PDF

Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 41,6 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X

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Principia Mathematica by Alfred North Whitehead,Bertrand Russell Pdf

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

Language and Mathematics

Marcel Danesi
Language and Mathematics Book PDF

Author : Marcel Danesi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 344 pages
File Size : 42,8 Mb
Release : 2016-06-06
Category : Language Arts & Disciplines
ISBN : 9781501500367

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Language and Mathematics by Marcel Danesi Pdf

This book explores the many disciplinary and theoretical links between language, linguistics, and mathematics. It examines trends in linguistics, such as structuralism, conceptual metaphor theory, and other relevant theories,to show that language and mathematics have a similar structure, but differential functions, even though one without the other would not exist.

Elementary Mathematics from a Higher Standpoint

Felix Klein
Elementary Mathematics from a Higher Standpoint Book PDF

Author : Felix Klein
Publisher : Springer
Page : 315 pages
File Size : 51,7 Mb
Release : 2016-06-29
Category : Education
ISBN : 9783662494455

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Elementary Mathematics from a Higher Standpoint by Felix Klein Pdf

These three volumes constitute the first complete English translation of Felix Klein’s seminal series “Elementarmathematik vom höheren Standpunkte aus”. “Complete” has a twofold meaning here: First, there now exists a translation of volume III into English, while until today the only translation had been into Chinese. Second, the English versions of volume I and II had omitted several, even extended parts of the original, while we now present a complete revised translation into modern English. The volumes, first published between 1902 and 1908, are lecture notes of courses that Klein offered to future mathematics teachers, realizing a new form of teacher training that remained valid and effective until today: Klein leads the students to gain a more comprehensive and methodological point of view on school mathematics. The volumes enable us to understand Klein’s far-reaching conception of elementarisation, of the “elementary from a higher standpoint”, in its implementation for school mathematics./div This volume II presents a paradigmatic realisation of Klein’s approach of elementarisation for teacher education. It is shown how the various geometries, elaborated particularly since the beginning of the 19th century, are revealed as becoming unified in a new restructured geometry. As Klein liked to stress: “Projective geometry is all geometry”. Non-Euclidean geometry proves to constitute a part of this unifying process. The teaching of geometry is discussed in a separate chapter, which provides moreover important information on the history of geometry teaching and an international comparison.