Paradoxes And Inconsistent Mathematics
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Paradoxes And Inconsistent Mathematics
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Author : Zach Weber
language : en
Publisher: Cambridge University Press
Release Date : 2021-10-21
Paradoxes And Inconsistent Mathematics written by Zach Weber and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-21 with Mathematics categories.
Why are there paradoxes? This book uses paraconsistent logic to develop the mathematics to find out.
Inconsistent Mathematics
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Author : C.E. Mortensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Inconsistent Mathematics written by C.E. Mortensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.
Mathematical Fallacies And Paradoxes
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Author : Bryan Bunch
language : en
Publisher: Courier Corporation
Release Date : 2012-10-16
Mathematical Fallacies And Paradoxes written by Bryan Bunch and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-16 with Mathematics categories.
Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.
Paradox And Paraconsistency
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Author : John Woods
language : en
Publisher: Cambridge University Press
Release Date : 2003
Paradox And Paraconsistency written by John Woods and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
In a world plagued by disagreement and conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible, systems. Do these disagreements admit of resolution? Can such resolution be achieved without disturbing assumptions that the theorems of logic and mathematics state objective truths about the real world? In this original and historically rich book John Woods explores apparently intractable disagreements in logic and the foundations of mathematics and sets out conflict resolution strategies that evade or disarm these stalemates. An important sub-theme of the book is the extent to which pluralism in logic and the philosophy of mathematics undermines realist assumptions. This book makes an important contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It will also be of interest to mathematicians and computer scientists.
The Sorites Paradox
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Author : Sergi Oms
language : en
Publisher: Cambridge University Press
Release Date : 2019-10-10
The Sorites Paradox written by Sergi Oms and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-10 with Philosophy categories.
Offers a systematic introduction and discussion of all the main solutions to the sorites paradox and its areas of influence.
Paraconsistency Logic And Applications
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Author : Koji Tanaka
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-26
Paraconsistency Logic And Applications written by Koji Tanaka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-26 with Philosophy categories.
A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.
Proofs And Research Programmes Lakatos At 100
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Author : Roman Frigg
language : en
Publisher: Springer Nature
Release Date : 2025-08-10
Proofs And Research Programmes Lakatos At 100 written by Roman Frigg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-10 with Science categories.
This open access book offers new insights into issues raised in philosophy of mathematics and in philosophy of science by Imre Lakatos. Lakatos was one of the most significant philosophers of the 20th Century, and his ideas remain important and relevant today. November 2022 saw the centenary of Lakatos’s birth, and the event was marked by an international conference held at the LSE – where Lakatos made his career after he had emigrated from Hungary to England. This volume consists of a selection of papers presented at the conference along with two additional contributions to debates about Lakatos’s continuing influence and importance.
Paradoxes From A To Z
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Author : Michael Clark
language : en
Publisher: Psychology Press
Release Date : 2002
Paradoxes From A To Z written by Michael Clark and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Philosophy categories.
'This sentence is false'. Is it? If a hotel with an infinite number of rooms is fully occupied, can it still accommodate a new guest? How can we have emotional responses to fiction, when we know that the objects of our emotions do not exist?
Principia Mathematica
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Author : Alfred North Whitehead
language : en
Publisher: Cambridge University Press
Release Date : 1927
Principia Mathematica written by Alfred North Whitehead and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Mathematics categories.
The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.
The Oxford Handbook Of Truth
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Author : Michael Glanzberg
language : en
Publisher: Oxford University Press
Release Date : 2018-07-04
The Oxford Handbook Of Truth written by Michael Glanzberg and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-04 with Philosophy categories.
Truth is one of the central concepts in philosophy, and has been a perennial subject of study. Michael Glanzberg has brought together 36 leading experts from around the world to produce the definitive guide to philosophical issues to do with truth. They consider how the concept of truth has been understood from antiquity to the present day, surveying major debates about truth during the emergence of analytic philosophy. They offer critical assessments of the standard theories of truth, including the coherence, correspondence, identity, and pragmatist theories. They explore the role of truth in metaphysics, with lively discussion of truthmakers, proposition, determinacy, objectivity, deflationism, fictionalism, relativism, and pluralism. Finally the handbook explores broader applications of truth in philosophy, including ethics, science, and mathematics, and reviews formal work on truth and its application to semantic paradox. This Oxford Handbook will be an invaluable resource across all areas of philosophy.