Mathematical Anti Realism And Modal Nothingism

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Mathematical Anti-Realism and Modal Nothingism

Author : Mark Balaguer
Publisher : Cambridge University Press
ISBN 13 : 1009346040
Total Pages : 151 pages
Book Rating : 4.0/5 (93 download)

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Book Synopsis Mathematical Anti-Realism and Modal Nothingism by : Mark Balaguer

Download or read book Mathematical Anti-Realism and Modal Nothingism written by Mark Balaguer and published by Cambridge University Press. This book was released on 2023-01-05 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element defends mathematical anti-realism against an underappreciated problem with that view-a problem having to do with modal truthmaking. Part I develops mathematical anti-realism, it defends that view against a number of well-known objections, and it raises a less widely discussed objection to anti-realism-an objection based on the fact that (a) mathematical anti-realists need to commit to the truth of certain kinds of modal claims, and (b) it's not clear that the truth of these modal claims is compatible with mathematical anti-realism. Part II considers various strategies that anti-realists might pursue in trying to solve this modal-truth problem with their view, it argues that there's only one viable view that anti-realists can endorse in order to solve the modal-truth problem, and it argues that the view in question-which is here called modal nothingism-is true.

Mathematical Pluralism

Author : Graham Priest
Publisher :
ISBN 13 : 1009089269
Total Pages : 82 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Mathematical Pluralism by : Graham Priest

Download or read book Mathematical Pluralism written by Graham Priest and published by . This book was released on 2024-04-16 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical pluralism is the view that there is an irreducible plurality of pure mathematical structures, each with their own internal logics; and that qua pure mathematical structures they are all equally legitimate. Mathematical pluralism is a relatively new position on the philosophical landscape. This Element provides an introduction to the position.

Mathematics and Explanation

Author : Christopher Pincock
Publisher : Cambridge University Press
ISBN 13 : 1009037412
Total Pages : 156 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Mathematics and Explanation by : Christopher Pincock

Download or read book Mathematics and Explanation written by Christopher Pincock and published by Cambridge University Press. This book was released on 2023-05-25 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element answers four questions. Can any traditional theory of scientific explanation make sense of the place of mathematics in explanation? If traditional monist theories are inadequate, is there some way to develop a more flexible, but still monist, approach that will clarify how mathematics can help to explain? What sort of pluralism about explanation is best equipped to clarify how mathematics can help to explain in science and in mathematics itself? Finally, how can the mathematical elements of an explanation be integrated into the physical world? Some of the evidence for a novel scientific posit may be traced to the explanatory power that this posit would afford, were it to exist. Can a similar kind of explanatory evidence be provided for the existence of mathematical objects, and if not, why not?

Phenomenology and Mathematics

Author : Michael Roubach
Publisher : Cambridge University Press
ISBN 13 : 1009002287
Total Pages : 149 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Phenomenology and Mathematics by : Michael Roubach

Download or read book Phenomenology and Mathematics written by Michael Roubach and published by Cambridge University Press. This book was released on 2023-11-30 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element explores the relationship between phenomenology and mathematics. Its focus is the mathematical thought of Edmund Husserl, founder of phenomenology, but other phenomenologists and phenomenologically-oriented mathematicians, including Weyl, Becker, Gödel, and Rota, are also discussed. After outlining the basic notions of Husserl's phenomenology, the author traces Husserl's journey from his early mathematical studies. Phenomenology's core concepts, such as intention and intuition, each contributed to the emergence of a phenomenological approach to mathematics. This Element examines the phenomenological conceptions of natural number, the continuum, geometry, formal systems, and the applicability of mathematics. It also situates the phenomenological approach in relation to other schools in the philosophy of mathematics-logicism, formalism, intuitionism, Platonism, the French epistemological school, and the philosophy of mathematical practice.

The Euclidean Programme

Author : A. C. Paseau
Publisher : Cambridge University Press
ISBN 13 : 100922199X
Total Pages : 153 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis The Euclidean Programme by : A. C. Paseau

Download or read book The Euclidean Programme written by A. C. Paseau and published by Cambridge University Press. This book was released on 2024-02-29 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Euclidean Programme embodies a traditional sort of epistemological foundationalism, according to which knowledge – especially mathematical knowledge – is obtained by deduction from self-evident axioms or first principles. Epistemologists have examined foundationalism extensively, but neglected its historically dominant Euclidean form. By contrast, this book offers a detailed examination of Euclidean foundationalism, which, following Lakatos, the authors call the Euclidean Programme. The book rationally reconstructs the programme's key principles, showing it to be an epistemological interpretation of the axiomatic method. It then compares the reconstructed programme with select historical sources: Euclid's Elements, Aristotle's Posterior Analytics, Descartes's Discourse on Method, Pascal's On the Geometric Mind and a twentieth-century account of axiomatisation. The second half of the book philosophically assesses the programme, exploring whether various areas of contemporary mathematics conform to it. The book concludes by outlining a replacement for the Euclidean Programme.

Number Concepts

Author : Richard Samuels
Publisher : Cambridge University Press
ISBN 13 : 100905967X
Total Pages : 100 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Number Concepts by : Richard Samuels

Download or read book Number Concepts written by Richard Samuels and published by Cambridge University Press. This book was released on 2024-02-07 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts.

Philosophical Uses of Categoricity Arguments

Author : Penelope Maddy
Publisher : Cambridge University Press
ISBN 13 : 1009432915
Total Pages : 75 pages
Book Rating : 4.0/5 (94 download)

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Book Synopsis Philosophical Uses of Categoricity Arguments by : Penelope Maddy

Download or read book Philosophical Uses of Categoricity Arguments written by Penelope Maddy and published by Cambridge University Press. This book was released on 2023-12-21 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element addresses the viability of categoricity arguments in philosophy by focusing with some care on the specific conclusions that a sampling of prominent figures have attempted to draw – the same theorem might successfully support one such conclusion while failing to support another. It begins with Dedekind, Zermelo, and Kreisel, casting doubt on received readings of the latter two and highlighting the success of all three in achieving what are argued to be their actual goals. These earlier uses of categoricity arguments are then compared and contrasted with more recent work of Parsons and the co-authors Button and Walsh. Highlighting the roles of first- and second-order theorems, of external and internal theorems, the Element concludes that categoricity arguments have been more effective in historical cases that reflect philosophically on internal mathematical matters than in recent questions of pre-theoretic metaphysics.

Iterative Conceptions of Set

Author : Neil Barton
Publisher : Cambridge University Press
ISBN 13 : 1009227254
Total Pages : 122 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Iterative Conceptions of Set by : Neil Barton

Download or read book Iterative Conceptions of Set written by Neil Barton and published by Cambridge University Press. This book was released on 2024-06-30 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many philosophers are aware of the paradoxes of set theory (e.g. Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages. This Element will examine possibilities for articulating this solution. In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best. Along the way, the author hopes to make some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers more widely and make their relationships to some other questions in philosophy perspicuous.

Fictionalism in Philosophy

Author : Bradley Armour-Garb
Publisher :
ISBN 13 : 0190689609
Total Pages : 257 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis Fictionalism in Philosophy by : Bradley Armour-Garb

Download or read book Fictionalism in Philosophy written by Bradley Armour-Garb and published by . This book was released on 2020 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects some of the most up-to-date work on philosophical fictionalism-the idea that a notion of pretense or fiction can help resolve certain puzzles or problems in philosophy. After a detailed discussion in the book's introductory chapter of how philosophers should think of fictionalism and its connection to metaontology more generally, the remaining chapters provide readers with arguments for and against this view from leading scholars in the fields of epistemology, ethics, metaphysics, philosophy of science, philosophy of language, and others.

Metaphysics, Sophistry, and Illusion

Author : Mark Balaguer
Publisher : Oxford University Press
ISBN 13 : 0192638831
Total Pages : 336 pages
Book Rating : 4.1/5 (926 download)

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Book Synopsis Metaphysics, Sophistry, and Illusion by : Mark Balaguer

Download or read book Metaphysics, Sophistry, and Illusion written by Mark Balaguer and published by Oxford University Press. This book was released on 2021-01-26 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metaphysics, Sophistry, and Illusion does two things. First, it introduces a novel kind of non-factualist view, and argues that we should endorse views of this kind in connection with a wide class of metaphysical questions, most notably, the abstract-object question and the composite-object question. (More specifically, Mark Balaguer argues that there's no fact of the matter whether there are any such things as abstract objects or composite objects—or material objects of any other kind.) Second, Metaphysics, Sophistry, and Illusion explains how these non-factualist views fit into a general anti-metaphysical view called neo-positivism, and explains how we could argue that neo-positivism is true. Neo-positivism is the view that every metaphysical question decomposes into some subquestions—call them Q1, Q2, Q3, etc.—such that, for each of these subquestions, one of the following three anti-metaphysical views is true of it: non-factualism, or scientism, or metaphysically innocent modal-truth-ism. These three views can be defined (very roughly) as follows: non-factualism about a question Q is the view that there's no fact of the matter about the answer to Q. Scientism about Q is the view that Q is an ordinary empirical-scientific question about some contingent aspect of physical reality, and Q can't be settled with an a priori philosophical argument. And metaphysically innocent modal-truth-ism about Q is the view that Q asks about the truth value of a modal sentence that's metaphysically innocent in the sense that it doesn't say anything about reality and, if it's true, isn't made true by reality

Shadows of Syntax

Author : Jared Warren
Publisher : Oxford University Press
ISBN 13 : 0190086165
Total Pages : 409 pages
Book Rating : 4.1/5 (9 download)

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Book Synopsis Shadows of Syntax by : Jared Warren

Download or read book Shadows of Syntax written by Jared Warren and published by Oxford University Press. This book was released on 2020-07-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Platonism and Anti-Platonism in Mathematics

Author : Mark Balaguer
Publisher :
ISBN 13 : 9780195143980
Total Pages : 234 pages
Book Rating : 4.1/5 (439 download)

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Book Synopsis Platonism and Anti-Platonism in Mathematics by : Mark Balaguer

Download or read book Platonism and Anti-Platonism in Mathematics written by Mark Balaguer and published by . This book was released on 2001 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible. (Philosophy)

Ontology and the Foundations of Mathematics

Author : Penelope Rush
Publisher : Cambridge University Press
ISBN 13 : 1108626564
Total Pages : 93 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Ontology and the Foundations of Mathematics by : Penelope Rush

Download or read book Ontology and the Foundations of Mathematics written by Penelope Rush and published by Cambridge University Press. This book was released on 2022-02-10 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element looks at the problem of inter-translation between mathematical realism and anti-realism and argues that so far as realism is inter-translatable with anti-realism, there is a burden on the realist to show how her posited reality differs from that of the anti-realist. It also argues that an effective defence of just such a difference needs a commitment to the independence of mathematical reality, which in turn involves a commitment to the ontological access problem – the problem of how knowable mathematical truths are identifiable with a reality independent of us as knowers. Specifically, if the only access problem acknowledged is the epistemological problem – i.e. the problem of how we come to know mathematical truths – then nothing is gained by the realist notion of an independent reality and in effect, nothing distinguishes realism from anti-realism in mathematics.

Free Will as an Open Scientific Problem

Author : Mark Balaguer
Publisher : MIT Press
ISBN 13 : 0262266156
Total Pages : 213 pages
Book Rating : 4.2/5 (622 download)

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Book Synopsis Free Will as an Open Scientific Problem by : Mark Balaguer

Download or read book Free Will as an Open Scientific Problem written by Mark Balaguer and published by MIT Press. This book was released on 2012-01-13 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: An argument that the problem of free will boils down to an open scientific question about the causal histories of certain kinds of neural events. In this largely antimetaphysical treatment of free will and determinism, Mark Balaguer argues that the philosophical problem of free will boils down to an open scientific question about the causal histories of certain kinds of neural events. In the course of his argument, Balaguer provides a naturalistic defense of the libertarian view of free will. The metaphysical component of the problem of free will, Balaguer argues, essentially boils down to the question of whether humans possess libertarian free will. Furthermore, he argues that, contrary to the traditional wisdom, the libertarian question reduces to a question about indeterminacy—in particular, to a straightforward empirical question about whether certain neural events in our heads are causally undetermined in a certain specific way; in other words, Balaguer argues that the right kind of indeterminacy would bring with it all of the other requirements for libertarian free will. Finally, he argues that because there is no good evidence as to whether or not the relevant neural events are undetermined in the way that's required, the question of whether human beings possess libertarian free will is a wide-open empirical question.

Sharpening Mathematical Analysis Skills

Author : Alina Sîntămărian
Publisher : Springer Nature
ISBN 13 : 3030771393
Total Pages : 543 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Sharpening Mathematical Analysis Skills by : Alina Sîntămărian

Download or read book Sharpening Mathematical Analysis Skills written by Alina Sîntămărian and published by Springer Nature. This book was released on 2021-10-25 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methods for proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises. Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren’t commonly seen in regular textbooks.

Pocket Dictionary of Apologetics & Philosophy of Religion

Author : C. Stephen Evans
Publisher : InterVarsity Press
ISBN 13 : 0830867015
Total Pages : 127 pages
Book Rating : 4.8/5 (38 download)

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Book Synopsis Pocket Dictionary of Apologetics & Philosophy of Religion by : C. Stephen Evans

Download or read book Pocket Dictionary of Apologetics & Philosophy of Religion written by C. Stephen Evans and published by InterVarsity Press. This book was released on 2010-03-17 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as a companion to the study of apologetics and philosophy of religion, this pocket dictionary by C. Stephen Evans offers 300 entries covering terms, apologists, philosophers, movements, apologetic arguments and theologies.

A Combinatorial Theory of Possibility

Author : D. M. Armstrong
Publisher : Cambridge University Press
ISBN 13 : 9780521377805
Total Pages : 174 pages
Book Rating : 4.3/5 (778 download)

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Book Synopsis A Combinatorial Theory of Possibility by : D. M. Armstrong

Download or read book A Combinatorial Theory of Possibility written by D. M. Armstrong and published by Cambridge University Press. This book was released on 1989-09-29 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface Part I. Non-Naturalist Theories of Possibility: 1. Causal argument 2. Non-Naturalist theories of possibility Part II. A Combinatorial and Naturalist Account of Possibility: 3. Possibility in a simple world 4. Expanding and contracting the world 5. Relative atoms 6. Are there de re incompatibilities and necessities? 7. Higher-order entities, negation and causation 8. Supervenience 9. Mathematics 10. Final questions: logic Works cited Appendix: Tractarian Nominalism Brian Skyrms Index.