Author : Graham Priest
Publisher : Cambridge University Press
Page : 93 pages
File Size : 19,11 MB
Release : 2024-04-30
Category : Philosophy
ISBN : 1009089080
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.
Author : Graham Priest
Publisher :
Page : 82 pages
File Size : 25,89 MB
Release : 2024-04-16
Category : Philosophy
ISBN : 1009089269
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.
Author : Michèle Friend
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 21,61 MB
Release : 2013-11-20
Category : Science
ISBN : 9400770588
This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word ‘pluralism’ with care.
Author : Bharath Sriraman
Publisher : Springer Nature
Page : 3221 pages
File Size : 30,26 MB
Release :
Category :
ISBN : 3031408462
Author : Justin Clarke-Doane
Publisher : Oxford University Press, USA
Page : 219 pages
File Size : 19,40 MB
Release : 2020-03-12
Category : Mathematics
ISBN : 0198823665
To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the "genealogy" of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together -- and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.
Author : Ahmet Cevik
Publisher : CRC Press
Page : 352 pages
File Size : 34,61 MB
Release : 2021-11-09
Category : Mathematics
ISBN : 1000468801
The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France
Author : Justin Clarke-Doane
Publisher : Cambridge University Press
Page : 105 pages
File Size : 28,18 MB
Release : 2022-06-30
Category : Science
ISBN : 1009002295
This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap's pragmatism, transposed to the key of realism.
Author : Michele Friend
Publisher :
Page : 312 pages
File Size : 16,12 MB
Release : 2013-09-30
Category :
ISBN : 9789400770591
Author : Christopher Cowie
Publisher : Routledge
Page : 224 pages
File Size : 17,69 MB
Release : 2019-09-24
Category : Philosophy
ISBN : 042984641X
Comparisons between morality and other ‘companion’ disciplines – such as mathematics, religion, or aesthetics – are commonly used in philosophy, often in the context of arguing for the objectivity of morality. This is known as the ‘companions in guilt’ strategy. It has been the subject of much debate in contemporary ethics and metaethics. This volume, the first full length examination of companions in guilt arguments, comprises an introduction by the editors and a dozen new chapters by leading authors in the field. They examine the methodology of companions in guilt arguments and their use in responding to the moral error theory, as well as specific arguments that take mathematics, epistemic norms, or aesthetics as a ‘companion’, and the use of the companions in guilt strategy to vindicate claims to moral knowledge. Companions in Guilt Arguments in Metaethics is essential reading for advanced students and researchers working in moral theory and metaethics, as well as those in epistemology and philosophy of mathematics concerned with the intersection of these subjects with ethics.
Author : Alan Bishop
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 45,37 MB
Release : 2003-06-30
Category : Education
ISBN : 9781402010088
This edition is an essential resource for students, researchers, teacher educators and curriculum policy makers in the field of mathematics education.
