Naturalizing Logico Mathematical Knowledge

Author : Sorin Bangu
Publisher : Routledge
Page : 319 pages
File Size : 54,8 Mb
Release : 2018-02-01
Category : Mathematics
ISBN : 9781351998444

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Naturalizing Logico-Mathematical Knowledge by Sorin Bangu Pdf

This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.

Author : Richard Samuels,Eric Snyder
Publisher : Cambridge University Press
Page : 179 pages
File Size : 51,7 Mb
Release : 2024-02-29
Category : Philosophy
ISBN : 9781009059473

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Number Concepts by Richard Samuels,Eric Snyder Pdf

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.

Author : Kim Byunghan,Brendle Jorg,Lee Gyesik,Liu Fenrong,Ramanujam R,Srivastava Shashi M,Tsuboi Akito,Yu Liang
Publisher : World Scientific
Page : 312 pages
File Size : 51,7 Mb
Release : 2019-01-16
Category : Mathematics
ISBN : 9789813237568

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Proceedings Of The 14th And 15th Asian Logic Conferences by Kim Byunghan,Brendle Jorg,Lee Gyesik,Liu Fenrong,Ramanujam R,Srivastava Shashi M,Tsuboi Akito,Yu Liang Pdf

The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields of mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere for an exchange of information and ideas. This combined proceedings volume represents works presented or arising from the 14th and 15th ALCs.

Author : Justin Clarke-Doane
Publisher : Oxford University Press
Page : 208 pages
File Size : 48,5 Mb
Release : 2020-03-12
Category : Philosophy
ISBN : 9780192556806

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Morality and Mathematics by Justin Clarke-Doane Pdf

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 : Mircea Pitici
Publisher : Princeton University Press
Page : 288 pages
File Size : 42,6 Mb
Release : 2019-11-05
Category : Crafts & Hobbies
ISBN : 9780691198354

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The Best Writing on Mathematics 2019 by Mircea Pitici Pdf

An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.

Author : Francesca Boccuni,Andrea Sereni
Publisher : Taylor & Francis
Page : 419 pages
File Size : 53,8 Mb
Release : 2021-11-29
Category : Mathematics
ISBN : 9781000508116

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Origins and Varieties of Logicism by Francesca Boccuni,Andrea Sereni Pdf

This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism. The essays, written by prominent scholars, are divided into three thematic sections. Part I focuses on major authors like Frege, Dedekind, and Russell, providing a historical and theoretical exploration of such figures in the philosophical and mathematical milieu in which logicist views were first expounded. Part II sheds new light on the interconnections between these founding figures and a number of influential other traditions, represented by authors like Hilbert, Husserl, and Peano, as well as on the reconsideration of logicism by Carnap and the logical empiricists. Finally, Part III assesses the legacy of such authors and of logicist themes for contemporary philosophy of mathematics, offering new perspectives on highly debated topics—neo-logicism and its extension to accounts of ordinal numbers and set-theory, the comparison between neo-Fregean and neo-Dedekindian varieties of logicism, and the relation between logicist foundational issues and empirical research on numerical cognition—which define the prospects of logicism in the years to come. This book offers a comprehensive account of the development of logicism and its contemporary relevance for the logico-philosophical foundations of mathematics. It will be of interest to graduate students and researchers working in philosophy of mathematics, philosophy of logic, and the history of analytic philosophy.

Author : Justin Clarke-Doane
Publisher : Cambridge University Press
Page : 105 pages
File Size : 44,5 Mb
Release : 2022-06-30
Category : Science
ISBN : 9781009002295

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Mathematics and Metaphilosophy by Justin Clarke-Doane Pdf

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 : Bharath Sriraman
Publisher : Springer Nature
Page : 3221 pages
File Size : 41,6 Mb
Release : 2024-06-03
Category : Electronic
ISBN : 9783031408465

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Handbook of the History and Philosophy of Mathematical Practice by Bharath Sriraman Pdf

Author : Carlo Cellucci
Publisher : Springer Nature
Page : 457 pages
File Size : 44,8 Mb
Release : 2022-03-07
Category : Mathematics
ISBN : 9783030897314

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The Making of Mathematics by Carlo Cellucci Pdf

This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.

Author : Andrew Aberdein,Matthew Inglis
Publisher : Bloomsbury Publishing
Page : 293 pages
File Size : 52,5 Mb
Release : 2019-05-02
Category : Philosophy
ISBN : 9781350039032

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Advances in Experimental Philosophy of Logic and Mathematics by Andrew Aberdein,Matthew Inglis Pdf

This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition.

Author : Insa Lawler,Kareem Khalifa,Elay Shech
Publisher : Taylor & Francis
Page : 429 pages
File Size : 48,5 Mb
Release : 2022-12-13
Category : Science
ISBN : 9781000782035

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Scientific Understanding and Representation by Insa Lawler,Kareem Khalifa,Elay Shech Pdf

This volume assembles cutting-edge scholarship on scientific understanding, scientific representation, and their delicate interplay. Featuring several articles in an engaging ‘critical conversation’ format, the volume integrates discussions about understanding and representation with perennial issues in the philosophy of science, including the nature of scientific knowledge, idealizations, scientific realism, scientific inference, and scientific progress. In the philosophy of science, questions of scientific understanding and scientific representation have only recently been put in dialogue with each other. The chapters advance these discussions from a variety of fresh perspectives. They range from case studies in physics, chemistry, and neuroscience to the representational challenges of machine learning models; from special forms of representation such as maps and topological models to the relation between understanding and explanation; and from the role of idealized representations to the role of representation and understanding in scientific progress. Scientific Understanding and Representation will appeal to scholars and advanced students working in philosophy of science, philosophy of physics, philosophy of mathematics, and epistemology.

Author : Antonio Vassallo
Publisher : Taylor & Francis
Page : 298 pages
File Size : 50,5 Mb
Release : 2022-09-30
Category : Science
ISBN : 9781000688009

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The Foundations of Spacetime Physics by Antonio Vassallo Pdf

This book provides an up-to-date overview of the foundations of spacetime physics. It features original essays written by world-class experts in the physics and philosophy of spacetime. The foundational questions regarding the origin and nature of spacetime are branching into new and exciting directions. These questions are not restricted to the quantum gravity program but also arise in the context of a well-established theory like general relativity. Against the background of these quick and diverse developments, this volume features a broad range of perspectives on spacetime. Part I focuses on the nature of spacetime in non-quantum theories, such as Newtonian mechanics and relativity. Part II explores some intriguing conceptual implications of developing a quantum theory of spacetime. The Foundations of Spacetime Physics is an essential resource for scholars and advanced students working in philosophy of physics, philosophy of science, and scientific metaphysics.

Author : Nicholas Shackel
Publisher : Taylor & Francis
Page : 390 pages
File Size : 41,5 Mb
Release : 2024-02-29
Category : Philosophy
ISBN : 9781003813354

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Bertrand’s Paradox and the Principle of Indifference by Nicholas Shackel Pdf

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. Bertrand's Paradox and the Principle of Indifference will appeal to scholars and advanced students working in the philosophy of mathematics, epistemology, philosophy of science, probability theory and mathematical physics.

Author : Kian Salimkhani
Publisher : Taylor & Francis
Page : 267 pages
File Size : 53,6 Mb
Release : 2023-10-06
Category : Science
ISBN : 9781000984637

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The Non-Fundamentality of Spacetime by Kian Salimkhani Pdf

This book argues that our current best theories of fundamental physics are best interpreted as positing spacetime as non-fundamental. It is written in accessible language and largely avoids mathematical technicalities by instead focusing on the key metaphysical and foundational lessons for the fundamentality of spacetime. According to orthodoxy, spacetime and spatiotemporal properties are regarded as fundamental structures of our world. Spacetime fundamentalism, however, faces challenges from speculative theories of quantum gravity – roughly speaking, the project of applying the lessons of quantum mechanics to gravitation and spacetime. This book demonstrates that the non-fundamentality of spacetime does not rely on speculative physics alone. Rather, one can give an interpretation of general relativity that supports some form of spacetime non-fundamentalism. The author makes the case for spacetime non-fundamentalism in three steps. First, he confronts the standard geometrical interpretation of general relativity with Brown and Pooley’s dynamical approach to relativity theory. Second, he considers an alternative derivation of the Einstein field equations, namely the classical spin-2 approach, and argues that it paves the way for a refined dynamical approach to general relativity. Finally, he argues that particle physics can serve as a continuity condition for the metaphysics of spacetime. The Non-Fundamentality of Spacetime will be of interest to scholars and advanced students working in philosophy of physics, philosophy of science, and metaphysics.

Author : Distinguished Professor of Anthropology Thomas Wynn,Thomas Wynn,Assistant Professor of Anthropology & Co-Director Karenleigh Overmann,Karenleigh Overmann,Frederick Coolidge
Publisher : Oxford University Press
Page : 1329 pages
File Size : 45,9 Mb
Release : 2024-03-27
Category : Psychology
ISBN : 9780192895950

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Oxford Handbook of Cognitive Archaeology by Distinguished Professor of Anthropology Thomas Wynn,Thomas Wynn,Assistant Professor of Anthropology & Co-Director Karenleigh Overmann,Karenleigh Overmann,Frederick Coolidge Pdf

This book showcases the theories, methods, and accomplishments of archaeologists who investigate the human mind through material forms. It encompasses the wide spectrum of cognitive archeology, showcasing contributions from scholars globally. It delivers analysis of material culture, from stone tools to ceramic and rock art of the past millennium.