The Metaphysics and Mathematics of Arbitrary Objects

The Metaphysics and Mathematics of Arbitrary Objects PDF

Author: Leon Horsten

Publisher: Cambridge University Press

Published: 2019-06-13

Total Pages: 251

ISBN-13: 110860143X

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Building on the seminal work of Kit Fine in the 1980s, Leon Horsten here develops a new theory of arbitrary entities. He connects this theory to issues and debates in metaphysics, logic, and contemporary philosophy of mathematics, investigating the relation between specific and arbitrary objects and between specific and arbitrary systems of objects. His book shows how this innovative theory is highly applicable to problems in the philosophy of arithmetic, and explores in particular how arbitrary objects can engage with the nineteenth-century concept of variable mathematical quantities, how they are relevant for debates around mathematical structuralism, and how they can help our understanding of the concept of random variables in statistics. This fully worked through theory will open up new avenues within philosophy of mathematics, bringing in the work of other philosophers such as Saul Kripke, and providing new insights into the development of the foundations of mathematics from the eighteenth century to the present day.

Metaphysics, Meaning, and Modality

Metaphysics, Meaning, and Modality PDF

Author: Mircea Dumitru

Publisher: Oxford University Press

Published: 2020-10-27

Total Pages: 431

ISBN-13: 0192598287

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This book is the first edited collection of papers on the work of one of the most seminal and profound contemporary philosophers. Over the last five decades, Kit Fine has made thought-provoking and innovative contributions to several areas of systematic philosophy, including philosophy of language, metaphysics, and the philosophy of mathematics, as well as to a number of topics in philosophical logic. These contributions have helped reshape the agendas of those fields and have given fresh impetus to a number of perennial debates. Fine's work is distinguished by its technical sophistication, philosophical breadth, and independence from current orthodoxy. A blend of sound common-sense combined with a virtuosity in argumentation and constructive thinking is part and parcel of Kit Fine's lasting contributions to current trends in analytic philosophy. Researchers and students in philosophy, logic, linguistics, and cognitive science will benefit alike from these critical contributions to Fine's novel theories on meaning and representation, arbitrary objects, essence, ontological realism, and the metaphysics of modality, and will come away with a better understanding of the issues within contemporary analytic philosophy with which they deal.

Objects, Structures, and Logics

Objects, Structures, and Logics PDF

Author: Gianluigi Oliveri

Publisher: Springer Nature

Published: 2022-03-08

Total Pages: 365

ISBN-13: 3030847063

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This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.

Metaphysics, Meaning, and Modality

Metaphysics, Meaning, and Modality PDF

Author: Mircea Dumitru

Publisher: Oxford University Press, USA

Published: 2020-02-27

Total Pages: 545

ISBN-13: 0199652627

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This is the first book on the provocative and innovative contributions to philosophy of language, metaphysics, the philosophy of mathematics, and logic made by Kit Fine, one of the world's foremost philosophers. Topics covered include meaning and representation, arbitrary objects, essence, ontological realism, and the metaphysics of modality.

The Tools of Metaphysics and the Metaphysics of Science

The Tools of Metaphysics and the Metaphysics of Science PDF

Author: Theodore Sider

Publisher: Oxford University Press

Published: 2020-02-19

Total Pages: 256

ISBN-13: 0192539450

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Metaphysics is sensitive to the conceptual tools we choose to articulate metaphysical problems. Those tools are a lens through which we view metaphysical problems, and the same problems will look different when we change the lens. In this book, Theodore Sider identifies how the shift from modal to "postmodal" conceptual tools in recent years has affected the metaphysics of science and mathematics. He highlights, for instance, how the increased consideration of concepts of ground, essence, and fundamentality has transformed the debate over structuralism in many ways. Sider then examines three structuralist positions through a postmodal lens. First, nomic essentialism, which says that scientific properties are secondary and lawlike relationships among them are primary. Second, structuralism about individuals, a general position of which mathematical structuralism and structural realism are instances, which says that scientific and mathematical objects are secondary and the pattern of relations among them is primary. And third, comparativism about quantities, which says that particular values of scientific quantities, such as having exactly 1000g mass, are secondary, and quantitative relations, such as being-twice-as-massive-as, are primary. Sider concludes these discussions by considering the meta-question of when theories are equivalent and how that impacts the debate over structuralism.

Identity

Identity PDF

Author: Erica Shumener

Publisher: Cambridge University Press

Published: 2022-09-15

Total Pages: 105

ISBN-13: 1009020153

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Identity criteria are powerful tools for the metaphysician. They tell us when items are identical or distinct. Some varieties of identity criteria also try to explain in virtue of what items are identical or distinct. This Element has two objectives: to discuss formulations of identity criteria and to take a closer look at one notorious criterion of object identity, Leibniz's Law. The first section concerns the form of identity criteria. The second section concerns the better-regarded half of Leibniz's Law, the indiscernibility of identicals. The third section turns to the more controversial half of Leibniz's Law, the identity of indiscernibles. The author considers alternatives to Leibniz's Law as well as the possibility that there are no adequate identity criteria to be found.

Formal Ontology

Formal Ontology PDF

Author: Jani Hakkarainen

Publisher:

Published: 2023-10-12

Total Pages: 81

ISBN-13: 1009069063

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This Element gives a systematic account of formal ontology as a branch of metaphysics and as an approach to metaphysics.

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