Objects, Structures, and Logics: FilMat Studies in the Philosophy of Mathematics

This edited collection explores central issues in contemporary philosophy of mathematics, such as realism/anti-realism, logic/metaphysics, and the nature of mathematics as a science of objects or structures. It features contributions from philosophers, logicians, and mathematicians from diverse backgrounds, making it valuable for researchers and students.

Format: Paperback / softback
Length: 363 pages
Publication date: 10 March 2023
Publisher: Springer Nature Switzerland AG

This edited collection delves into the core aspects of contemporary philosophy of mathematics, shedding light on pivotal debates such as realism versus anti-realism, the interplay between logic and metaphysics, and the nature of mathematics as a discipline focused on objects or structures. The discussions presented in the papers delve into intricate inquiries, encompassing notions of mathematical truth, proof, and grounding, while frequently emphasizing considerations related to mathematical practice. A notable hallmark of this book is its multicultural composition, featuring contributions from philosophers, logicians, and mathematicians of diverse backgrounds, all of whom have contributed high-quality articles that will be of immense value to researchers and students alike.

The realism/anti-realism dispute:
This debate revolves around the question of whether mathematics is a true representation of the underlying reality or merely a human-created construct. Realists argue that mathematics captures essential aspects of the world and provides a reliable means of understanding it. Anti-realists, on the other hand, contend that mathematics is a useful tool for reasoning and problem-solving but does not necessarily correspond to any external reality.

The relationship between logic and metaphysics:
Philosophers have long debated the relationship between logic and metaphysics, with some viewing them as separate disciplines and others as interrelated. Logicians, for their part, argue that logic is a fundamental discipline that provides a systematic framework for reasoning and that it can be applied to both philosophical and mathematical problems. Metaphysicians, on the other hand, seek to understand the fundamental nature of reality and the principles that govern it.

The question of whether mathematics is a science of objects or structures:
This question concerns the nature of mathematics and its relationship to other scientific disciplines. Some philosophers argue that mathematics is a science of objects, focusing on the properties and behaviors of mathematical objects such as numbers, symbols, and structures. Others argue that mathematics is a science of structures, emphasizing the patterns and relationships that exist between mathematical objects and other entities in the world.

Mathematical truth, proof, and grounding:
The discussions in this section explore the concepts of mathematical truth, proof, and grounding. Philosophers argue about the nature of mathematical truth, whether it is absolute or relative, and whether it can be discovered through empirical means or purely through reasoning. Logicians discuss the principles of proof and the criteria for validating mathematical statements. Mathematicians, in turn, explore the methods and techniques used to prove mathematical theorems and establish the validity of mathematical structures.

Considerations related to mathematical practice:
The papers in this collection also address considerations related to mathematical practice, such as the role of intuition in mathematical discovery, the use of mathematical models in scientific inquiry, and the ethical implications of mathematical research. Philosophers and mathematicians explore the ways in which mathematical practice shapes our understanding of the world and the ethical responsibilities that come with engaging in mathematical research.

Conclusion:
This edited collection provides a comprehensive and insightful exploration of central issues within contemporary philosophy of mathematics. The discussions offer a rich tapestry of perspectives, drawing from a diverse range of disciplines and offering valuable insights into the nature of mathematics and its relationship to other fields of inquiry. By examining the realism/anti-realism dispute, the relationship between logic and metaphysics, and the question of whether mathematics is a science of objects or structures, this book contributes to our understanding of the field and its potential applications. The multicultural nature of the community that has produced this book further highlights the importance of interdisciplinary collaboration in the pursuit of knowledge. Whether you are a researcher, student, or simply interested in the philosophical implications of mathematics, this collection is a must-read for anyone seeking to deepen their understanding of this fascinating subject.

Weight: 575g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030847081
Edition number: 1st ed. 2022