Elements in the Philosophy of Mathematics – serie
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55 produkter
A Concise History of Mathematics for Philosophers
Häftad, 2019
308 kr
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This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. …
Philosophy of Mathematics from Descartes to Kant
Av Emily Carson
Inbunden, 2026
791 kr
Kommande
The mathematical method and the nature of mathematical knowledge were subjects of intense philosophical discussion in the 17th and 18th centuries. In particular, there was a debate over whether metaphysical truths admit of distinct proof as geometrical truths do, and whether they may be known with …
Plato Was Not a Mathematical Platonist
Häftad, 2023
282 kr
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This Element shows that Plato keeps a clear distinction between mathematical and metaphysical realism and the knife he uses to slice the difference is method. The philosopher's dialectical method requires that we tether the truth of hypotheses to existing metaphysical objects. The mathematician's …
Mathematical Intuitionism
Av Carl J. Posy
Häftad, 2020
308 kr
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L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism - from …
Mathematics and Explanation
Häftad, 2023
406 kr
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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 …
Medieval Finitism
Häftad, 2025
308 kr
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Discussing various versions of two medieval arguments for the impossibility of infinity, this Element sheds light on early stages of the evolution of the notion of INFINITIES OF DIFFERENT SIZES. The first argument is called 'the Equality Argument' and relies on the premise that all infinities are …
Number Concepts
An Interdisciplinary Inquiry
Av Richard Samuels, Eric Snyder
Häftad, 2024
308 kr
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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 …
Elements of Purity
Av Andrew Arana
Häftad, 2025
308 kr
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A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, …
Introducing the Philosophy of Mathematical Practice
Häftad, 2025
302 kr
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This Element introduces a young field, the 'philosophy of mathematical practice'. We first offer a general characterisation of the approach to the philosophy of mathematics that takes mathematical practice seriously and contrast it with 'mathematical philosophy'. The latter is traced back to …
Mathematical Pluralism
Häftad, 2024
308 kr
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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 …
Definitions and Mathematical Knowledge
Häftad, 2025
302 kr
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This Element discusses the philosophical roles of definitions in the attainment of mathematical knowledge. It first focuses on the role of definitions in foundational programs, and then examines their major varieties, both as regards their origins, their potential epistemic roles, and their formal …
The Mereology of Classes
Häftad, 2024
308 kr
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This Element is a systematic study of the question of whether classes are composed of further parts. Mereology is the theory of the relation of part to whole, and we will ask how that relation applies to classes. One reason the issue has received attention in the literature is the hope that a clear …
Indispensability
Häftad, 2023
406 kr
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Our best scientific theories explain a wide range of empirical phenomena, make accurate predictions, and are widely believed. Since many of these theories make ample use of mathematics, it is natural to see them as confirming its truth. Perhaps the use of mathematics in science even gives us reason …
Mathematics is (mostly) Analytic
Häftad, 2025
308 kr
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This Element outlines and defends an account of analyticity according to which mathematics is, for the most part, analytic. The author begins by looking at Quine's arguments against the concepts of analyticity. He shows how Quine's position on analyticity is related to his view on explication and …
Philosophy of Mathematics from the Pythagoreans to Euclid
Häftad, 2025
292 kr
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This Element looks at the very beginning of the philosophy of mathematics in Western thought. It covers the first reflections on attempts to untie mathematics from its practical usage in administration, commerce, and land-surveying and discusses the first ideas to see mathematical structures as …
Husserl's Philosophy of Mathematical Practice
Häftad, 2025
240 kr
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Husserl's Philosophy of Mathematical Practice explores the applicability of the phenomenological method to philosophy of mathematical practice. The first section elaborates on Husserl's own understanding of the method of radical sense-investigation (Besinnung), with which he thought the mathematics …
The Euclidean Programme
Av A. C. Paseau, Wesley Wrigley
Häftad, 2024
282 kr
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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 …
Iterative Conceptions of Set
Av Neil Barton
Häftad, 2024
308 kr
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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 …
Mathematical Rigour and Informal Proof
Häftad, 2024
308 kr
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This Element looks at the contemporary debate on the nature of mathematical rigour and informal proofs as found in mathematical practice. The central argument is for rigour pluralism: that multiple different models of informal proof are good at accounting for different features and functions of the …
Mathematical Anti-Realism and Modal Nothingism
Häftad, 2023
308 kr
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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 …
Abstractionism
Av Francesca Boccuni, Luca Zanetti
Häftad, 2025
308 kr
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The aim of this Element is to provide an overview of abstractionism in the philosophy of mathematics. The authors distinguish between mathematical abstractionism, which interprets mathematical theories on the basis of abstraction principles, and philosophical abstractionism, which attributes a …
Lakatos and the Historical Approach to Philosophy of Mathematics
Häftad, 2023
308 kr
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The Element begins by claiming that Imre Lakatos (1922-74) in his famous paper 'Proofs and Refutations' (1963-64) was the first to introduce the historical approach to philosophy of mathematics. Section 2 gives a detailed analysis of Lakatos' ideas on the philosophy of mathematics. Lakatos died at …
Philosophical Uses of Categoricity Arguments
Av Penelope Maddy, Jouko Väänänen
Häftad, 2023
302 kr
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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 …
The Indeterminacy of Computation
Av Jack Copeland, Oron Shagrir
Häftad, 2026
282 kr
Kommande
This element describes an emerging and intriguing topic: computational indeterminacy. Indeterminacy occurs when a fixed physical system potentially computes several different functions, and there is no fact of the matter which of these is actually being computed by the system. The phenomenon of …
Phenomenology and Mathematics
Inbunden, 2023
911 kr
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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. …
Number Concepts
An Interdisciplinary Inquiry
Av Richard Samuels, Eric Snyder
Inbunden, 2024
911 kr
Lägg i varukorg
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 …
Philosophical Uses of Categoricity Arguments
Av Penelope Maddy, Jouko Väänänen
Inbunden, 2023
892 kr
Lägg i varukorg
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 …
Lakatos and the Historical Approach to Philosophy of Mathematics
Inbunden, 2023
911 kr
Lägg i varukorg
The Element begins by claiming that Imre Lakatos (1922-74) in his famous paper 'Proofs and Refutations' (1963-64) was the first to introduce the historical approach to philosophy of mathematics. Section 2 gives a detailed analysis of Lakatos' ideas on the philosophy of mathematics. Lakatos died at …
Mathematical Notations
Av Dirk Schlimm
Inbunden, 2025
911 kr
Lägg i varukorg
This Element lays the foundation, introduces a framework, and sketches the program for a systematic study of mathematical notations. It is written for everyone who is curious about the world of symbols that surrounds us, in particular researchers and students in philosophy, history, cognitive …
Mathematical Notations
Av Dirk Schlimm
Häftad, 2025
302 kr
Lägg i varukorg
This Element lays the foundation, introduces a framework, and sketches the program for a systematic study of mathematical notations. It is written for everyone who is curious about the world of symbols that surrounds us, in particular researchers and students in philosophy, history, cognitive …
