Details for: Boccuni F., Zanetti L. Abstractionism 2024

Boccuni F., Zanetti L. Abstractionism 2024

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Textbook in PDF format 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 philosophical significance to mathematical abstractionism. They then survey the main semantic, ontological, and epistemological theses that are associated with philosophical abstractionism. Finally, the authors suggest that the most recent developments in the debate pull abstractionism in different directions. Introduction Mathematical Abstractionism Introduction Second-Order Logic Frege’s Grundgesetze der Arithmetik Arithmetical Abstraction Real Number Abstraction Set Abstraction Invariance The Bad Company Problem Philosophical Abstractionism I: Semantics Introduction The Substantival View Nonsubstantival Views The Caesar Problem Philosophical Abstractionism II: Ontology Introduction The Existence of Mathematical Objects Real Definitions Philosophical Abstractionism III: Epistemology Introduction Puzzle 1: Epistemic Access Puzzle 2: Knowledge by Abstraction Epistemic Bad Company and Related Concerns New Directions in Philosophical Abstractionism Abstractionist Structuralism References Contributions Acknowledgements

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