- Title Pages
- Preface
- THE OXFORD HANDBOOK OF PHILOSOPHY OF MATHEMATICS AND LOGIC
- 1 Philosophy of Mathematics and Its Logic:
- A Priority and Application:
- Later Empiricism and Logical Positivism*
- Wittgenstein on Philosophy of Logic and Mathematics
- THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL
- Logicism in the Twenty‐first Century
- Logicism Reconsidered
- Formalism
- Intuitionism and Philosophy
- Intuitionism in Mathematics
- Intuitionism Reconsidered
- Quine and the Web of Belief
- Three Forms of Naturalism
- Naturalism Reconsidered
- Nominalism
- Nominalism Reconsidered
- Structuralism
- Structuralism Reconsidered
- Predicativity
- Mathematics—Application and Applicability
- Logical Consequence, Proof Theory, and Model Theory
- Logical Consequence: A Constructivist View
- Relevance in Reasoning
- No Requirement of Relevance
- Higher‐order Logic
- Higher‐order Logic Reconsidered
- Index

# Mathematics—Application and Applicability

# Mathematics—Application and Applicability

- Chapter:
- (p.625) Mathematics—Application and Applicability
- Source:
- The Oxford Handbook of Philosophy of Mathematics and Logic
- Author(s):
### Mark Steiner (Contributor Webpage)

- Publisher:
- Oxford University Press

This chapter discusses various senses in which mathematics is applied to the material world. It distinguishes between canonical and noncanonical applications of mathematics, the former being those for which the mathematics was developed to deal with in the first place. It also distinguishes between empirical and nonempirical applications, thus yielding four different kinds of applications. Examples of each are provided, and philosophical problems connected with each are treated.

*Keywords:*
mathematics, application, empirical

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- Title Pages
- Preface
- THE OXFORD HANDBOOK OF PHILOSOPHY OF MATHEMATICS AND LOGIC
- 1 Philosophy of Mathematics and Its Logic:
- A Priority and Application:
- Later Empiricism and Logical Positivism*
- Wittgenstein on Philosophy of Logic and Mathematics
- THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL
- Logicism in the Twenty‐first Century
- Logicism Reconsidered
- Formalism
- Intuitionism and Philosophy
- Intuitionism in Mathematics
- Intuitionism Reconsidered
- Quine and the Web of Belief
- Three Forms of Naturalism
- Naturalism Reconsidered
- Nominalism
- Nominalism Reconsidered
- Structuralism
- Structuralism Reconsidered
- Predicativity
- Mathematics—Application and Applicability
- Logical Consequence, Proof Theory, and Model Theory
- Logical Consequence: A Constructivist View
- Relevance in Reasoning
- No Requirement of Relevance
- Higher‐order Logic
- Higher‐order Logic Reconsidered
- Index