- 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

# A Priority and Application:

# A Priority and Application:

Philosophy of Mathematics in the Modern Period

- Chapter:
- (p.29) A Priority and Application:
- Source:
- The Oxford Handbook of Philosophy of Mathematics and Logic
- Author(s):
### Lisa Shabel (Contributor Webpage)

- Publisher:
- Oxford University Press

In the 17th and 18th centuries, mathematics was understood to be the science that systematized our knowledge of magnitude, or quantity. But the mathematical notion of magnitude and the methods used to investigate it underwent a period of radical transformation during the modern period, which forced philosophers of mathematics to confront a changing mathematical landscape. In this context, the modern philosopher of mathematics had to provide an account of the apriority and applicability of mathematical reasoning, as such reasoning was then understood. Early modern mathematical reasoning and the accounts of such reasoning offered by Newton, Descartes, Leibniz, and Kant are explained and discussed.

*Keywords:*
mathematics, magnitude, quantity, apriority, applicability, Newton, Descartes, Leibniz, Kant

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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