PhilSci Archive

Mathemtics and Metaphilosophy

Clarke-Doane, Justin (2022) Mathemtics and Metaphilosophy. Cambridge Elements.

[img]
Preview
Text
proofs of may 19 2022 (1) (1) (2) (1).pdf

Download (527kB) | Preview

Abstract

This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is intelligible. The book concludes with a complementary ‘pluralism’ about modality, logic and normative theory, highlighting its revisionary implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap’s pragmatism, transposed to the key of realism.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Clarke-Doane, Justinjc4345@columbia.edu
Keywords: knowledge, math, logic, set theory, pluralism, modal, indeterminacy, indefinite extensibility, Hartry Field, Gödel, Russell, Carnap, Quine, Benacerraf, normative, is/ought, justification, reliability, axiom, indispensability, debunking, abstract objects, methodology, pragmatism, deflationism,
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics > Proof
Specific Sciences > Mathematics > Values
General Issues > Scientific Metaphysics
Specific Sciences > Psychology > Evolutionary Psychology
General Issues > Causation
General Issues > Conventionalism
Specific Sciences > Physics > Fields and Particles
General Issues > Logical Positivism/Logical Empiricism
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
General Issues > Values In Science
Depositing User: Justin Clarke-Doane
Date Deposited: 12 Jun 2022 20:53
Last Modified: 12 Jun 2022 20:53
Item ID: 20728
Journal or Publication Title: Cambridge Elements
Publisher: Cambridge University Press
Official URL: https://www.cambridge.org/core/elements/abs/mathem...
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Methodology
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics > Proof
Specific Sciences > Mathematics > Values
General Issues > Scientific Metaphysics
Specific Sciences > Psychology > Evolutionary Psychology
General Issues > Causation
General Issues > Conventionalism
Specific Sciences > Physics > Fields and Particles
General Issues > Logical Positivism/Logical Empiricism
Specific Sciences > Physics > Quantum Gravity
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
General Issues > Values In Science
Date: 1 July 2022
URI: http://philsci-archive.pitt.edu/id/eprint/20728

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item