Morality and Mathematics

219 Pages·2020·1.638 MB·English

by  Justin Clarke-Doane

OUP CORRECTED PROOF – FINAL, 25/02/20, SPi
Morality and Mathematics
To what extent are the subjects of our thoughts and conversations real? This is the
question of realism.
Many hold that, while there are real mathematical facts out there to be discovered,
there are not real moral facts. Moral “facts,” if there are any, are just the products of
human invention. In this book, Justin Clarke-Doane argues that the situation is
much more subtle and explores the similarities and differences between morality
and mathematics, realistically construed. Although there are no real moral facts,
morality is objective in a paradigmatic respect. Conversely, while there are real
mathematical facts, mathematics fails to be objective. It follows from this that the
concepts of realism and objectivity, which have been widely identified, are actually
in tension. Our mathematical beliefs have no better claim to being self-evident or
provable than our moral beliefs, and nor do our mathematical beliefs have better
claim to being empirically justified than our moral beliefs. The book concludes with
a general account of areas of philosophical interest. Clarke-Doane applies the real-
ism/objectivity distinction across areas of inquiry and discusses its methodological
upshot, broaching key topics of broad interest such as self-evidence and proof, the
epistemological significance of disagreement, the philosophy/science comparison,
metaphysical possibility, the fact/value dichotomy, and deflationary conceptions of
philosophy.
“Justin Clarke-Doane identifies and explores the shocking parallelism between
morality and mathematics: on a surprising number of philosophical fronts, the two
disparate subjects seem to face common problems and analogous solutions and
rebuttals, whether the issue is realism, a priori justification, objectivity, naturalism
or pluralism. With consummate philosophical skill, Clarke-Doane teases apart the
differences and uncovers what is truly common and what is not. A remarkable
philosophical work.”
Joel David Hamkins (University of Oxford, UK)
OUP CORRECTED PROOF – FINAL, 25/02/20, SPi
“Morality and mathematics would seem to be significantly divergent fields of
inquiry. Justin Clarke-Doane is the rare philosopher with the requisite technical
mastery of both fields to see past the superficial differences and highlight the important
parallels lurking beneath, revealing how the issues of realism, objectivity, and justifi-
cation we face in moral philosophy have close analogues in the foundations of math-
ematics, while noting what differences remain intact. This is a provocative and
unique interdisciplinary contribution to how we understand truth and belief, with
wide-ranging philosophical implications.”
Sean Carroll (California Institute of Technology, US)
“Clarke-Doane’s book offers a coherent and plausible set of answers to the notori-
ous epistemological questions provoked by morality, and to the analogous ques-
tions that are provoked by mathematics. It is striking for its creativity, its rigorous
arguments, its many subtle but important distinctions, its unusual breadth of
expertise (covering philosophy of language, metaphysics, epistemology, philoso-
phy of mathematics, and meta-ethics), and its rational control of a daunting bat-
tery of interactings considerations from these various branches of the subject.
Exceptionally impressive philosophical talent and maturity are on display here.
Needless to say, we probably haven’t been given the final truth about these matters.
But it’s certain that anyone aiming to do better will have to grapple with Clarke-
Doane’s formidable arguments and conclusions.”
Paul Horwich (New York University, US)
OUP CORRECTED PROOF – FINAL, 25/02/20, SPi
Morality and
Mathematics
JUSTIN CLARKE-DOANE
1
OUP CORRECTED PROOF – FINAL, 25/02/20, SPi
1
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© Justin Clarke-Doane 2020
The moral rights of the author have been asserted
First Edition published in 2020
Impression: 1
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Library of Congress Control Number: 2019953283
ISBN 978–0–19–882366–7
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For Dad (1948–2017)
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Contents
Acknowledgments ix
Introduction 1
0.1 Science and Value 1
0.2 The Status of the Question 4
0.3 Overview of the Book 7
1. Realism, Ontology, and Objectivity 13
1.1 Individuating Areas 13
1.2 Bare-Bones Realism 15
1.3 Faithfulness 20
1.4 Knowledge 23
1.5 Ontology 24
1.6 Objectivity 27
1.7 Conclusions 33
2. Self-Evidence, Proof, and Disagreement 35
2.1 A Priori Justification 36
2.2 Axioms and Proofs 37
2.3 Self-Evidence 40
2.4 Plausibility and Disagreement 45
2.5 Extent of Disagreement 49
2.6 Philosophical Corruption 55
2.7 The Concept of Set 57
2.8 Error Theory 59
2.9 Philosophy Everywhere 62
3. Observation and Indispensability 66
3.1 Indispensability 67
3.2 The Quine–Putnam Thesis 68
3.3 Harman’s Thesis 70
3.4 Instrumentalism and Modality 76
3.5 Indispensable Mathematics and Metalogic 80
3.6 Perception 84
3.7 Justification and Explanation 88
3.8 Recreational Mathematics 91
3.9 A Priori/A Posteriori Revisited 95
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viii Contents
4. Genealogical Debunking Arguments 97
4.1 Harman’s Thesis as an Underminer 98
4.2 Three Constraints 102
4.3 Sensitivity 104
4.4 Safety 108
4.5 “Connection” 111
4.6 Modal Security 114
4.7 Conclusions 119
5. Explaining our Reliability 121
5.1 Justification and Reliability 122
5.2 Clarifying the Challenge 125
5.3 Causation, Explanation, and Connection 130
5.4 Counterfactual Dependence 133
5.5 Selection for Truth 135
5.6 The Mathematical Indifference of Evolution 138
5.7 The Inadequacy of the Sensitivity Challenge 143
5.8 Contingency 146
5.9 Pluralism and Safety 152
5.10 Conclusions 153
6. Realism, Objectivity, and Evaluation 156
6.1 Pluralism and Safety Again 156
6.2 Formulating Mathematical Pluralism 159
6.3 A Contrast 162
6.4 The Irrelevance of Semantics 164
6.5 Radicalizing the Open Question Argument 166
6.6 Objections and Replies 168
6.7 Realism, Objectivity, and Practical Safety 172
Conclusion 176
C.1 Key Themes 177
C.2 Toward Practical Philosophy 180
Bibliography 185
Index 205
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Acknowledgments
This manuscript has greatly benefited from the criticism of friends and
colleagues. I received written comments on chapters 1-6 at a workshop on
the manuscript hosted by Columbia University. Thanks to Wolfgang Mann
for making that happen, and to Russ Shafer-Landau, Paul Boghossian, Mary
Leng, Paul Horwich, Mark Balaguer, and Gideon Rosen for written comments
on Chapters 1 to 6, respectively. Thanks to the excellent oral comments
from participants, including, but not limited to, David Albert, Sean Carroll,
Jessica Collins, Hartry Field, Joel David Hamkins, Tamar Lando, Jennifer
McDonald, Michaela McSweeney, Thomas Nagel, Elliot Paul, Chris Peacocke,
Lisa Warenski, and Crispin Wright. Thanks to Vera Flocke, David Kaspar,
John Morrison, Olle Risberg, Katja Vogt, and an anonymous referee for
meticulous comments on the entire document. Matthew Bedke, Colin
Marshall, Conor Mayo-Wilson, and Michael Raven also offered penetrating
commentary on a draft at an author-meets-critics symposium at the June
2019 Canadian Philosophical Association meeting. Thanks to Christopher
Stephens for organizing that. Finally, I am grateful for the engaging discussion
of chapters 3-6 which took place in Elizabeth Harman’s and Sarah McGrath’s
Metaethics graduate seminar in Spring 2019.
Jens Haas, Brian Leiter, Peter Momtchiloff, Achille Varzi, and Katja Vogt
guided me through the process. I deeply appreciate their encouragement.
Thanks to Dan Baras, John Bengson, Betsy Clarke, Sinan Dogramaci, Emily
Fletcher, Martha Gibson, David Keyt, Patricia Kitcher, Philip Kitcher, Karen
Lewis, John Mackay, Farid Masrour, Christia Mercer, James Messina,
Michael Ridge, Chris Scambler, Anat Schechtman, Mark Schroeder, Alan
Sidelle, Alex Silk, Jon Simon, Neil Sinclair, Rob Streiffer, Bill Talbott, Mike
Titelbaum, Jack Woods, and Justin Zacek for helpful discussion. Thanks to
Matti Eklund for invigorating exchanges. Chapter 6 is indebted to them and
his work. Thanks to Rani Rachavelpula for compiling the index. Thanks,
finally, to Jenn McDonald, for everything.