What do you think?
Rate this book
Morality and Mathematics
To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the "genealogy" of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together -- and for a surprising reason. Moral questions, insofar
as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.
as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.
224 pages, Hardcover
Published May 25, 2020
3 people are currently reading
156 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 4 of 4 reviews
March 30, 2020
upshot: realist mathematical pluralism, anti-realist moral (practical) objectivism
January 26, 2025
Justin Clarke-Doane’s Morality and Mathematics is an ambitious and deeply technical work that seeks to clarify the parallels and distinctions between two traditionally distinct areas of philosophy: ethics and the philosophy of mathematics. The book systematically dismantles the common assumption that mathematics enjoys a more secure epistemological foundation than morality, ultimately arriving at the surprising conclusion that realism and objectivity, rather than reinforcing each other, are often in tension.
Bridging the Divide Between Ethics and Mathematics
Philosophy, Clarke-Doane argues, has become increasingly specialized, limiting interdisciplinary dialogue. His project is to bridge this gap by addressing a shared question in ethics and mathematics: realism. Are mathematical objects and moral truths independent of human minds? While many philosophers and scientists are comfortable with mathematical realism but reject moral realism, Clarke-Doane challenges the justifications for this asymmetry.
Defining Realism and Its Challenges (Chapter 1)
To assess whether an area is realist, Clarke-Doane establishes a minimalistic definition: realism requires aptness (most statements in the area are true or false), belief (they express beliefs, not attitudes or emotions), truth (some statements are true), independence (the truths are free from human minds and languages) and face-value (they need to be taken at their stated face value, not as proxies or metaphors). Importantly, he separates realism from objectivity—the idea that questions have unique answers. While common-sense realism might include notions of faithfulness, knowledge, or ontological commitment, Clarke-Doane rejects these as unnecessary complications.
Is Mathematics More Justifiable Than Morality? (Chapters 2–3)
The first epistemological challenge to moral realism is that mathematical truths appear better justified than moral truths. Chapter 2 explores a priori justification, arguing that mathematics is not uniquely self-evident. Foundational mathematical axioms (e.g., in set theory) are as debatable as moral principles. Chapter 3 extends this argument to a posteriori justification, examining the Quine-Putnam Indispensability argument, which suggests that mathematics is justified because it is indispensable to empirical science. Clarke-Doane challenges this by showing that moral beliefs might also enjoy empirical justification via quasi-perceptions.
Debunking Arguments and the Reliability Challenge (Chapters 4–5)
A major challenge to moral realism is genealogical debunking: the idea that the origins of our moral beliefs undermine their justification. Clarke-Doane rebuts this in Chapter 4, arguing that such arguments fail to show that moral beliefs are unreliable in a technical sense (e.g., failing sensitivity or safety conditions). Chapter 5 then examines the broader reliability challenge: can we explain why our beliefs match the truth? Neither causal, explanatory, nor evolutionary accounts convincingly justify mathematical reliability while undermining moral reliability. The only way to secure mathematical reliability, Clarke-Doane suggests, is to embrace pluralism.
Mathematical Pluralism and the Rejection of Moral Realism (Chapter 6)
The final chapter makes a striking claim: mathematical pluralism secures realism for mathematics but prevents it from being objective, while ethics, because it requires objective, prescriptive answers, cannot be pluralistic and therefore fails to be realist. This reverses a common assumption—rather than realism reinforcing objectivity, the two concepts are at odds.
Final Thoughts: A Thought-Provoking Contribution
Morality and Mathematics is a dense, technical work, but its implications are profound. Clarke-Doane forces us to reconsider long-held beliefs about realism, justification, and the structure of different areas of inquiry. His conclusion—that mathematics can be realist but non-objective while ethics can be objective but non-realist—is a significant challenge to conventional wisdom.
For readers with a background in philosophy, particularly epistemology and metaethics, Clarke-Doane offers an insightful, rigorous analysis. While the book’s technical arguments may be challenging for non-specialists, its core insights provide a fresh perspective on the nature of truth and justification across disciplines. Anyone interested in the philosophy of mathematics or metaethics will find this book a rewarding, if demanding, read.
On a personal note, I rather liked the book -I am very interested in both morality and mathematics, and on realism-. One handicap of the book though is its technicality, which is what stops me from giving it 5 stars. You probably need a degree in philosophy to be able to comfortably navigate the technical jargon, which extends to tortuous, logically motivated syntax at times. A background in questions of mathematical realism (which I had) also helps a lot. This is not the book’s fault, but it might mean that you as an average reader (like me) are probably not the intended audience, and it will make following some arguments really difficult.
Bridging the Divide Between Ethics and Mathematics
Philosophy, Clarke-Doane argues, has become increasingly specialized, limiting interdisciplinary dialogue. His project is to bridge this gap by addressing a shared question in ethics and mathematics: realism. Are mathematical objects and moral truths independent of human minds? While many philosophers and scientists are comfortable with mathematical realism but reject moral realism, Clarke-Doane challenges the justifications for this asymmetry.
Defining Realism and Its Challenges (Chapter 1)
To assess whether an area is realist, Clarke-Doane establishes a minimalistic definition: realism requires aptness (most statements in the area are true or false), belief (they express beliefs, not attitudes or emotions), truth (some statements are true), independence (the truths are free from human minds and languages) and face-value (they need to be taken at their stated face value, not as proxies or metaphors). Importantly, he separates realism from objectivity—the idea that questions have unique answers. While common-sense realism might include notions of faithfulness, knowledge, or ontological commitment, Clarke-Doane rejects these as unnecessary complications.
Is Mathematics More Justifiable Than Morality? (Chapters 2–3)
The first epistemological challenge to moral realism is that mathematical truths appear better justified than moral truths. Chapter 2 explores a priori justification, arguing that mathematics is not uniquely self-evident. Foundational mathematical axioms (e.g., in set theory) are as debatable as moral principles. Chapter 3 extends this argument to a posteriori justification, examining the Quine-Putnam Indispensability argument, which suggests that mathematics is justified because it is indispensable to empirical science. Clarke-Doane challenges this by showing that moral beliefs might also enjoy empirical justification via quasi-perceptions.
Debunking Arguments and the Reliability Challenge (Chapters 4–5)
A major challenge to moral realism is genealogical debunking: the idea that the origins of our moral beliefs undermine their justification. Clarke-Doane rebuts this in Chapter 4, arguing that such arguments fail to show that moral beliefs are unreliable in a technical sense (e.g., failing sensitivity or safety conditions). Chapter 5 then examines the broader reliability challenge: can we explain why our beliefs match the truth? Neither causal, explanatory, nor evolutionary accounts convincingly justify mathematical reliability while undermining moral reliability. The only way to secure mathematical reliability, Clarke-Doane suggests, is to embrace pluralism.
Mathematical Pluralism and the Rejection of Moral Realism (Chapter 6)
The final chapter makes a striking claim: mathematical pluralism secures realism for mathematics but prevents it from being objective, while ethics, because it requires objective, prescriptive answers, cannot be pluralistic and therefore fails to be realist. This reverses a common assumption—rather than realism reinforcing objectivity, the two concepts are at odds.
Final Thoughts: A Thought-Provoking Contribution
Morality and Mathematics is a dense, technical work, but its implications are profound. Clarke-Doane forces us to reconsider long-held beliefs about realism, justification, and the structure of different areas of inquiry. His conclusion—that mathematics can be realist but non-objective while ethics can be objective but non-realist—is a significant challenge to conventional wisdom.
For readers with a background in philosophy, particularly epistemology and metaethics, Clarke-Doane offers an insightful, rigorous analysis. While the book’s technical arguments may be challenging for non-specialists, its core insights provide a fresh perspective on the nature of truth and justification across disciplines. Anyone interested in the philosophy of mathematics or metaethics will find this book a rewarding, if demanding, read.
On a personal note, I rather liked the book -I am very interested in both morality and mathematics, and on realism-. One handicap of the book though is its technicality, which is what stops me from giving it 5 stars. You probably need a degree in philosophy to be able to comfortably navigate the technical jargon, which extends to tortuous, logically motivated syntax at times. A background in questions of mathematical realism (which I had) also helps a lot. This is not the book’s fault, but it might mean that you as an average reader (like me) are probably not the intended audience, and it will make following some arguments really difficult.
January 7, 2023
A brilliant work, easily one of my top ten books of 2021.
Displaying 1 - 4 of 4 reviews