Moral Mathematics Research Articles

Mistakes in the Moral Mathematics of Existential Risk

Mistakes in the Moral Mathematics of Existential Risk

2008's Harmless Torturers and Group Agents: The Moral Mathematics and Responsibilities of Financial Crises

After the 2008 Financial Crisis, there were widespread calls by politicians, policy-makers, and the general public to hold individuals accountable for the devastating harms that resulted. This yearning still remains alive and well in American culture despite the lack of criminal prosecutions or civil enforcement against individuals involved in 2008. By employing contemporary analytic philosophy, this paper argues, contrary to this commonly held belief, that it would be a moral mistake to hold individuals responsible for the Financial Crisis. Financial crises caused by amalgamation of systemic risk may be implemented by individuals, but they are undoubtedly programmed by corporations. Because of this, corporations and financial institutions are fit to be held morally responsible for 2008. As a result, they owe a moral duty to protect the right of all investors to reasonably rely on financial risks by monitoring through internal compliance programs how the actions taken by their individual employees contribute to systemic risks.

The Asymmetry of population ethics: experimental social choice and dual-process moral reasoning.

Population ethics is widely considered to be exceptionally important and exceptionally difficult. One key source of difficulty is the conflict between certain moral intuitions and analytical results identifying requirements for rational (in the sense of complete and transitive) social choice over possible populations. One prominent such intuition is the Asymmetry, which jointly proposes that the fact that a possible child's quality of life would be bad is a normative reason not to create the child, but the fact that a child's quality of life would be good is not a reason to create the child. This paper reports a set of questionnaire experiments about the Asymmetry in the spirit of economists' empirical social choice. Few survey respondents show support for the Asymmetry; instead respondents report that expectations of a good quality of life are relevant. Each experiment shows evidence (among at least some participants) of dual-process moral reasoning, in which cognitive reflection is statistically associated with reporting expected good quality of life to be normatively relevant. The paper discusses possible implications of these results for the economics of population-sensitive social welfare and for the conflict between moral mathematics and population intuition.

Affordability and Non-Perfectionism in Moral Action

One rationale policy-makers sometimes give for declining to fund a service or intervention is on the grounds that it would be ‘unaffordable’, which is to say, that the total cost of providing the service or intervention for all eligible recipients would exceed the budget limit. But does the mere fact that a service or intervention is unaffordable present a reason not to fund it? Thus far, the philosophical literature has remained largely silent on this issue. However, in this article, we consider this kind of thinking in depth. Albeit with certain important caveats, we argue that the use of affordability criteria in matters of public financing commits what Parfit might have called a ‘mistake in moral mathematics’. First, it fails to abide by what we term a principle of ‘non-perfectionism’ in moral action: the mere fact that it is practically impossible for you to do all the good that you have reason to do does not present a reason not to do whatever good you can do. And second, when used as a means of arbitrating between which services to fund, affordability criteria can lead to a kind of ‘numerical discrimination’. Various attendant issues around fairness and lotteries are also discussed.

The Asymmetry of Population Ethics: Experimental Social Choice and Dual-Process Moral Reasoning

Population ethics is widely considered to be exceptionally important and exceptionally difficult. One key source of difficulty is the conflict between certain moral intuitions and analytical results identifying requirements for rational (in the sense of complete and transitive) social choice over possible populations. One prominent such intuition is the Asymmetry, which jointly proposes that the fact that a possible child's quality of life would be bad is a normative reason not to create the child, but the fact that a child's quality of life would be good is not a reason to create the child. This paper reports a set of questionnaire experiments about the Asymmetry in the spirit of economists' empirical social choice. Few survey respondents show support for the Asymmetry; instead respondents report that expectations of a good quality of life are relevant. Each experiment shows evidence (among at least some participants) of dual-process moral reasoning, in which cognitive reflection is statistically associated with reporting expected good quality of life to be normatively relevant. The paper discusses possible implications of these results for the economics of population-sensitive social welfare and for the conflict between moral mathematics and population intuition.

Pragmatism, Utilitarianism, and the Stagnation of Analytical Moral Theory

This paper addresses the failure of analytical moral theory to recognize social conflict as driving perceptions of utility, the necessity of convergence of opposing positions to produce a consensual viewpoint, and of the transformation of moral reasoning for successful resolutions. Law provides an empirical context for understanding normative inquiry as an extended, dispute-driven inductive process. Leading utilitarian conceptions view the calculus of normative reasons as static, picturing all expected consequences as if visible at once, through a lens displaying prospective utility. Utilitarianism is blind to the revision of reasons that must take place if opposing positions are to converge. Pragmatism stresses the necessity of retirement of incommensurable reasons for success in conflict resolution. Derek Parfit has argued that all three “secular moral traditions” of mainstream philosophy (consequentialism, Kantianism, and contractualism) are “climbing the same mountain.” If so, all three are situated on a momentary, stationary conceptual landscape, attempting to perform what Parfit calls “moral mathematics” from a synchronic viewpoint. The analytical lens is blind to the often precarious world of engagement with specific moral problems, from which public acceptance and compliance must constantly be wrought, and on a piecemeal basis, not through a static global analytical rationale.

The Moral Mathematics of Strategic Games in The Unvanquished

The Moral Mathematics of Strategic Games in The Unvanquished

International Debt: The Constructive Implications of Some Moral Mathematics

Present arrangements governing the accumulation and discharge of debt by states are difficult to justify fully on the basis of underlying normative considerations. States are different from individuals in important respects, and the deontological justifications that explain why individuals have a strong burden to abide by promises to repay do not straightforwardly apply to countries. Consequentialist considerations must play a central role in determining what norms should govern the accumulation and discharge of sovereign debt. Modified background norms for the accumulation and discharge of international debt which permit countries’ repayments to be made formally contingent on specific circumstances and the reasons that these circumstances have arisen are more likely to be morally justifiable than the existing rules, which in general require countries to repay their debts according to an inflexible schedule. Modified rules for the accumulation and discharge of international sovereign debt can codify the moral and legal basis for existing ad hoc deviations and present a justifiable framework within which international lending and borrowing can take place.

International Debt: The Constructive Implications of Some Moral Mathematics

Present arrangements governing the accumulation and discharge of debt by states are difficult to justify fully on the basis of underlying normative considerations. States are different from individuals in important respects, and the deontological justifications that explain why individuals have a strong burden to abide by promises to repay do not straightforwardly apply to countries. Consequentialist considerations must play a central role in determining what norms should govern the accumulation and discharge of sovereign debt. Modified background norms for the accumulation and discharge of international debt which permit countries’ repayments to be made formally contingent on specific circumstances and the reasons that these circumstances have arisen are more likely to be morally justifiable than the existing rules, which in general require countries to repay their debts according to an inflexible schedule. Modified rules for the accumulation and discharge of international sovereign debt can codify the moral and legal basis for existing ad hoc deviations and present a justifiable framework within which international lending and borrowing can take place.

Climate Change and the Challenge of Moral Responsibility

The phenomenon of anthropogenic climate change—in which weather patterns and attendant ecological disruption result from increasing concentrations of greenhouse gases released into the atmosphere through human activities—challenges several conventional assumptions regarding moral responsibility. Multifarious individual acts and choices contribute (often imperceptibly) to the causal chain that is expected to produce profound and lasting harm unless significant mitigation efforts begin soon. Attributing responsibility for such harmful consequences is complicated by what Derek Parfit terms “mistakes in moral mathematics,” or failures to correctly assess the various individual contributions to collectively produced harm. Combined with the difficulties in attributingresponsibility to agents for spatially and temporally distant harmful effects and that of holding agents culpable for effects (resulting from socially-acceptable acts) about which they may be ignorant, this paper attempts to sort out several ethical problems surrounding the identification of responsible parties contributing to climate change.

International Debt: The Constructive Implications of Some Some Moral Mathematics

Present arrangements governing the accumulation and discharge of debt by states are difficult to justify fully on the basis of underlying normative considerations. States are different from individuals in important respects and the deontological justifications that explain why individuals have a strong burden to abide by promises to repay do not straightforwardly apply to countries. Consequentialist considerations must play a central role in determining what norms should govern the accumulation and discharge of sovereign debt. Modified background norms for the accumulation and discharge of international debt which permit countries' repayments to be made formally contingent on specific circumstances and the reasons that these circumstances have arisen are more likely to be morally justifiable than the existing rules, which in general require countries to repay their debts according to an inflexible schedule. Modified rules for the accumulation and discharge of international sovereign debt can codify the moral and legal basis for existing ad hoc deviations and present a justifiable framework within which international lending and borrowing can take place.

Augustus De Morgan and the propagation of moral mathematics

In the early nineteenth century, Henry Brougham endeavored to improve the moral character of England through the publication of educational texts. Soon after, Brougham helped form the Society for the Diffusion of Useful Knowledge to carry his plan of moral improvement to the people. Despite its goal of improving the nation’s moral character, the Society refused to publish any treatises on explicitly moral or religious topics. Brougham instead turned to a mathematician, Augustus De Morgan, to promote mathematics as a rational subject that could provide the link between the secular and religious worlds. Using specific examples gleaned from the treatises of the Society, this article explores both how mathematics was intended to promote the development of reason and morality and how mathematical content was shaped to fit this particular view of the usefulness of mathematics. In the course of these treatises De Morgan proposed a fundamentally new pedagogical approach, one which focused on the student and the role mathematics could play in moral education.

The Second Mistake in Moral Mathematics is not about the Worth of Mere Participation

‘The Second Mistake’ (TSM) is to think that if an act is right or wrong because of its effects, the only relevant effects are the effects of this particular act. This is not (as some think) a truism, since ‘the effects of this particular act’ and ‘its effects’ need not co-refer. Derek Parfit's rejection of TSM is based mainly on intuitions concerning sets of acts that over-determine certain harms. In these cases, each act belongs to the relevant set in virtue of a causal relation (other than marginal contribution) to a specific harmful event. This feature may make an act wrong, in a fashion consequentialists could admit. That explication of TSM does not rely on the questionable assumption that the set of acts is what harms here. Independently of this, there are several other reasons to prefer it to the ‘mere participation’ approach.

Is it better that ten guilty persons go free than that one innocent person be convicted?

I Introduction The relevance of answers depends, of course, on getting questions right. Sometimes, however, we are not quite sure we actually know what question is. The doctrine underlies title question to this essay is commonly ascribed to William Blackstone. in Commentaries on Laws of England (1769), Blackstone wrote the law holds is better ten guilty persons escape, than one innocent suffer. (1) This formulation is not only version of doctrine. For example, in his book on Evidence (1824), another British scholar, Thomas Starkie, insisted that is better ninety-nine ... offenders shall escape than one innocent man be condemned. (2) The various versions of this idea in circulation inspired Jeremy Bentham to make following skeptical comment in A Treatise on Judicial Evidence (1825): At first was said to be better to save several guilty men, than to condemn a single innocent man; others, to make maxim more striking, fixed on number ten, a third made this ten a hundred, and a fourth made a thousand. All these candidates for prize of humanity have been outstripped by I know not how many writers, who hold, that, in no case, ought an accused to be condemned, unless evidence amount to mathematical or absolute certainty. According to this maxim, nobody ought to be punished, lest an innocent man be punished. (3) II A Doctrine and Its Interpretation I shall take for granted no reasonable person could possibly endorse version implicitly ridiculed by Bentham: It is better all guilty persons go free than one innocent person be convicted. Nevertheless, in light of Bentham's remarks, seems equally clear would be futile to embark on an exercise in moral mathematics in order to fix and justify correct ratio of false acquittals of guilty to false convictions of I shall presuppose, moreover, any ratio one might come up with, say forty-two to one, (4) should not be taken to indicate is forty-two times worse to convict an innocent person than to acquit a guilty one. Rather, I think a more adequate interpretation of doctrine is to be found in a U.S. Supreme Court case from 1895, Coffin v. U.S. In this case, Justice White, who delivered opinion of court, dated doctrine back to Roman law. He quoted a Roman official who wrote it was better to let crime of a guilty person go unpunished than to condemn innocent. (5) I take this doctrine, which I shall call Roman doctrine, to articulate strong intuition of everyday morality: is worse to convict innocent people than to acquit guilty people. Significantly, to argue some phenomena are morally better than some other phenomena is to presuppose they are comparable with respect to some common moral standard of comparison, for example, a particular conception of criminal justice. There is no further need to presuppose a single scale of units of value allowing for quantification or measurement of how much better is to reduce number of false convictions rather than to reduce number of false acquittals. Most people take for granted Roman doctrine is basically sound, yet does not follow is easy to articulate a rationale for it. Still, in a certain narrow interpretation, seems as if doctrine is trivially true. Consider two comparable cases of murder, both of which are wrongly decided. In one case a murderer is acquitted, in another case an innocent person is convicted of murder. According to doctrine, outcome in former case is better, or rather, less worse or less bad, than outcome of latter case. How could fail to be true, we might ask. After all, by punishing innocent, guilty person is still out there enjoying his freedom. In TV series The Fugitive, when Dr. Kimble was wrongly convicted for murder of his wife, he was only person who kept looking for one-armed man. …

Does Participation Matter? An Inconsistency in Parfit's Moral Mathematics

Consequentialists typically think that the moral quality of one's conduct depends on the difference one makes. But consequentialists may also think that even if one is not making a difference, the moral quality of one's conduct can still be affected by whether one is participating (even if only ineffectually, or redundantly) in an endeavour that does make a difference. Derek Parfit discusses this issue – the moral significance of what I call ‘participation’ – in the chapter of Reasons and Persons that he devotes to what he calls ‘moral mathematics’. In my paper, I expose an inconsistency in Parfit's discussion of moral mathematics by showing how it gives conflicting answers to the question of whether participation matters. I conclude by showing how an appreciation of Parfit's error sheds some light on consequentialist thought generally, and on the debate between act- and rule-consequentialists specifically.

Economic analysis and moral philosophy

Introduction 1. Ethics and economics 2. Two examples Part I. Rationality and Morality: 3. Rationality 4. Rationality in positive and normative economics 5. Rationality, norms and morality Part II. Welfare and Consequences: 6. Welfare 7. Efficiency 8. Utilitarianism and consequentialism Part III. Libert, Rights, Equality and Justice: 9. Liberty, rights and libertarianism 10. Equality and egalitarianism 11. Justice and contractualism Part IV. Moral Mathematics: 12. Social choice theory 13. Game theory Part V. Conclusions: 14. Conclusions Appendix: How could ethics matter to economics?

Comment on Shrader-Frechette's "Parfit and Mistakes in Moral Mathematics

In a recent article in this journal' Shrader-Frechette discusses Parfit's arguments in Reasons and Persons2 with respect to issues in moral calculation. Although her analysis is reasonable, aspects of it need elaboration. The present note is an attempt to flesh out her response to Parfit. The issues are best illustrated with an example such as the one used by Parfit. He describes a scenario in which a thousand wounded soldiers in the desert need water, while in a second group of one thousand each individual is deciding whether or not to contribute his or her pint of water to be divided equally among the thirsty men. The effect of the equal division is that the pint contributed by a given altruist adds one thousandth of a pint to the amount each man receives. If it is assumed that this tiny fraction of the pint each person has to contribute is too small to be perceived by even a very thirsty individual, then each contributor may feel that his or her pint would avail nothing if distributed. The fact that many soldiers would each get slightly more water is irrelevant if none of them perceives any change. One thousand non-effects still constitute a non-effect. Yet, the benefit from the full contribution of the second thousand would certainly produce a noticeable alleviation of thirst. In a manner reminiscent of the Sorites problem, this is a situation in which each additional fraction of a pint makes at most an difference, but the sum of all such differences is quite perceptible. Parfit argues that there are indeed imperceptible benefits and that they must be counted as benefits in spite of this property. ShraderFrechette suggests that an analysis in terms of thresholds and probabilities of benefit would avoid the need to count them in this way. I agree, but I find her discussion somewhat preliminary. She does not spell out clearly how this might work.

De commodis litterarum atque incommodis

One of the principal aims of the Modern Humanities Research Association is declared to be 'to break down the barriers between scholars working in different disciplines, and to maintain the broader unity of humanistic scholarship in the face of increasing specialization'. If it had existed in the middle of the fifteenth century with these objectives, the Association could hardly have found a better candidate for the Presidency than the Italian Leon Battista Alberti, for he combined in a unique way a wide variety of disciplines in arts and sciences, including moral philosophy, law, social studies, literature, languages, optics, painting, sculpture, architecture, and mathematics. No studies were alien to him, whether practical or academic. He pursued knowledge not only for its intrinsic values but for its application to the benefit of the individual and society in general. He also pursued it with what we should term a strong research interest, constantly on the lookout for new ideas, new inventions, and new fields to explore, with a persistent confidence in human improvement towards self-fulfilment and happiness. His numerous works in Latin and Italian, both literary and technical, are obviously indebted to the classical tradition, but they also show a quite remarkable creativity and originality even during, and in spite of, those periods of pessimism which occurred frequently in his youth and continued sporadically into the changed circumstances of his later life. Whatever he subsequently became and wrote, he had many reasons not to be optimistic when he graduated from the University of Bologna in 1428 and soon afterwards wrote in Latin the work, whose title I have borrowed for this address, on the advantages and disadvantages of letters. His comments in their context are historically interesting, and they and their general themes are not irrelevant to our own. My object, therefore, is to explain and explore the content of Alberti's treatise for the light it throws on education and society in his times, and to invite reflection on its implications for our own studies. Alberti began life in I404 with two personal disadvantages, which were still there twenty-five years later, explicit or implicit, in his De commodis: illegitimacy and exile from Florence.1 The exile had just come to an end in I428. References in the work to Tuscan and Florentine attitudes, and to a Bologna recently left behind, suggest a probable date of composition of I429. We know that because of exile his education before university took place first in Venice, then in Padua in the school of Gasparino Barzizza, schoolmaster and university Professor of Rhetoric who was at that time introducing new material and methods into the teaching of the trivium, and in particular of grammar and rhetoric. These were the beginnings of humanistic teaching within the existing school curriculum and university system, pursuing,

Parfit and Mistakes in Moral Mathematics

In addition to the immediate and delayed fatalities and ailments following the Chernobyl explosion and the Bhopal toxic leak, numerous persons suffered allegedly imperceptible, painless, but slightly harmful effects. One question this raises is whether one ought to ignore acts causing allegedly imperceptible, but slightly harmful, effects on large numbers of persons. In Reasons and Persons (Mistakes in Moral Mathematics, pp. 6786), Parfit argues, correctly I think, that one ought not follow commonsense morality and ignore acts causing such imperceptible effects on large numbers of persons.' Although his conclusion is correct, Parfit's three main arguments (used to justify his account of imperceptible effects) are highly questionable. I call these the Mistaken Pain Defense, the Total Effect Defense, and the Simplicity Defense:

The Art of Being Human: The Humanities as a Technique for Living

The Art of Being Human: The Humanities as a Technique for Living