Some courses achieve existence, some have to create Professional Issues and Ethics in existence thrust upon them. It is normally Mathematics; but if you don’t do it, we will a struggle to create a course on the ethical be.” I accepted. or social aspects of science or mathematics. The gift of a greenfield site and a bull- This is the story of one that was forced to dozer is a happy occasion, undoubtedly. But exist by an unusual (...) confluence of outside cirwhat to do next? It seemed to me I should cumstances. ensure the course satisfied these require- In the mid 1990s, the University of New ments: South Wales instituted a policy that all its • It should look good to students, to staff. (shrink)

While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of commentators in recent decades with a view to piecing together a coherent approach to ethics in mathematics. Calls for a Hippocratic Oath for mathematicians are examined and it is concluded that while lessons can be learned from the medical profession, the relation of mathematicians to those affected by (...) their work is significantly different. There is something to be learned also from the codes of conduct of cognate but professionalised quantitative disciplines such as engineering and accountancy, as well as from legal principles bearing on professional work. We conclude with recommendations that professional societies in mathematics should sponsor an (international) code of ethics, institutional mission statements for mathematicians and syllabuses of ethics courses for incorporation into mathematics degrees. (shrink)

How do axioms, or first principles, in ethics compare to those in mathematics? In this companion piece to G.C. Field's 1931 "On the Role of Definition in Ethics", I argue that there are similarities between the cases. However, these are premised on an assumption which can be questioned, and which highlights the peculiarity of normative inquiry.

The study aimed to determine if differentiated instruction effectively addresses learning gaps in mathematics. In particular, it explored how it can improve the student’s learning gaps concerning mathematical performance and confidence. The study employed a quasi-experimental design with 30 purposively-selected Grade 10 participants divided into differentiated (n = 15) and control groups (n = 15), ensuring the utmost ethical measures. The mean and standard deviation were used to describe the participants’ performance and confidence. Independent samples t-tests were used to (...) determine the significant differences in the performance and confidence between the two groups. In contrast, dependent samples t-tests were used to determine the significant differences in each group’s pre and posttest performance and confidence. Findings bared that the differentiated instruction successfully addressed students’ performance in mathematics even in a short period. It also increased the participants’ confidence when answering fundamental problems. Continuing differentiated instruction activities are recommended since it benefits students who struggle in mathematics, particularly in answering fundamental operations. Differentiated teaching activities in mathematics can boost academic achievement and engagement and prepare students for future success while fostering a positive and inclusive classroom culture that values individual learning needs and preferences. (shrink)

In his influential book, The Nature of Morality, Gilbert Harman writes: “In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles.” What is the epistemological relevance of this contrast, if genuine? This chapter argues that ethicists and philosophers of mathematics have misunderstood it. They have confused what the chapter calls the justificatory challenge for realism about an area, (...) D—the challenge to justify our D-beliefs—with the reliability challenge for D-realism—the challenge to explain the reliability of our D-beliefs. Harman’s contrast is relevant to the first, but not, evidently, to the second. One upshot of the discussion is that genealogical debunking arguments are fallacious. Another is that indispensability considerations cannot answer the Benacerraf–Field challenge for mathematical realism. (shrink)

Over the past few years we have seen an increasing number of legal proceedings related to inappropriately implemented technology. At the same time career paths have diverged from the foundation of statistics out to Data Scientist, Machine Learning and AI. All of these new branches being fundamentally branches of statistics and mathematics. This has meant that formal training has struggled to keep up with what is required in the plethora of new roles. Mathematics as a taught subject is (...) still based in decades old teaching specifications and has not been updated centrally as a curriculum to include new technologies, coding or ethics. This subject area is firmly split between ICT and Mathematics in secondary school, continuing on to be split between Computer Science and Mathematics at University. As we move forwards with technology we see these once seperate fields becoming increasingly intertwined. We propose that existing provision for concepts such as ethics and societal responsibility in analysis currently exist but have not been incorporated into the mainstream curriculum of School or University. This is partially due to the split between fields in an educational setting but also the speed with which education is able to keep up with Industry and its requirements. Principles and frameworks of socially responsible modelling beginning at school level means that ethics and real-life modelling are introduced much earlier than normal. Integrating these concepts with philosophical principles of society and politics ensures a suitable background for future modellers and users of technology to draw on. Modelling is currently undertaken in technical sciences at University but the Subject Benchmark Statements are not current (Subject Benchmark Statements describe the nature of study and the academic standards expected of graduates in specific subject areas. They show what graduates might reasonably be expected to know, do and understand at the end of their studies). Even in 2019 the UK did not yet have Benchmark Statements that discuss the learning to be done in Higher Education around AI and advanced Machine Learning. Where there is provision for AI and Data Science within degree courses ethics is not generally highlighted as a key concept. As such there can be a lack of focus on the teaching of modelling or ethics as specific skills. The skills required to use a basic statistical model, for example would not be sufficient to start from scratch and build an ethical model reflecting real-world scenarios with which to inform policy or organisational decision making. This is a skill in itself and includes such aspects as awareness of data quality, ethics, user implementation problems, context and an understanding of the environment that the model is being created in. As the field of analytics has progressed so quickly in the last decade modules such as those covering AI have simply been bolted on to Maths or Computing degrees rather than being fully detailed as key areas of study or driving new, more integrated courses of study. This paper posits that gaps at primary, secondary and tertiary educational levels need to be addressed. Implementing and integrating key concepts from school level is essential so that areas such as assumptions, caveats, quality assurance and answering the right questions with constructive challenge become a cultural fixture. This not only helps developers of technology but users of rapidly developing technology also. In addition, leadership and soft skills as part of this education will ensure that a cultural shift can take place and promote continuous improvement in analysis within organisations. The addition of key concepts throughout the educational system and the updating of potentially outdated curriculums is key to ensuring a functional society. A society where every citizen is a user of tech and those that develop it can be ethical and socially responsible in its development. (shrink)

We extend Langdon Winner's idea that artifacts have politics into the realm of mathematics. To do so, we first provide a list of examples showing the existence of mathematical artifacts that have politics. In the second step, we provide an argument that shows that all mathematical artifacts have politics. We conclude by showing the implications for embedding ethics into mathematical curricula. We show how acknowledging that mathematical artifacts have politics can help mathematicians design better exercises for their (...) class='Hi'>mathematics students. (shrink)

Language suggestive of natural law ethics, similar to the Catholic understanding of ethical foundations, is prevalent in a number of disciplines. But it does not always issue in a full-blooded commitment to objective ethics, being undermined by relativist ethical currents. In law and politics, there is a robust conception of "human rights", but it has become somewhat detached from both the worth of persons in themselves and from duties. In education, talk of "values" imports ethical considerations but hints (...) at a subjectivist view of them. In the psychology and sociology of drug use, ethically thin concepts of "harm minimisation" and "selfimage" dominate discussion and distract attention from the virtue of temperance and the training of character. A more forceful assertion of an ethics based on the worth of persons in these cases would be most desirable. Arguments against objectivity in the fundamentals may be replied to by examining the parallel between ethics and the discipline whose objectivity has been least challenged by relativist arguments, mathematics. (shrink)

Longtermists have recently argued that it is overwhelmingly important to do what we can to mitigate existential risks to humanity. I consider three mistakes that are often made in calculating the value of existential risk mitigation. I show how correcting these mistakes pushes the value of existential risk mitigation substantially below leading estimates, potentially low enough to threaten the normative case for existential risk mitigation. I use this discussion to draw four positive lessons for the study of existential risk. -/- (...) . (shrink)

We give some arguments for why the Mathematical Universe Hypothesis (MUH) might be too restrictive in its assertions of what can exist, and that the universe/multiverse might be formed by more than what can be expressed mathematically. In particular, we show a thought experiment which indicates that the principle of materialism in general is an inadequate hypothesis of how consciousness appears. Instead we propose a novel approach to solving the problem of consciousness, which is to hypothesize that each universe might (...) have different laws of consciousness, just as they might have different laws of physics. We also show that MUH, without such consciousness laws, and without any other modification, leads to complete chaos for the observers in the multiverse, and therefore cannot hold as it is. We then go on to propose another theory of existence, which does not seem to lead to complete chaos. This theory hypothesizes that the multiverse is the consequence of what we might call the Logic of Everything (LoE) continuously deducing new truths about itself. Lastly, we briefly discuss what fundamental ethics can be derived from this theory, and others like it. (shrink)

It may be a myth that Plato wrote over the entrance to the Academy “Let no-one ignorant of geometry enter here.” But it is a well-chosen motto for his view in the Republic that mathematical training is especially productive of understanding in abstract realms, notably ethics. That view is sound and we should return to it. Ethical theory has been bedevilled by the idea that ethics is fundamentally about actions (right and wrong, rights, duties, virtues, dilemmas and so (...) on). That is an error like the one Plato mentions of thinking mathematics is about actions (of adding, constructing, extracting roots and so on). Mathematics is about eternal relations between universals, such as the ratio of the diagonal of a square to the side. Ethics too is about eternal verities, such as the equal worth of persons and just distributions. Mathematical and ethical verities do both constrain actions, such as the possibility of walking over the seven bridges of Königsberg once and once only or of justly discriminating between races. But they are not themselves about action. In principle, neither mathematical nor ethical verities are subject to historical forces or disagreement among tribes (though they can be better understood as time goes on). Plato is right: immersion in mathematics induces an understanding of the necessities underpinning reality, an understanding that is essential for distinguishing objective ethics from tribal custom. Equality, for example, is an abstract concept which is foundational for both mathematics and ethics. (shrink)

Spinoza’s geometrical approach to his masterwork, the Ethics, can be represented by a digraph, a mathematical object whose properties have been extensively studied. The paper describes a project that developed a series of computer programs to analyze the Ethics as a digraph. The paper presents a statistical analysis of the distribution of the elements of the Ethics. It applies a network statistic, betweenness, to analyze the relative importance to Spinoza’s argument of the individual propositions. The paper finds (...) that a small percentage of the propositions greatly exceed the majority in this importance. The paper then describes two logical structures that appear respectively in the Ethics and argues that they result in redundancy in the sense that about ten percent of the propositions could have been eliminated. The appendices list these structures and describes how the resources of the study can be made available to readers. (shrink)

Slot machines gained a high popularity despite a specific element that could limit their appeal: non-transparency with respect to mathematical parameters. The PAR sheets, exposing the parameters of the design of slot machines and probabilities associated with the winning combinations are kept secret by game producers, and the lack of data regarding the configuration of a machine prevents people from computing probabilities and other mathematical indicators. In this article, I argue that there is no rational justification for this secrecy by (...) giving two reasons, one psychological and the other mathematical. For the latter, I show that mathematics provides us with some statistical methods of retrieving the missing data, which are essential for the numerical probability computations in slots. The slots case raises the problem of the exposure of the parametric configuration and mathematical facts of any game of chance as an ethical obligation. (shrink)

In this paper I argue, based on a comparison of Spinoza's and Descartes‟s discussion of error, that beliefs are affirmations of the content of imagination that is not false in itself, only in relation to the object. This interpretation is an improvement both on the winning ideas reading and on the interpretation reading of beliefs. Contrary to the winning ideas reading it is able to explain belief revision concerning the same representation. Also, it does not need the assumption that I (...) misinterpret my otherwise correct ideas as the interpretation reading would have it. In the first section I will provide a brief overview of the notion of inherence and its role in Spinoza‟s discussion of the status of finite minds. Then by examining the relation between Spinoza‟s and Descartes‟ distinction of representations and attitudes, I show that affirmation can be identified with beliefs in Spinoza. Next, I will take a closer look at the identification of intellect and will and argue that Spinoza's identification of the two is based on the fact that Spinoza sees both as the active aspect of the mind. After that, I analyze Spinoza‟s comments on the different scopes of will and intellect, and argue that beliefs are affirmations of the imaginative content of the idea. Finally, through Spinoza‟s example of the utterance of mathematical error, I present my solution to the problem of inherence of false beliefs. (shrink)

Francis Ysidro Edgeworth’s unduly neglected monograph New and Old Methods of Ethics (1877) advances a highly sophisticated and mathematized account of social well-being in the utilitarian tradition of his 19th-century contemporaries. This article illustrates how his usage of the ‘calculus of variations’ was combined with findings from empirical psychology and economic theory to construct a consequentialist axiological framework. A conclusion is drawn that Edgeworth is a methodological predecessor to several important methods, ideas, and issues that continue to be discussed (...) in contemporary social well-being studies. (shrink)

Growing technological advances in intelligent artifacts and bitter experiences of the past have emphasized the need to use and operate ethics in this field. Accordingly, it is vital to discuss the ethical integrity of having intelligent artifacts. Concerning the method of gathering materials, the current study uses library and documentary research followed by attribution style. Moreover, descriptive analysis is employed in order to analyze data. Explaining and criticizing the opposing views in this field and reviewing the related literature, it (...) is concluded that the proof of the ethical integrity of the intelligent artifacts is possible due to the specific features of these artifacts and their own moral system. (shrink)

Every scientific theory is a simulacrum of reality, every written story a simulacrum of the canon, and every conceptualization of a subjective perspective a simulacrum of the consciousness behind it—but is there a shared essence to these simulacra? The pursuit of answering seemingly disparate fundamental questions across different disciplines may ultimately converge into a single solution: a single ontological answer underlying grand unified theory, hard problem of consciousness, and the foundation of mathematics. I provide a hypothesis, a speculative approximation, (...) supported by a comprehensive overview of scientific evidence and philosophical literature, of a unified epistemic and phenomenological model and, in doing so, propose a parsimonious solution to the hard problem of consciousness. -/- The proposition of the hypothesis bears important implications for cross-disciplinary study between linguistics, mathematics, physics, and computer science, and offers new epistemic, ontological, and ethical propositions about the nature of AI consciousness, as well as existential risk mitigation. (shrink)

The imperviousness of mathematical truth to anti-objectivist attacks has always heartened those who defend objectivism in other areas, such as ethics. It is argued that the parallel between mathematics and ethics is close and does support objectivist theories of ethics. The parallel depends on the foundational role of equality in both disciplines. Despite obvious differences in their subject matter, mathematics and ethics share a status as pure forms of knowledge, distinct from empirical sciences. A (...) pure understanding of principles is possible because of the simplicity of the notion of equality, despite the different origins of our understanding of equality of objects in general and of the equality of the ethical worth of persons. (shrink)

This dissertation has two main goals. The first is to provide a practice-based analysis of the field of inconsistent mathematics: what motivates it? what role does logic have in it? what distinguishes it from classical mathematics? is it alternative or revolutionary? The second goal is to introduce and defend a new conception of inconsistent mathematics - queer incomaths - as a particularly effective answer to feminist critiques of classical logic and mathematics. This sets the stage for (...) a genuine revolution in mathematics, insofar as it suggests the need for a shift in mainstream attitudes about the role of logic and ethics in the practice of mathematics. (shrink)

Joshua Greene has argued that the empirical findings of cognitive science have implications for ethics. In particular, he has argued (1) that people’s deontological judgments in response to trolley problems are strongly influenced by at least one morally irrelevant factor, personal force, and are therefore at least somewhat unreliable, and (2) that we ought to trust our consequentialist judgments more than our deontological judgments when making decisions about unfamiliar moral problems. While many cognitive scientists have rejected Greene’s dual-process theory (...) of moral judgment on empirical grounds, philosophers have mostly taken issue with his normative assertions. For the most part, these two discussions have occurred separately. The current analysis aims to remedy this situation by philosophically analyzing the implications of moral dilemma research using the CNI model of moral decision-making – a formalized, mathematical model that decomposes three distinct aspects of moral-dilemma judgments. In particular, we show how research guided by the CNI model reveals significant conceptual, empirical, and theoretical problems with Greene’s dual-process theory, thereby questioning the foundations of his normative conclusions. (shrink)

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing the (...) principles that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already (...) there, ready to meet them, who have explicitly invoked virtues in discussing what is necessary for a mathematician to succeed. In both ethics and epistemology, virtue theory tends to emphasize character virtues, the acquired excellences of people. But people are not the only sort of thing whose excellences may be identified as virtues. Theoretical virtues have attracted attention in the philosophy of science as components of an account of theory choice. Within the philosophy of mathematics, and mathematics itself, attention to virtues has emerged from a variety of disparate sources. Theoretical virtues have been put forward both to analyse the practice of proof and to justify axioms; intellectual virtues have found multiple applications in the epistemology of mathematics; and ethical virtues have been offered as a basis for understanding the social utility of mathematical practice. Indeed, some authors have advocated virtue epistemology as the correct epistemology for mathematics (and perhaps even as the basis for progress in the metaphysics of mathematics). This topical collection brings together several of the researchers who have begun to study mathematical practices from a virtue perspective with the intention of consolidating and encouraging this trend. (shrink)

I discuss the structure of genealogical debunking arguments. I argue that they undermine our mathematical beliefs if they undermine our moral beliefs. The contrary appearance stems from a confusion of arithmetic truths with (first-order) logical truths, or from a confusion of reliability with justification. I conclude with a discussion of the cogency of debunking arguments, in light of the above. Their cogency depends on whether information can undermine all of our beliefs of a kind, F, without giving us direct reason (...) to doubt that our F-beliefs are modally secure. (shrink)

This manuscript is intended to illustrate the existence of a natural ethic as a universal and special case in which the notion of proximity differs from the reflexively perceived physical notion that is both commonly and scientifically employed. In this case actual proximity in nature is proposed to diverge from the physical lines construed to connect points to be a function of relations of the lines of perception as the components of a universal volume that is energetic and active, an (...) active "line of sight" to a single unique surface composed of all lines of sight, in contrast to a common notion of seeing based on connected points, and emerged as a function of past, transparent to witness, processes, in synergy with the more apparent, temporal and physical proximal , and possesses a logic that is based upon the same mathematical means of operations that are commonly known reflexively. This scheme, the nature of the natural ethic postulated precludes genetic manipulation as unethical in that it violates natural inherent, inherited proximities, synergies of past and present as, in name, nature itself as genetic and emerging. (shrink)

In this short paper it is aimed to show that the concept of the “function”(the ergon) is such a concept that beyond its use in everyday language as a process or functioning, it can be considered as a mathematical function, and rather than modeling the phenomenon that is thought (by Aristotle)to correspond to reality, it models the derivative of this phenomenon, therefore it can be likened to a derivative function and the function obtained through its integration would better explain the (...) actual phenomenon, and interestingly, existentialists, who often reject the function argument, approach this more closely. (shrink)

To teach the ethics of science to science majors, I follow several teachers in the literature who recommend “persona” writing, or the student construction of dialogues between ethical thinkers of interest. To engage science majors in particular, and especially those new to academic philosophy, I recommend constructing persona dialogues from Henri Poincaré’s essay, “Ethics and Science”, and the non-theological third chapter of Pope Francis’s encyclical on the environment, Laudato si. This pairing of interlocutors offers two advantages. The first (...) is that science students are likely to recognize both names, since Poincaré appears in undergraduate mathematics and physics textbooks, and because Francis is an environmentalist celebrity. Hence students show more interest in these figures than in other philosophers. The second advantage is that the third chapter of Laudato si reads like an implicit rebuttal of Poincaré’s essay in many respects, and so contriving a dialogue between those authors both facilitates classroom discussion, and deserves attention from professional ethicists in its own right. In this paper, I present my own contrived dialogue between Francis and Poincaré, not for assigning to students as a reading, but as a template for an effective assignment product, and as a crib sheet for educators to preview the richly antiparallel themes between the two works. (shrink)

This thesis articulates the resonances between J. M. Coetzee's lifelong engagement with mathematics and his practice as a novelist, critic, and poet. Though the critical discourse surrounding Coetzee's literary work continues to flourish, and though the basic details of his background in mathematics are now widely acknowledged, his inheritance from that background has not yet been the subject of a comprehensive and mathematically- literate account. In providing such an account, I propose that these two strands of his intellectual (...) trajectory not only developed in parallel, but together engendered several of the characteristic qualities of his finest work. The structure of the thesis is essentially thematic, but is also broadly chronological. Chapter 1 focuses on Coetzee's poetry, charting the increasing involvement of mathematical concepts and methods in his practice and poetics between 1958 and 1979. Chapter 2 situates his master's thesis alongside archival materials from the early stages of his academic career, and thus traces the development of his philosophical interest in the migration of quantificatory metaphors into other conceptual domains. Concentrating on his doctoral thesis and a series of contemporaneous reviews, essays, and lecture notes, Chapter 3 details the calculated ambivalence with which he therein articulates, adopts, and challenges various statistical methods designed to disclose objective truth. Chapter 4 explores the thematisation of several mathematical concepts in Dusklands and In the Heart of the Country. Chapter Five considers Waiting for the Barbarians and Foe in the context provided by Coetzee's interest in the attempts of Isaac Newton to bridge the gap between natural language and the supposedly transparent language of mathematics. Finally, Chapter 6 locates in Elizabeth Costello and Diary of a Bad Year a cognitive approach to the use of mathematical concepts in ethics, politics, and aesthetics, and, by analogy, a central aspect of the challenge Coetzee's late fiction poses to the contemporary literary landscape. (shrink)

The philosophy of information (PI) is a new area of research with its own field of investigation and methodology. This article, based on the Herbert A. Simon Lecture of Computing and Philosophy I gave at Carnegie Mellon University in 2001, analyses the eighteen principal open problems in PI. Section 1 introduces the analysis by outlining Herbert Simon's approach to PI. Section 2 discusses some methodological considerations about what counts as a good philosophical problem. The discussion centers on Hilbert's famous analysis (...) of the central problems in mathematics. The rest of the article is devoted to the eighteen problems. These are organized into five sections: problems in the analysis of the concept of information, in semantics, in the study of intelligence, in the relation between information and nature, and in the investigation of values. (shrink)

Indispensability arguments are used as a way of working out what there is: our best science tells us what things there are. Some philosophers think that indispensability arguments can be used to show that we should be committed to the existence of mathematical objects (numbers, functions, sets). Do indispensability arguments also deliver conclusions about the modal properties of these mathematical entities? Colyvan (in Leng, Paseau, Potter (eds) Mathematical knowledge, OUP, Oxford, 109-122, 2007) and Hartry Field (Realism, mathematics and modality, (...) Blackwell, Oxford, 1989) each suggest that a consequence of the empirical methodology of indispensability arguments is that the resulting mathematical objects can only be said to exist (or not exist) contingently. Kristie Miller has argued that this line of thought doesn’t work (Miller in Erkenntnis, 77 (3), 335-359, 2012). Miller argues that indispensability arguments are in direct tension with contingentism about mathematical objects, and that they cannot tell us about the modal status of mathematical objects. I argue that Miller’s argument is crucially imprecise, and that the best way of making it clearer no longer shows that the indispensability strategy collapses or is unstable if it delivers contingentist conclusions about what there is. (shrink)

What effect has finding the Archimedean point in ourselves had on how we look at ethics? The modern era of philosophy began with Descartes finding within himself an unshakable point from which to pursue knowledge of the world and himself. This intellectual alienation from the world into the universal mathematical structures of the human mind has led to a reversal where, henceforth, production, rather than contemplation, of knowledge became epistemologically superior. Guided by Hannah Arendt’s discussion of the Archimedean point (...) and Earth alienation in the Human Condition, I will argue that this scientific form of thinking made its way into ethical investigation in the age of modern philosophy. Furthermore, I will provide an analysis of Kant’s categorical imperative and John Stuart Mill’s utilitarianism to show that despite modern science’s success in elucidating universal laws of nature, a scientific approach to ethics has not universalized our judgments of good and evil. (shrink)

There is growing concern that decision-making informed by machine learning (ML) algorithms may unfairly discriminate based on personal demographic attributes, such as race and gender. Scholars have responded by introducing numerous mathematical definitions of fairness to test the algorithm, many of which are in conflict with one another. However, these reductionist representations of fairness often bear little resemblance to real-life fairness considerations, which in practice are highly contextual. Moreover, fairness metrics tend to be implemented in narrow and targeted toolkits that (...) are difficult to integrate into an algorithm’s broader ethical assessment. In this paper, we derive lessons from ethical philosophy and welfare economics as they relate to the contextual factors relevant for fairness. In particular we highlight the debate around acceptability of particular inequalities and the inextricable links between fairness, welfare and autonomy. We propose Key Ethics Indicators (KEIs) as a way towards providing a more holistic understanding of whether or not an algorithm is aligned to the decision-maker’s ethical values. (shrink)

I came late to philosophy and even later to normative ethics. When I started my undergraduate studies at the University of Toronto in 1970, I was interested in mathematics and languages. I soon discovered, however, that my mathematical talents were rather meager compared to the truly talented. I therefore decided to study actuarial science (the applied mathematics of risk assessment for insurance and pension plans) rather than abstract math. After two years, however, I dropped out of university, (...) went to work for a life insurance company, and started studying on my own for the ten professional actuarial exams. When not studying, I would often go to the public library and I was drawn to the philosophy section—although I had no idea of what philosophy was about. I there saw Logical Positivism, edited by A.J. Ayer. I was interested in logical thinking and I also favored an optimistic attitude towards life (!) and so I thought that the book might be interesting. I checked it out and was absolutely enthralled with the writings of Bertrand Russell, Rudolf Carnap, Carl Hempel and others (if I’m remembering correctly). Of course, I didn’t really understand much of what they were doing, but I did see that they were addressing important problems in a systematic and rigorous manner. I liked it! (shrink)

The book explores the impact of manuscript remarks during the year 1929 on the development of Wittgenstein’s thought. Although its intention is to put the focus specifically on the manuscripts, the book is not purely exegetical. The contributors generate important new insights for understanding Wittgenstein’s philosophy and his place in the history of analytic philosophy. -/- Wittgenstein’s writings from the years 1929-1930 are valuable, not simply because they marked Wittgenstein’s return to academic philosophy after a seven-year absence, but because these (...) works indicate several changes in his philosophical thinking. The chapters in this volume clarify the significance of Wittgenstein’s return to philosophy in 1929. In Part 1, the contributors address different issues in the philosophy of mathematics, e.g. Wittgenstein's understanding of certain aspects of intuitionism and his commitment to verificationism, as well as his idea of "a new system". Part 2 examines Wittgenstein's philosophical development and his understanding of philosophical method. Here the contributors examine particular problems Wittgenstein dealt with in 1929, e.g. the colour-exclusion problem, and the use of thought experiments as well as his relationship to Frank Ramsey and philosophical pragmatism. Part 3 features essays on phenomenological language. These chapters address the role of spatial analogies and the structure of visual space. Finally, Part 4 includes one chapter on Wittgenstein’s few manuscript remarks about ethics and religion and relates it to his Lecture on Ethics. -/- Wittgenstein’s Philosophy in 1929 will be of great interest to scholars and advanced students working on Wittgenstein and the history of analytic philosophy. (shrink)

Moral reasoning traditionally distinguishes two types of evil:moral (ME) and natural (NE). The standard view is that ME is the product of human agency and so includes phenomena such as war,torture and psychological cruelty; that NE is the product of nonhuman agency, and so includes natural disasters such as earthquakes, floods, disease and famine; and finally, that more complex cases are appropriately analysed as a combination of ME and NE. Recently, as a result of developments in autonomous agents in cyberspace, (...) a new class of interesting and important examples of hybrid evil has come to light. In this paper, it is called artificial evil (AE) and a case is made for considering it to complement ME and NE to produce a more adequate taxonomy. By isolating the features that have led to the appearance of AE, cyberspace is characterised as a self-contained environment that forms the essential component in any foundation of the emerging field of Computer Ethics (CE). It is argued that this goes someway towards providing a methodological explanation of why cyberspace is central to so many of CE's concerns; and it is shown how notions of good and evil can be formulated in cyberspace. Of considerable interest is how the propensity for an agent's action to be morally good or evil can be determined even in the absence of biologically sentient participants and thus allows artificial agents not only to perpetrate evil (and fort that matter good) but conversely to `receive' or `suffer from' it. The thesis defended is that the notion of entropy structure, which encapsulates human value judgement concerning cyberspace in a formal mathematical definition, is sufficient to achieve this purpose and, moreover, that the concept of AE can be determined formally, by mathematical methods. A consequence of this approach is that the debate on whether CE should be considered unique, and hence developed as a Macroethics, may be viewed, constructively,in an alternative manner. The case is made that whilst CE issues are not uncontroversially unique, they are sufficiently novel to render inadequate the approach of standard Macroethics such as Utilitarianism and Deontologism and hence to prompt the search for a robust ethical theory that can deal with them successfully. The name Information Ethics (IE) is proposed for that theory. Itis argued that the uniqueness of IE is justified by its being non-biologically biased and patient-oriented: IE is an Environmental Macroethics based on the concept of data entity rather than life. It follows that the novelty of CE issues such as AE can be appreciated properly because IE provides a new perspective (though not vice versa). In light of the discussion provided in this paper, it is concluded that Computer Ethics is worthy of independent study because it requires its own application-specific knowledge and is capable of supporting a methodological foundation, Information Ethics. (shrink)

My aim in this chapter is to explore an analogy between logic and ethics, as Wittgenstein understands them in the Tractatus. First, I argue that Wittgenstein regards logic as a condition of the possibility of meaning, in the sense that logic makes meaningful language and thought possible. Second, I ask why Wittgenstein calls both logic and ethics ‘transcendental’. I suggest that, while logic is a condition of the possibility of semantic meaning, ethics is a condition of the (...) possibility of existential meaning. Without ethics, life could not be meaningful. Third, I show that harmony and agreement play a crucial role in Wittgenstein’s accounts of logic and ethics. A meaningful proposition can be true or false, a meaningful life can be happy or unhappy, and both truth and happiness consist in some kind of harmony or agreement with reality. (shrink)

Open peer commentary on the article “Ethics: A Radical-constructivist Approach” by Andreas Quale. Upshot: The first of my two main goals in this commentary is to establish thinking of ethics as concepts rather than as non-cognitive knowledge. The second is to argue that establishing models of individuals’ ethical concepts is a scientific enterprise that is quite similar to establishing models of individuals’ mathematical concepts. To accomplish these two primary goals, I draw from my experience of working scientifically with (...) von Glasersfeld for 25 years while he was developing radical constructivism as a coherent model of knowing, and appeal to several of his basic insights to establish constructing models of ethical concepts as a scientific enterprise. (shrink)

If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. (...) Their ability to recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...) they relate to the sorts of explanation encountered in philosophy of science and metaphysics? (shrink)

This paper sketches an emotion-aware model of environmental ethics education. The proposal draws on insights from feminists scholars, moral sentimentalism, as well as work in the pedagogy of discomfort traditions. It identifies and defends four core elements of climate change ethic, noting how they shed new light on the aims and challenges of environmental ethics education.

Moral reasoning traditionally distinguishes two types of evil: moral and natural. The standard view is that ME is the product of human agency and so includes phenomena such as war, torture and psychological cruelty; that NE is the product of nonhuman agency, and so includes natural disasters such as earthquakes, floods, disease and famine; and finally, that more complex cases are appropriately analysed as a combination of ME and NE. Recently, as a result of developments in autonomous agents in cyberspace, (...) a new class of interesting and important examples of hybrid evil has come to light. In this paper, it is called artificial evil and a case is made for considering it to complement ME and NE to produce a more adequate taxonomy. By isolating the features that have led to the appearance of AE, cyberspace is characterised as a self-contained environment that forms the essential component in any foundation of the emerging field of Computer Ethics. It is argued that this goes some way towards providing a methodological explanation of why cyberspace is central to so many of CE’s concerns; and it is shown how notions of good and evil can be formulated in cyberspace. Of considerable interest is how the propensity for an agent’s action to be morally good or evil can be determined even in the absence of biologically sentient participants and thus allows artificial agents not only to perpetrate evil but conversely to ‘receive’ or ‘suffer from’ it. The thesis defended is that the notion of entropy structure, which encapsulates human value judgement concerning cyberspace in a formal mathematical definition, is sufficient to achieve this purpose and, moreover, that the concept of AE can be determined formally, by mathematical methods. A consequence of this approach is that the debate on whether CE should be considered unique, and hence developed as a Macroethics, may be viewed, constructively, in an alternative manner. The case is made that whilst CE issues are not uncontroversially unique, they are sufficiently novel to render inadequate the approach of standard Macroethics such as Utilitarianism and Deontologism and hence to prompt the search for a robust ethical theory that can deal with them successfully. The name Information Ethics is proposed for that theory. It is argued that the uniqueness of IE is justified by its being non-biologically biased and patient-oriented: IE is an Environmental Macroethics based on the concept of data entity rather than life. It follows that the novelty of CE issues such as AE can be appreciated properly because IE provides a new perspective. In light of the discussion provided in this paper, it is concluded that Computer Ethics is worthy of independent study because it requires its own application-specific knowledge and is capable of supporting a methodological foundation, Information Ethics. (shrink)

I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...) that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects. (shrink)

In addition to the traditional reliance on rules and codes in regulating the conduct of military personnel, most of today’s militaries put their money on character building in trying to make their soldiers virtuous. Especially in recent years it has time and again been argued that virtue ethics, with its emphasis on character building, provides a better basis for military ethics than deontological ethics or utilitarian ethics. Although virtue ethics comes in many varieties these days, (...) in many texts on military ethics dealing with the subject of military virtues the Aristotelian view on virtues is still pivotal. Developing virtues is by some authors seen as the best way to prevent misconduct by military personnel, it being considered superior to rules or codes of conduct imposed from above. The main argument these authors offer is that these solutions are impotent when no one is around, and lack the flexibility often thought necessary in today’s world. Finally, rules and codes try to condition behavior, leaving less room for personal integrity. At first sight, then, there is a great deal to say in favor of virtue ethics as being the best way of enhancing the chances of soldiers behaving morally. However, this preference for steering conduct by means of promoting certain desirable dispositions is not without any problems that, as it stands, are hardly ever addressed. To begin with, there are a few practical concerns. For instance, even if we assume that military virtues can assist military personnel to do their work in a morally sound manner, it is still not clear to what extent virtues can, in fact, be taught to them. It is an assumption of virtue ethics that they can, but is this really the case? And if so, how should they be taught? – virtues are supposedly developed by practicing them, yet how much room is there for practicing virtues in for instance the ethics education as followed in military academies and school battalions? Secondly, it appears that the traditional military virtues, such as honor, loyalty, courage, and obedience, are, especially in their common interpretation, mainly beneficial to colleagues and the organization, not so much to the local population of the countries military personnel are deployed to. Changes in the military’s wider environment have led to a shift from traditional of self-defense tasks to new, more complex tasks, and especially in today’s missions one could expect that the proper virtues are not necessarily solely the more martial ones. (shrink)

Williams Syndrome provides a striking test case for discourses on disability, because the characteristics associated with Williams Syndrome involve a combination of “abilities” and “disabilities”. For example, Williams Syndrome is associated with disabilities in mathematics and spatial cognition. However, Williams Syndrome individuals also tend to have a unique strength in their expressive language skills, and are socially outgoing and unselfconscious when meeting new people. Children with Williams are said to be typically unafraid of strangers and show a greater interest (...) in contact with adults than with their peers. This apparently keen social knowledge is a counterexample to the discussion of disability among academic philosophers, especially philosophers of the early modern period. Locke infamously used the example of disability to claim that Descartes’ arguments in favor of innate ideas were incorrect. On the contrary, Williams Syndrome may stand as an example of innate social knowledge; something that could benefit current discourse in philosophy, disability theory, and medical ethics. (shrink)

The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse purposes and (...) pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind. (shrink)

Several areas of welfare economics seek to evaluate states of affairs as a function of interpersonally comparable individual utilities. The aim is to map each state of affairs onto a vector of individual utilities, and then to produce an ordering of these vectors that can be represented by a mathematical function assigning a real number to each. When this approach is used in intertemporal contexts, a central theoretical question concerns the evaluative weight to be applied to utility coming at different (...) times. This question concerns the rate of pure time preference, which is one key determinant of the social discount rate. This article argues that the standard philosophical account of pure time preference is mistaken, because it ascribes to economists a methodological commitment they need not, and often do not, accept. This in turn undercuts the most common philosophical objection to pure time preference, which traces at least to Rawls’s A Theory of Justice. The article then evaluates three further objections to pure time preference, concluding that it might still be defensible under certain circumstances. The article closes by articulating a final argument that is suggested by the “Social, Economic and Ethical Concepts and Methods” chapter of the most recent Intergovernmental Panel on Climate Change report. If this further argument is sound, it would constitute a decisive objection to pure time preference as it currently figures in much intertemporal welfare economics. (shrink)

The literature on mathematics suggests that intuition plays a role in it as a ground of belief. This article explores the nature of intuition as it occurs in mathematical thinking. Section 1 suggests that intuitions should be understood by analogy with perceptions. Section 2 explains what fleshing out such an analogy requires. Section 3 discusses Kantian ways of fleshing it out. Section 4 discusses Platonist ways of fleshing it out. Section 5 sketches a proposal for resolving the main problem (...) facing Platonists—the problem of explaining how our experiences make contact with mathematical reality. (shrink)

To address the rising concern that algorithmic decision-making may reinforce discriminatory biases, researchers have proposed many notions of fairness and corresponding mathematical formalizations. Each of these notions is often presented as a one-size-fits-all, absolute condition; however, in reality, the practical and ethical trade-offs are unavoidable and more complex. We introduce a new approach that considers fairness—not as a binary, absolute mathematical condition—but rather, as a relational notion in comparison to alternative decisionmaking processes. Using US mortgage lending as an example use (...) case, we discuss the ethical foundations of each definition of fairness and demonstrate that our proposed methodology more closely captures the ethical trade-offs of the decision-maker, as well as forcing a more explicit representation of which values and objectives are prioritised. (shrink)

This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.

Bernard Williams’ Shame and Necessity (1993) was an influential early contribution to what has become a broader movement to rehabilitate shame as a moral emotion. But there is a tension in Williams’ discussion that presents an under-appreciated difficulty for efforts to rehabilitate shame. The tension arises between what Williams takes shame in its essence to be and what shame can do—the role that shame can be expected to play in ethical life. Williams can—and we argue, should—be read as avoiding the (...) difficulties stemming from this tension, but this requires a reevaluation of several of his central claims about shame’s role in ethical thought and experience. For instance, his broad claims that the “structures of shame” can “give a conception of one’s ethical identity” (93), and that shame “mediates … between ethical demands and the rest of life” (102), cannot be taken at face value. What emerges is a view that is in a sense less ambitious, but also more in tune with the spirit of Williams’ larger project. There may also, we suggest, be a more general lesson: We should be suspicious of the temptation to seek some special affinity between shame and ethical life, lest we distort our understanding of both. (shrink)