There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby establishing (...) an even more general impossibility theorem. (shrink)

I provide a characterization of weakly pseudo-rationalizable choice functions---that is, choice functions rationalizable by a set of acyclic relations---in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions.

Everything we do in life involves a connection with information, experience and know-how: together these represent the most valuable of intangible human assets encompassing our history, cultures and wisdom. However, the more easily new technologies gather information, the more we are confronted with our limited capacity to distinguish between what is essential, important or merely ‘nice-to-have’. This article presents the case study of a multilingual Knowledge Management System, the Business enabling e-Platform that gathers and protects tacit knowledge, as the key (...) to developing structured intellectual capital, while acknowledging the urgent need here to integrate Ethics-by-design alongside AI-by-design, in view of the far-reaching consequences involved, for good or ill. It also explains how a beneficial Circular Economy of Knowledge depends on evidence-based answers, and how harmonising taxonomies, terminology and standards promotes global trust as the basis for the unhindered transfer of tacit knowledge between generations in a way that benefits everyone. (shrink)

The focus of this paper is employee ownership, specifically the role of employee ownership in value creation. Based on a sample of 163 French companies, we have measured the impact of employee share ownership on value creation for both shareholders and stakeholders. Only companies with a sustained employee ownership policy over a 5-year period (from 2001 to 2005), as defined by the French Federation of Employee and Former Employee Shareholders (FAS), have been considered. The results indicate that employee share ownership (...) plans have no effect on shareholders’ or stakeholders’ value creation. (shrink)

Rush Rhees (1905-1989) was a philosopher, and a pupil and close friend of Ludwig Wittgenstein. While some of Rhees's own published papers became classics, most of his work remained unpublished during his lifetime. After his death, his papers were found to comprise sixteen thousand pages of manuscript on every aspect of philosophy, from philosophical logic to Simone Weil. This collection of unpublished papers, edited by D. Z. Phillips, includes Rhees's outstanding work on philosophy and religion. Written over an academic (...) lifetime, some of the papers are sympathetic to religion while others are not. It is Rhees's ability to interweave the personal and philosophical, and his integrity and intellectual honesty, which make this one of the most impressive books in twentieth-century philosophy of religion. (shrink)

The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...) Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus. (shrink)

For much of its history, philosophy was not merely a theoretical discipline but a way of life, an "art of living." This practical aspect of philosophy has been much less dominant in modernity than it was in ancient Greece and Rome, when philosophers of all stripes kept returning to Socrates as a model for living. The idea of philosophy as an art of living has survived in the works of such major modern authors as Montaigne, Nietzsche, and Foucault. Each of (...) these writers has used philosophical discussion as a means of establishing what a person is and how a worthwhile life is to be lived. In this wide-ranging, brilliantly written account, Alexander Nehamas provides an incisive reevaluation of Socrates' place in the Western philosophical tradition and shows the importance of Socrates for Montaigne, Nietzsche, and Foucault. Why does each of these philosophers—each fundamentally concerned with his own originality—return to Socrates as a model? The answer lies in the irony that characterizes the Socrates we know from the Platonic dialogues. Socratic irony creates a mask that prevents a view of what lies behind. How Socrates led the life he did, what enabled or inspired him, is never made evident. No tenets are proposed. Socrates remains a silent and ambiguous character, forcing readers to come to their own conclusions about the art of life. This, Nehamas shows, is what allowed Montaigne, Nietzsche, and Foucault to return to Socrates as a model without thereby compelling them to imitate him. This highly readable, erudite study argues for the importance of the tradition within Western philosophy that is best described as "the art of living" and casts Montaigne, Nietzsche, and Foucault as the three major modern representatives of this tradition. Full of original ideas and challenging associations, this work will offer new ways of thinking about the philosophers Nehamas discusses and about the discipline of philosophy itself. (shrink)

In these discussions, Rush Rhees, who was a student and close friend of Wittgenstein, works out what he has learned from Wittgenstein's personal teaching and from study of his published and (at the time) unpublished writings. Some are review articles of books on Wittgenstein, and these are devoted to exposition of Wittgenstein's views. Others are independent discussions of special points in Wittgenstein's philosophy. The longest article, here published for the first time, is an account or record of what Wittgenstein (...) said about continuity in private discussion in 1938. (shrink)

In many assessment problems—aptitude testing, hiring decisions, appraisals of the risk of recidivism, evaluation of the credibility of testimonial sources, and so on—the fair treatment of different groups of individuals is an important goal. But individuals can be legitimately grouped in many different ways. Using a framework and fairness constraints explored in research on algorithmic fairness, I show that eliminating certain forms of bias across groups for one way of classifying individuals can make it impossible to eliminate such bias across (...) groups for another way of dividing people up. And this point generalizes if we require merely that assessments be approximately bias-free. Moreover, even if the fairness constraints are satisfied for some given partitions of the population, the constraints can fail for the coarsest common refinement, that is, the partition generated by taking intersections of the elements of these coarser partitions. This shows that these prominent fairness constraints admit the possibility of forms of intersectional bias. (shrink)

Essays offer a glimpse of the Vienna-born philosopher's personality, character, and life's work.

Four years after the publication of Wittgenstein's Investigations, Rush Rhees began writing critical reflections on the masterpiece he had helped to edit. In this edited collection of his previously unpublished writings, Rhees argues, contra Wittgenstein, that although language lacks the unity of a calculus it is not simply a family of language games. The unity of language is found in its dialogical character. It is in this context that we say something, and grow in understanding: notions not captured in (...) Wittgenstein's emphasis on language games, following rules, and using language. Rhees develops Wittgenstein's notion that to imagine a language is to image a form of life, without suggesting that we are all engaged in an all-inclusive conversation. The result is not only a major contribution to Wittgenstein scholarship, but an original discussion of central philosophical questions concerning the possibility of discourse. (shrink)

Our aim here is to present a result that connects some approaches to justifying countable additivity. This result allows us to better understand the force of a recent argument for countable additivity due to Easwaran. We have two main points. First, Easwaran’s argument in favour of countable additivity should have little persuasive force on those permissive probabilists who have already made their peace with violations of conglomerability. As our result shows, Easwaran’s main premiss – the comparative principle – is strictly (...) stronger than conglomerability. Second, with the connections between the comparative principle and other probabilistic concepts clearly in view, we point out that opponents of countable additivity can still make a case that countable additivity is an arbitrary stopping point between finite and full additivity. (shrink)

Recent impossibility theorems for fair risk assessment extend to the domain of epistemic justice. We translate the relevant model, demonstrating that the problems of fair risk assessment and just credibility assessment are structurally the same. We motivate the fairness criteria involved in the theorems as also being appropriate in the setting of testimonial justice. Any account of testimonial justice that implies the fairness/justice criteria must be abandoned, on pain of triviality.

In this book, Rhees brings out the continuity in Wittgenstein's thought, and the radical character of his conclusions.

This essay provides an explanation and interpretation of the undertreatment of pain by discussing some of the scientific, clinical, cultural, and philosophical aspects of this problem. One reason why pain continues to be a problem for medicine is that pain does not conform to the scientific approach to health and disease, a philosophy adopted by most health care professionals. Pain does not fit this philosophical perspective because (1) pain is subjective, not objective; (2) the causal basis of pain is often (...) poorly understood; (3) pain is often regarded as a mere symptom, not as a disease; (4) there often are no magic bullets for pain; (5) pain does not fit the expert knowledge model. In order for health care professionals to do a better job of treating pain, some changes need to occur in medical philosophy, education, and practice. (shrink)

Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. (...) We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling. (shrink)

This paper generalizes rationalizability of a choice function by a single acyclic binary relation to rationalizability by a set of such relations. Rather than selecting those options in a menu that are maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function selects those options that are maximal with respect to at least one binary relation in a given set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple functional properties. This result also (...) generalizes Aizerman and Malishevski's characterization of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total orders. (shrink)

When in May 1930, the Council of Trinity College, Cambridge, had to decide whether to renew Wittgenstein's research grant, it turned to Bertrand Russell for an assessment of the work Wittgenstein had been doing over the past year. His verdict: The theories contained in this new work... are novel, very original and indubitably important. Whether they are true, I do not know. As a logician who like simplicity, I should like to think that they are not, but from what I (...) have read of them I am quite sure that he ought to have the opportunity to work them out, since, when completed, they may easily prove to constitute a whole new philosophy. (shrink)

Rush Rhees questions the viability of moral theories and the general claims they make in ethics. He shows how one can both be concerned with knowing what one ought to do while recognizing that one's answer is a personal one. These insights, arrived at in a distinctive style, characteristic of Rhees, are then applied to issues of life and death, human sexuality, and our relations to animals. To recognize why philosophy cannot answer such questions for us is an affirmation, (...) not a denial, of their importance. (shrink)

We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be nontrivially Bayes-compatible. We show by contrast that geometric pooling can be nontrivially Bayes-compatible. Indeed, we show that, under certain assumptions, geometric and (...) Bayes-compatible pooling are equivalent. Granting supra-Bayesianism its usual normative status, one upshot of our study is thus that, in a certain class of epistemic contexts, geometric pooling enjoys a normative advantage over linear pooling as a social learning mechanism. We discuss the philosophical ramifications of this advantage, which we show to be robust to variations in our statement of the Bayes-compatibility problem. (shrink)

The paper discusses the foundation and genesis of the political society according to Locke, elaborating why the relationship between the civil society and the government is not defined in contractual terms, but by the notion of “trust”. Rehm argues against the view that Locke supports a liberal proceduralism, stressing that consent for him is indeed the necessary, but not the sufficient condition of legitimate political power: what needs to be added is action in accordance with the law of nature.

This text has as a purpose the realization of a comparative analysis between two points view about the history of science. Ilya Prigogine (Nobel Prize 1977) and Eduardo Nicol (Mexican-Spanish philosopher) discuss about time and history of science, allowing us to find a coincidence between physics an..

Our challenge begins with America's aversion to science. The problem is, of course, that nonscientists could understand scientific thinking, and would understand it, if they were encouraged and expected to do so. Though Members of Congress and their staff may avoid science, the institution itself cannot. Until the day comes when science is fully integrated into education for all, and even Members of Congress and congressional staff Members can deal with technical subjects, we will need special help for our legislation. (...) Likewise, ensuring that good science informs and infuses good public policy requires scientists engage in the process of self-governance. Science should not only be a tool of public policy, it should be its foundation. With a scientifically literate society and public policy grounded in sound science, America can maintain its leadership in the emerging global knowledge economy. Without these, America will lose the very things that have fueled its greatness. (shrink)

The paper is an analysis of Rousseau’s concept of property. It shows that Rousseau wants to draft a new system of politics that will not forbid private property but will limit its scale. It aims to clarify that Rousseau owes much to John Locke’s theory and even adopts Locke’s definition that it is a basic purpose of the social contract to protect the citizen’s property. It is argued that in spite of these similarities Rousseau’s account differs fundamentally from Locke’s. Having (...) a right of ownership to something for Locke means to be entitled to exclude anybody else from it: to say “this is mine” in Locke is synonymous to “it is not yours”. For Rousseau having a right of ownership to something implies a self-limitation by the proprietor: to say “this is mine” in Rousseau signifies “everything else is not mine”. While property rights in Locke have the purpose of legitimizing “pleonexia” and economic inequality, Rousseau tries to use them as restrictions to citizens’ desires and greed. (shrink)

The paper is devoted to demonstrating the systematic value of the “Two Treatises of Government”. Even though their genesis is rooted in the political circumstances of Locke’s life-time, the “Treatises” are not simply a pamphlet designed to support the Whig cause, as Locke’s political ideas are derived from his theoretical philosophy and from his concept of natural law.

A distinguished discussion of Weil's views on social philosophy, science, ethics, and religion.

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

Is Rousseau an advocate of natural law or not? The purpose of Rehm’s paper is to suggest a positive answer to this controversially discussed question. On the one hand, Rousseau presents a critical history of traditional natural law theory which in his view is based on flawed suppositions: not upon natural, but on artificial qualities of man, and even rationality and sociability are counted among the latter. On the other hand he presents the self-confident manifesto for a fresh start (...) in natural law theory, founded on what to Rousseau’s mind is the true idea of human nature. The paper intends to show that the only natural qualities which can be seen as anthropological constants are those that keep man flexible, namely perfectibility and freedom of will. It is argued that these are exactly the qualities which according to Rousseau serve as the standard of natural law for the system of politics and its laws: Only a state based upon the free consent of individuals can do justice to man’s perfectibility and freedom of will. Rehm stresses that because of perfectibility and freedom of will, this self-commitment has to be revisable, which is why the republic of the “Social Contract” should not have a constitution, or any law that the citizens cannot alter. It is demonstrated that in Rousseau’s view, this republic is the enabling condition of natural liberty. -/- . (shrink)

An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...) context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

The purpose of this article is to explore Thomas Hobbes’ renunciation of a prominent concept of the social contract that distinguishes between two different contracts, namely, “pactum associationis” and “pactum subiectionis”.

In the face of an impossibility result, some assumption must be relaxed. The Mere Addition Paradox is an impossibility result in population ethics. Here, I explore substantially weakening the decision-theoretic assumptions involved. The central finding is that the Mere Addition Paradox persists even in the general framework of choice functions when we assume Path Independence as a minimal decision-theoretic constraint. Choice functions can be thought of either as generalizing the standard axiological assumption of a binary “betterness” relation, or as providing (...) a general framework for a normative (rather than axiological) theory of population ethics. Path Independence, a weaker assumption than typically (implicitly) made in population ethics, expresses the idea that, in making a choice from a set of alternatives, the order in which options are assessed or considered is ethically arbitrary and should not affect the final choice. Since the result establishes a conflict between the relevant ethical principles and even very weak decision-theoretic principles, we have more reason to doubt the ethical principles. (shrink)

This paper studies a generalization of rational choice theory. I briefly review the motivations that Helzner gives for his conditional choice construction . Then, I focus on the important class of conditional choice functions with vacuous second tiers. This class is interesting for both formal and philosophical reasons. I argue that this class makes explicit one of conditional choice’s normative motivations in terms of an account of neutrality advocated within a certain tradition in decision theory. The observations recorded—several of which (...) are generalizations of central results in the standard theory of rational choice—are intended to provide further insight into how conditional choice generalizes the standard account and are offered as additional evidence of the fruitfulness of the conditional choice framework. (shrink)

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is “completely (...) ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting? (shrink)

We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...) LEM is intrumental in the proof of Cantor's Theorem, and we then argue that this is based on a more general form than can be reasonably justified. We briefly consider the impact of our approach on arithmetic and naive set theory, and compare it with intuitionist mathematics and briefly with recursive mathematics. Our "Four Basic Logical Issues" paper would provide useful background, the current paper being an application of the some of the ideas in it. (shrink)

The claim of this paper is to show that the “Discourse on the Arts and Sciences” does not propose a general critique of progress as such, but a critique of the idea of progress as promoted by the 18th century “philosophers”. It is argued that Rousseau is no proponent of a Counter-Enlightenment, on the contrary he aims to go further than other thinkers of his time by scrutinizing even progress itself, Enlightenment’s pet notion. In defining arts and sciences as the (...) very driving forces of progress, the “philosophers” according to Rousseau are fostering inequality, because only an elite will be able to succeed in them. By contrast, talking about progress in Rousseau’s view only makes sense if “progress” is defined in moral and political terms, as enabling all men to participate in the promotion of everybody’s well-being. The paper intends to show that Rousseau’s answer to the shortcomings of civilization is not a “return to nature”, but the advancement of artificial institutions: namely, the egalitarian republic. (shrink)

Between 1937 and 1951 Wittgenstein had numerous philosophical conversations with his student and close friend, Rush Rhees. This article is composed of Rhees’s notes of twenty such conversations — namely, all those which have not yet been published — as well as some supplements from Rhees’s correspondence and miscellaneous notes. The principal value of the notes collected here is that they fill some interesting and important gaps in Wittgenstein ’s corpus. Thus, firstly, the notes touch on a wide range (...) of subjects, a number of which are only briefly addressed by Wittgenstein elsewhere, if at all. The subjects discussed include: explanation, ethics, anarchism, contradiction, psychoanalysis, colour, religion, concepts, classification, seeing-as, evolution, the relation between science and philosophy, and free will, amongst others. Secondly, the notes contain references to, and brief remarks about, philosophers of whom Wittgenstein otherwise says very little, if anything — such as Brentano, Heidegger, Aquinas, and Marx, amongst others. And thirdly, the notes provide us with valuable examples of Wittgenstein ’s use of some key ‘Wittgensteinian’ terms of art which are surprisingly rare in his written works, such as ‘surface-’ and ‘depth-grammar’, and ‘centres of variation’. (shrink)