Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist (...) there when the last of their radiant host shall have fallen from heaven." In What is Mathematics, Really?, renowned mathematician Rueben Hersh takes these eloquent words and this pervasive philosophy to task, in a subversive attack on traditional philosophies of mathematics, most notably, Platonism and formalism. Virtually all philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of the book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, David Hilbert, Rudolph Carnap, and Willard V.O. Quine--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, Peirce, Dewey, and Lakatos. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. He contends that Platonism and elitism fit well together, that Platonism in fact is used to justify the claim that "some people just can't learn math." The humanist philosophy, on the other hand, links mathematics with geople, with society, and with history. It fits with liberal anti-elitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge and culture. Thus Hersh's argument has educational and political ramifications. Written by the co-author of The Mathematical Experience, which won the American Book Award in 1983, this volume reflects an insider's view of mathematical life, based on twenty years of doing research on advanced mathematical problems, thirty-five years of teaching graduates and undergraduates, and many long hours of listening, talking to, and reading philosophers. A clearly written and highly iconoclastic book, it is sure to be hotly debated by anyone with a passionate interest in mathematics or the philosophy of science. (shrink)

The ever-increasing application of algorithms to decision-making in a range of social contexts has prompted demands for algorithmic accountability. Accountable decision-makers must provide their decision-subjects with justifications for their automated system’s outputs, but what kinds of broader principles should we expect such justifications to appeal to? Drawing from political philosophy, I present an account of algorithmic accountability in terms of the democratic ideal of ‘public reason’. I argue that situating demands for algorithmic accountability within this justificatory framework enables us to (...) better articulate their purpose and assess the adequacy of efforts toward them. (shrink)

In this paper, I use interventionist causal models to identify some novel Newcomb problems, and subsequently use these problems to refine existing interventionist treatments of causal decision theory. The new Newcomb problems that make trouble for existing interventionist treatments involve so-called ‘exotic choice’—that is, decision-making contexts where the agent has evidence about the outcome of her choice. I argue that when choice is exotic, the interventionist can adequately capture causal decision-theoretic reasoning by introducing a new interventionist approach to updating on (...) exotic evidence. But I also argue that this new updating procedure is principled only if the interventionist trades in the typical interventionist conception of choice for an alternative Ramseyan conception. I end by arguing that the guide to exotic choice developed here may, despite its name, be useful in some everyday contexts. (shrink)

Decisions based on algorithmic, machine learning models can be unfair, reproducing biases in historical data used to train them. While computational techniques are emerging to address aspects of these concerns through communities such as discrimination-aware data mining and fairness, accountability and transparency machine learning, their practical implementation faces real-world challenges. For legal, institutional or commercial reasons, organisations might not hold the data on sensitive attributes such as gender, ethnicity, sexuality or disability needed to diagnose and mitigate emergent indirect discrimination-by-proxy, such (...) as redlining. Such organisations might also lack the knowledge and capacity to identify and manage fairness issues that are emergent properties of complex sociotechnical systems. This paper presents and discusses three potential approaches to deal with such knowledge and information deficits in the context of fairer machine learning. Trusted third parties could selectively store data necessary for performing discrimination discovery and incorporating fairness constraints into model-building in a privacy-preserving manner. Collaborative online platforms would allow diverse organisations to record, share and access contextual and experiential knowledge to promote fairness in machine learning systems. Finally, unsupervised learning and pedagogically interpretable algorithms might allow fairness hypotheses to be built for further selective testing and exploration. Real-world fairness challenges in machine learning are not abstract, constrained optimisation problems, but are institutionally and contextually grounded. Computational fairness tools are useful, but must be researched and developed in and with the messy contexts that will shape their deployment, rather than just for imagined situations. Not doing so risks real, near-term algorithmic harm. (shrink)

Although excess blood collection has characterized U.S. national disasters, most dramatically in the case of September 11, periodic shortages of blood have recurred for decades. In response, I propose a new model of medical philanthropy, one that specifically uses charitable contributions to health care as blood donation incentives. I explain how the surge in blood donations following 9/11 was both transient and disaster-specific, failing to foster a greater continuing commitment to donate blood. This underscores the importance of considering blood donation (...) incentives. I defend charitable incentives as an alternative to financial incentives, which I contend would further extend neoliberal market values into health care. I explain my model's potential appeal to private foundations or public–private partnerships as a means for expanding both the pool of blood donors and the prosocial benefit of each act of blood donation. Finally I link my analysis to the empirical literature on blood donation incentives. (shrink)

Kim’s causal exclusion argument purports to demonstrate that the non-reductive physicalist must treat mental properties (and macro-level properties in general) as causally inert. A number of authors have attempted to resist Kim’s conclusion by utilizing the conceptual resources of Woodward’s interventionist conception of causation. The viability of these responses has been challenged by Gebharter, who argues that the causal exclusion argument is vindicated by the theory of causal Bayesian networks (CBNs). Since the interventionist conception of causation relies crucially on CBNs (...) for its foundations, Gebharter’s argument appears to cast significant doubt on interventionism’s anti-reductionist credentials. In the present article, we both (1) demonstrate that Gebharter’s CBN-theoretic formulation of the exclusion argument relies on some unmotivated and philosophically significant assumptions (especially regarding the relationship between CBNs and the metaphysics of causal relevance), and (2) use Bayesian networks to develop a general theory of causal inference for multi-level systems that can serve as the foundation for an anti-reductionist interventionist account of causation.1. (shrink)

"This new collection of essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive ...

This thesis explores the merits and limits of John Hawthorne’s contextualist analysis of free will. First, I argue that contextualism does better at capturing the ordinary understanding of ‘free will’ than competing views because it best accounts for the way in which our willingness to attribute free will ordinarily varies with context. Then I consider whether this is enough to conclude that the contextualist has won the free will debate. I argue that this would be hasty, because the contextualist, unlike (...) her competitors, cannot tell us whether any particular agent is definitively free, and therefore cannot inform any practices that are premised on whether a particular agent is morally responsible. As such, I argue that whether the contextualist “wins the free will debate” depends on whether it is more important to capture the ordinary understanding of ‘free will’ or more important to inform our practices of ascribing moral responsibility. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2014 Heft: 202 Seiten: 395-424.

Jim Joyce has argued that David Lewis’s formulation of causal decision theory is inadequate because it fails to apply to the “small world” decisions that people face in real life. Meanwhile, several authors have argued that causal decision theory should be developed such that it integrates the interventionist approach to causal modeling because of the expressive power afforded by the language of causal models, but, as of now, there has been little work towards this end. In this paper, I propose (...) a variant of Lewis’s causal decision theory that is intended to meet both of these demands. Specifically, I argue that Lewis’s causal decision theory can be rendered applicable to small world decisions if one analyzes his dependency hypotheses as causal hypotheses that depend on the interventionist causal modeling framework for their semantics. I then argue that this interventionist variant of Lewis’s causal decision theory is preferable to interventionist causal decision theories that purportedly generalize Lewis’s through the use of conditional probabilities. This is because Lewisian interventionist decision theory captures the causal decision theorist’s conviction that any correlation between what the agent does and cannot cause should be irrelevant to the agent’s choice, while purported generalizations do not. (shrink)

As government pressure on major technology companies builds, both firms and legislators are searching for technical solutions to difficult platform governance puzzles such as hate speech and misinformation. Automated hash-matching and predictive machine learning tools – what we define here as algorithmic moderation systems – are increasingly being deployed to conduct content moderation at scale by major platforms for user-generated content such as Facebook, YouTube and Twitter. This article provides an accessible technical primer on how algorithmic moderation works; examines some (...) of the existing automated tools used by major platforms to handle copyright infringement, terrorism and toxic speech; and identifies key political and ethical issues for these systems as the reliance on them grows. Recent events suggest that algorithmic moderation has become necessary to manage growing public expectations for increased platform responsibility, safety and security on the global stage; however, as we demonstrate, these systems remain opaque, unaccountable and poorly understood. Despite the potential promise of algorithms or ‘AI’, we show that even ‘well optimized’ moderation systems could exacerbate, rather than relieve, many existing problems with content policy as enacted by platforms for three main reasons: automated moderation threatens to further increase opacity, making a famously non-transparent set of practices even more difficult to understand or audit, further complicate outstanding issues of fairness and justice in large-scale sociotechnical systems and re-obscure the fundamentally political nature of speech decisions being executed at scale. (shrink)

Contrary to stockholder theories that place the interests of profit-seeking owners above all else, stakeholder theorists argue that corporate executives have moral and ethical obligations to consider equally the interests of a wide range of stakeholders affected by the actions of a corporation. This paper argues that the stakeholder approach is particularly appropriate for the governance of news media companies and outlines an ethical framework to guide news company executives.

There are two distinct meanings to ‘mathematical proof’. The connection between them is an unsolved problem. The first step in attacking it is noticing that it is an unsolved problem.

This paper defends an ontology of weak entity realism for homeostatic property cluster (HPC) theories of natural kinds, adapted from Bird’s (Synthese 195(4):1397–1426, 2018) taxonomy of such theories. Weak entity realism about HPC kinds accepts the existence of natural kinds. Weak entity realism denies two theses: that (1) HPC kinds have mind-independent essences, and that (2) HPC kinds reduce to entities, such as complex universals, posited only by metaphysical theories. Strong entity realism accepts (1) and (2), whereas moderate entity realism (...) accepts only (1). Given its commitment to (2), strong entity realism is more theoretically complex than weak entity realism, with little explanatory payoff. Given their commitment to (1), moderate and strong entity realisms cannot explain how the identity conditions of HPC kinds are to be straightforwardly knowable. I argue that weak entity realism avoids such epistemic difficulties. I further rebut two plausible criticisms of weak entity realism, namely that weak entity realism cannot account for quantification over kinds, and that weak entity realism cannot provide identity conditions for HPC kinds which are both scientifically useful and objective. Given the theoretical costs of strong and moderate entity realism, and weak entity realism’s adequate response to its most plausible challenges, weak entity realism about HPCs is to be preferred, especially for biological and chemical kinds. (shrink)

Meek and Glymour use the graphical approach to causal modeling to argue that one and the same norm of rational choice can be used to deliver both causal-decision-theoretic verdicts and evidential-decision-theoretic verdicts. Specifically, they argue that if an agent maximizes conditional expected utility, then the agent will follow the causal decision theorist’s advice when she represents herself as intervening, and will follow the evidential decision theorist’s advice when she represents herself as not intervening. Since Meek and Glymour take no stand (...) on whether agents should represent themselves as intervening, they provide more general advice than standard causal decision theorists and evidential decision theorists. But I argue here that even Meek and Glymour’s advice is not sufficiently general. This is because their advice is not sensitive to the distinct ways in which agents can fail to intervene, and there are decision-making contexts in which agents can reasonably have non-extreme confidence that they are intervening. I then show that the most natural extension of Meek and Glymour’s framework fails, but offer a generalization of my “Interventionist Decision Theory” that does not suffer from the same problems. (shrink)

It is explained that, in the sense of the sociologist Erving Goffman, mathematics has a front and a back. Four pervasive myths about mathematics are stated. Acceptance of these myths is related to whether one is located in the front or the back.

McGee argues that it is sometimes reasonable to accept both x and x-> without accepting y->z, and that modus ponens is therefore invalid for natural language indicative conditionals. Here, we examine McGee's counterexamples from a Bayesian perspective. We argue that the counterexamples are genuine insofar as the joint acceptance of x and x-> at time t does not generally imply constraints on the acceptability of y->z at t, but we use the distance-based approach to Bayesian learning to show that applications (...) of modus ponens are nevertheless guaranteed to be successful in an important sense. Roughly, if an agent becomes convinced of the premises of a modus ponens argument, then she should likewise become convinced of the argument's conclusion. Thus we take McGee's counterexamples to disentangle and reveal two distinct ways in which arguments can convince. Any general theory of argumentation must take stock of both. (shrink)

Brentano is often considered the originator of the fitting-attitudes analysis of value, on which to be valuable is to be that which it’s fitting to value. But there has been comparatively little attention paid to Brentano’s argument for this analysis. That argument advances the stronger claim that fittingness is part of the analysis of normativity. Since the argument rests on an analogy between truth and fittingness, its impact may seem limited by the idiosyncratic features of Brentano’s later notion of truth. (...) I argue, however, that the Brentanian argument is defensible even if fittingness is analogized to a more typical realist account of truth. The result is what I call the worldly Brentanian account of normativity. I defend this account as a form of naturalistic realism. I then show how the account can fare better than prominent alternatives against two kinds of error-theoretic arguments. (shrink)

The study of social change has neglected the dynamics motivating individuals to join mass movements. Particularly obscure is how apathetic people are transformed into social activists. Considering this problem the author suggests three stages of development through which the individual progresses in attaining a higher level of personal and social maturity. The first stage - dreaming -emerges when the individual aspires to change while wishing to avoid the risks involved. The second - the illusion of power - occurs when the (...) hunger for power and the fear of it are mediated. The third - real power - is promoted by the yearning for self-respect and social acceptance and is manifested by competence in gaining supremacy and actual experience in struggle. As a consequence of this process the individual advances from a subjective self-image to perceiving himself as a social being; society is humanized by the greater participation of individuals. (shrink)

Though common sense says that causes must temporally precede their effects, the hugely influential interventionist account of causation makes no reference to temporal precedence. Does common sense lead us astray? In this paper, I evaluate the power of the commonsense assumption from within the interventionist approach to causal modeling. I first argue that if causes temporally precede their effects, then one need not consider the outcomes of interventions in order to infer causal relevance, and that one can instead use temporal (...) and probabilistic information to infer exactly when X is causally relevant to Y in each of the senses captured by Woodward’s interventionist treatment. Then, I consider the upshot of these findings for causal decision theory, and argue that the commonsense assumption is especially powerful when an agent seeks to determine whether so-called “dominance reasoning” is applicable. (shrink)

Adopting Kantor’s Masochean turn within Levinas, this article challenges the anthropocentrically limited purview of Levinas’s ethical relation. Incorporating Kantor’s legalistic reading of Levinas, informed through his literary analysis of Sacher-Masoch’s ‘Venus in Furs’, the article details the inescapable, legalistic plight that is to be the Levinasian ethical subject. Extending upon Kantor’s introductory conceptualisation of the Levinasian subject through Masoch, reveals a subject for whom suffering and sacrifice must be embraced; necessary acts of penitence before an irrepressible Other who they adore. (...) The Other is presented through Masoch’s text as an insatiable, inescapable deity of Law who cannot be refused and demands subservience. A god manifest in Exteriority whose influence upon the subject extends beyond the frame of the interhuman relation and is a necessary component of the subject’s existence and, more broadly, their world. The Levinasian subject’s relation with alterity poetically portraying all the potency, affirmation and urgency of dear Severin’s with his Venus, a relation which destroys, haunts and affirms the subject completely as only Law can. (shrink)