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)

RAAAF [Rietveld Architecture-Art-Affordances] is an interdisciplinary studio that operates at the crossroads of visual art, experimental architecture and philosophy. RAAAF makes location- and context-specific artworks, an approach that derives from the respective backgrounds of the founding partners: Prix de Rome laureate Ronald Rietveld and Socrates Professor in Philosophy Erik Rietveld.

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)

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)

Absolutism about mass within Newtonian gravity claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Defenders of comparativism promise to recover all the empirical and theoretical virtues of absolutism, but at a lower ‘metaphysical cost’. This article develops a Machian form of comparativism about mass in Newtonian gravity, obtained by replacing Newton’s constant in the law of universal gravitation by another constant divided by the sum over all masses. Although this form of comparativism is indeed empirically (...) equivalent to the absolutist version of Newtonian gravity—thereby meeting the challenge posed by the comparativist’s bucket argument—it is argued that the explanatory power and metaphysical parsimony of comparativism are highly questionable. (shrink)

Here, Rhonda Martens offers the first extended study of Kepler's philosophical views and shows how those views helped him construct and justify the new astronomy.

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)

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)

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

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)

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)

This paper scrutinises the tenability of a strict conceptual distinction between space and matter via the lens of the debate between modified gravity and dark matter. In particular, we consider Berezhiani and Khoury's novel 'superfluid dark matter theory' as a case study. Two families of criteria for being matter and being spacetime, respectively, are extracted from the literature. Evaluation of the new scalar field postulated by SFDM according to these criteria reveals that it is as much matter as anything could (...) possibly be, but alsoꟷbelow the critical temperature for superfluidityꟷas much spacetime as anything could possibly be. A sequel paper examines possible interpretations of SFDM in light of this result, as well as the consequences for our understanding of the modified gravity/ dark matter distinction and the broader spacetime–matter distinction. (shrink)

Absolutism about mass claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Dasgupta, Oxford studies in metaphysics, Oxford University Press, Oxford, 2013) argues for comparativism about mass, in the context of Newtonian Gravity. Such an argument requires proving that comparativism is empirically adequate. Dasgupta equates this to showing that absolute masses are undetectable, and attempts to do so. This paper develops an argument by Baker to the contrary: absolute masses are in fact empirically meaningful, that is (...) detectable. Additionally, it is argued that the requirement of empirical adequacy should not be cashed out in terms of undetectability in the first place. The paper closes by sketching the possible strategies that remain for the comparativist. Along the way a framework is developed that is useful for thinking about these issues: Ozma games—how could one explain to an alien civilisation what an absolute mass is? (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)

The debate concerning the ontological status of spacetime is standardly construed as a dilemma between substantivalism and relationalism. I argue that a trilemma is more appropriate, emergent spacetime theories being the third category. Traditional philosophical arguments do not distinguish between emergent spacetime and substantivalism. It is arguments from physics that suggest giving up substantivalism in favour of emergent spacetime theories. The remaining new dilemma is between emergent spacetime and relationalism. I provide a list of questions, which one should consider when (...) discussing emergent spacetime theories, and apply them to a quantum superfluid toy model of emergent spacetime. (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)

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)

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.

In my article on proof [Philosophia Mathematica (3) 5 (1997), 153—165], I suggested or intimated that computer proofs of mathematical theorems had been found only for relatively simple or trivial theorems. I am obligated to Martin Davis and R. S. Boyer for the information that this suggestion or intimation is incorrect. For instance, a machine proof of quadratic reciprocity was published by D. M. Russinoff in J. Automated Reasoning 8 (1992), 3–21. A machine proof of the unsolvability of the halting (...) problem has been published by R S. Boyer and J. S. Moore. This and many other examples are presented in Chapter 1 of their book, A Computational Logic Handbook, Academic Press, 1990. A second edition of this book is expected shortly. (shrink)

Recently, there has been increasing interest in the use of heavily restricted randomization designs which enforce balance on observed covariates in randomized controlled trials. However, when restrictions are strict, there is a risk that the treatment effect estimator will have a very high mean squared error. In this article, we formalize this risk and propose a novel combinatoric-based approach to describe and address this issue. First, we validate our new approach by re-proving some known properties of complete randomization and restricted (...) randomization. Second, we propose a novel diagnostic measure for restricted designs that only use the information embedded in the combinatorics of the design. Third, we show that the variance of the MSE of the difference-in-means estimator in a randomized experiment is a linear function of this diagnostic measure. Finally, we identify situations in which restricted designs can lead to an increased risk of getting a high MSE and discuss how our diagnostic measure can be used to detect such designs. Our results have implications for any restricted randomization design and can be used to evaluate the trade-off between enforcing balance on observed covariates and avoiding too restrictive designs. (shrink)

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)

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)

In diesem biografisch gesättigten Essay entfaltet der Philosoph Rainer Marten vor dem Hintergrund des neoliberalen Zeitgeists der Silicon Valley-Gegenwart die Essenz seines Denkens in kraftvollen Zügen. Im Angesicht des eigenen Lebensendes legt er an unsere Zeit den Maßstab überzeitlicher Lehren der Philosophie, Theologie und Lebenskunst. Mit wachem Blick für die Verwerfungen unserer Zeit tritt er ein für die Schönheit des fragilen Lebens, dessen Grund er in der Poesie der Notwendigkeit sieht. Im Nachdenken über Technomessianismus, Verführung des Bösen und Künstliche Intelligenz (...) stärkt er sein Konzept des Humanums, plädiert für das Leben als Kunstwerk und gegen dessen Instrumentalisierung. (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)

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.

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)

Among the many common criticisms of the Turing test, a valid criticism concerns its scope. Intelligence is a complex and multi-dimensional phenomenon that will require testing using as many different formats as possible. The Turing test continues to be valuable as a source of evidence to support the inductive inference that a machine possesses a certain kind of intelligence and when interpreted as providing a behavioural test for a certain kind of intelligence. This paper raises the novel criticism that the (...) Turing test represents an example of Goodhart’s Law operating in the field of artificial intelligence. As one measure towards the goal of creating genuinely intelligent machines, the Turing test must not be confused with the goal itself. Moreover, the Turing test ought to be augmented such that through its use additional evidence could be secured to support the strong inference that a machine, were it to pass the Turing Test, could think like a human. (shrink)

This paper pushes back against the Democritean-Newtonian tradition of assuming a strict conceptual dichotomy between spacetime and matter. Our approach proceeds via the more narrow distinction between modified gravity/spacetime and dark matter. A prequel paper argued that the novel field Φ postulated by Berezhiani and Khoury's 'superfluid dark matter theory' is as much matter as anything could possibly be, but also below the critical temperature for superfluidity as much spacetime as anything could possibly be. Here we introduce and critically evaluate (...) three groups of interpretations that one should consider for such Janus-faced theories. The consubstantiality interpretation holds that Φ is both matter and a modification of spacetime, analogously to the sense in which Jesus is both human and god. The fundamendalist interpretations consider for each of these roles whether they are instantiated fundamentally or emergently. The breakdown interpretations focus on the question of whether Φ signals the breakdown, in some sense to be specified, of the MG-DM dichotomy and perhaps even the broader spacetime–matter distinction. More generally, it is argued that hybrid theories urge a move towards a single space of theories, rather than two separate spaces of spacetime theories and matter theories, respectively. (shrink)

An increasingly number of patients in Western civilizations suffer from weak authenticity structure which is characterized by a lack of self-realization, autonomy, character strength, stereotype behavior, inability to use (internal) dialogue in order to learn about oneself and defining oneself as a individual, and so on. In this paper a theoretical model of fragile authenticity structure and some suggestions to regain a more authentic attitude are presented.