Neutral monism is a position in metaphysics defended by Mach, James, and Russell in the early twentieth century. It holds that minds and physical objects are essentially two different orderings of the same underlying neutral elements of nature. This paper sets out some of the central concepts, theses and the historical background of ideas that inform this doctrine of elements. The discussion begins with the classic neutral monism of Mach, James, and Russell in the first part of the paper, then (...) considers recent neo-Russellian versions in the second half. The chances for a revival of neutral monism are probably slight; its key ideas and starting points lie far from those in contemporary philosophy of mind. A better route might be through the philosophy of science and a deeper understanding of causation. (shrink)

Grete Hermann’s essay “Die naturphilosophischen Grundlagen der Quantenmechanik” has received much deserved scholarly attention in recent years. In this paper, I follow the lead of Elise Crull who sees in Hermann’s work the general outlines of a neo-Kantian interpretation of quantum theory. In full support of this view, I focus on Hermann’s central claim that limited spatio-temporal, and even analogically causal, representations of events exist within an overall relational structure of entangled quantum mechanical states that defy any unified spatio-temporal description. (...) In my view, Hermann also advances an important transcendental argument that perspectival spatio-temporal representations of nature have their foundations in general relational networks that are not spatio-temporal. The key point is that the adoption of a perspectival system within the general network induces the representation but only for that context. These ideas are consistent with a perspectival subject–object principle in Kant and also with Weyl’s work on Lie groups and their representations. (shrink)

A look at the dynamical concept of space and space-generating processes to be found in Kant, J.F. Herbart and the mathematician Bernhard Riemann's philosophical writings.

Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.

This paper, for two upcoming volumes, makes what I consider to be the definitive textual case for finally rejecting the phenomenalist interpretation of Ernst Mach's works, and his customary association with the Vienna Circle, in favor of a stronger realistic neutral monist reading connecting him to James, Russell and the American realist movement and today's neutral monism (for example my 2014). I hope that this reading will eventually supplant the previously mistaken view of Mach's work and that his views of (...) science and philosophy of space and time can be revised as well. (shrink)

This article distinguishes between Machian empiricism and the logical positivism of the Vienna Circle and associated philosophers. Mach's natural philosophy was a first order attempt to reform and reorganize physics, not a second order reconstruction of the "language" of physics. Mach's elements were not sense data but realistic events in the natural world and in minds, and Mach admitted unobserved elements as part of his world view. Mach's critique of metaphysics was far more subtle and concerned the elimination of sensory (...) visual imagery from natural science, leaving only concrete elements and functions, very much an inspiration to the young Einstein and Heisenberg and a useful engine of theory construction in physics. (shrink)

William James' Radical Empiricist essays offer a unique and powerful argument for direct realism about our perceptions of objects. This theory can be completed with some observations by Kant on the intellectual preconditions for a perceptual judgment. Finally James and Kant deliver a powerful blow to the representational theory of perception and knowledge, which applies quite broadly to theories of representation generally.

This paper for an upcoming journal volume examines Grete Hermann's Naturphilosophischen Grundlagen der Quantenmechanik (1935) and the relative context, or perspectival, interpretation of standard quantum mechanics found therein. I find an argument for the emergence of limited spatio-temporal and retrocausal stories, from a chosen experimental perspective, within a larger set of entangled systems not subject to a spatio-temporal interpretation. This argument can be read in reverse as giving some of the necessary preconditions of spatio-temporal representations as based upon perspectival relations, (...) carrying on a Kantian transcendental argument on one hand, and on the other hand, looking forward to Weyl's use of symmetry groups, Lie algebras and their representations in quantum mechanics. (shrink)

I examine Mach's influence on American philosophy from 1890-1910, on Carus, James, Peirce, the American Realists and J.B. Stallo. I also consider the question of whether Mach was a pragmatist in the sense of Peirce and James. I conclude that early pragmatism was a method-centric theory whereas Mach's empiricism prized agreement with experience and downplayed the significance of inductive-scientific methods in general as a guide to discovery.

This paper offers a "tu quoque" defense of strong AI, based on the argument that phenomena of self-consciousness and intentionality are nothing but the "negative space" drawn around the concrete phenomena of brain states and causally connected utterances and objects. Any machine that was capable of concretely implementing the positive phenomena would automatically inherit the negative space around these that we call self-consciousness and intention. Because this paper was written for a literary audience, some examples from Greek tragedy, noir fiction, (...) science fiction and Dada are deployed to illustrate the view. (shrink)

A look at Mach's work on monocular stereoscopy with relation to Mach Bands and the sensation of space.

Bertrand Russell in "My Philosophical Development" claimed he converted to neutral monism in 1919, in the essay "On Propositions." I question whether Russell was really a complete neutral monist in the style of Mach and James and conclude that he was not. Russell's lingering commitment to image propositions and a linguistic theory of meaning and truth and falsity separate him from the more naturalistic causal theory of knowledge and error one finds in James and Mach.

An overview of the problem of constructing extension combinatorially from qualities cum dispositional powers. In the model recommended here, Grassmann's algebra provides the combinatorial structure while Machian elements give the content.

Two types of formal models - landscape search tasks and two-armed bandit models - are often used to study the effects that various social factors have on epistemic performance. I argue that they can be understood within a single framework. In this unified framework, I develop a model that may be used to understand the effects of functional and demographic diversity and their interaction. Using the unified model, I find that the benefit of demographic diversity is most pronounced in a (...) functionally homogeneous group, and decreases with the increase of functional diversity. (shrink)

(Expected) adverse effects of the ‘ICT Revolution’ on work and opportunities for individuals to use and develop their capacities give a new impetus to the debate on the societal implications of technology and raise questions regarding the ‘responsibility’ of research and innovation (RRI) and the possibility of achieving ‘inclusive and sustainable society’. However, missing in this debate is an examination of a possible conflict between the quest for ‘inclusive and sustainable society’ and conventional economic principles guiding capital allocation (including the (...) funding of research and innovation). We propose that such conflict can be resolved by re-examining the nature and purpose of capital, and by recognising mainstream economics’ utilitarian foundations as an unduly restrictive subset of a wider Aristotelian understanding of choice. (shrink)

A 2012 review article for Metascience which explains Mach's realistic brand of empiricism, contrasting it with the common phenomenalist reading of Mach by John Blackmore in two recent books.

In the literature on expert trust, it is often assumed that track records are the gold standard for evaluating expertise, and the difficulty of expert identification arises from either the lack of access to track records, or the inability to assess them. I show, using a computational model, that even in an idealized environment where agents have a God’s eye view on track records, they may fail to identify experts. Under plausible conditions, selecting testimony based on track records ends up (...) reducing overall accuracy, and preventing the community from identifying the real experts. (shrink)

ABSTRACT Objectives There is little research on moral uncertainties and distress of palliative and hospice care providers (PHCPs) working in jurisdictions anticipating legalising voluntary assisted dying (VAD). This study examines the perception and anticipated concerns of PHCPs in providing VAD in the State of Queensland, Australia prior to legalisation of the practice in 2021. The findings help inform strategies to facilitate training and support the health and well-being of healthcare workers involved in VAD. Design The study used a qualitative approach (...) to examine and analyse the perception and anticipated concerns of PHCPs regarding challenges of providing assisted dying in Queensland. Fourteen PHCPs were recruited using a purposive sampling strategy to obtain a broad representation of perspectives including work roles, geographical locations and workplace characteristics. Data were collected via one in-depth interview per participant. The transcripts were coded for patterns and themes using an inductive analysis approach following the tradition of Grounded Theory. Setting The study was conducted in hospital, hospice, community and residential aged care settings in Queensland, Australia. These included public and private facilities, secular and faith-based facilities, and regional/rural and urban facilities. Participants Interviews were conducted with fourteen PHCPs: 10 nurses and 4 physicians; 11 female and 3 male. The median number of years of palliative care practice was 17, ranging from 2 to 36 years. For inclusion, participants had to be practising palliative and hospice care providers. Results PHCPs are divided on whether VAD should be considered part of palliative care. Expectations of moral distress and uncertainty about practising VAD were identified in five areas: handling requests, assessing patient capacity, arranging patient transfers and logistical issues, managing unsuccessful attempts, and dealing with team conflicts and stigma. Conclusions The possibility of having to practise VAD causes moral distress and uncertainty for some PHCPs. Procedural clarity can address some uncertainties; moral and psychological distress, however, remains a source of tension that needs support to ensure ongoing care of both patients and PHCPs. The introduction of VAD post-legalisation may present an occasion for further moral education and development of PHCPs. (shrink)

This chapter describes the potential far‐reaching consequences of contemplative higher education for the fields of science and medicine.

Achieving space situational awareness requires, at a minimum, the identification, characterization, and tracking of space objects. Leveraging the resultant space object data for purposes such as hostile threat assessment, object identification, and conjunction assessment presents major challenges. This is in part because in characterizing space objects we reference a variety of identifiers, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, operational processes, operational statuses, and so forth, which tend to be defined in highly heterogeneous and sometimes inconsistent (...) ways. The Space Domain Ontologies are designed to provide a consensus-based realist framework for formulating such characterizations in a way that is both consistent and computable. Space object data are aligned with classes and relations in a suite of ontologies built around the existing Space Object Ontology. They are stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space situational awareness and the needs of spacecraft operators and analysts. This paper provides an overview of the Space Domain Ontologies and their development and use. It presents the motivation for and advantages of the Space Domain Ontologies, including the benefits they provide for enhancing and maintaining long-term space situational awareness. (shrink)

Objective: To examine the current ethical review process of ethics committees in a non-pharmacological trial from the perspective of a clinical investigator.Design: Prospective collection of data at the Study Centre of the German Surgical Society on the duration, costs and administrative effort of the ERP of a randomised controlled multicentre surgical INSECT Trial between November 2003 and May 2005.Setting: Germany.Participants: 18 ethics committees, including the ethics committee handling the primary approval, responsible overall for 32 clinical sites throughout Germany. 8 ethics (...) committees were located at university medical schools and 10 at medical chambers. Duration was measured as days between submission and receipt of final approval, costs in euros and administrative effort by calculation of the product of the total number of different types of documents and the mean number of copies required .Results: The duration of the ERP ranged from 1 to 176 days. The median duration was 26 days at MSUs compared with 34 days at medical chambers. The total cost was €2947. 1 of 8 ethics committees at universities and 8 of 10 at medical chambers charged a median fee of €162 . The administrative effort for primary approval was 30. Four ethics committees required a higher administrative effort for secondary approval .Conclusion: The ERP for non-pharmacological multicentre trials in Germany needs improvement. The administrative process has to be standardised: the application forms and the number and content of the documents required should be identical or at least similar. The fees charged vary considerably and are obviously too high for committees located at medical chambers. However, the duration of the ERP was, with some exceptions, excellent. A centralised ethics committee in Germany for multicentre trials such as the INSECT Trial can simplify the ERP for clinical investigators in and outside the country. (shrink)

May lethal autonomous weapons systems—‘killer robots ’—be used in war? The majority of writers argue against their use, and those who have argued in favour have done so on a consequentialist basis. We defend the moral permissibility of killer robots, but on the basis of the non-aggregative structure of right assumed by Just War theory. This is necessary because the most important argument against killer robots, the responsibility trilemma proposed by Rob Sparrow, makes the same assumptions. We show that the (...) crucial moral question is not one of responsibility. Rather, it is whether the technology can satisfy the requirements of fairness in the re-distribution of risk. Not only is this possible in principle, but some killer robots will actually satisfy these requirements. An implication of our argument is that there is a public responsibility to regulate killer robots ’ design and manufacture. (shrink)

Functional diversity holds the promise of understanding ecosystems in ways unattainable by taxonomic diversity studies. Underlying this promise is the intuition that investigating the diversity of what organisms actually do—i.e. their functional traits—within ecosystems will generate more reliable insights into the ways these ecosystems behave, compared to considering only species diversity. But this promise also rests on several conceptual and methodological—i.e. epistemic—assumptions that cut across various theories and domains of ecology. These assumptions should be clearly addressed, notably for the sake (...) of an effective comparison and integration across domains, and for assessing whether or not to use functional diversity approaches for developing ecological management strategies. The objective of this contribution is to identify and critically analyze the most salient of these assumptions. To this aim, we provide an “epistemic roadmap” that pinpoints these assumptions along a set of historical, conceptual, empirical, theoretical, and normative dimensions. (shrink)

This article is part of a For-Discussion-Section of Methods of Information in Medicine about the paper "Biomedical Informatics: We Are What We Publish", written by Peter L. Elkin, Steven H. Brown, and Graham Wright. It is introduced by an editorial. This article contains the combined commentaries invited to independently comment on the Elkin et al. paper. In subsequent issues the discussion can continue through letters to the editor.

This is the short version, in French translation by Anne Querrien, of the originally jointly authored paper: Müller, Vincent C., ‘Autonomous killer robots are probably good news’, in Ezio Di Nucci and Filippo Santoni de Sio, Drones and responsibility: Legal, philosophical and socio-technical perspectives on the use of remotely controlled weapons. - - - L’article qui suit présente un nouveau système d’armes fondé sur des robots qui risque d’être prochainement utilisé. À la différence des drones qui sont manoeuvrés à distance (...) mais comportent une part importante de discernement humain, il s’agit de machines programmées pour défendre, attaquer, ou tuer de manière autonome. Les auteurs, philosophes, préfèrent prévenir de leur prochaine diffusion et obtenir des Nations Unies leur régulation. Une campagne internationale propose plutôt leur interdiction. (shrink)

Three separate churches erected in Constantinople were all dedicated to the wisdom of Christ and erected on the same site one after the other. These churches were built between 360 and 537 AD by three different emperors: Constantius II, Theodosius the Younger, and Justinian I. The first two churches were consumed in flames after relatively short lives, but the final and greatest church still stands today, despite a history of extensive damage. This final edifice is the main focus of this (...) paper, owing to its 1500 year longevity and unprecedented architecture. If the entire History of Justinian's church is to considered, it is inaccurate to refer to it as a “church,” because although it remained a church for the first 900 years after its audacious construction, it was later converted into a mosque. Today it is a museum, in remembrance of its long history. (24). (shrink)

Lethal Autonomous Weapon Systems are here. Technological development will see them become widespread in the near future. This is in a matter of years rather than decades. When the UN Convention on Certain Conventional Weapons meets on 10-14th November 2014, well-considered guidance for a decision on the general policy direction for LAWS is clearly needed. While there is widespread opposition to LAWS—or ‘killer robots’, as they are popularly called—and a growing campaign advocates banning them outright, we argue the opposite. LAWS (...) may very well reduce suffering and death in war. Rather than banning them, they should be regulated, to ensure both compliance with international humanitarian law, and that this positive outcome occurs. This policy memo sets out the basic structure and content of the regulation required. (shrink)

REMARKS ON EVOLUTION AND TIME-SCALES, Graham Cairns-Smith; HODGSON'S BLACK BOX, Thomas Clark; DO HODGSON'S PROPOSITIONS UNIQUELY CHARACTERIZE FREE WILL?, Ravi Gomatam; WHAT SHOULD WE RETAIN FROM A PLAIN PERSON'S CONCEPT OF FREE WILL?, Gilberto Gomes; ISOLATING DISPARATE CHALLENGES TO HODGSON'S ACCOUNT OF FREE WILL, Liberty Jaswal; FREE AGENCY AND LAWS OF NATURE, Robert Kane; SCIENCE VERSUS REALIZATION OF VALUE, NOT DETERMINISM VERSUS CHOICE, Nicholas Maxwell; COMMENTS ON HODGSON, J.J.C. Smart; THE VIEW FROM WITHIN, Sean Spence; COMMENTARY ON HODGSON, Henry Stapp.

Financial gerontology can be defined as investigating relations between finances and aging. Authors such as Neal E. Cutler, Kouhei Komamura, Davis W. Gregg, Shinya Kajitani, Kei Sakata, and Colin McKenzie affirm that financial literacy is an effect of aging with concern about the issue of finances, as well as stating that it is the effect of longevity and aging on economies or the financial resilience of older people.

Financial gerontology can be defined as investigating relations between finances and aging. Authors such as Neal E. Cutler, Kouhei Komamura, Davis W. Gregg, Shinya Kajitani, Kei Sakata, and Colin McKenzie affirm that financial literacy is an effect of aging with concern about the issue of finances, as well as stating that it is the effect of longevity and aging on economies or the financial resilience of older people.

Common everyday materials such as textiles, foodstuffs, soil or skin can have complex, mutable and varied appearances. Under typical viewing conditions, most observers can visually recognize materials effortlessly, and determine many of their properties without touching them. Visual material perception raises many fascinating questions for vision researchers, neuroscientists and philosophers, yet has received little attention compared to the perception of color or shape. Here we discuss some of the challenges that material perception raises and argue that further philosophical thought should (...) be directed to how we see materials. (shrink)

Results: We analyzed 1,402 surveys and 15 in-depth interviews. Many (32%) CL participants reported greater difficulty refilling medications and a minority (14%) reported greater difficulty accessing HIV care during the pandemic. Most (99%) Opt4Mamas participants reported no difficulty refilling medications or accessing HIV/pregnancy care. Among the CL participants, older women were less likely (aOR = 0.95, 95% CI: 0.92–0.98) and women with more children were more likely (aOR = 1.13, 95% CI: 1.00–1.28) to report difficulty refilling medications. Only 2% of (...) CL participants reported greater difficulty managing FP and most (95%) reported no change in likelihood of using FP or desire to get pregnant. Qualitative analysis revealed three major themes: (1) adverse organizational/economic implications of the pandemic, (2) increased importance of pregnancy prevention during the pandemic, and (3) fear of contracting COVID-19. (shrink)

This chapter demonstrates that G.W. Leibniz and Michal Polanyi’s creative work in multiple fields of attention may serve a twenty first century in need of scholars willing to put daring and speculative imaginative inter–disciplinary risks in play. Such a cultural development would activate a general and cross–cultural sensibility that may salvage knowledge work, which is often predicated on property and power, for instead intellectual work that would serve the production of multiple truths that may enliven the world and inspire it.

Deep Brain Stimulation (DBS) is a relatively new, experimental treatment for patients suffering from treatment-refractory Obsessive Compulsive Disorder (OCD). The effects of treatment are typically assessed with psychopathological scales that measure the amount of symptoms. However, clinical experience indicates that the effects of DBS are not limited to symptoms only: patients for instance report changes in perception, feeling stronger and more confident, and doing things unreflectively. Our aim is to get a better overview of the whole variety of changes that (...) OCD patients experience during DBS treatment. For that purpose we conducted in-depth, semi-structured interviews with 18 OCD patients. In this paper, we present the results from this qualitative study.We list the changes grouped in four domains: with regard to (a) person, (b) (social) world, (c)characteristics of person-world interactions, and (d) existential stance. We subsequently provide an interpretation of these results. In particular, we suggest that many of these changes can be seen as different expressions of the same process; namely that the experience of anxiety and tension gives way to an increased basic trust and increased reliance on one’s abilities. We then discuss the clinical implications of our findings, especially with regard to properly informing patients of what they can expect from treatment, the usefulness of including CBT in treatment, and the limitations of current measures of treatment success. We end by making several concrete suggestions for further research. (shrink)

This book presents new research into key areas of the work of German philosopher and mathematician Gottfried Wilhelm Leibniz (1646-1716). Reflecting various aspects of Leibniz's thought, this book offers a collection of original research arranged into four separate themes: Science, Metaphysics, Epistemology, and Religion and Theology. With in-depth articles by experts such as Maria Rosa Antognazza, Nicholas Jolley, Agustín Echavarría, Richard Arthur and Paul Lodge, this book is an invaluable resource not only for readers just beginning to discover Leibniz, but (...) also for scholars long familiar with his philosophy and eager to gain new perspectives on his work. (shrink)

Most models of generational succession in sexually reproducing populations necessarily move back and forth between genic and genotypic spaces. We show that transitions between and within these spaces are usually hidden by unstated assumptions about processes in these spaces. We also examine a widely endorsed claim regarding the mathematical equivalence of kin-, group-, individual-, and allelic-selection models made by Lee Dugatkin and Kern Reeve. We show that the claimed mathematical equivalence of the models does not hold. *Received January 2007; revised (...) April 2008. †To contact the authors, please write to: Elisabeth Lloyd, Department of History and Philosophy of Science, 130 Goodbody Hall, Indiana University, Bloomington, IN 47405; e-mail: [email protected]; Richard Lewontin, Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, MA 02138; Marcus Feldman, Department of Biological Sciences, Stanford University, Stanford, CA 94305; e-mail: [email protected]. (shrink)

There is growing interest in the use of technology to enhance the tracking and quality of clinical information available for patients in disaster settings. This paper describes the design and evaluation of the Wireless Internet Information System for Medical Response in Disasters (WIISARD).

Erik Banks does several things in this slender yet substantial book on realistic empiricism (aka neutral monism). First, he encapsulates the main ideas of this tradition. While he goes into greater depth on some of these ideas than other introductions do, these pages are still accessible to nonspecialists. Second, he traces the the history of this tradition through the Austrian scientist, Ernst Mach, the American psychologist, William James, the British philosopher, Bertrand Russell, and others. These four chapters are a (...) valuable source for readers seeking to understand neutral monism in depth. Third, he develops his own version of neutral monism to deal with problems in the philosophies of mind and science. Most of my commentary will pertain to his own theory, which has some similar roots to my own. (shrink)

Neuroscience hasn’t shown how quite similar sensory circuits encode quite different colors and other qualia, nor how the unified pictorial form of images is encoded, nor how these codes yield conscious images. Neuroscience’s fixation here on cortical codes may be the culprit. Treating conscious images partly as retinal substances may avoid these problems. The evidence for conscious retinal images is that (a) the cortical codes for images are quite problematic, (b) injecting retinas with certain genes turns dichromats into trichromats without (...) cortical help, (c) retinas can discern colors by themselves without cortex, (d) retinal distortions appear in images but cortical distortions don’t, (e) retinal detectors support finely detailed colors, but V4 detectors don’t, due to their big receptive fields, (f) retinal activity has pictorial form, but viable cortical codes for pictorial form don’t exist. So, the colors and unified pictorial form of images arguably arise mainly across arrays of retinal detectors—not from abstract cortical codes. Images may be hidden in retinal activity beyond what EEGs show of it (cf. Strawson’s monism). Also, cortex refines these retinal images but cortical impairment (anesthesia, lesions, etc.) blocks awareness of them, for they’re no longer accessible to the mind’s subject-centered consciousness, resident in cortex. This proposal is largely testable and based in recent evidence. It avoids neuroscience’s elusive, problematic coded images and enigmatic explanations of how they become conscious. (shrink)

Conventional wisdom has it that truth is always evaluated using our actual linguistic conventions, even when considering counterfactual scenarios in which different conventions are adopted. This principle has been invoked in a number of philosophical arguments, including Kripke’s defense of the necessity of identity and Lewy’s objection to modal conventionalism. But it is false. It fails in the presence of what Einheuser (2006) calls c-monsters, or convention-shifting expressions (on analogy with Kaplan’s monsters, or context-shifting expressions). We show that c-monsters naturally (...) arise in contexts, such as metalinguistic negotiations, where speakers entertain alternative conventions. We develop an expressivist theory—inspired by Barker (2002) and MacFarlane (2016) on vague predications and Einheuser (2006) on counterconventionals—to model these shifts in convention. Using this framework, we reassess the philosophical arguments that invoked the conventional wisdom. (shrink)

There can be no doubt that discrimination based on sex, race, ethnicity, religion or beliefs should not be tolerated in academia. Surprisingly, however, in recent years, policies of Diversity, Inclusion and Equity(DIE), officially introduced to counteract discrimination, have increasingly led to quite the opposite result: the exclusion of individuals who do not share a radical 'woke' ideology on identity politics (feminism, other gender activisms, critical race theory, etc.), and to the suppression of the academic freedom to discuss such dogmas. This (...) subversion of academia ― disguised Trojan-horse style as universal human rights advocacy ― is unacceptable because academia must be politically neutral and protect freedom of speech, a cornerstone of professional scholarly activity without which universities as we know them will slowly but surely suffocate. -/- Our purpose here is to put together some particularly illustrative cases of such repression in a single book, testifying to a ubiquitous trend within western culture, irreducible to a few isolated complaints. The essays contained here illustrate the abuse of power, censorship and witch-hunts at many universities and research centres in the name of DIE. -/- List of coauthors in alphabetical order: Dorian Abbot, Tomonori Agoh, Gerhard Amendt, Ivar Arpi, David Benatar, Peter Boghossian, Civitas Research Team, David Díaz Pardo de Vera, Pedro Domingos, Janice Fiamengo, Étienne Forest, Jorge Gibert Galassi, Norman Goldstuck, José L. González Quirós, Lawrence M. Krauss, Patrick LaBelle, Martín López Corredoira, Heather Mac Donald, Martin Malmgren, Erik. J. Olsson, Jordan Peterson, Constantin Polychronakos, Philip C. Salzman, Alessandro Strumia, Tom Todd, Andrei Yafaev. (shrink)

The revival of the philosophy of mathematics in the 60s following its post-1931 slump left us with two conflicting positions on arithmetic’s ontological relationship to set theory. W.V. Quine’s view, presented in 'Word and Object' (1960), was that numbers are sets. The opposing view was advanced in another milestone of twentieth-century philosophy of mathematics, Paul Benacerraf’s 'What Numbers Could Not Be' (1965): one of the things numbers could not be, it explained, was sets; the other thing numbers could not be, (...) even more dramatically, was objects. Curiously, although Benacerraf’s article appeared in the heyday of Quine’s influence, it declined to engage the Quinean position squarely, even seemed to think it was not its business to do so. Despite that, in my experience, most philosophers believe that Benacerraf’s article put paid to the reductionist view that numbers are sets (though perhaps not the view that numbers are objects). My chapter will attempt to overturn this orthodoxy. (shrink)