Chapter 20 David Kovacs’ “Essence, Grounding, and Explanation” sets out four different ways in which essence might be taken to relate to the notion of grounding or metaphysical explanation, i.e., the type of connection that is often expressed by means of non-causal “in virtue of” or “because”-claims: (i) Unity: essence and grounding belong to a unified set of explanatory concepts; (ii) Supplementation: essence and grounding both contribute in their own way to a distinctive type of explanation; (iii) Independence: essence is (...) a sui generis notion with no straightforward conceptual links to grounding; and (iv) Irrelevance: essence is not an explanatory notion at all and therefore should not be viewed as connected to explanatory notions like grounding. As Kovacs brings out in the chapter, a wide variety of attitudes are represented in the literature even among philosophers who are sympathetic to the recent “hyperintensional” turn in metaphysics when it comes to the question of how the notions of essence and grounding interact with one another. (shrink)

In this paper, I argue for a novel reading of Spinoza’s position in his exchangewith Boyle about Boyle’s experiment with nitre. Boyle claimed to have shownthrough experiments that nitre ceased to be nitre after heating. Spinozadisagreed and proposed the alternative hypothesis that nitre has changed itsstate and not its nature. Spinoza’s position was construed in the literature asrational scepticism denying that experiments can yield knowledge ofessences because all sensory experience is underdetermined and open tomultiple interpretations. I argue for an alternative (...) reading of Spinoza’sposition which focuses on Bacon’s notion of crucial instance. According tothis reading, Spinoza did not deny the possibility of knowing byexperimentation whether nitre has changed its nature, he asked for a crucialinstance, i.e. an experiment that would refute the hypothesis that nitre haschanged merely its state. Spinoza’s argumentative strategy shows that,contrary to the mainstream reading, the representational content of sensoryideas can be determined even if it does not represent the essence of theobject: we can know with absolute, rather than merely moral, certaintywhether nitre ceased to be nitre without knowing what nitre is. (shrink)

Kant's theory of transcendental ideas can be conceived as a sort of model theory for an empirical first-order object theory. The main features of Kant's theory of transcendental ideas (especially its antinomies and their solutions) can be recognized, in a modified way, in a religious discourse as exemplified in the dialogue of Jesus and the Samaritan woman (John 4). In this way, what is by Kant meant merely as regulative ideas obtains a sort of objective reality and becomes a religiously (...) founded metaphysics. A metaphysical theory of religious dialogue is formalized on the basis of an extended justification logic of evidence and wish agents. (shrink)

A first-order logic of belief with identity is proposed, primarily to give an account of possible de re contradictory beliefs, which sometimes occur as consequences of de dicto non-contradictory beliefs. A model has two separate, though interconnected domains: the domain of objects and the domain of appearances. The satisfaction of atomic formulas is defined by a particular S-accessibility relation between worlds. Identity is non-classical, and is conceived as an equivalence relation having the classical identity relation as a subset. A tableau (...) system with labels, signs, and suffixes is defined, extending the basic language $\mathscr{L}_{\mathbf{QB}}$ by quasiformulas (to express the denotations of predicates). The proposed logical system is paraconsistent since $\phi \wedge \neg\phi$ does not ``explode'' with arbitrary syntactic consequences. (shrink)

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Popular culture continues fuelling public imagination with things, human and non-human, that we might beco-me or confront. Besides robots, other significant tropes in popular fiction that generated images include non-human humans and cyborgs, wired into his-torically varying sociocultural realities. Robots and artificial intelligence are re-defining the natural order and its hierar-chical structure. This is not surprising, as natural order is always in flux, shaped by new scientific discoveries, especially the reading of the genetic code, that reveal and redefine relationships between (...) life forms. However, for the first time, a new, artificial, species is being introduced into the existing diagrams, and, for the first time, it appears to hybridise the anthro-pocentric natural world order. (shrink)

Christine Overall has argued that miracles, if they exist, would be an evil committed by God and therefore disprove the existence of God. However, her notion of a miracle as an intervention presupposes a view about the relation between God and creation that posits God as an ‘outsider.’ Such a view has not been held by all theists. It was not held by Thomas Aquinas. I show that Aquinas ’s conception is not susceptible to Overall’s criticisms. The upshot is that (...) theists should avoid any view of God as an ‘outsider,’ if they wish to avoid Overall’s criticisms. (shrink)

Plotinus criticizes the view that individual human souls are parts of the world-soul arguing that they would lack individual agency since their alleged actions would have to be attributed to the whole they are parts of (iii.1.4). He nevertheless holds that individual souls are parts of a larger whole, the so-called hypostasis soul, a soul that does not ensoul any body but encompasses and produces all individual souls including the world-soul (iv.3.4.14–21; iv.8.36–12; iv.9.5). In this paper, I ask whether Plotinus, (...) in the face of his own arguments, can consistently attribute agency to individual souls and hold that they are parts of the hypostasis soul. I argue that Plotinus’ model of intelligible mereology (vi.2.20) allows individual souls to depend on the hypostasis soul as parts in a way that grounds their agency by providing them with the capacity for rational thought. (shrink)

The article focuses on Kant's formal logic (formal theory of concepts, judgments, and inference, general methodology) in the systematic order of logical forms and presents the main characteristics of his transcendental logic (theory of categories and transcendental ideas). Kant's problem of the foundations of logic and its completeness is addressed. The relevance and influence of Kant's account of logic in the development of modern logic is outlined. The article gives a selection of primary and secondary sources.

In this paper I argue against Michael Morris’ claim, that the Tractatus view involves holding that the possibility of truth-functional combination is prior to the possibility for sentential constituents to combine with one another. I provide an alternative interpretation in which I deny the presence of any distinction in the Tractatus between these two possibilities. I then turn to Adrian Moore’s ‘disjunctivist’ account of sentencehood, itself inspired by the Tractatus view. I argue that Moore’s account need not involve a commitment (...) to the kind of priority Morris describes, and that it need not involve a commitment to transcendental idealism. (shrink)

The aim of the present study was to examine whether offspring at high and low familial risk for depression differ in the immediate and more lasting behavioural and physiological effects of hedonica...

A systematic treatment of Hume's conception of imagination in all the main topics of his philosophy.

Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (shrink)

Explainable artificial intelligence (XAI) seeks to produce explanations for those machine learning methods which are deemed opaque. However, there is considerable disagreement about what this means and how to achieve it. Authors disagree on what should be explained (topic), to whom something should be explained (stakeholder), how something should be explained (instrument), and why something should be explained (goal). In this paper, I employ insights from means-end epistemology to structure the field. According to means-end epistemology, different means ought to be (...) rationally adopted to achieve different epistemic ends. Applied to XAI, different topics, stakeholders, and goals thus require different instruments. I call this the means-end account of XAI. The means-end account has a descriptive and a normative component: on the one hand, I show how the specific means-end relations give rise to a taxonomy of existing contributions to the field of XAI; on the other hand, I argue that the suitability of XAI methods can be assessed by analyzing whether they are prescribed by a given topic, stakeholder, and goal. (shrink)

Immanuel Kant is often considered to be the source of the contemporary idea of human dignity, but his conception of human dignity and its relation to human value and to the requirement to respect others have not been widely understood. Kant on Human Dignity offers the first in-depth study in English of this subject. Based on a comprehensive analysis of all the passages in which Kant uses the term ;dignity, as well as an analysis of the most prominent arguments for (...) a value of human beings in the Kant literature, the book carefully examines different ways of construing the relationship between dignity, value and respect for others. It takes seriously Kant s Copernican Revolution in moral philosophy: Kant argues that moral imperatives cannot be based on any values without yielding heteronomy. Instead it is imperatives of reason that determine what is valuable. The requirement to respect all human beings is one such imperative. Respect for human beings does not follow from human dignity for this would violate autonomy but is an unconditional command of reason. Following this train of thought yields a unified account of Kant s moral philosophy. (shrink)

The UN Global Compact is a voluntary initiative designed to help fashion a more humane world by enlisting business to follow ten principles concerning human rights, labor, the environment, and corruption. Although the four-year-old Compact is a relatively successful initiative, having signed up over eleven hundred companies and more than two hundred of the large multinationals, and having begun some important projects on globalization issues, there is a serious problem in that very few of the major U.S. companies have joined. (...) While the premier U.S. companies are interested in meeting the legitimate expectations of society, there is concerncentering around accountability issues. The accountability issues are in four major areas: 1. Accountability showing that the globalization of the economy actually helps the poor. 2. Accountability showing the corporate performance matches rhetoric. 3. Accountability that provides legitimacy to a two-tier pricing system and other measures that are designed to assist the poor in developing countries. 4. Accountability in the human rights area; what societal expectations are multinational companies accountablefor? The article outlines the problems that the Compact brings to the fore and offers some insight from the ethical literature that may address U.S. company concerns or provide new ways of thinking about the issues. It further argues that the forum provided by the Compact may be the most effective means to gain consensus of the role of business in society. (shrink)

This paper reviews the hole argument as an argument against spacetime substantivalism. After a careful presentation of the argument itself, I critically review possible responses.

The Lorentz transformation relates the Einstein-defined measures, associated with two inertial frames, of the space and time coordinates of a body or event. From such information relative velocities and accelerations may be deduced, and their appropriate transformations derived. All other transformations of special relativity are derived from the Lorentz transformation and hence depend on the coordinate measures related by the transformation. In particular, the transformation of forces depends on that for accelerations; hence it may not be appropriately applicable to equilibrium (...) phenomena involving null-acceleration. It is suggested that this is the root of the apparent paradox which arises when the conventional force transformation is applied to the consideration of a right-angled lever in equilibrium in its proper inertial frame. It is shown that this paradox is resolved by the employment of a nonconventional but appropriate special relativistic transformation for forces not associated with corresponding accelerations. (shrink)

Im Folgenden stellen wir drei aktuelle Forschungsbereiche zur formalen Logik bei Kant allgemeinverständlich dar und greifen dabei auf die trans zendentale Logik nur dann zurück, wenn sie ein besseres Verständnis der formalen Logik ermöglicht: Zunächst wird Kants Beitrag zur Rezeption und Weiterentwicklung von Euler-artigen Diagrammen dargestellt. Diese Diagramme wurden in den 1990er Jahren wiederentdeckt, als formales System interpretiert und werden heute insbes. in der Didaktik, in den Kognitionswissenschaften, in der Linguistik, in KI-Bereichen wie der (Logik-basierten) Wissensrepräsentation eingesetzt, und auch in (...) der Philosophie verwendet (Kapitel 2). Mehrere Studien haben in den letzten Jahren gezeigt, dass Kant in weiten Teilen seines Systems Oppositionsverhältnisse verwendet, die der Struktur des logischen Quadrats entsprechen. Das logische Quadrat ist heute Gegenstand intensiver Forschung, da es neben der klassischen, auch die paravollständige und parakonsistente Negation abbildet (Kap. 3). Jüngst wurde zudem die Implementierbarkeit der kantischen Logik in ein formalisiertes deduktives System bewiesen. Die Bedeutung dieses Ergebnisses wird insbesondere im Hinblick auf die formalisierte Umsetzung der Sätze vom Widerspruch, vom zureichenden Grund und der Ausschließung des Mittleren erläutert (Kap. 4). Abschließend möchten wir ein paar Perspektiven für die Forschung zur formalen Logik bei Kant nennen (Kap. 5). -- -/- Note: No financial support acknowledged by the second autor (S. Kovač). (shrink)

ABSTRACT The use of broad consent for genomics research raises important ethical questions for the conduct of genomics research, including relating to its acceptability to research participants and comprehension of difficult scientific concepts. To explore these and other challenges, we conducted a study using qualitative methods with participants enrolled in an H3Africa Rheumatic Heart Disease genomics study (the RHDGen network) in Zambia to explore their views on broad consent, sample and data sharing and secondary use. In-depth interviews were conducted with (...) RHDGen participants (n = 18), study staff (n = 5) and with individuals who refused to participate (n = 3). In general, broad consent was seen to be reasonable if reasons for storing the samples for future research use were disclosed. Some felt that broad consent should be restricted by specifying planned future studies and that secondary research should ideally relate to original disease for which samples were collected. A few participants felt that broad consent would delay the return of research results to participants. This study echoes findings in other similar studies in other parts of the continent that suggested that broad consent could be an acceptable consent model in Africa if careful thought is given to restrictions on re-use. (shrink)

Several authors have argued that traumatic experiences are processed and remembered in a qualitatively different way from neutral events. To investigate this issue, we interviewed 121 Croatian war veterans diagnosed with posttraumatic stress disorder about amnesia, intrusions , and the sensory qualities of their most horrific war memories. Additionally, they completed a self-report scale measuring dissociative experiences. In contrast to what one would expect on the basis of theories emphasizing the special status of traumatic memories, amnesia, and high frequency intrusions (...) were not particularly typical for our sample of traumatized individuals. Moreover, traumatic memories were not qualitatively different from neutral memories with respect to their stability and sensory qualities. The severity of PTSD symptoms was not significantly correlated with dissociative experiences. Our findings do not support the existence of special memory mechanisms that are unique to experiencing traumatic events. (shrink)

In his paper ``What is Structural Realism?'' James Ladyman drew a distinction between epistemological structural realism and metaphysical (or ontic) structural realism. He also drew a suggestive analogy between the perennial debate between substantivalist and relationalist interpretations of spacetime on the one hand, and the debate about whether quantum mechanics treats identical particles as individuals or as `non-individuals' on the other. In both cases, Ladyman's suggestion is that an ontic structural realist interpretation of the physics might be just what is (...) needed to overcome the stalemate. The main thesis of this paper is that, whatever the interpretative difficulties of generally covariant spacetime physics are, they do not support or suggest structural realism. In particular, I hope to show that there is in fact no analogy that supports a similar interpretation of the metaphysics of spacetime points and of quantum particles. (shrink)

Many research fields concerned with the processing of information contained in human faces would benefit from face stimulus sets in which specific facial characteristics are systematically varied while other important picture characteristics are kept constant. Specifically, a face database in which displayed expressions, gaze direction, and head orientation are parametrically varied in a complete factorial design would be highly useful in many research domains. Furthermore, these stimuli should be standardised in several important, technical aspects. The present article presents the freely (...) available Radboud Faces Database offering such a stimulus set, containing both Caucasian adult and children images. This face database is described both procedurally and in terms of content, and a validation study concerning its most important characteristics is presented. In the validation study, all frontal images were rated with respect to the shown facial expression, intensity of expression, clarity of expression, genuineness of expression, attractiveness, and valence. The results show very high recognition of the intended facial expressions. (shrink)

Philosophy in the English-speaking world is dominated by analytic approaches to its problems and projects; but theology has been dominated by alternative approaches. Many would say that the current state in theology is not mere historical accident, but is, rather, how things ought to be. On the other hand, many others would say precisely the opposite: that theology as a discipline has been beguiled and taken captive by 'continental' approaches, and that the effects on the discipline have been largely deleterious. (...) The methodological divide between systematic theologians and analytic philosophers of religion is ripe for exploration. The present volume represents an attempt to begin a much-needed interdisciplinary conversation about the value of analytic philosophical approaches to theological topics. Most of the essays herein are sympathetic toward the enterprise the editors are calling analytic theology; but, with an eye toward balance, the volume also includes essays and an introduction that try to offer more critical perspectives on analytic theology. (shrink)

This paper develops the Diachronic Self-Making View, the view that we are the non-accidentally best candidate referents of our ‘I’-beliefs. A formulation and defence of DSV is followed by an overview of its treatment of familiar puzzle cases about personal identity. The rest of the paper focuses on a challenge to DSV, the Puzzle of Inconstant ‘I’-beliefs: the view appears to force on us inconsistent verdicts about personal identity in cases that we would naturally describe as changes in one’s de (...) se beliefs. To solve this problem, the paper defends the possibility of overlapping people, and addresses a number of objections to this idea. (shrink)

What is morality? How many moral values are there? And what are they? According to the theory of morality-as-cooperation, morality is a collection of biological and cultural solutions to the problems of cooperation recurrent in human social life. This theory predicts that there will be as many different types of morality as there are different types of cooperation. Previous research, drawing on evolutionary game theory, has identified at least seven different types of cooperation, and used them to explain seven different (...) types of morality: family values, group loyalty, reciprocity, heroism, deference, fairness and property rights. Here we explore the conjecture that these simple moral ‘elements’ combine to form a much larger number of more complex moral ‘molecules’, and that as such morality is a combinatorial system. For each combination of two elements, we hypothesise a candidate moral molecule, and successfully locate an example of it in the professional and popular literature. These molecules include: fraternity, blood revenge, family pride, filial piety, gavelkind, primogeniture, friendship, patriotism, tribute, diplomacy, common ownership, honour, confession, turn taking, restitution, modesty, mercy, munificence, arbitration, mendicancy, and queuing. These findings indicate that morality – like many other physical, biological, psychological and cultural systems – is indeed a combinatorial system. Thus morality-as-cooperation provides a principled and powerful theory, that explains why there are many moral values, and successfully predicts what they will be; and it generates a systematic framework that has the potential to explain all moral ideas, possible and actual. Pursuing the many implications of this theory will help to place the study of morality on a more secure scientific footing. (shrink)

Many philosophers embrace grounding, supposedly a central notion of metaphysics. Grounding is widely assumed to be irreflexive, but recently a number of authors have questioned this assumption: according to them, it is at least possible that some facts ground themselves. The primary purpose of this paper is to problematize the notion of self-grounding through the theoretical roles usually assigned to grounding. The literature typically characterizes grounding as at least playing two central theoretical roles: a structuring role and an explanatory role. (...) Once we carefully spell out what playing these roles includes, however, we find that any notion of grounding that isn’t irreflexive fails to play these roles when they are interpreted narrowly, and is redundant for playing them when they are interpreted more broadly. The upshot is that no useful notion of grounding can allow a fact to ground itself. (shrink)

Negative theology or apophasis - the idea that God is best identified in terms of 'absence', 'otherness', 'difference' - has been influential in modern Christian thought, resonating as it does with secular notions of negation developed in continental philosophy. Apophasis also has a strong intellectual history dating back to the early Church Fathers. Silence and the Word both studies the history of apophasis and examines its relationship with contemporary secular philosophy. Leading Christian thinkers explore in their own way the extent (...) to which the concept of the apophatic illumines some of the deepest doctrinal structures of Christian faith, and of Christian self-understanding both in terms of its historical and contemporary situatedness, showing how a dimension of negativity has characterised not only traditional mysticism but most forms of Christian thought over the years. (shrink)

We give reasons for our judgements of works of art. (2) Reasons are inherently general, and hence dependent on principles. (3) There are no principles of aesthetic evaluation. Each of these three propositions seems plausible, yet one of them must be false. Illusionism denies (1). Particularism denies (2). Generalism denies (3). We argue that illusionism depends on an unacceptable account of the use of critical language. Particularism cannot account for the connection between reasons and verdicts in criticism. Generalism comes in (...) two forms: reversible generalism is the thesis that there are meaningful generalizations in criticism that admit of exceptions; irreversible generalism is the thesis that such generalizations cannot admit of exceptions. It is argued that Frank Sibley's defence of reversible generalism cannot provide a criterion for distinguishing valenced from non-valenced properties, and thus fails. Irreversible generalism is correct: it is logically cogent and fits our critical practices. (shrink)

The UN Global Compact is a voluntary initiative designed to help fashion a more humane world by enlisting business to follow ten principles concerning human rights, labor, the environment, and corruption. Although the four-year-old Compact is a relatively successful initiative, having signed up over eleven hundred companies and more than two hundred of the large multinationals, and having begun some important projects on globalization issues, there is a serious problem in that very few of the major U.S. companies have joined. (...) While the premier U.S. companies are interested in meeting the legitimate expectations of society, there is concerncentering around accountability issues. The accountability issues are in four major areas: 1. Accountability showing that the globalization of the economy actually helps the poor. 2. Accountability showing the corporate performance matches rhetoric. 3. Accountability that provides legitimacy to a two-tier pricing system and other measures that are designed to assist the poor in developing countries. 4. Accountability in the human rights area; what societal expectations are multinational companies accountablefor? The article outlines the problems that the Compact brings to the fore and offers some insight from the ethical literature that may address U.S. company concerns or provide new ways of thinking about the issues. It further argues that the forum provided by the Compact may be the most effective means to gain consensus of the role of business in society. (shrink)

Diffeomorphism invariance is sometimes taken to be a criterion of background independence. This claim is commonly accompanied by a second, that the genuine physical magnitudes (the ``observables'') of background-independent theories and those of background-dependent (non-diffeomorphism-invariant) theories are essentially different in nature. I argue against both claims. Background-dependent theories can be formulated in a diffeomorphism-invariant manner. This suggests that the nature of the physical magnitudes of relevantly analogous theories (one background free, the other background dependent) is essentially the same. The temptation (...) to think otherwise stems from a misunderstanding of the meaning of spacetime coordinates in background-dependent theories. (shrink)

How is grounding related to metaphysical explanation? The standard view is that the former somehow “backs”, “undergirds” or “underlies” the latter. This view fits into a general picture of explanation, according to which explanations in general hold in virtue of a certain elite group of “explanatory relations” or “determinative relations” that back them. This paper turns the standard view on its head: grounding doesn't “back” metaphysical explanation but is in an important sense downstream from it. I call this view “grounding (...) idealism”, since it structurally resembles an analogous view about causation that is known as “causal idealism” and has been endorsed by philosophers like Michael Scriven and Philip Kitcher. I formulate a specific version of grounding idealism, Metaphysical Explanation‐First Idealism (MEFI), according to which the semantic value of ‘grounding’ is an abundant, gerrymandered relation settled by the metaphysical explanation facts. Then I offer some theoretical considerations that support MEFI over rival accounts of the relation between grounding and metaphysical explanation. Finally, I address the question of what role is left for grounding to play, if not that of “backing” metaphysical explanations. (shrink)

The use of broad consent for genomics research raises important ethical questions for the conduct of genomics research, including relating to its acceptability to research participants and comprehension of difficult scientific concepts. To explore these and other challenges, we conducted a study using qualitative methods with participants enrolled in an H3Africa Rheumatic Heart Disease genomics study in Zambia to explore their views on broad consent, sample and data sharing and secondary use. In-depth interviews were conducted with RHDGen participants, study staff (...) and with individuals who refused to participate. In general, broad consent was seen to be reasonable if reasons for storing the samples for future research use were disclosed. Some felt that broad consent should be restricted by specifying planned future studies and that secondary research should ideally relate to original disease for which samples were collected. A few participants felt that broad consent would delay the return of research results to participants. This study echoes findings in other similar studies in other parts of the continent that suggested that broad consent could be an acceptable consent model in Africa if careful thought is given to restrictions on re-use. (shrink)

Since its founding in 1950, the Metaphysical Society of America has remained a pluralistic community dedicated to rigorous philosophical inquiry into the most basic metaphysical questions. At each year’s conference, the presidential address offers original insights into metaphysical questions. Both the insights and the questions are as perennial as they are relevant to contemporary philosophers. This volume collects eighteen of the finest representatives from those presidential addresses, including contributions from George Allan, Richard Bernstein, Norris Clarke, Vincent Colapietro, Frederick Ferré, Jorge (...) J. E. Gracia, Joseph Grange, Marjorie Grene, George Klubertanz, Ivor Leclerc, Ralph McInerny, Ernan McMullin, Joseph Owens, John Herman Randall, Jr., Nicholas Rescher, Stanley Rosen, John E. Smith, and Robert Sokolowski. Also included are Paul Weiss’s inaugural address to the Society, an introduction chronicling the history of the Society, and an original Foreword by William Desmond and Epilogue by Robert Neville. (shrink)

We make some remarks on the mathematics and metaphysics of the hole argument, in response to a recent article in this journal by Weatherall ([2018]). Broadly speaking, we defend the mainstream philosophical literature from the claim that correct usage of the mathematics of general relativity `blocks' the argument.

English has plural terms as well as singular terms. But our standard formal languages, e.g., the predicate calculus, feature only singular terms. How can the plural idiom be formalized?‘Changing the subject’ is by far the most common plurals strategy among both philosophers and linguists: a plural term is replaced by a singular term standing for some complex object that ‘contains’ the individuals to which the plural term alludes. For example, one might simply replace ‘A, B imply C’ with ‘{A, B} (...) implies [singular] C’. We uncover a surprising variety of ways to change the subject, of ever‐increasing complexity and ingenuity. Our question is whether any can made to work. (shrink)