I discuss three recent counterexamples to the transitivity of grounding due to Jonathan Schaffer. I argue that the counterexamples don’t work and draw some conclusions about the relationship between grounding and explanation.

Most authors on metaphysical grounding have taken full grounding to be an internal relation in the sense that it's necessary that if the grounds and the grounded both obtain, then the grounds ground the grounded. The negative part of this essay exploits empirical and provably nonparadoxical self-reference to prove conclusively that even immediate full grounding isn't an internal relation in this sense. The positive, second part of this essay uses the notion of a “completely satisfactory explanation” to shed light on (...) the logic of ground in the presence of self-reference. This allows us to develop a satisfactory logic of ground and recover a sense in which grounding is still an internal relation. (shrink)

This paper evaluates the proof-theoretic definition of ground developed by Poggiolesi in a range of recent publications and argues that her proposed definition fails. The paper then outlines an alternative approach where logical consequence relations and the logical operations are defined in terms of ground.

I systematically defend a novel account of the grounds for identity and distinctness facts: they are all uniquely zero‐grounded. First, this Null Account is shown to avoid a range of problems facing other accounts: a relation satisfying the Null Account would be an excellent candidate for being the identity relation. Second, a plenitudinist view of relations suggests that there is such a relation. To flesh out this plenitudinist view I sketch a novel framework for expressing real definitions, use this framework (...) to give a definition of identity, and show how the central features of the identity relation can be deduced from this definition. (shrink)

A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta. In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground can be extended to the many-many case, giving rise to the Pure Logic (...) of Many-Many Ground. In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete. (shrink)

Fine (2012) is a pluralist about grounding. He holds that there are three fundamentally distinct notions of grounding: metaphysical, normative, and natural. Berker (2017) argues for monism on the grounds that the pluralist cannot account for certain principles describing how the distinct notions of grounding interact. This paper defends pluralism. By building on work by Fine (2010) and Litland (2015) I show how the pluralist can systematically account for Berker's interaction principles.

Wilhelm has recently shown that widely accepted principles about immediate ground are inconsistent with some principles of propositional identity. This note responds to this inconsistency by developing two ground-theoretic accounts of propositional individuation. On one account some of the grounding principles are incorrect; on the other account, the principles of propositional individuation are incorrect.

Could φ’s partially grounding ψ itself be a partial ground for ψ? I show that it follows from commonly accepted principles in the logic of ground that this sometimes happens. It also follows from commonly accepted principles that this never happens. I show that this inconsistency turns on different principles than the puzzles of ground already discussed in the literature, and I propose a way of resolving the inconsistency.

This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead (...) simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations. (shrink)

How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show how (...) epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework.  We will also present a complete axiomatization of the logic we recommend to both epistemicists and local supervaluationists. . (shrink)

Using only uncontentious principles from the logic of ground I construct an infinitely descending chain of ground without a lower bound. I then compare the construction to the constructions due to Dixon and Rabin and Rabern.

Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of ground. In this paper—drawing on graph-theoretic and topological ideas—I develop a general framework in which various theories of decycling can be compared. This allows us to improve on proposals made earlier by Fine and Litland. However, it turns out (...) that there is no unique method of decycling. An important upshot is that the notion of asymmetric ground may be indeterminate. (shrink)

This article develops the Pure Logic of Iterated Full Ground (PLIFG), a logic of ground that can deal with claims of the form “ϕ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truth ϕ when there is an explanatory argument (of a certain sort) from premisses Γ to conclusion ϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we can give introduction rules for operators (...) for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle. (shrink)

In “Proof-Theoretic Justification of Logic”, building on work by Dummett and Prawitz, I show how to construct use-based meaning-theories for the logical constants. The assertability-conditional meaning-theory takes the meaning of the logical constants to be given by their introduction rules; the consequence-conditional meaning-theory takes the meaning of the logical constants to be given by their elimination rules. I then consider the question: given a set of introduction rules \, what are the strongest elimination rules that are validated by an assertability (...) conditional meaning-theory based on \? I prove that the intuitionistic introduction rules are the strongest rules that are validated by the intuitionistic elimination rules. I then prove that intuitionistic logic is the strongest logic that can be given either an assertability-conditional or consequence-conditional meaning-theory. In “Grounding Grounding” I discuss the notion of grounding. My discussion revolves around the problem of iterated grounding-claims. Suppose that \ grounds \; what grounds that \ grounds that \? I argue that unless we can get a satisfactory answer to this question the notion of grounding will be useless. I discuss and reject some proposed accounts of iterated grounding claims. I then develop a new way of expressing grounding, propose an account of iterated grounding-claims and show how we can develop logics for grounding. In “Is the Vagueness Argument Valid?” I argue that the Vagueness Argument in favor of unrestricted composition isn’t valid. However, if the premisses of the argument are true and the conclusion false, mereological facts fail to supervene on non-mereological facts. I argue that this failure of supervenience is an artifact of the interplay between the necessity and determinacy operators and that it does not mean that mereological facts fail to depend on non-mereological facts. I sketch a deflationary view of ontology to establish this. (shrink)

Jon Erling Litland’s “Meta-Ground” is concerned with the question: If A grounds B, what grounds the fact that A grounds B? His chapter begins by discussing what turns on this question. The chapter then compares the two main existing solutions to the problem of meta-ground. It ends by discussing how the problem of meta-ground is connected to other issues in the theory of ground and what are the main issues for future research.

The Problem of Iterated Ground is to explain what grounds truths about ground: if Γ grounds φ, what grounds that Γ grounds φ? This paper develops a novel solution to this problem. The basic idea is to connect ground to explanatory arguments. By developing a rigorous account of explanatory arguments we can equip operators for factive and non-factive ground with natural introduction and elimination rules. A satisfactory account of iterated ground falls directly out of the resulting logic: non- factive grounding (...) claims, if true, are zero-grounded in the sense of Fine. (shrink)

This volume of essays is very much a sequel to the two earlier collections by Jon Elster, Ulysses and the Sirens and Sour Grapes. His topic is rationality - its scope, its limitations, and its failures. Elster considers rational responses to the insufficiency of reason itself, and to the 'indeterminacies' in deploying rational-choice theory and discusses the irrationality of not seeing when, where, and what these are. A key essay which gives the collection its title examines disputes in cases of (...) child custody, which are paradigmatically indeterminate. Leaving aside cases where one parent is patently unfit and assuming that protracted dispute is against the immediate interests of the child, Elster argues that three options present themselves: a strong presumption in favour of the mother, a strong presumption in favour of the primary caretaker (also likely to be the mother), and tossing a coin. Though the first two options may be preferable in the short/medium term, Elster argues that there is a case for randomisation in the long term. The book will be read with interest by anyone concerned with political and social science. (shrink)

I, player : the puzzle of personal identity (MMORPGS and Virtual Communities) -- The game inside the mind, the mind inside the game (The Nintendo Wii Gaming Console) -- Realistic blood and gore : do violent games make violent gamers? (First-person Shooters) -- Games and God's goodness (World-builder and Tycoon Games) -- The metaphysics of interactive art (Puzzle and Adventure Games) -- Artificial and human intelligence (Single-player RPGS) -- Epilogue: Video games and the meaning of life.

Profound transformations in the composition, performance and reception of modernist music have taken place in recent decades. This collection brings fresh perspectives to bear upon key questions surrounding the forms that musical modernism takes today, how modern music is performed and heard, and its relationship to earlier music. In sixteen chapters, leading figures in the field and emerging scholars examine modernist music from the inside, in terms of changing practices of composition, musical materials and overarching aesthetic principles, and from the (...) outside, in terms of the changing contextual frameworks in which musical modernism has taken place and been understood. Shaped by a 'rehearing' of modernist music, the picture that emerges redraws the map of musical modernism as a whole and presents a full-scale re-evaluation of what the modernist movement has all been about. (shrink)

This volume tackles the slippery subject of 'meaning'.

While some authors have published excellent essays on various chapters and aspects of the book, few authors have successfully tackled the whole.In The Unity of ...

In this paper, we reply to Eric Moore’s argument that Lance Armstrong did not cheat, at least according to one, standard account of cheating. If that is the case, we argue, so much the worse for th...

This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.

The semeiotic of Charles Sanders Peirce is irreducibly triadic, positing that a sign mediates between the object that determines it and the interpretant that it determines. He eventually holds that each sign has two objects and three interpretants, standardizing quickly on immediate and dynamical for the objects but experimenting with a variety of names for the interpretants. The two most prominent terminologies are immediate/dynamical/final and emotional/energetic/logical, and scholars have long debated how they are related to each other. This paper seeks (...) to shed new light on the matter by reviewing the numerous manuscript drafts where Peirce develops the latter nomenclature while attempting to introduce his pragmatism to a general audience. It then goes on to examine an additional set of interpretants, intentional/effectual/communicational, and shows that the three different trichotomies can be understood as complementary, rather than redundant or conflicting. (shrink)

A concise and comprehensive introduction to Marx's social, political and economic thought for the beginning student. Jon Elster surveys in turn each of the main themes of marxist thought: methodology, alienation, economics, exploitation, historical materialism, classes, politics, and ideology; in a final chapter he assesses 'what is living and what is dead in the philosophy of Marx'. The emphasis throughout is on the analytical structure of Marx's arguments and the approach is at once sympathetic, undogmatic, and rigorous.

This book brings together several directions of work in model theory between the late 1950s and early 1980s.

Coming from a Nordic environment, professionally working in teacher education, both authors engaged in developmental work and research in the Uluguru mountains in Tanzania. The research is carried out in a community-based organization for vulnerable youth, Mgeta Orphan Education Foundation, which builds on principles of action learning and action research. We have followed and participated in the development of the organization since 2010, and this article builds on data gathered in 2016-17. We will show and discuss some of the transformations (...) we have witnessed, mainly in the older members. The transformations seem to have an emergent character, and we examine further factors we have seen as crucial for transforming the lives of the young people in the orphan education project. Surprisingly, duty was a factor coming forth in the data. The youth perceived duty in a relational way, mainly caused by inner motivation nurtured by the example of their coordinator, Solomon, and by facing the continuous, emergent need for assistance in their local communities. Less surprisingly, belonging transpired as a fundamental factor. Previously, we have analyzed the transformational learning among the youngsters, and identified a set of transformational tools. Building on the transformational tools, we have derived a model for Relational Transformation. Transformative action research is the approach we follow, and one aim of this article is to contribute to the understanding of the reciprocity of transformative processes in transformative research. (shrink)

The increasing application of artificial intelligence (AI) to healthcare raises both hope and ethical concerns. Some advanced machine learning methods provide accurate clinical predictions at the expense of a significant lack of explainability. Alex John London has defended that accuracy is a more important value than explainability in AI medicine. In this article, we locate the trade-off between accurate performance and explainable algorithms in the context of distributive justice. We acknowledge that accuracy is cardinal from outcome-oriented justice because it helps (...) to maximize patients’ benefits and optimizes limited resources. However, we claim that the opaqueness of the algorithmic black box and its absence of explainability threatens core commitments of procedural fairness such as accountability, avoidance of bias, and transparency. To illustrate this, we discuss liver transplantation as a case of critical medical resources in which the lack of explainability in AI-based allocation algorithms is procedurally unfair. Finally, we provide a number of ethical recommendations for when considering the use of unexplainable algorithms in the distribution of health-related resources. (shrink)

Presents a mathematically rigorous, philosophically sound foundation for a science of information.