This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)

Distinctions in fundamentality between different levels of description are central to the viability of contemporary decoherence-based Everettian quantum mechanics (EQM). This approach to quantum theory characteristically combines a determinate fundamental reality (one universal wave function) with an indeterminate emergent reality (multiple decoherent worlds). In this chapter I explore how the Everettian appeal to fundamentality and emergence can be understood within existing metaphysical frameworks, identify grounding and concept fundamentality as promising theoretical tools, and use them to characterize a system of explanatory (...) levels (with associated laws of nature) for EQM. This Everettian level structure encompasses and extends the ‘classical’ levels structure. The ‘classical’ levels of physics, chemistry, biology, etc. are recovered, but they are emergent in character and potentially variable across Everett worlds. EQM invokes an additional fundamental level, not present in the classical levels picture, and a novel potential role for self-location in interlevel metaphysics. When given a modal realist interpretation, EQM also makes trouble for supervenience-based approaches to levels. (shrink)

The aim of this paper is to introduce, elucidate and defend the usefulness of a variant of grounding, or metaphysical explanation, that has the feature that the grounds explain of some states of affairs that one of them obtains without explaining which one obtains. I will dub this variant arbitrary grounding. After informally elucidating the basic idea in the first section, I will provide three metaphysical hypotheses that are best formulated in terms of arbitrary grounding in the second section. The (...) third section will be concerned with the relation between arbitrary grounding and non-arbitrary grounding. The fourth section will compare arbitrary grounding to two extant proposals in the literature. (shrink)

This paper develops a view on which: (a) all fundamental facts are absolute, (b) some facts do not supervene on the fundamental facts, and (c) only relative facts fail to supervene on the fundamental facts.

Explanatory realism is the view that explanations work by providing information about relations of productive determination such as causation or grounding. The view has gained considerable popularity in the last decades, especially in the context of metaphysical debates about non-causal explanation. What makes the view particularly attractive is that it fits nicely with the idea that not all explanations are causal whilst avoiding an implausible pluralism about explanation. Another attractive feature of the view is that it allows explanation to be (...) a partially epistemic, context-dependent phenomenon. In spite of its attractiveness, explanatory realism has recently been subject to criticism. In particular, Taylor :197–219, 2018). has presented four types of explanation that the view allegedly cannot account for. This paper defends explanatory realism against Taylor’s challenges. We will show that Taylor’s counterexamples are either explanations that turn out to provide information about entities standing in productive determination relations or that they are not genuine explanations in the first place. (shrink)

What grounds facts of ground? Some metaphysicians invoke fundamental grounding laws to answer this question. These are general principles that link grounded facts to their grounds. The main business of this paper is to advance the debate about the metaphysics of grounding laws by exploring the prospects of a plausible yet underexplored minimalist account, one which is structurally analogous to a familiar Humean conception of natural laws. In the positive part of this paper, I articulate such a novel view and (...) argue for its merits. The minimalist account shuns essences and takes laws to be unmysterious elite regularities. Therefore, it is a promising alternative for theorists of ground who spurn the acceptance of essentialism about the grounding laws but think that these are needed in our theorizing. In the negative part, I argue that widely accepted principles of ground, coupled with the tenets of minimalism, jeopardize the fundamentality of the grounding laws. I discuss two immediately available and prima facie appealing strategies to evade this threat. However, I show that both have undesirable theoretical costs. I conclude by casting doubts on whether the benefits of a minimalist account of fundamental grounding laws outweigh such costs. (shrink)

In contemporary metaphysics, the doctrine that the fundamental facts are those which are wholly ungrounded is the received view or something near enough. Against this radical brutalism, several metaphysicians argued in favour of the existence of fundamental facts that are moderately brute or merely partially grounded. However, the arguments for moderately brute facts rely on controversial metaphysical scenarios. This paper aims to counteract the tendency in favour of radical brutalism on scientific grounds. It does so by showing that naturalistic metaphysicians (...) can appeal to plausible considerations from physical theory to establish the existence of moderately brute facts. But should the naturalistic metaphysician embrace moderate brutalism, namely the view that the fundamental facts are those which are merely partially ungrounded? Here I argue for a negative answer, recommending a more inclusive pluralism about the kinds of brute facts we can expect to find in nature. (shrink)

Pluralists argue for the distinctness of coinciding objects on the grounds that they have different properties. The grounding problem is the problem of explaining how the supposed difference in properties can arise in the first place. This paper considers this problem as an instance of a more general phenomenon, namely, the problem of dealing with underdetermination in asymmetrical systems admitting of non-trivial automorphisms. It argues in favour of primitivism by developing an account of stochastic grounding that makes room for non-fundamental (...) bruteness and substantially mitigates the costs of primitivism. (shrink)

This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn't arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the $\lambda$-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a (...) diagrammatic representation, and a logical representation in a novel language. In the latter half of the paper I turn to some technical questions concerning the treatment of quantification, and demonstrate various equivalences between the diagrammatic and logical representations, and a fragment of the $\lambda$-calculus. (shrink)

The notion of fundamentality, as it is used in metaphysics, aims to capture the idea that there is something basic or primitive in the world. This metaphysical notion is related to the vernacular use of “fundamental”, but philosophers have also put forward various technical definitions of the notion. Among the most influential of these is the definition of absolute fundamentality in terms of ontological independence or ungroundedness. Accordingly, the notion of fundamentality is often associated with these two other technical notions.