Hamkins’ multiverse view is a prominent position on the nature of set theory. It is posited against the universe view and proposed as a philosophical theory explaining current set-theoretic practice. This paper confronts the multiverse view with the results of an interview study investigating current set-theoretic practice. The study reveals a heterogeneity of set-theoretic research practices. The multiverse view is found to align well with pluralist research practices but not with absolutist practices. The generalisation claim of the (...) multiverse view fails because of this heterogeneity; only a reduced interpretation of the multiverse view might hold generally. Furthermore, Hamkins’ prediction that the community as a whole will not adopt axioms deciding the continuum hypothesis is found probably true, but for different reasons: although part of the community has already accepted axioms beyond ZFC, another part of the community will withdraw from doing so. In conclusion, I argue that Hamkins’ multiverse view is best interpreted as a valuable perspective on pluralist set-theoretic practices. (shrink)

The multiverse theodicy proposes to reconcile the existence of God and evil by supposing that God created all and only the creation-worthy universes and that some universes like ours are, despite their evils, creation-worthy. Drawing on work in population ethics, this paper develops a novel challenge to the multiverse theodicy. Roughly, the challenge contends that the axiological underpinnings of the multiverse theodicy harbor a ‘mere addition paradox’: the assumption that creating creation-worthy universes would always make the world (...) better turns out to have morally repugnant consequences akin to those of the assumption that adding worthwhile lives to a population would always make the overall welfare of the population better. Further, the challenge leverages this difficulty into an argument against God’s having created all and only the creation-worthy universes, and hence against the multiverse theodicy. Responses to this challenge are considered but found wanting, largely because of commitments of the multiverse theodicy that have no analogs in population ethics. (shrink)

According to standard cosmology, the universe underwent a brief period of inflation within the first second of its existence. The cosmological multiverse is grounded in an extrapolation of this idea known as “eternal inflation.” This paper argues that the physics of eternal inflation is far less secure than inflation itself, and that a multiverse generated from eternal inflation should not inherit support from inflation alone. After explaining inflation, the anomalies it was intended to explain, and the mechanism by (...) which eternal inflation is supposed to produce pocket universes, the paper surveys a range of difficulties from both philosophy and physics. No single objection is decisive. Rather, the accumulation of problems reveals a research program sustained more by theoretical extrapolation than empirical evidence. These problems include the measure problem, the relocation rather than resolution of fine-tuning, trans-Planckian worries, the presupposed quantum-to-classical transition, and swampland constraints tied to quantum gravity. At present, the existence of the multiverse based on eternal inflation warrants skepticism rather than belief. (shrink)

We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with (...) regard to the universe of sets, then we discuss the Zermelian view, featuring a ‘vertical’ multiverse, and give special attention to this multiverse conception in light of the hyperuniverse programme introduced in Arrigoni and Friedman (2013). We argue that the distinctive feature of the multiverse conception chosen for the hyperuniverse programme is its utility for finding new candidates for axioms of set theory. (shrink)

Can multiverse hypotheses ever receive empirical support? Critics argue that multiverse scenarios posit unobservable entities, face severe underdetermination, or fall outside the bounds of science. This chapter challenges that view by offering a naturalistic metaphysical counterpoint to Bayesian approaches, distinguishing fragmented from holistic multiverses. Scientific proposals are almost always holistic: they embed universes within a unifying physical or metaphysical structure that can, in principle, leave empirical signatures inside the universes. I develop a typology of such signatures and show (...) how it applies to leading scenarios from quantum theory, cosmology, and string theory. This framework clarifies why objections such as the `this universe' objection and a newly articulated generalization, the epistemic isolation objection, fail against scientifically motivated multiverses. The upshot is a qualified defence: while fragmented multiverses remain empirically inaccessible, certain holistic multiverses could, in principle, be supported by the same epistemic standards used elsewhere in physics. (shrink)

A multiverse is comprised of many universes, which quickly leads to the question: How many universes? There are either finitely many or infinitely many universes. The purpose of this paper is to discuss two conceptions of infinite number and their relationship to multiverses. The first conception is the standard Cantorian view. But recent work has suggested a second conception of infinite number, on which infinite numbers behave very much like finite numbers. I will argue that that this second conception (...) of infinite number is the correct one, and analyze what this means for multiverses. (shrink)

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account (...) of reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position. (shrink)

If the laws of nature are fine-tuned for life, can we infer other universes with different laws? How could we even test such a theory without empirical access to those distant places? Can we believe in the multiverse of the Everett interpretation of quantum theory or in the reality of other possible worlds, as advocated by philosopher David Lewis? At the intersection of physics and philosophy of science, this book outlines the philosophical challenge to theoretical physics in a measured, (...) well-grounded manner. The origin of multiverse theories are explored within the context of the fine-tuning problem and a systematic comparison between the various different multiverse models are included. Cosmologists, high energy physicists, and philosophers including graduate students and researchers will find a systematic exploration of such questions in this important book. (shrink)

In reply to the problem of evil, some suggest that God created an infinite number of universes—for example, that God created every universe that contains more good than evil. I offer two objections to these multiverse theodicies. First, I argue that, for any number of universes God creates, he could have created more, because he could have created duplicates of universes. Next, I argue that multiverse theodicies can’t adequately account for why God would create universes with pointless suffering, (...) and hence they don’t solve the problem of evil. (shrink)

As a candidate theory of quantum gravity, the popularity of string theory has waxed and waned over the past four decades. One current source of scepticism is that the theory can be used to derive, depending upon the input geometrical assumptions that one makes, a vast range of different quantum field theories, giving rise to the so-called landscape problem. One apparent way to address the landscape problem is to posit the existence of a multiverse; this, however, has in turn (...) drawn heightened attention to questions regarding the empirical testability and predictivity of string theory. We argue first that the landscape problem relies on dubious assumptions and does not motivate a multiverse hypothesis. Nevertheless, we then show that the multiverse hypothesis is scientifically legitimate and could be coupled to string theory for other empirical reasons. Looking at various cosmological approaches, we offer an empirical criterion to assess the scientific status of multiverse hypotheses. (shrink)

I provide the account of divine creation found in multiverse theorists Donald Turner, Klaas Kraay, and Tim O’Connor. I show that the accounts Kraay and Turner offer are incoherent. God does not survey all possible worlds and necessarily actualize those universes in the (on balance) good worlds or the worthy worlds. If God necessarily actualizes the multiverse, we have no idea which universes are parts of that multiverse. I show next that Tim O’Connor’s multiverse account of (...) creation is also incoherent. I argue that a preferable multiverse would include a much greater variety of universes than are included in Turner, Kraay or O’Connor. In the last section I offer some concluding remarks. (shrink)

The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous range of set-theoretic possibilities, a phenomenon that challenges (...) the universe view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for. (shrink)

This paper isolates a surprising range of multiverse positions, revealing their sometimes-dubious metaphysical underpinnings and demonstrating that the distinction between multiversism and universism is often muddier than it might appear. Setting metaphysics aside, the operative questions cluster around Axiomatic Universism versus Multiversism—should our fundamental theory be couched in terms of sets or in terms of sets and classes?—and Heuristic Universism versus Multiversism—should set-theoretic practice be guided by an intuitive picture of an iterative hierarchy or of a collection of such (...) hierarchies? It concludes that the mathematical benefits of a switch from (extensions of) ZFC to (extensions of) a multiverse theory like Steel’s MV have yet to be demonstrated and that a truly metaphysics-free perspective should happily welcome the heuristic benefits of both intuitive pictures. (shrink)

In this article, I develop a novel version of the multiverse theory of sets called hierarchical pluralism by introducing the notion of “degrees of intentionality” of theories. The presented view is articulated for the purpose of reconciling epistemological realism and the multiverse theory of sets so as to preserve a considerable amount of epistemic objectivity when working with the multiverse theory. I give some arguments in favor of a hierarchical picture of the multiverse in which theories (...) or models are thought to be ordered with respect to their plausibility as a manifestation of endorsing the idea that some set theories are more plausible than others. The proposed multiverse account settles the pluralist’s dilemma, the dichotomy that there is a trade-off between the richness of mathematical ontology and the objectivity of mathematical truth. The view also extends and serves as an alternative position to Balaguer’s intention-based Platonism, from which he claims that a certain version of mathematical pluralism follows. (shrink)

The intended title was “Universe Oriented Ontology” or “Multiverse Oriented Ontology”, or “Universe or Multiverse Metaphysics”. I mention this as it gives an idea about the meaning and intention of the title and the work as well as the titles I considered and why I moved away from them to the present one. The sub-title provides a further hint towards the intentions of the work, namely: ” Beyond Earth- and Human-centricity’. I opted for ‘transcending’ rather than beyond, as (...) I am still in the process of describing the process of transcending and many of the ideas I am obliged to use from our conceptual system and practices are still earth- and anthropo-centered, And, they have not yet gone to a state beyond those two -isms. I say something about universe-centeredness, then about planet earth as point and frame of reference and anthropo-centricity. The socio-cultural practice of philosophy and the doing of philosophy is merely one of many human, social and cultural practices. I post different notions of philosophy by a number of writers, some of them philosophers. These notions are about their perceptions of what philosophy is. Few of them go into detail about the subject-matter of philosophy. No one really deal with the aims, purposes and objectives of the discipline and none deal with the nature of the doing of philosophy or philosophizing. Activities that I suggest resemble certain features of the processes of theorizing. I end with explorations of possible characteristics of original- and creative thinkers. I do this by mentioning a number of themes of meta-philosophy listed and described by Peter Suber. I make a number of comments in them and highlight aspects relevant to these type of thinkers. One find them of course in all disciplines and socio-cultural [racticesand disciplines be they the arts,humanities, sciences, etc. I am of course specifically concerned with original andcreative thinkers inthe Western tradition of philosophy. As I am a radical and absolute sceptic, I end with an article on this theme. It is said by everyone, for example Hume, Russell and Pascal, that such a radical position is psychologically impossible and that it cannot be lived 24/7. Pascal for example opted for believe or faith and he and a number of writers suggest that that is the only way out and the final position of radical sceptics. I disagree with him. (shrink)

Given recent scientific findings suggesting that our world is part of a multiverse, Leland Harper argues that we ought to abandon the idea of an active God in Judeo-Christian theism. This shift results in a more coherent, cohesive and, ultimately, better account of God than is currently offered by the Judeo-Christian monotheistic tradition.

"God may be a — humanly incomprehensible — eternal cosmic existence, intimately related to the endlessness of space, to the nature of the deepest common substance of matter and energy, to this common substance’s unceasing motion responsible for time, and to the basic laws of their allness, letting love transform this allness to an ordered Multiverse with a Soul: the — scientifically approachable — Soul of Multiverse inspired to guard these laws and equip their order with direction and (...) morals while imbuing the cosmos with the potential of lives evolving, at the right spatial and temporal distances, to embrace the sense of the divine, thus justifying the existence of God.”. (shrink)

The generic multiverse was introduced in [74] and [81] to explicate the portion of mathematics which is immune to our independence techniques. It consists, roughly speaking, of all universes of sets obtainable from a given universe by forcing extension. Usuba recently showed that the generic multiverse contains a unique definable universe, assuming strong large cardinal hypotheses. On the basis of this theorem, a non-pluralist about set theory could dismiss the generic multiverse as irrelevant to what set theory (...) is really about, namely that unique definable universe. Whatever one’s attitude towards the generic multiverse, we argue that certain impure proofs ensure its ongoing relevance to the foundations of set theory. The proofs use forcing-fragile theories and absoluteness to prove ${\mathrm {ZFC}}$ theorems about simple “concrete” objects. (shrink)

This chapter explores the place of neurodivergence in feminist, queer, abolitionist, and decolonial worldmaking with a focus on the history and reclamation of witchcraft. The first part of the chapter lays out a theoretical framework, organized around the concepts of “tending,” “esoterism,” and “multiverse,” that supports a method of “reading through” witchcraft to subjunctive esoterisms accompanying it. The second section examines the role of “madness” or “hysteria” in feminist accounts of witchcraft by Barbara Ehrenreich and Dierdre English, Silvia Federici, (...) and Kathleen Skott-Myhre, finding in them a “disjunctive” approach that downplays or disavows neurodivergence. The third section dwells with the poetics of JJJJJerome Ellis, whose Aster of Ceremonies offers a non-disjunctive mood for thinking about politics, knowledge, spirituality, and neurodivergence as co-constitutive of a world. The final section uses Ellis’s mood to speculatively make room for thinking about witchcraft’s history and future in a way that is feminist, spiritual, and affirming of neurodivergent worlding. (shrink)

In this article I go through the history of the notion of a multiverse, and compare how it has been used in non-fiction (in philosophy and natural science), and in science fiction. Within non-fiction I discuss, among others, modal realism and theories of branching space-time in metaphysics, and within natural science, the many worlds interpretation of quantum mechanics and the theories of cosmic inflation and braneworlds. In fiction I look (among other subjects) at Victorian precursors of the notion of (...) multiverse, Michael Moorcock’s multiverse, super-hero multiverses, and utopias and dystopias that make use of a multiverse. I also discuss the danger of nihilism raised by many versions of a theory of a multiverse. I also examine and critique, in the light of philosophy and natural science, the feasibility of some common tropes of this type of narrative—like that of a person meeting duplicates or counterparts when traveling through the multiverse. (shrink)

Multiverses are predictions based on theories. Focusing on each theory’s assumptions is key to evaluating a proposed multiverse. Although accepted theories of particle physics and cosmology contain non-intuitive features, multiverse theories entertain a host of “strange” assumptions classified as metaphysical topics such as: infinity, duplicate yous, hypothetical fields, more than three space dimensions, Hilbert space, advanced civilizations, and reality established by mathematical relationships. It is easy to confuse multiverse proposals because many divergent models exist. This overview defines (...) the characteristics of eleven popular multiverse proposals. The characteristics compared are: initial conditions, values of constants, laws of nature, number of space dimensions, number of universes, and fine tuning explanations. Future scientific experiments may validate selected assumptions; but until they do, proposals by philosophers may be as valid as theoretical scientific theories. (shrink)

In this article we analyze the method of forcing from a more philosophical perspective. After a brief presentation of this technique we outline some of its philosophical imports in connection with realism. We shall discuss some philosophical reactions to the invention of forcing, concentrating on Mostowski’s proposal of sharpening the notion of generic set. Then we will provide an overview of the notions of multiverse and the related philosophical debate on the foundations of set theory. In conclusion, we connect (...) this modern debate and Mostowski’s proposal, suggesting a way to analyze the notion of genericity within the framework of a multiverse structure. (shrink)

Recent advances in string theory and inflationary cosmology have led to a surge of interest in the possible existence of an ensemble of cosmic regions, or “universes”, among the members of which key physical parameters, such as the masses of elementary particles and the coupling constants, might assume different values. The observed values in our cosmic region are then attributed to an observer selection effect (the so-called anthropic principle). The assemblage of universes has been dubbed “the multiverse”. In this (...) paper we review the multiverse concept and the criticisms that have been advanced against it on both scientific and philosophical grounds. (shrink)

Some analytic philosophers of religion argue that theists should embrace the hypothesis of the multiverse to address the problem of evil and make the concept of a “best possible creation” plausible. I discuss what classical theists, such as Augustine, Anselm, and Aquinas, might make of the multiverse hypothesis including issues such as: the principle of plenitude, what a classical theist multiverse could look like, and how a classical theist multiverse could deal with the problem of evil (...) and the question of a best possible creation. (shrink)

We argue that Kraay's "theistic multiverse" response to the objections to theism [Kraay 2011] is unsuccessful as it simply shifts the problems leveled against theism from the level of possible worlds to the level of possible universes. Furthermore, when we restate the objections at the level of possible universes, we can show how Kraay's conclusion about the uniqueness of the theistic multiverse is undermined.

The multiverse hypothesis is one of the leading proposed explanations of cosmic fine‐tuning for life. One common objection to the multiverse hypothesis is that, even if it were true, it would not explain why this universe, our universe, is fine‐tuned for life. To think it would so explain is allegedly to commit “the inverse gambler's fallacy.” This paper presents what the inverse gambler's fallacy is supposed to be, then surveys the discussion of it in the philosophical literature of (...) the last 35 years. (shrink)

The set-theoretic multiverse has fundamentally reshaped contemporary founda tions of mathematics by overturning the dogma of a single, absolute universe of sets. While this pluralistic framework has vastly expanded the space of mathemati cal possibility, it has simultaneously exposed a foundational deficiency: the absence of an explicit and principled criterion of identity across universes. The multiverse generates plurality, but it does not, by itself, regulate identity. Building on the Co-Equal Structure Thesis (CEST) and its formal development, this paper (...) introduces the Axiom of Structural Identity (ASI) as a necessary law governing identity within and across set-theoretic universes. ASI grounds identity in the co-equal invariants of cardinality and ordinality, elevating a practice already implicit in contemporary set theory to the level of an explicit axiom. The central claim defended here is that ASI is not an optional philosophical refinement, but a structural requirement for the intelligibility of the multiverse itself. With ASI in place, plurality is preserved without arbitrariness, forcing ex tensions become structurally comparable, and the multiverse is transformed from an unconstrained proliferation of models into a disciplined structural cosmos. (shrink)

I discuss the multiverse response to fine-tuning arguments for theism. In particular, I focus on the 'this-universe objection' (Hacking 1987, White 2000): the contention that inference to a multiverse from fine-tuning commits the inverse gambler's fallacy. I contend that the objection is successful. But I leave open whether non-fine-tuning-related arguments for a multiverse—in particular, those from the existence of our universe or from self-locating evidence—may succeed. I then consider White's subsidiary thesis: if we know a multiverse (...) exists independently from fine-tuning, then fine-tuning is no longer evidence for theism. Following work from Rota and Metcalf, I show that that thesis is false. As such, even if a multiverse exists, the fine-tuning argument for theism is no worse for wear in a multiverse context than a single universe one. (shrink)

Width multiverse approaches to set theory (like Joel David Hamkins’ influential proposal in [Joel Hamkins The multiverse perspective in set theory, 2013]) reject the idea that there’s an intended width hierarchy of sets which contains ‘all possible subsets’ of the sets that it contains. In this paper, I raise an explanatory indispensability worry for the multiverse theorist and distinguish three different possible styles of response to this worry. I will argue that each approach faces some serious prima (...) facie problems. And I’ll suggest that, by clarifying their response to this puzzle about applications, multiverse theorists can helpfully clarify their proposals concerning pure mathematics. (shrink)

While the present information ecosystem is still undergoing a tsunami of repeated algorithmic superintelligence (ASI) achievement claims linked to the motif of the epistemic perpetuum mobile (EPM), will the laterally emerging and slowly propagating quantum ASI hype finally lead to a multiversal fear of missing out? Instead of adding novel entries to the already large enough and growing set of prophecies about the future promulgated in the deepfake era, this paper written for purposes of self-education utilizes a recent epistemic complexity (...) theory to answer the following natural scientific question: could the impossibility to build a multiversal ASI be amenable to experimental problematization? (shrink)

Recent developments in cosmology and particle physics have led to speculation that our universe is merely one of a multitude of universes. While this notion, the multiverse hypothesis, is highly contested as legitimate science, it has nonetheless struck many physicists as a necessary consequence of the effort to construct a final, unified theory. In Process and Reality (1929), his magnum opus, Alfred North Whitehead advanced a cosmology as part of his general metaphysics of process. Part of this project involved (...) a theory of cosmic epochs which bears a remarkable affinity to current cosmological speculation. This paper demonstrates how the basic framework of a multiverse theory is already present in Whitehead’s cosmology and defends the necessity of speculation in the quest for an explanatory description. (shrink)

The problem at stake: Can the scholastic notion of contingency be put in correspondence with a concept drawn from the conceptual equipment of the modern sciences in such a way that this time-honoured concept may be useful in our thinking about the world? It appears that the evolution of the idea constitutes something of a bridge connecting the medieval idea of contingency with the current scientific context, namely thinking about the place of humankind in the universe and the problem of (...) the beginning of the universe. The current scientific context in this respect is shaped by the concept of the multiverse. One can say that in current cosmological speculations, a single universe can be regarded as contingent, because it has no explanation, while the multiverse can be regarded as non-contingent, because it does not need any explanation. We discuss the correctness of this reasoning together with certain connected theological aspects. (shrink)

In this paper I apply the concept of _inter-Model Inconsistency in Set Theory_ (MIST), introduced by Carolin Antos (this volume), to select positions in the current universe-multiverse debate in philosophy of set theory: I reinterpret H. Woodin’s _Ultimate L_, J. D. Hamkins’ multiverse, S.-D. Friedman’s hyperuniverse and the algebraic multiverse as normative strategies to deal with the situation of de facto inconsistency toleration in set theory as described by MIST. In particular, my aim is to situate these (...) positions on the spectrum from inconsistency avoidance to inconsistency toleration. By doing so, I connect a debate in philosophy of set theory with a debate in philosophy of science about the role of inconsistencies in the natural sciences. While there are important differences, like the lack of threatening explosive inferences, I show how specific philosophical positions in the philosophy of set theory can be interpreted as reactions to a state of inconsistency similar to analogous reactions studied in the philosophy of science literature. My hope is that this transfer operation from philosophy of science to mathematics sheds a new light on the current discussion in philosophy of set theory; and that it can help to bring philosophy of mathematics and philosophy of science closer together. (shrink)

In a recent paper in this journal, Jason Megill (2011) offers an innovative meta-argument which deploys considerations about multiple universes in an effort to block all arguments from evil. In what follows, I contend that Megill has failed to establish a key premise in his meta-argument. I also offer a rival account of the effect of multiverse models on the debate about evil.

Cosmological models that invoke a multiverse - a collection of unobservable regions of space where conditions are very different from the region around us - are controversial, on the grounds that unobservable phenomena shouldn't play a crucial role in legitimate scientific theories. I argue that the way we evaluate multiverse models is precisely the same as the way we evaluate any other models, on the basis of abduction, Bayesian inference, and empirical success. There is no scientifically respectable way (...) to do cosmology without taking into account different possibilities for what the universe might be like outside our horizon. Multiverse theories are utterly conventionally scientific, even if evaluating them can be difficult in practice. (shrink)

A debated issue in the mathematical foundations in at least the last two decades is whether one can plausibly argue for the merits of treating undecidable questions of mathematics, e.g., the Continuum Hypothesis (CH), by relying on the existence of a plurality of set-theoretical universes except for a single one, i.e., the well-known set-theoretical universe V associated with the cumulative hierarchy of sets. The multiverse approach has some varying versions of the general concept of multiverse yet my intention (...) is to primarily address ontological multiversism as advocated, for instance, by Hamkins or Väätänen, precisely for the reason that they proclaim, to the one or the other extent, ontological preoccupations for the introduction of respective multiverse theories. Taking also into account Woodin’s and Steel’s multiverse versions, I take up an argumentation against multiversism, and in a certain sense against platonism in mathematical foundations, mainly on subjectively founded grounds, while keeping an eye on Clarke-Doane’s concern with Benacerraf’s challenge. I note that even though the paper is rather technically constructed in arguing against multiversism, the non-negligible philosophical part is influenced to a certain extent by a phenomenologically motivated view of the matter. (shrink)

The multiverse hypothesis is growing in popularity among theistic philosophers because some view it as the preferable way to solve certain difficulties presented by theistic belief. In this paper, I am concerned specifically with its application to Rowe’s problem of no best world, which suggests that God’s existence is impossible given the fact that the world God actualizes must be unsurpassable, yet for any given possible world, there is one greater. I will argue that, as a solution to the (...) problem of no best world, the multiverse hypothesis fails. To defend my thesis, I will first define the multiverse hypothesis and articulate the problem of no best world and how the multiverse hypothesis is thought to solve it. I will then show that the solution fails by articulating two problems that have been mentioned, but not developed, in the literature—what I call the problem of no highest standard and the problem of multiverse cardinality. In each case, after articulating the problem, I will offer possible responses to the problem and show why those responses are inadequate. (shrink)

Several philosophers contend that a theistic multiverse (TM), a collective of all possible universes worthy of divine creation, is the best possible world, and that this fact proves helpful to theism in the face of various objections. Almeida (2017), however, argues that proposed theories of TM are incoherent. After presenting TM, I distinguish three objections Almeida raises against it: God cannot create universes corresponding to other possible worlds, we cannot know whether TM includes only worthwhile universes, and TM violates (...) the principle of plenitude. I show that none of these undermine TM’s potential to address various objections to theism. (shrink)

The objective of this paper is analyzing to which extent the multiverse hypothesis provides a real explanation of the peculiarities of the laws and constants in our universe. First we argue in favor of the thesis that all multiverses except Tegmark’s “mathematical multiverse” are too small to explain the fine tuning, so that they merely shift the problem up one level. But the “mathematical multiverse" is surely too large. To prove this assessment, we have performed a number (...) of experiments with cellular automata of complex behavior, which can be considered as universes in the mathematical multiverse. The analogy between what happens in some automata (in particular Conway’s “Game of Life") and the real world is very strong. But if the results of our experiments can be extrapolated to our universe, we should expect to inhabit—in the context of the multiverse—a world in which at least some of the laws and constants of nature should show a certain time dependence. Actually, the probability of our existence in a world such as ours would be mathematically equal to zero. In consequence, the results presented in this paper can be considered as an inkling that the hypothesis of the multiverse, whatever its type, does not offer an adequate explanation for the peculiarities of the physical laws in our world. (shrink)

We develop an untyped framework for the multiverse of set theory. $\mathsf {ZF}$ is extended with semantically motivated axioms utilizing the new symbols $\mathsf {Uni}(\mathcal {U})$ and $\mathsf {Mod}(\mathcal {U, \sigma })$, expressing that $\mathcal {U}$ is a universe and that $\sigma $ is true in the universe $\mathcal {U}$, respectively. Here $\sigma $ ranges over the augmented language, leading to liar-style phenomena that are analyzed. The framework is both compatible with a broad range of multiverse conceptions and (...) suggests its own philosophically and semantically motivated multiverse principles. In particular, the framework is closely linked with a deductive rule of Necessitation expressing that the multiverse theory can only prove statements that it also proves to hold in all universes. We argue that this may be philosophically thought of as a Copernican principle that the background theory does not hold a privileged position over the theories of its internal universes. Our main mathematical result is a lemma encapsulating a technique for locally interpreting a wide variety of extensions of our basic framework in more familiar theories. We apply this to show, for a range of such semantically motivated extensions, that their consistency strength is at most slightly above that of the base theory $\mathsf {ZF}$, and thus not seriously limiting to the diversity of the set-theoretic multiverse. We end with case studies applying the framework to two multiverse conceptions of set theory: arithmetic absoluteness and Joel D. Hamkins’ multiverse theory. (shrink)

This paper establishes the final synthesis of the Co-Equal Structure Thesis (CEST) and the Axiom of Structural Identity (ASI), moving beyond model-relative pluralism toward the concept of the Set-Theoretic Multiverse as a Concrete Universal. We demonstrate that local identity definitions are mathematically insufficient due to path-dependence and the subsequent global instability in forcing chains, a failure that necessi tates a systemic totality. By characterizing Structural Negentropy as an invariance condition on transitions, we show (at the meta-inferential level) that mathematical (...) reason is essentially trans-model. We conclude that the Absolute Idea is realized in the identity of the Objectified Proof (Set) and the Subjectified Structure (Proof-Skeleton). We emphasize that this does not imply that sets are reducible to proofs, but that their actuality is intelligible only through invariant inferential structure. (shrink)

Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the (...) class='Hi'>multiverse seems to be crucial, and show how one may provide responses to Maddy's concerns based on a careful analysis of 'multiverse practice'. (shrink)

This paper argues that multiverses that expand in a divine meta-time are plausible candidates for unsurpassable worlds. Proponents of the exhaustive theistic multiverse claim that the best possible world is a world in which god creates all and only the universes that are worth being created. The cardinality objection, one of the most pressing objections against this conception of an unsurpassable world, is based on the assumptions that for every cardinal number κ, there can be more than κ creation-worthy (...) universes and that necessarily, there are not proper class many universes. This paper introduces expanding theistic multiverses as novel candidates for unsurpassable worlds. In an expanding theistic multiverse creation takes place in a divine meta-time. This allows to hold that at no point in meta-time there are more than proper-class many universes, but every cardinal number κ is such that at some point in meta time there will be more than κ universes. These features of expanding theistic multiverses will be shown to defuse the cardinality objection if it is assumed that the expanding multiverses have an expansionist metaphysics of meta-time according to which the domain of universes increases when meta-time passes. (shrink)

Abstract This paper develops a structural analysis of proofs in ZFC that distinguishes between their inferential identity and their ordinal modes of justification across models of set theory. While forcing extensions preserve the validity of proofs, they disperse the ordinal grounds on which those proofs can be justified. I introduce the notion of a proof skeleton, isolating the inferential core of a proof from its semantic parameters, and prove that this skeleton is invariant under forcing. I then define the ordinal (...) support spectrum of a proof and measure its dispersion via an entropic invariant. My main technical result establishes an upper bound on this entropy in terms of the proof-theoretic complexity of the proof itself. These results show that the set-theoretic multiverse is neither chaotic nor ar bitrary: dispersion is real but controlled. The multiverse supports a form of dis tributed rationality in which proofs retain their identity while acquiring a modal profile that cannot be expressed within low-entropy universes such as L. (shrink)

Our universe seems to be miraculously fine-tuned for life. Multiverse theories have been proposed as an explanation for this on the basis of probabilistic arguments, but various authors have objected that we should consider our total evidence that this universe in particular has life in our inference, which would block the argument. The debate thus crucially hinges on how Bayesian background and evidence are distinguished and on how indexical or demonstrative terms are analysed. The aim of this article is (...) to take a step back and examine these various aspects of Bayesian reasoning and how they affect the arguments. The upshot is that there are reasons to resist the fine-tuning argument for the multiverse, but the “this-universe-objection” is not one of them. (shrink)

Problems in moral philosophy and philosophy of religion can take on new forms in light of contemporary physical theories. Here we discuss how the problem of evil is transformed by the Everettian ‘Many-Worlds’ theory of quantum mechanics. We first present an Everettian version of the problem and contrast it to the problem in single-universe physical theories such as Newtonian mechanics and Bohmian mechanics. We argue that, pace Turner and Zimmerman, the Everettian problem of evil is no more extreme than the (...) Bohmian one. The existence and multiplicity of (morally) terrible branches in the Everettian multiverse in contrast to the mere possibility of them in the Bohmian universe does not entail there is ‘more evil’ in the former than in the latter. Low probability in the Bohmian case and low branch weight in the Everettian case should modulate how we respond to them in exactly the same way. We suggest that the same applies to the divine decision of creating an Everettian multiverse. For an empirically adequate Everettian quantum mechanics that justifies the Born rule, there is no special problem of evil. In order for there to be a special Everettian problem of evil, the Everettian interpretation must already have been exposed to decisive refutation. In the process, we hope to show how attention to the details of physical and metaphysical theories can and should impact the way we think about problems in moral philosophy and philosophy of religion. (shrink)

David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.

Suppose that reality consists of parallel universes of every variety imaginable. No path through space and time leads from one to another, and each universe is causally isolated from the rest. Some physicists believe a ‘multiverse’ hypothesis not terribly distant from this one simplifies quantum mechanics and provides an elegant explanation of why our universe has its particular laws. Suppose as science advances we come to accept the multiverse hypothesis, so construed.

In the Marvel Cinematic Universe (MCU), according to the Ancient One, magic is created by drawing energy from the other dimensions of the multiverse. This sounds like a concept from science fiction, but the idea that people are living in a vast multiverse is very possibly science fact. A recurring and especially important theme in Doctor Strange is the role that human beings are supposed to play in the universe. The concept of the multiverse is well established (...) in the Marvel comics and has officially been introduced into the MCU, and the way it is introduced touches on central issues in the philosophy of physics. Quantum mechanics is hands‐down one of the greatest accomplishments of science. Understanding the apparent collapse of the wave function upon observation is the core of the measurement problem. There are different ways of explaining this, which are called “interpretations” of quantum mechanics. (shrink)

According to the Self-Indication Assumption (SIA), learning that you are an observer should make you more confident in hypotheses that posit more observers. SIA suggests a straightforward argument for multiverse hypotheses. The argument is of distinctive interest because it supports multiverse hypotheses using a mundane observation, not fine-tuning, quantum mechanics, or modal metaphysics. However, SIA is controversial: whereas many worry that SIA yields overly strong armchair verdicts about matters that call for empirical investigation, others are drawn to SIA (...) as an antidote to the doomsday argument. This chapter contests the standard story about SIA’s motivations and problems and offers an alternative approach to SIA: we argue that SIA can be understood as a form of induction, that we should compromise between different versions of SIA, and that this approach offers solutions to problems for SIA and an appropriately modest version of the SIA argument for multiverse hypotheses. (shrink)