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)

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 progression of theories suggested for our world, from ego- to geo- to helio-centric models to universe and multiverse theories and beyond, shows one tendency: The size of the described worlds increases, with humans being expelled from their center to ever more remote and random locations. If pushed too far, a potential theory of everything (TOE) is actually more a theories of nothing (TON). Indeed such theories have already been developed. I show that including observer localization into such (...) theories is necessary and sufficient to avoid this problem. I develop a quantitative recipe to identify TOEs and distinguish them from TONs and theories in-between. This precisely shows what the problem is with some recently suggested universal TOEs. (shrink)

Some scientists or philosophers argue that multiverse theories are unfalsifiable and thus not scientific. However, some advocates of multiverse theories have recently argued that although the multiverse is not observable, multiverse theories are indeed falsifiable in principle. Therefore, they share similar features with a conventional scientific theory. On the other hand, the proposals of an epistemic shift and nonempirical theory assessment have possibly revived the discussions of the scientific nature of multiverse theories. In (...) this article, I revisit the falsifiable arguments made by the advocates of multiverse theories and show that these arguments do not justify arguing the scientific nature of such theories. Moreover, even if we accept the proposals of the epistemic shift and the nonempirical theory assessment, I argue that multiverse theories still cannot pass or satisfy the required assessments based on the new theoretical virtues and the nonempirical arguments. (shrink)

This article has two main parts. The first part argues in favor of a multiverse theodicy. God has created our particular universe because it contains unique goods. While God could have made our universe better, that would in fact have turned our universe into another universe, which God has also created. Our universe remains as it is to actualize its specific goals. The second part uses this basis to defend why God's revelation is so vague. It could have been (...) clearer, which again would have turned our universe into another universe, which also exists. Since our kind of independent universe with vague revelation actualizes unique goods, God has created our universe where the vague revelation serves specific purposes. (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)

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.

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.

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)

From a physical point of view, the no-boundary Hartle-Hawking model put forward in 1983 was an attempt to demonstrate that the incorporation of quantum effects into the general theory of relativity would solve the problem of singularities that make the theory of relativity incomplete. This was achieved by imposing the so called “no-boundary conditions” whereby the Universe could emerge with non-zero probability from a non-existing state. Stephen Hawking quickly turned this result into a metaphysical claim that physical laws (...) explained away the necessity of the Divine intervention at the origin of the Universe. This paper offers an inquiry into the line of arguments presented by Hawking and Mlodinow in their book The Grand Design and supported with the claim that the yet unknown versionof the superstring theory, the M-theory, is an ultimate theory of the Universe. The upshot of the paper is that although the argument in the Grand Design relies on the newer achievements of physics embedded in the controversial multi-verse setting, it does not escape the question of the origin of the most general laws of physics that bring the Universe into existence. (shrink)

Finetuning and Naturalness are extra-empirical theory assessments that reflect our expectation how scientific theories should provide an intuitive understanding about the foundations underlying the observed phenomena. Recently, the absence of new physics at the LHC and the theoretical evidence for a multiverse of alternative physical realities, predicted by our best fundamental theories, have casted doubts about the validity of these concepts. In this essay we argue that the discussion about Finetuning should not predominantly concentrate on the desired features (...) a fundamental theory is expected to have, but rather on the question what a theory needs to qualify as fundamental in the first place. By arguing that a fundamental description of the Universe should possess zero entropy, we develop a ‘holistic’ concept for the most fundamental layer of reality: The fundamental description of the Universe is the Universe itself, understood as an entangled quantum state. Adopting a universal applicability of quantum mechanics, in this framework the behavior of subsystems can be understood as the perspectival experience of an entangled quantum Universe perceived through the “lens of decoherence”. In this picture the fundamental reality is non-local, and finetuned coincidences in effective theories may be understood in a way similar to EPR-correlations. This notion provides a fresh view on the topic of Naturalness and Finetuning since it suggests that Finetuning problems and hints for anthropic explanations are an artifact of theories building up on subsystems rather than on the fundamental description. Recent work in quantum gravity aiming at an understanding of spacetime geometry from entanglement entropy could be interpreted as a first sign of such a paradigm shift. (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)

The article analyzes the problem of physical theory nature and its criteria in the context of several concepts of modern physics. Such physical concepts allow multiple possible universes (the last usually happens to be a random consequence of the theory). Since the study requires several universe models, which basic principles (physical laws) can vary, the two theories have become the objects of analysis: the first, which includes the concept of eternal inflation, the second – the string cosmology (the (...) string landscape). Both theories allow for a large variation of physical laws (no matter, whether these are fundamentally different physical laws or different versions of the same basic principles). The amount of dark energy (cosmological constant) has been selected as a physical law parameter, changing its value in possible universes.The analysis of the physical theories, which allow a multiplicity of universes, has shown that the standard requirements for the theory, which connect its veracity with the criteria of observability and the need for validation of our universe basic principles, are not entirely consistent. Theoretical physics is moving towards the formulization of models that become a real (in some cases, apparently irresistible) challenge for experimental verification. The article proves that such verification probably can not be required in several physical theories, since, in particular, the postulation of this kind of connection between theory and reality is no more than a manifestation of anthropocentrism. However, the theory can trace more general grounds that lie beyond the scope of human observation. (shrink)

This paper has two aims. First, we argue that Wittgenstein’s notion of petrification can be used to explain phenomena in advanced mathematics, sometimes better than more popular views on mathematics, such as formalism, even though petrification usually suffers from a diet of examples of a very basic nature (in particular a focus on addition of small numbers). Second, we analyse current disagreements on the absolute undecidability of CH under the notion of petrification and hinge epistemology. We argue that in contemporary (...) set theory the usage of construction techniques for set-theoretic models in which the Continuum Hypothesis holds and those in which it fails have petrified into the normative demand that CH remain undecidable. That is, the continuous and successful practices involving the construction of various set-theoretic models now act as a normative hinge shared among practitioners, i.e., have normative force in the discipline. However, not all hinges are universal, which is why we find disagreements in set theory. We will show that this is a refinement of, and partially conflicts with, the arguments presented by set theorist Joel David Hamkins. (shrink)

Anthropic arguments in multiverse cosmology and string theory rely on the weak anthropic principle (WAP). We show that the principle, though ultimately a tautology, is nevertheless ambiguous. It can be reformulated in one of two unambiguous ways, which we refer to as WAP_1 and WAP_2. We show that WAP_2, the version most commonly used in anthropic reasoning, makes no physical predictions unless supplemented by a further assumption of "typicality", and we argue that this assumption is both misguided and (...) unjustified. WAP_1, however, requires no such supplementation; it directly implies that any theory that assigns a non-zero probability to our universe predicts that we will observe our universe with probability one. We argue, therefore, that WAP_1 is preferable, and note that it has the benefit of avoiding the inductive overreach characteristic of much anthropic reasoning. (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)

Alfred North Whitehead advanced a version of multiverse theory in 1929 that bears a remarkable affinity to the revolutionary ideas of current cosmological speculation. He postulated his theory for some of the very same reasons as those advanced today by leading cosmologists and physicists such as Martin Rees, Lee Smolin, Stephen Hawking, Max Tegmark and Steven Weinberg, but his theory has largely gone unnoticed.

Jim Stone has argued that a multiversal version of Modal Realism together with Counterpart Theory cannot account for a certain intuitive possibility. Roughly, it is the possibility that all free moral choices of a certain sort are the right choices in all cases in the multiverse. The present work offers an explanation of how the metaphysics in question can account for the intuitive possibility in question.

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)

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)

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)

The paper is devoted to the problem of describing reality in the language of mathematics and logic in connection with intellectual intuition. The question raised is how the basic requirements of mathematical theory and logic will change if some of the multiverse models of modern physics are taken as the basis. Mathematics is considered in the context of various historical approaches. It is shown that some of the well-known requirements of a formal theory (such as consistency) may (...) begin to play a different role if the multiverse hypothesis is accepted. In the framework of theories based on the idea of multiple worlds, the logical consequence, the natural law of Duns Scotus, the law of excluded middle, and other well-known facts of classical logic which in some cases cause controversy due to their intuitive unacceptability are resolved. The paper discusses an approach based on paraconsistent logics: such logics can be considered the first to correspond to multiverse theories. (shrink)

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)

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)

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)

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)

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)

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)

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)

We have, then, a theory which is objectively causal and continuous, while at the same time subjectively probabilistic and discontinuous. It can lay claim to a certain completeness, since it applies to all systems, of whatever size, and is still capable of explaining the appearance of the macroscopic world. The price, however, is the abandonment of the concept of the uniqueness of the observer, with its somewhat disconcerting philosophical implications.

Presents a comprehensive history of multiverse theory, reviewing the discoveries that shaped astrophysicists' current consensus view while showing that the multiverse is able to be explained entirely in naturalistic terms.

This paper explores the idea that human consciousness perceives itself as the "main character" due to the structure of the multiverse. If every decision branches into a new reality, then an individual’s memory and experience are biased toward the timeline where they continue to exist. This could lead to a form of subjective immortality, where consciousness shifts to realities where survival and satisfaction persist. The implications of this perspective are examined through the lenses of quantum mechanics, philosophy, and cognitive (...) psychology. (shrink)

In recent decades, there has been astonishing growth in scientific theorizing about multiverses. Once considered outré or absurd, multiple universe theories appear to be gaining considerable scientific respectability. There are, of course, many such theories, including (i) Everett’s (1957) many worlds interpretation of quantum mechanics, defended by Deutsch (1997) and others; (ii) Linde’s (1986) eternal inflation view, which suggests that universes form like bubbles in a chaotically inflating sea; (iii) Smolin’s (1997) fecund universe theory, which proposes that universes are (...) generated through black holes; (iv) the cyclic model, recently defended using string/M theory by Steinhardt and Turok (2007), which holds that distinct universes are formed in a never-ending sequence of Big Bangs and Big Crunches; and (v) Tegmark’s (2007) “Level IV” multiverse, which contains many universes governed by distinct mathematical and scientific laws. While not all of these preclude each other, the details and implications of each one are hotly contested. In one area within the philosophy of religion (the debate concerning the “fine-tuning” argument), scientific multiverse theories are widely held to be hostile to theism. This is because such theories appear to account for the relevant data – the biophilic parameters of the universe we inhabit – without appeal to an intelligent designer. Yet, in recent years, several philosophers and one physicist have offered reasons for thinking that if theism is true, the actual world comprises (or probably comprises) many universes. I first set out some requirements – both scientific and otherwise – for such a theory. I then survey some problems such theories are held to face, and some prospects they are thought to have. Finally, I examine arguments both for and against the claim that multiverse theories can help theists respond to the problem of evil. I conclude that such theories advantage neither the theist or the atheist in the debate about evil: they merely require reframing arguments from evil. (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 (2016) and Zimmerman (2017), 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)

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)

In recent decades, scientific theories have postulated the existence of many universes beyond our own. The details and implications of these theories are hotly contested. Some philosophers argue that these scientific models count against the existence of God. Others, however, argue that if God exists, a multiverse is precisely what we should expect to find. Moreover, these philosophers claim that the idea of a divinely created multiverse can help believers in God respond to certain arguments for atheism. These (...) proposals are, of course, also extremely controversial. This volume collects together twelve newly published essays – two by physicists, and ten by philosophers – that discuss various aspects of this issue. Some of the essays support the idea of a divinely created multiverse; others oppose it. Scientific, philosophical, and theological issues are considered. (shrink)

The Multiverse Thesis is a proposed solution to the Grandfather Paradox. It is popular and well promulgated, found in fiction, philosophy and (most importantly) physics. I first offer a short explanation on behalf of its advocates as to why it qualifies as a theory of time travel (as opposed to mere 'universe hopping'). Then I argue that the thesis nevertheless has an unwelcome consequence: that extended objects cannot travel in time. Whilst this does not demonstrate that the (...) class='Hi'>Multiverse Thesis is false, the consequence should give pause for concern. Even if it does not lead one to reject the thesis, I briefly detail some reasons to think it is interesting nonetheless. (shrink)

Penelope Maddy has recently addressed the set-theoretic multiverseset-theoretic multiverse, and expressed reservations on its status and merits Foundations of mathematics. Essays in honor of W. Hugh Woodin’s 60th birthday. Contemporary mathematics. American Mathematical Society, Providence, pp. 289–322, 2017). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalismset-theoretic naturalism. I first distinguish three main forms of ‘multiversism’multiversism, and then I proceed to analyse MaddyMaddy’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 multiverse seems to be crucial, and show how one may provide responses to MaddyMaddy’s concerns based on a careful analysis of ‘multiverse practice’. (shrink)

Few topics in cosmology are as hotly debated as the Multiverse: for some it is untestable and hence unscientific; for others it is unavoidable and a natural extension of previous science. A third position is that it is seen to follow from other theories, but those other theories might themselves be seen as too speculative. The idea of fine-tuning has a similar status. Some of this disagreement might be due to misunderstanding, in particular the degree to which probability distributions (...) are necessary to interpret conclusions based on the Multiverse, especially with regard to the Anthropic Principle. I present undisputed facts, discuss some common misunderstandings, and investigate the role played by probability. The Multiverse is perhaps an important component necessary for interpreting cosmological and other physical parameters. (shrink)

Does the claimed fine-tuning of the constants of nature for life give reason to think that there are many other universes in which the constants have different values? Or does the inference from fine-tuning to a multiverse commit what Hacking calls the inverse gambler’s fallacy? The present paper considers two fine-tuning problems that seem promising to consider because they are in many respects analogous to the problem of the fine-tuned constants. Reasoning that parallels the inference from fine-tuning to a (...) multiverse seems prima facie adequate in these problems. However, it turns out that in both cases there are independent empirical reasons to believe the hypotheses that are analogous to the multiverse hypothesis. In the absence of such evidence, it would be coherent to raise the inverse gambler’s fallacy charge against the inference from fine-tuning to these multiverse-type hypotheses. In response to this finding, I suggest taking the possibility seriously that established standards of rationality may not allow us to decide whether the inference from fine-tuning to a multiverse is fallacious or not. The paper concludes by sceptically assessing the prospects for obtaining independent empirical evidence for concrete multiverse theories. (shrink)

If ZFC is consistent, then the collection of countable computably saturated models of ZFC satisfies all of the Multiverse Axioms of Hamkins.

This paper critically examines two arguments against the generic multiverse, both of which are due to W. Hugh Woodin. Versions of the first argument have appeared a number of times in print, while the second argument is relatively novel. We shall investigate these arguments through the lens of two different attitudes one may take toward the methodology and metaphysics of set theory; and we shall observe that the impact of these arguments depends significantly on which of these attitudes (...) is upheld. Our examination of the second argument involves the development of a new model for Steel’s multiverse theory, which is delivered in the Appendix. (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 (...) 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)

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)

In extracting predictions from theories that describe a multiverse, we face the difficulty that we must assess probability distributions over possible observations, prescribed not just by an underlying theory, but by a theory together with a conditionalization scheme that allows for selection effects. This means we usually need to compare distributions that are consistent with a broad range of possible observations, with actual experimental data. One controversial means of making this comparison is by invoking the 'principle of (...) mediocrity': that is, the principle that we are typical of the reference class implicit in the conjunction of the theory and the conditionalization scheme. In this paper, I quantitatively assess the principle of mediocrity in a range of cosmological settings, employing 'xerographic distributions' to impose a variety of assumptions regarding typicality. I find that for a fixed theory, the assumption that we are typical gives rise to higher likelihoods for our observations. If, however, one allows both the underlying theory and the assumption of typicality to vary, then the assumption of typicality does not always provide the highest likelihoods. Interpreted from a Bayesian perspective, these results support the claim that when one has the freedom to consider different combinations of theories and xerographic distributions, one should favor the framework that has the highest posterior probability; and then from this framework one can infer, in particular, how typical we are. In this way, the invocation of the principle of mediocrity is more questionable than has been recently claimed. (shrink)

The forcing method is a powerful tool to prove the consistency of set-theoretic assertions relative to the consistency of the axioms of set theory. Laver’s theorem and Bukovský’s theorem assert that set-generic extensions of a given ground model constitute a quite reasonable and sufficiently general class of standard models of set-theory.In Sects. 2 and 3 of this note, we give a proof of Bukovsky’s theorem in a modern setting ). In Sect. 4 we check that the multiverse (...) of set-generic extensions can be treated as a collection of countable transitive models in a conservative extension of ZFC. The last section then deals with the problem of the existence of infinitely-many independent buttons, which arose in the modal-theoretic approach to the set-generic multiverse by Hamkins and Loewe :1793–1817, 2008). (shrink)