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.

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)

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)

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)

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)

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-Friedman :77–96, 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)

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, 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)

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)

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.

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)

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 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)

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)

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)

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)

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)

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)

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)

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)

Privileged-perspective realism (PPR) is a version of metaphysical realism that takes certain irreducibly perspectival facts to be partly constitutive of reality. PPR asserts that there is a single metaphysically privileged standpoint from which these perspectival facts obtain. This chapter discusses several views that fall under the category of privileged-perspective realism. These include presentism, which is PPR about tensed facts, and non-multiverse interpretations of quantum mechanics, which the chapter argues, constitute PPR about world-indexed facts. Using the framework of the bird (...) perspective and the frog perspective, it argues that PPR views methodologically treat the frog perspective as metaphysically primary. This chapter considers case studies of metaphysical interpretations of special relativity and quantum mechanics in order to demonstrate that such motivations for PPR are non-naturalistic. Further, it considers psychological factors that motivate the appeal of PPR views and offers naturalistic explanations of why we should not expect them to produce an adequate metaphysics of science. (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, 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)

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)

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)

I present and defend an “indexical” version of the Fine-Tuning Argument. I begin by outlining the dialectic between the Fine-Tuning Argument, the Multiverse Objection, and the This-Universe Reply. Next, I sketch an indexical fine-tuning argument and defend it from two new objections. Then, I show that such an argument is immune to the Multiverse Objection. I explain how a further augmentation to the argument allows it to avoid an objection I call the “Indifference Objection.” I conclude that my (...) indexical version of the Fine-Tuning Argument is no less cogent than the standard version, and yet it is immune to the Multiverse Objection. (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)

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.

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 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)

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 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)

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)

In this paper, an evolutionary multiverse argument against naturalism is presented: E1. In an evolutionary multiverse, phenomena have variable evolutionary ages. E2. After some time T, the development of the empirical sciences will be evolutionarily conserved. E3. The phenomena with an evolutionary age above T are methodologically supernatural. Entities are classified according to whether they are physical and spatiotemporal, causally efficacious, and either observed by or explanatorily necessary for the empirical sciences. While the conjunction of and is taken (...) to be sufficient for existence in reality, the negation of defines methodological supernaturalness. EMAAN uses a generalization of evolutionary theory, namely cosmological natural selection, to argue that phenomena evolve that fulfill conditions and, but not. This shows that methodologically supernatural phenomena have a clear epistemology according to a theory that is grounded in the commitments of naturalism. Supernatural phenomena are not observed by the empirical sciences because the empirical sciences themselves are supernaturally guided and predestined to develop according to an evolutionarily conserved plan. In spite of this scientific plan, there is room for afterlives and supernaturality in the everyday experience. (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.

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.

Timothy O’Connor and Philip Woodward defend a version of a compositional theory, according to which an incarnate deity has two natures, each of which is a distinct component of its being. They then extend this model to permit multiple incarnations. Finally, they consider an objection to this model based on the theological idea that Christ’s work is necessary for ushering in a united community of all divine-image-bearing creatures. In response, they speculate that no such all-encompassing community would be possible, given (...) the vast differences between such creatures. Accordingly, they speculate that each incarnation could help to bring about a unified community of the relevant sort of divine-image-bearing creatures, and that each of these communities would, in its own way, participate in the common goal of union with God. (shrink)

"Methodological Solipsism and the Multiverse" defends the many-universes interpretation of quantum physics, but draws attention to a major philosophical obstacle to the interpretation's acceptance: the question of why, if there are many universes, all on a par with one another, at a particular time the 'I' is manifest in only one. This is known as the 'preferred basis' problem. The so-called methodological solipsism approach, introduced by Driesch and employed by philosophers, such as Putnam and Fodor, is used to answer (...) the question. (shrink)

Beginning with ancient Atomist and Stoic philosophies, Mary-Jane Rubenstein links contemporary models of the multiverse to their forerunners and explores their current emergence.

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)

In the absence of a fundamental theory that precisely predicts values for observable parameters, anthropic reasoning attempts to constrain probability distributions over those parameters in order to facilitate the extraction of testable predictions. The utility of this approach has been vigorously debated of late, particularly in light of theories that claim we live in a multiverse, where parameters may take differing values in regions lying outside our observable horizon. Within this cosmological framework, we investigate the efficacy of top-down anthropic (...) reasoning based on the weak anthropic principle. We argue contrary to recent claims that it is not clear one can either dispense with notions of typicality altogether or presume typicality, in comparing resulting probability distributions with observations. We show in a concrete, top-down setting related to dark matter, that assumptions about typicality can dramatically affect predictions, thereby providing a guide to how errors in reasoning regarding typicality translate to errors in the assessment of predictive power. We conjecture that this dependence on typicality is an integral feature of anthropic reasoning in broader cosmological contexts, and argue in favour of the explicit inclusion of measures of typicality in schemes invoking anthropic reasoning, with a view to extracting predictions from multiverse scenarios. (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)

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)

The multiverse is a hypothesis for which there is no evidence, and perhaps can never be any evidence. It is only since 1998 that it has leapt off the blackboards of a few physicists doing esoteric mathematics and lodged itself in the popular imagination. As is the way with popular science, it is easy to move from speculating that there might have been more than one big bang to proceeding on the basis that there has been more than one (...) big bang. (shrink)