It is impossible to deduce the properties of a strongly emergent whole from a complete knowledge of the properties of its constituents, according to C. D. Broad, when those constituents are isolated from the whole or when they are constituents of other wholes. Elanor Taylor proposes the Collapse Problem. Macro-level property p supposedly emerges when its micro-level components combine in relation r. However, each component has the property that it can combine with the others in r to produce p. (...) Broad’s nondeducibility criterion is not met. This article argues that the amount of information required for r is physically impossible. Strong Emergence does not collapse. But the Collapse Problem does. Belief in Strong Emergence is strongly warranted. Strong Emergence occurs whenever it is physically impossible to deduce how components, in a specific relation, would combine to produce a whole with p. Almost always, that is impossible. Strong Emergence is ubiquitous. Word counts. (shrink)

In recent years the doctrine of divine simplicity has become a topic of interest in the philosophical theological community. In particular, the modal collapse argument against divine simplicity has garnered various responses from proponents of divine simplicity. Some even claiming that the modal collapse argument is invalid. It is our contention that these responses have either misunderstood or misstated the argument, and have thus missed the force of the objection. Our main aim is to clarify what the modal collapse argument (...) in fact says, and explain why the recent responses do not succeed. In order to argue our case, we will proceed in several steps. First, we aim to systematically articulate the doctrine of divine simplicity. Second, articulate the Christian conviction that God is free to create any feasible world or no world at all. Third, argue that divine simplicity suffers a modal collapse and thus undermines God's freedom. Fourth, respond to potential objections to modal collapse. Fifth, we offer some concluding remarks. (shrink)

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many (...) authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory. (shrink)

Wavefunction collapse models modify Schrödinger's equation so that it describes the rapid evolution of a superposition of macroscopically distinguishable states to one of them. This provides a phenomenological basis for a physical resolution to the so-called “measurement problem.” Such models have experimentally testable differences from standard quantum theory. The most well developed such model at present is the Continuous Spontaneous Localization (CSL) model in which a universal fluctuating classical field interacts with particles to cause collapse. One “side effect” of (...) this interaction is that the field imparts energy to the particles: experimental evidence on this has led to restrictions on the parameters of the model, suggesting that the coupling of the classical field to the particles must be mass-proportional. Another “side effect” is that the field imparts momentum to particles, causing a small blob of matter to undergo random walk. Here we explore this in order to supply predictions which could be experimentally tested. We examine the translational diffusion of a sphere and a disc, and the rotational diffusion of a disc, according to CSL. For example, we find that the rms distance an isolated 10−5 cm radius sphere diffuses is ≈(its diameter, 5 cm) in (20 sec, a day), and that a disc of radius 2 ⋅ 10−5 cm and thickness 0.5 ⋅ 10−5 cm diffuses through 2πrad in about 70 sec (this assumes the “standard” CSL parameter values). The comparable rms diffusions of standard quantum theory are smaller than these by a factor 10−3±1. It is shown that the CSL diffusion in air at STP is much reduced and, indeed, is swamped by the ordinary Brownian motion. It is also shown that the sphere's diffusion in a thermal radiation bath at room temperature is comparable to the CSL diffusion, but is utterly negligible at liquid He temperature. Thus, in order to observe CSL diffusion, the pressure and temperature must be low. At the low reported pressure of 5 ⋅ 10−17 Torr, achieved at 4.2°K, the mean time between air molecule collisions with the (sphere, disc) is ≈(80, 45)min. This is ample time for observation of the putative CSL diffusion with the standard parameters and, it is pointed out, with any parameters in the range over which the theory may be considered viable. This encourages consideration of how such an experiment may actually be performed, and the paper closes with some thoughts on this subject. (shrink)

Quantum mechanics, with its revolutionary implications, has posed innumerable problems to philosophers of science. In particular, it has suggested reconsidering basic concepts such as the existence of a world that is, at least to some extent, independent of the observer, the possibility of getting reliable and objective knowledge about it, and the possibility of taking (under appropriate circumstances) certain properties to be objectively possessed by physical systems. It has also raised many others questions which are well known to those involved (...) in the debate on the interpretation of this pillar of modern science. One can argue that most of the problems are not only due to the intrinsic revolutionary nature of the phenomena which have led to the development of the theory. They are also related to the fact that, in its standard formulation and interpretation, quantum mechanics is a theory which is excellent (in fact it has met with a success unprecedented in the history of science) in telling us everything about what we observe, but it meets with serious difficulties in telling us what is. We are making here specific reference to the central problem of the theory, usually referred to as the measurement problem, or, with a more appropriate term, as the macro-objectification problem. It is just one of the many attempts to overcome the difficulties posed by this problem that has led to the development of Collapse Theories, i.e., to the Dynamical Reduction Program (DRP). As we shall see, this approach consists in accepting that the dynamical equation of the standard theory should be modified by the addition of stochastic and nonlinear terms. The nice fact is that the resulting theory is capable, on the basis of a unique dynamics which is assumed to govern all natural processes, to account at the same time for all well-established.. (shrink)

The thesis that nature is composed of metaphysical levels is commonly understood in terms of emergence. In this paper, I uncover a problem for accounts of emergence, the collapse problem. The collapse problem suggests that emergence merely tracks relations between arbitrary groups of properties and so cannot be used in service of the levels view. I reject several failed attempts to solve the collapse problem and argue for an alternative solution according to which emergence is not (...) a distinction between metaphysical levels, but instead tracks the unavailability of scientific explanations. (shrink)

The existence of spacetime singularities is one of the biggest problems of nowadays physics. According to Penrose, each physical singularity should be covered by a “cosmic censor” which prevents any external observer from perceiving their existence. However, classical models describing the gravitational collapse usually results in strong curvature singularities, which can also remain “naked” for a finite amount of advanced time. This proceedings studies the modifications induced by asymptotically safe gravity on the gravitational collapse of generic Vaidya spacetimes. It will (...) be shown that, for any possible choice of the mass function, quantum gravity makes the internal singularity gravitationally weak, thus allowing a continuous extension of the spacetime beyond the singularity. (shrink)

For any putative excuse, why not recast it as a justification rendering one’s wrongful conduct ultimately permissible? This paper confronts the worry that many, perhaps all, excuses might collapse into justifications – either in morality or criminal law. It is an especially pressing problem for normative expectations views, on which excuses speak to a lower standard than justifications. I argue that the prospects for decisively blocking collapse within morality look bleak – at least if we adhere to an important (...) constraint of the present project. I want to see if we can block collapse without appealing to a substantive theory of moral wrongness or taking on robust theoretical commitments about interpersonal morality. This is especially important for criminal law purposes, though I concede that blocking collapse in morality likely requires substantive commitments. Accordingly, I develop a more ecumenical way to block collapse within the criminal law, although not morality. The key is to attend to differences in how the legislature can legitimately assign weight to reasons in determining which actions it deems to be wrong vs. how individuals can fairly be expected to assign weight to reasons, which is key to assessing culpability. Institutional considerations impact the former but not the latter. (shrink)

God is traditionally taken to be a necessarily existing being who is unsurpassably powerful, knowledgeable, and good. The familiar problem of actual evil claims that the presence of gratuitous suffering in the actual world constitutes evidence against the existence of such a being. In contrast, the problem of possible evil claims that the possibility of bad worlds constitutes evidence against theism. How? It seems plausible to suppose that there are very bad possible worlds. But if God exists in (...) every world, then God exists in those, too. And if God exists in very bad worlds, some say, God is culpable for not ensuring that they are better. In what follows, I consider this argument, survey some responses, and offer a novel solution. Along the way, I argue that theists should maintain that the actual world is a multiverse featuring all and only universes worthy of being created and sustained by God, and – more controversially – I suggest that theists should embrace modal collapse: the claim that this multiverse is the only possible world. (shrink)

For any putative excuse, why not recast it as a justification rendering one’s wrongful conduct ultimately permissible? This paper confronts the worry that many, perhaps all, excuses might collapse into justifications – either in morality or criminal law. It is an especially pressing problem for normative expectations views, on which excuses speak to a lower standard than justifications. I argue that the prospects for decisively blocking collapse within morality look bleak – at least if we adhere to an important (...) constraint of the present project. I want to see if we can block collapse without appealing to a substantive theory of moral wrongness or taking on robust theoretical commitments about interpersonal morality. This is especially important for criminal law purposes, though I concede that blocking collapse in morality likely requires substantive commitments. Accordingly, I develop a more ecumenical way to block collapse within the criminal law, although not morality. The key is to attend to differences in how the legislature can legitimately assign weight to reasons in determining which actions it deems to be wrong vs. how individuals can fairly be expected to assign weight to reasons, which is key to assessing culpability. Institutional considerations impact the former but not the latter. (shrink)

For any putative excuse, why not recast it as a justification rendering one’s wrongful conduct ultimately permissible? This paper confronts the worry that many, perhaps all, excuses might collapse into justifications – either in morality or criminal law. It is an especially pressing problem for normative expectations views, on which excuses speak to a lower standard than justifications. I argue that the prospects for decisively blocking collapse within morality look bleak – at least if we adhere to an important (...) constraint of the present project. I want to see if we can block collapse without appealing to a substantive theory of moral wrongness or taking on robust theoretical commitments about interpersonal morality. This is especially important for criminal law purposes, though I concede that blocking collapse in morality likely requires substantive commitments. Accordingly, I develop a more ecumenical way to block collapse within the criminal law, although not morality. The key is to attend to differences in how the legislature can legitimately assign weight to reasons in determining which actions it deems to be wrong vs. how individuals can fairly be expected to assign weight to reasons, which is key to assessing culpability. Institutional considerations impact the former but not the latter. (shrink)

According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the principle of general covariance of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space–time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the (...) exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. The reason is that the conflict or the problem of ill-definedness for a superposition of different space–time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and the preferred basis are also problematic. (shrink)

One of the most serious challenges (if not the most serious challenge) for interactive psycho-physical dualism (henceforth interactive dualism or ID) is the so-called ‘interaction problem’. It has two facets, one of which this article focuses on, namely the apparent tension between interactions of non-physical minds in the physical world and physical laws of nature. One family of approaches to alleviate or even dissolve this tension is based on a collapse solution (‘consciousness collapse/CC) of the measurement problem in (...) quantum mechanics (QM). The idea is that the mind brings about the collapse of a superposed wave function onto one of its eigenstates. Thus, it is claimed, can the mind change the course of things without violating any law figuring in physical theory. I will first show that this hope is premature because energy and momentum are probably not conserved in collapse processes, and that even if this can be dealt with, the violations are either severe or produce further ontological problems. Second, I point out several conceptual difficulties for interactionist CC. I will also present solutions for those problems, but it will become clear that those solutions come at a high cost. Third, I shall briefly list some empirical problems which make life even harder for interactionist CC. I conclude with remarks about why no- collapse interpretations of QM don’t help either and what the present study has shown is the real issue for ID: namely to find a plausible integrative view of dualistic mental causation and laws of nature. (shrink)

Spontaneous collapse theories of quantum mechanics require an interpretation if their claim to solve the measurement problem is to be vindicated. The most straightforward interpretation rule, the fuzzy link, generates a violation of common sense known as the counting anomaly. Recently, a consensus has developed that the mass density link provides an appropriate interpretation of spontaneous collapse theories that avoids the counting anomaly. In this paper, I argue that the mass density link violates common sense in just as striking (...) a way as the fuzzy link, and hence should not be regarded as a problem-free alternative to the fuzzy link. Hence advocates of spontaneous collapse theories must accept some violation of common sense, although this is not necessarily fatal to their project. (shrink)

Position measurement-induced collapse states are shown to provide a unified quantum description of diffraction of particles passing through a single slit. These states, which we here call ‘quantum location states’, are represented by the conventional rectangular wave function at the initial time of position measurement. We expand this state in terms of the position eigenstates, which in turn can be represented as a linear combination of energy eigenfunctions of the problem, using the closure property. The time-evolution of the location (...) states in the case of free particles is shown to have position probability density patterns closely resembling diffraction patterns in the Fresnel region for small times and the same in Fraunhofer region for large times. Using the quantum trajectory representations in the de Broglie–Bohm, modified de Broglie–Bohm and Floyd–Faraggi–Matone formalisms, we show that Fresnel and Fraunhofer diffractions can be described using a single expression. We also discuss how to obtain the probability density of location states for the case of particles moving in a general potential, detected at some arbitrary point. In the case of the harmonic oscillator potential, we find that they have oscillatory properties similar to that of coherent states. (shrink)

According to a particular interpretation of quantum mechanics, the causal role of human consciousness in the measuring process is called upon to solve a foundational problem called the “measurement problem.” Traditionally, this interpretation is tied up with the metaphysics of substance dualism. As such, this interpretation of quantum mechanics inherits the dualist’s mind-body problem. Our working hypothesis is that a process-based approach to the consciousness causes collapse interpretation (CCCI) ---leaning on Whitehead’s solution to the mind-body problem--- (...) offers a better metaphysical understanding of consciousness and its role in interpreting quantum mechanics. This article is the kickoff for such a research program in the metaphysics of science. (shrink)

Spontaneous collapse models are modifications of standard quantum mechanics in which a physical mechanism is responsible for the collapse of the wavefunction, thus providing a way to solve the so-called “measurement problem”. The two most famous of these models are the Ghirardi–Rimini–Weber (GRW) model and the Continuous Spontaneous Localisation (CSL) models. Here, we propose a new kind of non-relativistic spontaneous collapse model based on the idea of collapse points situated at fixed spacetime coordinates. This model shares properties of both (...) GRW and CSL models, while starting from different assumptions. We show that it can lead to a dynamics quite similar to that of the GRW model while also naturally solving the problem of indistinguishable particles. On the other hand, we can also obtain the same master equation of the CSL models. Then, we show how our proposed model solves the measurement problem in a manner conceptually similar to the GRW model. Finally, we show how the proposed model can also accommodate for Newtonian gravity by treating the collapses as gravitational sources. (shrink)

Peter Lewis ([1997]) has recently argued that the wavefunction collapse theory of GRW (Ghirardi, Rimini and Weber [1986]) can only solve the problem of wavefunction tails at the expense of predicting that arithmetic does not apply to ordinary macroscopic objects. More specifically, Lewis argues that the GRW theory must violate the enumeration principle: that 'if marble 1 is in the box and marble 2 is in the box and so on through marble n, then all n marbles are in (...) the box' ([1997], p. 321). Ghirardi and Bassi ([1999]) have replied that it is meaningless to say that the enumeration principle is violated because the wavefunction Lewis uses to exhibit the violation cannot persist, according to the GRW theory, for more than a split second ([1999], p. 709). On the contrary, we argue that Lewis's argument survives Ghirardi and Bassi' s criticism unscathed. We then go on to show that, while the enumeration principle can fail in the GRW theory, the theory itself guarantees that the principle can never be empirically falsified, leaving the applicability of arithmetical reasoning to both micro- and macroscopic objects intact. (shrink)

Classical theism is often said to suffer from the problem of modal collapse: if God is necessary and simple then all of his effects (creatures) are also necessary. Many classical theists have turned to extrinsic predication in response: God’s simple and necessary act is compatible with any number of possible effects or no effects, and is only said to be an act of creating in virtue of the existence of the universe itself. Leftow and Schmid criticize this solution for (...) leading to “providential collapse”: God would not have control over which creation obtains if all his intrinsic features are compatible with any possible universe. Thomistic classical theism avoids both modal collapse and providential collapse by utilizing the metaphysics of relations. With no differences within his simple essence/act, God can relate himself differently to his possible effects, willing some and not willing others. These relations determine whether or not the effects will exist. Thomistic classical theism’s version of divine simplicity is not incompatible with God having a multiplicity of relations, for the three divine persons are distinct relations within God. Divine simplicity is only incompatible with a multiplicity of absolute items within God. Furthermore, not all differences of relation are grounded in the different absolute characteristics of their relata. Rather, sometimes differences of relation themselves ground differences in the absolute characteristics of their relata. God’s divine act is thus said to be an act of willing this creation rather than that in virtue of his chosen, contingent relation to possible creatures, rather than in virtue of the creatures themselves. (shrink)

Energy nonconservation is a serious problem of dynamical collapse theories. In this paper, we propose a discrete model of energy-conserved wavefunction collapse. It is shown that the model is consistent with existing experiments and our macroscopic experience.

Theories of mind draw on processes that represent mental states and their computational connections; simulation, in addition, draws on processes that replicate (Heal 1986 ) a sequence of mental states. Moreover, mental simulation can be triggered by input from imagination instead of real perceptions. To avoid confusion between mental states concerning reality and those created in simulation, imagined contents must be quarantined. Goldman bypasses this problem by giving pretend states a special role to play in simulation (Goldman 2006 ). (...) We argue that this path leads to the resurgence of the threat of collapse (Davies 1994 ), diluting the principled distinction between simulation and theory use. Exploration of a related method of real-mental states operating in a pretend mode leads to a factually untenable model. Our main goal here is to raise this problem as a challenge for Goldman’s reconfigured simulation theory. Only at the end we will briefly sketch a possible alternative way of quarantine that preserves the replicative element of simulation and avoids collapse. Figure 1 provides a guide to our argument. (shrink)

Acclaimed cultural critic Curtis White examines current fissures in Western Buddhism and argues against the growth of scientific and corporate dharma, particularly in Stephen Batchelor's Secular Buddhist movement. In Transcendent, celebrated cultural critic Curtis White, asks what Buddhism will look like in the future. Do we want a secular Buddhism that looks like corporations and neuroscience? Or do we want a Buddhism that still provides refuge from the debased world of money and things? Transcendence is not about magic realms where (...) spirits fly about; the world is, as Shunryu Suzuki put it, its own magic. We only need to reclaim it and reclaim our humanity while we’re at it. The problem White suggests is a culture that recognizes only "things," capitalist things and science things, and aggressively denies the idea that the world of things has a beyond. We're told by science ideologues like the New Atheists that we live in a secular age and that philosophy is dead, and art is only an amusement, and transcendence is not wanted because science can provide all the wonder and beauty we need. Transcendent is a call for the re-enchantment not only of Buddhism but also of our Western art traditions. White recalls the risks and the raptures of the English Romantics, Beat poets, and the children of the counterculture, all in the name of a living world, and in defiance of our current world of climate catastrophe, contagious disease, and social collapse. (shrink)

It is a received view that superluminal signaling is prohibited in collapse theories of quantum mechanics. In this paper, I argue that this may be not the case. I propose two possible mechanisms of superluminal signaling in collapse theories. The first one is based on the well-accepted solution to the tails problem, and the second one is based on certain assumptions about the minds of observers. Finally, I also discuss how collapse theories can avoid such superluminal signaling.

This paper examines three meta-ontological deflationary approaches – frameworks, verbal disputes, and metalinguistic negotiation – and applies them to ontological debates in philosophy of mind. An intriguing consequence of this application is that it reveals a deep, systematic problem for mental deflationism – specifically, a problem of cognitive collapse. This is surprising; cognitive collapse problems are usually reserved for serious ontological views such as eliminative materialism and mental fictionalism, not deflationism. This paper investigates why deflationism about the mental (...) is particularly problematic, and provides an explanation as to why mental fictionalism is in principle better equipped to address collapsing problems than deflationism is. (shrink)

Crete in the Early Iron Age and Archaic periods presents a number of very particular problems for the ancient historian. Most educated lay people associate Crete with its Bronze Age civilization, the so-called Minoans, and most historians of ancient Greece tend to be more familiar with Athens and the Peloponnese. That is, after all, where the great events that Herodotus and Thucydides describe took place. Most of our literary sources for ancient Crete take the form of philosophical reflections or antiquarian (...) tidbits, and focus not on events but institutions. These facts make a conventional narrative history, an histoire éventielle, of ancient Crete more or less an impossibility. It is nonetheless precisely in the institutions of ancient Crete—the law codes, the andreion, the agele, and the persistence of oligarchy throughout the historical period—that the historical interest lies. This literary perspective emphasizes Cretan difference: Cretan exceptionalism within the Greek-speaking Mediterranean. And the study of Crete begs the question: why did democracy not emerge more often? And, more specifically, if widespread literacy and the publication of law are the keys to democracy, why did it not emerge first in Crete and not in Athens? (shrink)

A familiar interpretation of quantum mechanics (one of a number of views sometimes labeled the "Copenhagen interpretation'"), takes its empirical apparatus at face value, holding that the quantum wave function evolves by the Schrödinger equation except on certain occasions of measurement, when it collapses into a new state according to the Born rule. This interpretation is widely rejected, primarily because it faces the measurement problem: "measurement" is too imprecise for use in a fundamental physical theory. We argue that this (...) is a weak objection, as there may be many ways of making "measurement" precise. However, measurement-collapse interpretations face a more serious objection: a dilemma tied to the quantum Zeno effect. Is measurement itself an observable that can enter superpositions? If yes, then the standard measurement-collapse dynamics is ill-defined. If no, then (at least if measurement is an observable), measurements can never start or finish. The best way out is to deny that measurement is an observable, but this leads to strong and revisionary consequences. This reinforces the view that there is no nonrevisionary interpretation of quantum mechanics. (shrink)

Theistic modal realism argues for an extension of Lewis's modal realism capable of accommodating a theistic God. By affording elegant solutions to many atheistic challenges, the view is of great theoretical utility for the theist. However, it has been objected that within a Lewisian framework God cannot be causally efficacious on pain of collapsing intuitively distinct modal notions. In this article I explain why these worries are ill-founded and show how God's existence and causal power over the pluriverse can (...) be consistently understood. If successful, the proposal offers a congenial theistic way to adopt modal realism and address the atheological problems. (shrink)

Lewis 313) has recently presented an argument claiming that, under the Ghirardi–Rimini–Weber theory of quantum mechanics, arithmetic does not apply to ordinary macroscopic objects such as marbles . In this paper, I disentangle two different lines of Lewis's argument, one devoted to what I call the standard GRW interpretation and the other to the mass density interpretation . I present both strains of Lewis's argument, and move on to criticise Lewis's position, focusing on his argument with respect to MDI. I (...) analyse the structure of his argument, and follow this with a novel refutation of Lewis's argument, drawing on the original presentation of MDI as developed by Ghirardi et al. 5). I briefly consider the debate that ensued between Bassi and Ghirardi and Clifton and Monton and interpret it within the context of my analysis. I conclude that Lewis's Counting Anomaly fails to generate a genuine problem. (shrink)

I discuss the interpretation of spontaneous collapse theories, with particular reference to Bell's suggestion that the stochastic jumps in the evolution of the wave function should be considered as local beables of the theory. I develop this analogy in some detail for the case of non-relativistic GRW-type theories, using a generalisation of Bell's notion of beables to POV measures. In the context of CSL-type theories, this strategy appears to fail, and I discuss instead Ghirardi and co-workers' mass-density interpretation and its (...) relation to Schrödinger's original charge-density interpretation. This discussion is extended to relativistic CSL-type theories. A few remarks on Everett's interpretation conclude the paper. (shrink)

Contrasting accounts of physicalism and strong emergentism face two problems. According to the neutrality problem, contrasting supervenience-based formulations of these positions cannot be neutral with respect to certain unrelated metaphysical commitments. According to the collapse problem, emergent properties can be accounted for using an appropriately expansive physical ontology, rendering strong emergentism metaphysically suspect. I argue that both these problems can be solved with a principled distinction between emergent causal laws and physical laws. I propose such a distinction based (...) on a finite discontinuity in the behavior of fundamental physical constituents as a function of complexity. (shrink)

We show that arithmetical transfinite recursion is equivalent to a suitable formalization of the following: For every ordinal \alpha there exists an ordinal /beta such that 1 + \beta \cdot (\beta + \alpha) admits an almost order preserving collapse into \beta. Arithmetical comprehension is equivalent to a statement of the same form, with \beta \cdot \alpha at the place of \beta \cdot (\beta + \alpha). We will also characterise the principles that any set is contained in a countable coded ω-model (...) of arithmetical transfinite recursion and arithmetical comprehension, respectively. (shrink)

I critically examine the claim that modal collapse arguments against the traditional doctrine of divine simplicity (DDS) are in general fallacious. In a recent paper, Christopher Tomaszewski alleges that modal collapse arguments against DDS are invalid, owing to illicit substitutions of nonrigid singular terms into intensional contexts. I show that this is not, in general, the case. I show, further, that where existing modal collapse arguments are vulnerable to this charge the arguments can be repaired without any apparent dialectical impropriety. (...) I conclude that the genuine debate over modal collapse and divine simplicity and modal collapse is substantially a controversy over the metaphysics of divine action, and that this constitutes a fruitful direction in which to take future discussions of the subject. (shrink)

I present and explain the Bohmian account of collapse in quantum mechanics.

The measurement problem concerns an apparent conflict between the two fundamental principles of quantum mechanics, namely the Schrödinger equation and the measurement postulate. These principles describe inconsistent behavior for quantum systems in so-called "measurement contexts." Many theorists have thought that the measurement problem can only be resolved by proposing a mechanistic explanation of (genuine or apparent) wavefunction collapse that avoids explicit reference to "measurement." However, I argue here that the measurement problem dissolves if we accept Humeanism about (...) laws of nature. On a Humean metaphysics, there is no conflict between the two principles, nor is there any inherent problem with the concept of "measurement" figuring into the account of collapse. (shrink)

We show that it is independent whether club $\kappa $ -Miller forcing preserves $\kappa ^{++}$. We show that under $\kappa ^{ \kappa $, club $\kappa $ -Miller forcing collapses $\kappa ^{<\kappa }$ to $\kappa $. Answering a question by Brendle, Brooke-Taylor, Friedman and Montoya, we show that the iteration of ultrafilter $\kappa $ -Miller forcing does not have the Laver property.

Collapse models predict the spontaneous collapse of the wave function, in order to avoid the emergence of macroscopic superpositions. In their mass-dependent formulation, they claim that the collapse of any system’s wave function depends on its mass. Neutral K, D, B mesons are oscillating systems that are given by Nature as superposition of two distinct mass eigenstates. Thus they are unique laboratory for testing collapse models that are sensitive to the mass. In this paper we derive—for the single mesons and (...) bipartite entangled mesons—the effect of the mass-proportional CSL (Continuous Spontaneous Localization) collapse model on the dynamics on neutral mesons. We compare the theoretical prediction with experimental data from different accelerator facilities. (shrink)

After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse of time. As (...) a result, modal collapse should not be conceived in Gödel so much as a deficit, but rather as a kind of the rise of modalities to the “perfect” being. We further show that, in accordance with Gödel’s ontology, the concepts of modality and time should be derived in terms of the “fundamental philosophical concept” of cause. To give an example of how a formalization of such causative Gödelian ontology and ontological proof might look, we propose the transformation of GO into a kind of causally re-interpreted justification logic. (shrink)

There have been many attempts to undertand the connections between quantum theory and Whiteheadian process philosophy. However, due to the ontological considerations, it is very important to specify which interpretation of quantum theory one embraces before inquiring into the details of Whitehead`s philosophy of organism. In this article, I argue that Ghirardi-Rimini-Weber (GRW) collapse interpretation of quantum theory serves as a suitable point of departure for future endeavors. Comparisons with many-worlds interpretation and decoherence approach have also been provided.

We are preoccupied with survival and gratification at the expense of human suffering and concern. This is the denial of the psyche: a levelling-out of meanings and values.

Despite growing interest in risks of societal collapse due to anthropogenic climate change, there exists no consensus about how collapse should be understood. In this article, we critically examine existing definitions and argue that none adequately address the challenges for conceptualizing collapse that climate change presents. We therefore propose an alternative conception, which regards collapse as a reduction of collective capacity resulting in a pervasive and difficult-to-reverse loss of basic functionality. Our conception is dynamic in that it focuses on the (...) interrelations of constituent subsystems. It also distinguishes collapse from transformations needed to address climate change and provides insight into the relationship between collapse and sustainability. [Open access]. (shrink)

In this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to the three parts of the paper. In any empirical science, the first two features are obviously connected but, as is well known, among the different formulations and interpretations of non-relativistic quantum mechanics, only collapse models, as the paper well illustrates with a richness of details, (...) have experimental consequences. Finally, we show that a clarification of the ontological intimations of collapse models is needed for at least three reasons: (1) to respond to the indispensable task of answering the question ’what are collapse models (and in general any physical theory) about?’; (2) to achieve a deeper understanding of their different formulations; (3) to enlarge the panorama of possible readings of a theory, which historically has often played a fundamental heuristic role. (shrink)

We define what it means for a function on ω1 to be a collapsing function for λ and show that if there exists a collapsing function for +, then there is no precipitous ideal on ω1. We show that a collapsing function for ω2 can be added by forcing. We define what it means to be a weakly ω1-Erdös cardinal and show that in L[E], there is a collapsing function for λ iff λ is less than (...) the least weakly ω1-Erdös cardinal. As a corollary to our results and a theorem of Neeman, the existence of a Woodin limit of Woodin cardinals does not imply the existence of precipitous ideals on ω1. We also show that the following statements hold in L[E]. The least cardinal λ with the Chang property ↠ is equal to the least ω1-Erdös cardinal. In particular, if j is a generic elementary embedding that arises from non-stationary tower forcing up to a Woodin cardinal, then the minimum possible value of j is the least ω1-Erdös cardinal. (shrink)

The relation between quantum collapse, consciousness and superluminal communication is analyzed. As we know, quantum collapse, if exists, can result in the appearance of quantum nonlocality, and requires the existence of a pre- ferred Lorentz frame. This may permit the realization of quantum superluminal communication (QSC), which will no longer result in the usual causal loop in case of the existence of a preferred Lorentz frame. The possibility of the existence of QSC is further analyzed under the assumption that quantum (...) collapse is a real process. We demonstrate that the combination of quantum collapse and the consciousness of the observer will permit the observer to distinguish nonorthogonal states in principle. This provides a possible way to realize QSC. Some implications of the existence of QSC are briefy discussed. (shrink)

We introduce the Easton collapse and show that the two-stage iteration of Easton collapses gives a model in which the successor of a regular cardinal carries a strongly saturated filter. This allows one to get a model in which many successor cardinals carry saturated filters just by iterating Easton collapses.

Our worldview assumes that people are morally responsible. Consider our emotions regarding other people or ourselves. We often feel anger, gratitude, pride, and shame toward them or ourselves. Consider religious beliefs. Jews and Christians believe that God cares whether a person does right by others and freely loves him. Consider moral values. We value dignity, freedom, and rights. The above emotions, beliefs, and values assume that people are responsible. In particular, they assume that a person is responsible for what she (...) thinks and does, and that this is a good thing. This book argues that the above worldview is false. No one is responsible. -/- I provide four arguments for this conclusion. -/- (1) Foundation. No one is responsible because there is no foundation for responsibility. A foundation for responsibility is something for which a person is responsible but not by being responsible for something else. -/- (2) Epistemic Condition. No one is responsible because no one fulfills the epistemic condition necessary for blameworthiness. -/- (3) Internalism. If a person were responsible, then she would be responsible for, and only for, what goes on in her head. Most of the evidence for responsibility says the opposite. -/- (4) Amount. No one is responsible because we cannot make sense of what makes a person more or less praiseworthy (or blameworthy). -/- The above arguments cohere with each other, explain the responsibility-skepticism literature, and have disturbing implications. (shrink)

We present a novel spontaneous collapse model where size is no longer the property of a physical system which determines its rate of collapse. Instead, we argue that the rate of spontaneous localization should depend on a system’s quantum Integrated Information, a novel physical property which describes a system’s capacity to act like a quantum observer. We introduce quantum Integrated Information, present our QII collapse model and briefly explain how it may be experimentally tested against quantum theory.

This paper presents a view of the process of transition from planned command socialism to mixed market capitalism involving nonlinear complex dynamical phenomena. After the former institutional structure disappears a coordination failure can bring about macroeconomic collapse as in almost all of the former Soviet bloc or macroeconomic boom as in China. A closely linked phenomenon is the rise of the underground economy as inflation and income inequality increase. This can lead to a jump from one equilibrium to a very (...) different one as nonlinear social feedback processes operate in the transition. (shrink)

We examine the differences between three standard classes of forcing notions relative to the way they collapse the continuum. It turns out that proper and semi-proper posets behave differently in that respect from the class of posets that preserve stationary subsets of \.