The most serious objection to Beall and Restall’s case-based logical pluralism is the so-called collapse argument. According to the collapse argument, logical pluralism is not genuinely pluralistic and collapses into a single privileged relation of logical consequence. In response, Caret offered an account of logical contextualism that supposedly maintains the merits of Beall and Restall’s case-based logical pluralism while circumventing the collapse argument. In this paper, I first point out a gap in the collapse argument in (...) that it does not affect pluralists who assume that there is no uniquely strongest admissible consequence relation. This gap, then, is closed by an improved version of the collapse argument, which makes use of Eklund’s classification of types of pluralism. Finally, I discuss how Caret’s logical contextualism cannot hold up against this new formulation of the collapse argument unless implausible assumptions about the contents of normative operators are made. Moreover, by reformulating the collapse argument, I determine the extent to which logical monism and pluralism oppose each other, paving the way for fruitful future discussion. (shrink)

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

One of the most pressing objections against Divine simplicity is that it entails what is commonly termed a ‘modal collapse’, wherein all contingency is eliminated and every true proposition is rendered necessarily true. In this paper, I show that a common form of this argument is in fact famously invalid and examine three ways in which the opponent of Divine simplicity might try to repair the argument. I conclude that there is no clear way of repairing the argument that (...) does not beg the question against the doctrine of Divine simplicity. (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)

The collapse of the wavefunction is arguably the least understood process in quantum mechanics. A plethora of ideas—macro-micro divide, many worlds and even consciousness—have been put forth to resolve the issue. Contrary to the standard Copenhagen interpretation, objective collapse models modify the Schrödinger equation with nonlinear and stochastic terms in order to explain the collapse of the wavefunction. In this paper we propose a collapse model in which a particle’s wavefunction has a possibility of collapsing when (...) it interacts with macroscopic objects, without the intervention of a conscious observer. We propose four possible conditions of collapse of the wavefunction and make testable predictions which differ from standard quantum mechanics. (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)

It is commonplace today to hear climate change identified as the single most important challenge facing humanity. Consider the headlines from COP24, the United Nations Climate Change Conference held in Poland in December 2018. U.N. Secretary-General António Guterres opened the proceedings by calling climate change “the most important issue we face” (PBS 2018). The Secretary-General’s remarks paraphrase the opening line of the U.N.’s climate change web page, which announces that “[c]limate Change is the defining issue of our time and we (...) are at a defining moment” (United Nations n.d.). Such statements about the singular significance of climate change—the most important, the defining issue—are often followed by proclamations about what hangs in the balance, and this was the case at COP24. There, the celebrated British naturalist Sir David Attenborough warned that “collapse of our civilizations and the extinction of much of the natural world is on the horizons,” amounting to, in his words, “disaster of global scale, our greatest threat in thousands of years” (PBS 2018). (shrink)

The concept of collapse in history is one of the normative conceptions through which human past gets a shape. There is no necessary incompatibility between progress and decline, because the decline of some things can itself be interpreted as a mark of progress. This chapter provides an overview of philosophers like Alasdair MacIntyre, Friedrich Nietzsche, and Darwin on this issue. This chapter tries to illustrate through an example the differences between Christian morality and Nietzsche's concept of morality. Nietzsche claimed (...) that the cultural dominance of the Christian ascetic ideal in which self-negation is cultivated at the expense of the aristocratic virtue of self-assertion has come to an end. (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.

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)

In this article, we claim that recent developments in climate science and renewable energy should prompt a reframing of debates surrounding climate change mitigation. Taken together, we argue that these developments suggest (1) global climate collapse in this century is a non-negligible risk, (2) mitigation offers substantial benefits to current generations, and (3) mitigation by some can generate social tipping dynamics that could ultimately make renewables cheaper than fossil fuels. We explain how these claims undermine familiar framings of climate (...) change, wherein mitigation is understood as self-sacrifice that individuals and governments must be morally persuaded or incentivized to undertake. [Open access]. (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)

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.

After decades of Cold War stability, most participants experienced the collapse of communism in 1989-90 as an unforeseen “return of history.”1 The deep freeze of the Cold War made it seem that the East-West division had become permanent and that the best one could hope for was a gradual softening of the iron curtain. Repeated suppression of East European revolts by Soviet tanks and the failure of the communist parties in the West appeared to indicate that the domestic order (...) of the competing blocs would remain unchangeable. Just when most people had accepted the permanence of the post-war system. Gorbachev's…. (shrink)

GRW theory offers precise laws for the collapse of the wave function. These collapses are characterized by two new constants, \ and \ . Recent work has put experimental upper bounds on the collapse rate, \ . Lower bounds on \ have been more controversial since GRW begins to take on a many-worlds character for small values of \ . Here I examine GRW in this odd region of parameter space where collapse events act as natural disasters (...) that destroy branches of the wave function along with their occupants. Our continued survival provides evidence that we don’t live in a universe like that. I offer a quantitative analysis of how such evidence can be used to assess versions of GRW with small collapse rates in an effort to move towards more principled and experimentally-informed lower bounds for \. (shrink)

Recently a number of works in meta-ontology have used a variant of J.H. Harris's collapse argument in the philosophy of logic as an argument against Eli Hirsch's quantifier variance. There have been several responses to the argument in the literature, but none of them have identified the central failing of the argument, viz., the argument has two readings: one on which it is sound but doesn't refute quantifier variance and another on which it is unsound. The central lesson I (...) draw is that arguments against quantifier variance must pay strict attention to issues of translation and interpretation. The paper also has a substantial appendix in which I prove the equivalence of plural mereological nihilism and standard first-order atomistic mereology; results of this kind are often appealed to in the literature on quantifier variance but without many details on the nature or proof of the result. (shrink)

This brief essay describes the significance of Hillary Putnam's "Collapse of the Fact/Value Dichotomy" for Catholic thinkers who are inspired by Thomas Aquinas.

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 \.

The Collapse of the Rule of Law. The Messina Earthquake and the State of Exception Messina, a Sicilian town, was devasteted by an earthquake in1908. It was an hecatomb. Stricken through this unfathomable disgrace Messina’s institutions and civil society collapsed and a sort of wild natural state replaced the rule of law. In this situation there was a first intervention of the Russian Czarist navy who came to help but immediately enforced cruel emergency measures. The Italian army followed and (...) there was a formal declaration of an ‘emergency situation.’ Around this event and the several exceptional measures taken by the government a debate took place about the legality of those exceptional measures. The article tries to reconstruct the historical context and the content of that debate and in a broader perspective thematizes how law (and morality) could be brought to meet the breaking of normality and ordinary life by an unexpected and catastrophic event. (shrink)

The following introduction offers a broad survey of the history of quantum physics. It then outlines the position of each contributor in this Special Focus Section concerning the collapse of the quantum wave function and defines three important terms (Hilbert space, Schrödinger’s cat, and decoherence) used in discussing this topic.

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)

A physical theory of experiments carried out in a space-time region can accommodate a detector localized in another space-like separated region, in three, not necessarily exclusive, ways: (1) the detector formally collapses physical states across space-like separations, (2) the detector enables superluminal signals, and (3) the theory becomes logically inconsistent. If such a theory admits autonomous evolving states, the space-like collapse must be instantaneous. Time-like separation does not allow such conclusions. We also prove some simple results on structural stability: (...) within the set of all possible theories, under a weak empirical topology, the set of all theories with superluminal signals and the set of all theories with retrograde signals are both open and dense. (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)

A collection of 17 meditative essays and 52 weekly reflections, this book is for readers who are concerned about the daunting future humankind has created and who seek inspiration, wisdom, and spiritual purpose in the face of the collapse of industrial civilization.

In this paper I argue that the attempt to develop practice dependence as a middle path between cosmopolitanism and social liberalism ultimately fails. In particular, I contend that the only type of practice dependence that can coherently be defended collapses into cosmopolitanism. I trace the origin of practice dependence theory from Cohen and Sabel’s work through Sangiovanni and Valentini. After discussing the various different types of practice dependence, I argue that the only type of practice dependence that stands up to (...) scrutiny is functionalism, but that if functionalism is true, it commits us to cosmopolitanism. (shrink)

On some views, we can be sure that parties to a dispute over the logic of ‘exists’ are not talking past each other if they can characterise ‘exists’ as the only monadic predicate up to logical equivalence obeying a certain set of rules of inference. Otherwise, we ought to be suspicious about the reality of their disagreement. This is what we call a proof- theoretic argument. Pace some critics, who have tried to use proof-theoretic arguments to cast doubts about the (...) reality of disagreements about the logic of ‘exists’, we argue that proof-theoretic arguments can be deployed to establish the reality of several such disagreements. Along the way, we will also utilise this technique to establish similar results about some disagreements over the logic of identity. (shrink)

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)

This article proposes that cosmetic minimally-invasive procedures – Botox injections, soft-tissue fillers, microdermabrasion, chemical peels and laser treatments – are an under-researched area and provide a number of promising paths for skin studies research. I argue that cosmetic minimally-invasive procedures collapse the difference between the surfaces of the photograph and the skin – the primary surfaces of cosmetic surgery – more successfully than cosmetic surgical procedures. More precisely, I maintain that the difference between photograph and skin is collapsed in (...) two ways: first, through narrating the transformation of the skin’s surface in a way that more closely matches the photographic promises of the cosmetic surgery industry; and, second, by depicting the surgical penetration of the skin through advertising photography. The article concludes by suggesting that further investigation into cosmetic minimally-invasive procedures could offer a new way to think about relationships between ‘normative’ and ‘non-normative’ skin modification practices. (shrink)

In this paper we we will argue against the orthodox definition of quantum entanglement which has been implicitly grounded on several widespread presuppositions which have no relation whatsoever to the formalism of QM. We will show how these presuppositions have been introduced through a naive interpretation of the quantum mathematical structure which assumes dogmatically that the theory talks about "small particles" represented by pure states which suddenly "collapse" when a measurement takes place. In the second part of this paper (...) we will present a non-collapse approach to QM which makes no use whatsoever of particle metaphysics, escaping the need to make reference to space-time separability or the restriction to certain predictions of definite valued binary properties. Our paper ends up concluding the essential need to redefine the notion of quantum entanglement, at least in the cases of: i) non-collapse interpretations of QM; or, ii) any other interpretation which abandons the idea that QM makes reference to "small particles". (shrink)

Eugene Wigner and others have speculated that the “collapse of the state vector” during an observation might be a physically real process so that some modification of current quantum theory would be required to describe the interaction with a conscious observer appropriately.Experimental reports on the “psychokinetic effect” as a mental influence on the outcome of quantum jumps suggest that perhaps this effect might be vital for an understanding of the observer's role in quantum mechanics.Combining these two speculations we introduce (...) a reduction principle that provides for the gradual reduction of a macroscopically ambiguous state and allows simultaneously for the occurrence of some psychokinetic effect in the process of observation.The resulting model leads to many of the paradoxical, but logically consistent, features of the psychokinetic effect that have been reported, and makes further testable predictions.The model does not touch on the more profound questions of consciousness. But the model implies that the result of a conscious observation, the collapse of the state vector, becomes accessible to the experimenter, with the psychokinetic effect as probe: Whether Schrödinger's cat has not or has collapsed the state vector determines whether or not the later human observer can still exert a psychokinetic influence on the result. (shrink)

This essay addresses the collapse/incoherence problem for normative frameworks that contain both fundamental values and rules for promoting those values. The problem is that in some cases, we would bring about more of the fundamental value by violating the framework’s rules than by following them. In such cases, if the framework requires us to follow the rules anyway, then it appears to be incoherent; but if it allows us to make exceptions to the rules, then the framework “collapses” into (...) one that doesn’t make use of rules in the first place. The chapter begins with an examination of happiness and truth as fundamental values in Mill’s work, which lead into parallel versions of the collapse/incoherence problem in ethics and epistemology. It then sets out the collapse problem for rule-consequentialist approaches in ethics, truth-directed accounts of justification in epistemology, and epistemological approaches to argument cogency. The chapter closes with discussion of two potential solutions to the problem. (shrink)

The honeybee, Apis mellifera, has excited both literary and scientific interest since ancient times, and even modern entomological investigation has not entirely dispelled the mystery surrounding the corporate intelligence of the beehive. Yet this lingering mystique has not prevented the wholesale exploitation of the honeybee as pollinator of choice in present-day industrial agriculture. In the context of this industrialization of the apiary, honeybees around the world are succumbing to the condition known as “colony collapse disorder.” The consequent disappearance of (...) honeybees on a massive scale poses the question, what do honeybees mean to us? Is their loss a moral loss, and if so, is it merely a moral loss, or something more? Does the loss of honeybees portend further losses that will amount to the loss of the basic conditions for meaning, and hence for morality, per se? (shrink)

In this article we attempt to bring out some significant general aspects of what we call collapse-induced quantum nonlocal effects resulting from the use of the hypothesis of wave function collapse.

The collapse models of arithmetic are inconsistent, nontrivial models obtained from ℕ and set out in the Logic of Paradox (LP). They are given a general treatment by Priest (Priest, 2000). Finite collapse models are decidable, and thus axiomatizable, because finite. LP, however, is ill-suited to normal axiomatic reasoning, as it invalidates Modus Ponens, and almost all other usual conditional inferences. I set out a logic, A3, first given by Avron (Avron, 1991), and give a first order axiom (...) system for the finite collapse models. I present some standard arithmetical axioms in addition to a cyclic axiom and prove that these axioms are sound and complete for the cyclic models, reporting a similar result for the heap models. The state of the situation for the each of the kinds of infinite collapse model is, however, left an open question. (shrink)

An overview of the collapse theories of quantum mechanics. Written by distinguished physicists and philosophers of physics, it discusses the origin and implications of wave-function collapse, the controversies around collapse models and their ontologies, and new arguments for the reality of wave function collapse.

This essay redefines the crisis of historicism as a collapse of trust. Following Friedrich Jaeger, it suggests that this crisis should be understood, not as a crisis caused by historicist methods, but as a crisis faced by the classical historicist tradition of Ranke. The "nihilism" and "moral relativism" feared by Troeltsch's generation did not primarily refer to the view that moral universals did not exist; rather, they expressed that the historical justification of bildungsbürgerliche values offered by classical historicism did (...) no longer work. In Niklas Luhmann's vocabulary, this is to say that moral values could no longer be trusted on historical grounds. But when the "reduction of complexity" offered by classical historicism collapsed, Troeltsch's generation faced a justification problem: what other modes of justification, if any at all, were available in a time of increasing secularization and growing feelings of discontinuity with the past? In identifying the crisis of historicism with this moral justification problem, this essay helps explain why such debts of despair could be reached in the early-twentieth-century disputes over historicism. (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)

This paper makes an analysis of the recent collapse of Fortis, a major European bank, from the perspective of shareholder activism and social movement theory to illustrate the limits of corporate governance. Some specific issues of the Fortis affair – and more especially the chaotic events at the general assembly - illustrate the application of social movement theory to shareholder activism, besides agency theory problems and conflicts of interests. Paradoxes between legal constraints and principles of good corporate governance are (...) presented. The Fortis case illustrates the limits of the juridical bureaucracy in situations of urgency. The case illustrates the limits of corporate governance. Governance systems need to find appropriate mechanisms to align the voting rights with the long-term interests of the company. We argue for new criteria that will restrict representation to loyal shareholders with a long-term commitment. Good governance mechanisms should prevent opportunistic behaviour and encourage a responsible attitude. (shrink)

The Lottery Paradox has been thought to provide a reductio argument against probabilistic accounts of inductive inference. As a result, much work in artificial intelligence has concentrated on qualitative methods of inference, including default logics, which are intended to model some varieties of inductive inference. It has recently been shown that the paradox can be generated within qualitative default logics. However, John Pollock's qualitative system of defeasible inference, does avoid the Lottery Paradox by incorporating a rule designed specifically for that (...) purpose. I shall argue that Pollock's system instead succumbs to a worse disease: it fails to allow for induction at all. (shrink)

Assuming that GCH holds and [Formula: see text] is [Formula: see text]-supercompact, we construct a generic extension [Formula: see text] of [Formula: see text] in which [Formula: see text] remains strongly inaccessible and [Formula: see text] for every infinite cardinal [Formula: see text]. In particular the rank-initial segment [Formula: see text] is a model of ZFC in which [Formula: see text] for every infinite cardinal [Formula: see text].

We compute the effect of collapse models on neutrino oscillations. The effect of the collapse is to modify the evolution of the spatial part of the wave function and we will show that this indirectly amounts to a change on the flavor components. For the analysis we use the mass proportional CSL model, and perform the calculation to second order perturbation theory. As we will show, the CSL effect is very small—mainly due to the very small mass of (...) neutrinos—and practically undetectable. (shrink)

Virtue ethics is normally taken to be an alternative to consequentialist and Kantian moral theories. I shall discuss what I think is the most interesting version of virtue ethics – Rosalind Hursthouse's. I shall then argue that her version is inadequate in ways that suggest revision in the direction of a kind of rule-consequentialism.

This article addresses a neglected problem in Searle’s social ontology, namely, how human civilization may collapse. In the first section, I provide the theoretical framework. In the second section, I offer the key elements to understanding Searle’s ontology as well as his philosophy of society, emphasizing the role of constitutive rules and deontic powers. In the third section I examine how they improve trust and co-operation. Global and local natural disasters are distinguished in the fourth section, because the former (...) is sufficient to undermine pacts, promises, constitutive rules and deontic powers, while the latter is neither sufficient nor necessary. In the fifth and final section, I put forward an argument via a thought experiment that allows us to anticipate what would occur if people did not keep promises and pacts, on the one hand, and did not respect constitutive rules and deontic powers, on the other hand. Such events, I argue, would result in the collapse of civilization. (shrink)

The Hilbert program was actually a specific approach for proving consistency, a kind of constructive model theory. Quantifiers were supposed to be replaced by ε-terms. εxA(x) was supposed to denote a witness to ∃xA(x), or something arbitrary if there is none. The Hilbertians claimed that in any proof in a number-theoretic system S, each ε-term can be replaced by a numeral, making each line provable and true. This implies that S must not only be consistent, but also 1-consistent. Here we (...) show that if the result is supposed to be provable within S, a statement about all Pi-0-2 statements that subsumes itself within its own scope must be provable, yielding a contradiction. The result resembles Gödel's but arises naturally out of the Hilbert program itself. (shrink)

According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than (...) the original view. It is a major improvement that should be embraced by all logical pluralists. (shrink)

A simple quantum model describing the onset of time is presented. This is combined with a simple quantum model of the onset of space. A major purpose is to explore the interpretational issues which arise. The state vector is a superposition of states representing different “instants.” The sample space and probability measure are discussed. Critical to the dynamics is state vector collapse: it is argued that a tenable interpretation is not possible without it. Collapse provides a mechanism whereby (...) the universe size, like a clock, is narrowly correlated with the quantized time eigenvalues. (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)

This paper raises the question under what circumstances a plurality forms a set. My main point is that not always all things form sets. A provocative way of presenting my position is that, as a result of my approach, there are more pluralities than sets. Another way of presenting the same thesis claims that there are ways of talking about objects that do not always collapse into sets. My argument is related to expressive powers of formal languages. Assuming classical (...) logic, I show that if all plurality form a set and the quantifiers are absolutely general, then one gets a trivial theory. So, by reductio, one has to abandon one of the premiss. Then, I argue against the collapse of the pluralities into sets. What I am advocating is that the thesis of collapse limits important applications of the plural logic in model theory, when it is assumed that the quantifiers are absolutely general. (shrink)