The problem of statistical inference based on a partial measurement (“coarse-graining”) requires the specification of an a priori distribution. We reformulate the ordinary theory such as to encompass systematically a wide range of a priori distributions (“relative coarse-graining”). This is done in a mathematical setting which admits an interpretation in both classical probability and quantum mechanics. The formalism is illustrated in a few simple examples, such as the die whose geometrical shape is known, the spin in thermal (...) equilibrium with an unknown reservoir, and the position measurement of a one-dimensional particle. It is shown that some of the limitations of the usual theory are a consequence of the fact that it is restricted to “equidistributed” (symmetric) a priori states. (shrink)

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal (...) quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories. (shrink)

While the fundamental laws of physics are time-reversal invariant, most macroscopic processes are irreversible. Given that the fundamental laws are taken to underpin all other processes, how can the fundamental time-symmetry be reconciled with the asymmetry manifest elsewhere? In statistical mechanics, progress can be made with this question. What I dub the ‘Zwanzig–Zeh–Wallace framework’ can be used to construct the irreversible equations of SM from the underlying microdynamics. Yet this framework uses coarse-graining, a procedure that has faced much criticism. (...) I focus on two objections in the literature: claims that coarse-graining makes time-asymmetry ‘illusory’ and ‘anthropocentric’. I argue that these objections arise from an unsatisfactory justification of coarse-graining prevalent in the literature, rather than from coarse-graining itself. This justification relies on the idea of measurement imprecision. By considering the role that abstraction and autonomy play, I provide an alternative justification and offer replies to the illusory and anthropocentric objections. Finally, I consider the broader consequences of this alternative justification: the connection to debates about inter-theoretic reduction and the implication that the time-asymmetry in SM is weakly emergent. 1Introduction 1.1Prospectus2The Zwanzig–Zeh–Wallace Framework3Why Does This Method Work? 3.1The special conditions account3.2When is a density forwards-compatible?4Anthropocentrism and Illusion: Two Objections 4.1The two objections in more detail4.2Against the justification by measurement imprecision5An Alternative Justification 5.1Abstraction and autonomy5.2An illustration: the Game of Life6Reply to Illusory7Reply to Anthropocentric8The Wider Landscape: Concluding Remarks 8.1Inter-theoretic relations8.2The nature of irreversibility. (shrink)

This article considers the popular thesis that a more proportional relationship between a cause and its effect yields a more abstract causal explanation of that effect, which in turn produces a deeper explanation. This thesis is taken to have important implications for choosing the optimal granularity of explanation for a given explanandum. In this article, I argue that this thesis is not generally true of probabilistic causal relationships. In light of this finding, I propose a pragmatic, interest-relative measure of explanatory (...) depth. This measure uses a decision-theoretic model of information pricing to determine the optimal granularity of explanation for a given explanandum, agent, and decision problem. (shrink)

There is a received view on measurement scales. It includes both a classification of scales and a set of prescriptions regarding measurement inferences. This article casts doubt on the adequacy of this received view. To do this, I propose an epistemic characterization of the ordinal/interval distinction, that is, one in terms of researchers’ beliefs. This novel characterization reveals the ordinal/interval distinction as too coarse grained and thus the received view as too restrictive of a framework for (...) measurement research. (shrink)

Prevention of age-related disorders is increasingly in focus of health policies, and it is hoped that early intervention on processes of deterioration can promote healthier and longer lives. New opportunities to slow down the aging process are emerging with new fields such as personalized nutrition. Data-intensive research has the potential to improve the precision of existing risk factors, e.g., to replace coarse-grained markers such as blood cholesterol with more detailed multivariate biomarkers. In this paper, we follow an attempt (...) to develop a new aging biomarker. The vision among the project consortium, comprising both research and industrial partners, is that the new biomarker will be predictive of a range of age-related conditions, which may be preventable through personalized nutrition. We combine philosophical analysis and ethnographic fieldwork to explore the possibilities and challenges of managing aging through bodily signs that are not straightforwardly linked to symptomatic disease. We document how the improvement of measurement brings about new conceptual challenges of demarcating healthy and unhealthy states. Moreover, we highlight that the reframing of aging as risk has social and ethical implications, as it is generative of normative notions of what constitutes successful aging and good citizenship. (shrink)

In this paper I first argue that the objection which is most commonly levelled against the coarse-graining approach-viz. that it introduces an element of subjectivity into what ought to be a purely objective formalism-is ultimately unfounded. I then proceed to argue that two different objections to the coarse-graining approach indicate that it is an inadequate approach to statistical mechanics. The first objection is based on the fact that the appeal to appearances by the coarse-graining approach fails to (...) justify the coarse-graining strategy of ignoring the physical differences between so-called quasi-equilibrium distributions and equilibrium distributions. The second objection is centred on the notion of a coarse-grained entropy. I will argue that the required increase in the coarse-grained entropy is obtained by disregarding the dynamical constraints on the system. This undermines the very task statistical mechanics has set out to accomplish, viz. to provide a microdynamical underpinning of thermodynamics. (shrink)

The emergence of macroscopic variables can be effected through coarse graining. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse grains has been considered problematic. We provide objective selection methods, deriving from the existence of relatively slow dynamical time scales. Using a framework for nonequilibrium statistical mechanics developed by us, we show the emergence of both spatial variables and order parameters. Although significant objective criteria are introduced (...) in the coarse graining, we do not provide a unique prescription. Most significantly, the grains, and by implication entropy, are only defined modulo a characteristic time scale of observation. (shrink)

Explaining the emergence of individuality in the process of evolution remains a challenge; it faces the difficulty of characterizing adequately what ‘emergence’ amounts to. Here, I present a pragmatic account of individuality in which I take up this challenge. Following this account, individuals that emerge from an evolutionary transition in individuality are coarse-grained entities: entities that are summaries of lower-level evolutionary processes. Although this account may _prima facie_ appear to ultimately rely on epistemic considerations, I show that it (...) can be used to vindicate the emergence of individuals in a quasi-ontological sense. To this end, I discuss a recent account of evolutionary transitions in individuality proposed by Godfrey-Smith and Kerr (Brit J Philos Sci 64(1):205–222, 2013) where a transition occurs through several stages, each with an accompanying model. I focus on the final stage where higher-level entities are ascribed a separate fitness parameter, while they were not in the previous stages. In light of my account, I provide some justification for why such a change in parameters is necessary and cannot be dismissed as merely epistemic. (shrink)

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational (...) import on grounds of lack of rigor. (shrink)

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory, but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational (...) import on grounds of lack of rigor. (shrink)

Dariusz Łukasiewicz has investigated in depth the “Argument from Chance” which argues that the data revealing chance in the world are incompatible with Divine Providence. Łukasiewicz agrees that these data undermine the traditional model of Providence—a fine-grained model in which every single detail is controlled by God—but maintains that they are not incompatible with a coarse-grained model—in which God leaves to chance many aspects of history (including some horrendous evils). Furthermore, Łukasiewicz provides independent reasons to prefer this (...) coarse-grained model. Even though I agree that a maximally fine-grained model is undermined by the scientific data, I argue that this is no sufficient reason to adopt a model as coarse-grained as Łukasiewicz’s. I propose a model of intermediate level of fine-grainedness which could avoid the drawbacks of both extremes, and seems to me to provide a more traditional approach to the problem of evil. (shrink)

ABSTRACT McCabe [2021: 137–40] identifies a crucial ambiguity in the terms ‘learns’ and ‘knows’. Such terms can be read as either ‘perfective’ or ‘imperfective’. This is an aspect difference. The former indicates a settled state, the latter a directed process. McCabe uses this insight to show how Socrates can rebut the sophists’ view of meaning, render compelling Socrates’ self-refutation arguments, and explain the Socratic connections between learning, knowledge, and how one should live. In the final section of the Euthydemus, Euthydemus (...) offers the ‘Omniscience Sophism’, and the related, rather cheeky, ‘Father Sophisms’. McCabe [ibid.: 140–2] suggests that the Omniscience Sophism might be addressed by identifying an aspect ambiguity, but does not follow up her point in detail. In this response, I argue that McCabe’s instinct is good and that a relative term, such as ‘knowledgeable’, can be understood as having two senses. That distinction is between what I call ‘fine-grained’ and ‘coarse-grained’ senses of ‘knowledgeable’. I suggest that this distinction that tracks McCabe’s aspect distinction between senses of ‘learns’ and best explains the fallacy committed in the Omniscience Sophism. (shrink)

Plasmids are a major type of mobile genetic elements (MGEs) that mediate horizontal gene transfer. The stable maintenance of plasmids plays a critical role in the functions and survival for microbial populations. However, predicting and controlling plasmid persistence and abundance in complex microbial communities remain challenging. Computationally, this challenge arises from the combinatorial explosion associated with the conventional modeling framework. Recently, a plasmid‐centric framework (PCF) has been developed to overcome this computational bottleneck. This framework enables the derivation of a simple (...) metric, the persistence potential, to predict plasmid persistence and abundance. Here, we discuss how PCF can be extended to account for plasmid interactions. We also discuss how such model‐guided predictions of plasmid fates can benefit from the development of new experimental tools and data‐driven computational methods. (shrink)

Neuroimaging showing brain abnormalities is increasingly being introduced in criminal court proceedings to argue that a defendant could not control his behavior and should not be held responsible for it. But imaging has questionable probative value because it does not directly capture brain function or a defendant’s mental states at the time of a criminal act. Advanced techniques could transform imaging from a coarse-grained measure of correlations between brain states and behavior to a fine-grained measure of causal (...) connections between them. Even if this occurs, bias and other attitudes may unduly influence jurors’ interpretation of the data. Moreover, judges’ decisions about whether neuroimaging data is legally relevant and admissible are normative decisions based on more than empirical evidence. Advanced neuroimaging will better inform assessments of criminal responsibility but will not supplant or explain away the psychological and normative foundation of the criminal law. (shrink)

This paper aims to distinguish two main types of coarse graining, and reveal the relationship between the notions of coarse graining and emergence. In physics, some forms of coarse graining seem to be indispensable to show a physical property, and the other merely changes our descriptions of the system. To clarify the notion of coarse graining, this article investigates the cases of the renormalization group method and irreversibility, both of which have been important topics in philosophy (...) of science, and the case of the rigid body in classical mechanics, which is an elementary case including coarse graining. The case studies reveal the distinction between substantial and mere coarse-graining. This distinction clarifies the relationships between the notions of coarse graining and emergence and further provides some implications for the issues about emergence. (shrink)

We study uncertainty relations for a general class of canonically conjugate observables. It is known that such variables can be approached within a limiting procedure of the Pegg–Barnett type. We show that uncertainty relations for conjugate observables in terms of generalized entropies can be obtained on the base of genuine finite-dimensional consideration. Due to the Riesz theorem, there exists an inequality between norm-like functionals of two probability distributions in finite dimensions. Using a limiting procedure of the Pegg–Barnett type, we take (...) the infinite-dimensional limit right for this inequality. Hence, uncertainty relations are derived in terms of generalized entropies. In particular, the case of measurements with a finite precision is addressed. It takes into account that in any experiment an accuracy of performed measurements is always limited. (shrink)

The paper takes up Bell's “Everett theory” and develops it further. The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. This many-particle system as a whole performs random jumps through 3N-dimensional configuration space – hence “Tychistic Bohmian Mechanics”. The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. Contra Bell, the theory is argued to satisfy the minimal desiderata for (...) a Bohmian theory within the Primitive Ontology framework. TBM's formalism is that of ordinary Bohmian Mechanics, without the postulate of continuous particle trajectories and their deterministic dynamics. This “rump formalism” receives, however, a different interpretation. We defend TBM as an empirically adequate and coherent quantum theory. Objections voiced by Bell and Maudlin are rebutted. The “for all practical purposes”-classical, Everettian worlds exist sequentially in TBM. In a temporally coarse-grained sense, they quasi-persist. By contrast, the individual particles themselves cease to persist. (shrink)

In this article, monist values are expressed as preferences like in economics and decision making. On the basis of this formalization, various ways of defining value disagreement of agents within a group are investigated. Twelve notions of categorical value disagreement are laid out. Since these are too coarse-grained for many purposes, known distance-based approaches like Kendall’s Tau and Spearman’s footrule are generalized from linear orders to preorders and position-sensitive variants are developed. The account is further generalized to allow (...) for agents with incomplete information. The article ends with a discussion of known limitations of preference-based accounts of values and how these might be overcome by accounting for parity and essential incompleteness. It is also shown that one intuitively compelling notion of disagreement does not give rise to a proper distance measure. (shrink)

I analyse two different methods for the retrieval of a classical notion of spacetime from the theory of quantum cosmology in terms of the different means they employ to bring about the necessary loss of coherence. One method employs a direct coarse graining of the appropriate phase space, whereas the other method is based on decohering the system by the interaction with an environment. Although these methods are equivalent on a phenomenological level, I argue that conceptually the decoherence approach (...) is superior. The coarse graining approach construes the necessary loss of coherence in epistemic terms, whereas the method based on decohering the system by interaction with an environment provides a dynamical explanation for the emergence of classical notions of spacetime. On the latter account the emergence of classical behaviour is an objective property of the physical system under consideration, in contradistinction with the subjective coarse graining account of the retrieval of a classical spacetime in terms of measurements made by an observer. (shrink)

We introduce a simple model for so-called spin-echo experiments. We show that the model is a mincing system. On the basis of this model we study fine-grained entropy and coarse-grained entropy descriptions of these experiments. The coarse-grained description is shown to be unable to provide an explanation of the echo signals, as a result of the way in which it ignores dynamically generated correlations. This conclusion is extended to the general debate on the foundations of (...) statistical mechanics. We emphasize the need for an appropriate mechanism to explain the gradual suppression over time of the correlations in a thermodynamic system. We argue that such a mechanism can only be provided by the interventionist approach, in which the interaction of the system with its environment is taken into account. Irreversible behavior is then seen to arise not as a result of limited measurement accuracy , but as a result of the fact that thermodynamic systems are limited systems which interact with their environment. A detailed discussion is given of recent objections to the interventionist approach in the literature. (shrink)

I analyse two different methods for the retrieval of a classical notion of spacetime from the theory of quantum cosmology in terms of the different means they employ to bring about the necessary loss of coherence. One method employs a direct coarse graining of the appropriate phase space, whereas the other method is based on decohering the system by the interaction with an environment. Although these methods are equivalent on a phenomenological level, I argue that conceptually the decoherence approach (...) is superior. The coarse graining approach construes the necessary loss of coherence in epistemic terms, whereas the method based on decohering the system by interaction with an environment provides a dynamical explanation for the emergence of classical notions of spacetime. On the latter account the emergence of classical behaviour is an objective property of the physical system under consideration, in contradistinction with the subjective coarse graining account of the retrieval of a classical spacetime in terms of measurements made by an observer. (shrink)

The second law of thermodynamics is traditionally interpreted as a coarse-grained result of classical mechanics. Recently its relation with quantum mechanical processes such as decoherence and measurement has been revealed in literature. In this paper we will formulate the second law and the associated time irreversibility following Everett’s idea: systems entangled with an object getting to know the branch in which they live. Accounting for this self-locating knowledge, we get two forms of entropy: objective entropy measuring the (...) uncertainty of the state of the object alone, and subjective entropy measuring the information carried by the self-locating knowledge. By showing that the summation of the two forms of entropy is a conserved and perspective-free quantity, we interpret the second law as a statement of irreversibility in knowledge acquisition. This essentially derives the thermodynamic arrow of time from the subjective arrow of time, and provides a unified explanation for varieties of the second law, as well as the past hypothesis. (shrink)

The interpretation of the concept of reduced state is a subtle issue that has relevant consequences when the task is the interpretation of quantum mechanics itself. The aim of this paper is to argue that reduced states are not the quantum states of subsystems in the same sense as quantum states are states of the whole composite system. After clearly stating the problem, our argument is developed in three stages. First, we consider the phenomenon of environment-induced decoherence as an example (...) of the case in which the subsystems interact with each other; we show that decoherence does not solve the measurement problem precisely because the reduced state of the measuring apparatus is not its quantum state. Second, the non-interacting case is illustrated in the context of no-collapse interpretations, in which we show that certain well-known experimental results cannot be accounted for due to the fact that the reduced states of the measured system and the measuring apparatus are conceived as their quantum states. Finally, we prove that reduced states are a kind of coarse-grained states, and for this reason they cancel the correlations of the subsystem with other subsystems with which it interacts or is entangled. (shrink)

Through the kindness of Professor K. T. Erim of New York University I have the opportunity to offer the following note on a fragment of a Lydian inscription found recently during his excavations at Aphrodisias in Caria. The description and details of the archaeological context I owe to Professor Erim and to Miss Joyce Reynolds.The fragment came to light in July 1968, re-used in one of the ruined modern houses on the northern slope of the so-called acropolis when they were (...) being demolished in preparation for the full-scale excavation of the Theatre there. It is of medium- to coarse-grained marble, greyish in colour, probably from the Aphrodisias quarries themselves, and measures 0·11 × 0·75 × 0·165 m.; no original edges survive, but it is likely that the original left edge was very close to the surviving left edge.What remains of the inscribed surface is approximately trapezoidal in shape and carries traces of three lines of text; in the first only the lower tips of the letters survive and these cannot be securely interpreted, but in the second five complete letters can be read, although they have suffered from slight surface chipping, and in the third the upper two-thirds of five letters survives and these also can be read perfectly well. The inscription was firmly and deftly, if lightly, cut, with trenches c. 0·001 deep, very slightly triangular in profile and showing some tendency to broaden a little on the base line. Judging from the position of the last letters in Il. 2, 3, it seems probable that each line ended with a completed word. (shrink)

In this paper we study the emergence of Minkowski space–time from a discrete causal network representing a classical information flow. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity—including space–time—be defined through precise measurement procedures. Topological homogeneity is a requirement for having space–time metric emergent from the pure topology of causal connections, whereas physically homogeneity (...) corresponds to the universality of the physical law. We analyze in detail the case of 1+1 dimensions. If we consider the causal connections as an exchange of classical information, we can establish coordinate systems via an Einsteinian protocol, and this leads to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can be regarded as the synchronization with a global clock of the calls to independent subroutines in a parallel distributed computation. Thus the Lorentz time-dilation emerges as an increased density of leaves within a single tic-tac of a clock, whereas space-contraction results from the corresponding decrease of density of events per leaf. The operational procedure of building up the coordinate system introduces an in-principle indistinguishability between neighboring events, resulting in a network that is coarse-grained, the thickness of the event being a function of the observer's clock. The illustrated simple classical construction can be extended to space dimension greater than one, with the price of anisotropy of the maximal speed, due to the Weyl-tiling problem. This issue is cured if the causal network is quantum, as e.g. in a quantum cellular automaton, and isotropy is recovered by quantum coherence via superposition of causal paths. We thus argue that in a causal network description of space–time, the quantum nature of the network is crucial. (shrink)

When a jazz, rock, or hip-hop drummer strikes certain notes in each measure slightly late, instead of hearing the degree to which those notes are late, we typically hear the effects of those variations; namely, a groove, the "feel" of a rhythm. Slight variations of pitch function similarly. In this essay, I argue that certain analytic theorists go astray due to their preoccupation with the variations themselves. By invoking Maurice Merleau- Ponty's insights into subtle visual perceptions, and his notion of (...) perceptual indeterminacy, I avoid an account of musical subtlety suggested by Daniel Dennett that is too coarse-grained, as well as the bleak conclusion that certain musical subtleties are ineffable, Diana Raffman's view. I conclude that elements of music that are perceived ambiguously can perform a positive function in such aesthetic experiences: they can mediate or foster emergent qualities; moreover, they must be perceived in this way to do so. (shrink)

(1992). Grain packing in early standard capacity measures: Evidence from the scottish dry capacity standards. Annals of Science: Vol. 49, No. 4, pp. 337-350.

In talking about the compatibility of quantum observables, discussions often center on the question of whether the corresponding operators commute—even though commutativity is a coarse-grained notion that largely fails to capture the salient “nonclassical” features of quantum theory. Often, too, such discussions involve the issue of whether the operators in question satisfy a Heisenberg-like inequality, of the form ΔA·ΔB≥r>0—even though such inequalities are specific to unbounded operators and (for this and other reasons) are typically not a useful way (...) to discuss joint uncertainty in quantum mechanics. In the present paper we emphasize a simpler dichotomy, in which operator pairs (A, B) are classified according to whether or not states can be found with arbitrarily small dispersions in both A and B. If A and B cannot be made arbitrarily dispersionless simultaneously, then we call A and B an uncertainty pair. Otherwise, we call A and B a certainty pair. An interesting feature of uncertainty pairs in particular is that they are stable, in the sense that if A and B form an uncertainty pair, then slight enough perturbations of A and B must also form an uncertainty pair. This stability, obvious in the finite-dimensional case, follows in general from an operator inequality derived herein. A consequence of this inequality is that perturbed position and momentum operators X+δX and P+δP cannot share an eigenvector unless |δX|·|δP|≥ℏ/2. (Here vertical bars denote the operator norm.) This, despite the fact that (as we show) arbitrarily slight perturbations of X and P can fail to satisfy a Heisenberg inequality—a fact which raises interesting measurement issues in its own right. (shrink)

The purpose of this paper is to review and clarify the quantum “measurement problem.” The latter originates in the ambivalent nature of the “observer”: Although the observer is not described by the Schrödinger equation, it should nevertheless be possible to “quantize” him and include him in the wave function if quantum theory is universally valid. The problem is to prove that no contradiction may arise in these two conflicting descriptions. The proof invokes the notion of irreversibility. The validity of (...) the latter is questionable, because the standard rationale for classical irreversibility, namely mixing and coarse graining, does not apply to quantum theory. There is no chaos in a closed, finite quantum system. However, when a system is large enough, it cannot be perfectly isolated from its “environment,” namely from external (or even internal) degrees of freedom which are not fully accounted for in the Hamiltonian of that system. As a consequence, the long-range evolution of such a quantum system is essentially unpredictable. It follows that the notion of irreversibility is a valid one in quantum theory and the “measurement problem” can be brought to a satisfactory solution. (shrink)

This dissertation aims to determine the optimal level of granularity for the variables used in probabilistic causal models. These causal models are useful for generating explanations in a number of scientific contexts. In Chapter 1, I argue that there is rarely a unique level of granularity at which a given phenomenon can be causally explained, thereby rejecting various causal exclusion arguments. In Chapter 2, I consider several recent proposals for measuring the explanatory power of causal explanations, and show that these (...) measures fail to track the comparative depth of explanations given at different levels of granularity. In Chapter 3, I offer a pragmatic account of how to partition the measure space of a causal variable so as to optimally explain its effect. My account uses the decision-theoretic notion of value of information, and indexes the relative depth of an explanation to a particular agent faced with a particular decision problem. Chapter 4 applies this same decisiontheoretic framework to answer the epistemic question of how to discover constitutive relationships in nature. In Chapter 5, I describe the formal details of the relationship between random variables that are meant to be coarse-grained and fine-grained representations of the same type of phenomenon. I use this formal framework to rebut a popular argument for the view that special science probabilities can be objective chances. Chapter 6 discusses challenges related to the causal interpretation of Bayes nets that use imprecise rather than precise probabilities. (shrink)

Peter Brössel and Franz Huber in 2015 argued that the Bayesian concept of confirmation had no use. I will argue that it has both the uses they discussed—it can be used for making claims about how worthy of belief various hypotheses are, and it can be used to measure the epistemic value of experiments. Furthermore, it can be useful in explanations. More generally, I will argue that more coarse-grained concepts can be useful, even when we have more fine- (...) class='Hi'>grained concepts available. (shrink)

This paper describes how the entire universe might be considered an eigenstate determined by classical limiting conditions within it. This description is in the context of an approach in which the path of each relativistic particle in spacetime represents a fine-grained history for that particle, and a path integral represents a coarse-grained history as a superposition of paths meeting some criteria. Since spacetime paths are parametrized by an invariant parameter, not time, histories based on such paths do (...) not evolve in time but are rather histories of all spacetime. Measurements can then be represented by orthogonal states that correlate with specific points in such coarse-grained histories, causing them to decohere, allowing a consistent probability interpretation. This conception is applied here to the analysis of the two slit experiment, scattering and, ultimately, the universe as a whole. The decoherence of cosmological states of the universe then provides the eigenstates from which our “real” universe can be selected by the measurements carried out within it. (shrink)