A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the “virtual” paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born’s rule; therefore, Bell’s type (...) inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system. (shrink)

Adams' Thesis states that the probability of a conditional is the probability of the consequent conditional on the antecedent. S. Kaufmann introduced a rival method, the so-called ``local interpretation'', for calculating the probability of a conditional that, according to a purported majority, squares better with intuition in some circumstances. He also gives an example purporting to show that this new method sometimes corresponds to rational action. We challenge the intuitions and expose a mathematical error in the example. We (...) also offer a model for the local interpretivist semantics. This model puts theoretical local interpretivists on ground as solid as that of Thesis abiders for whom conditionals have truth conditions. (shrink)

Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in (...) which initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest. (shrink)

This is the first of two papers reviewing and analysing the approach to locality and to mind-body dualism proposed in Everett interpreta- tions of quantum mechanics. The planned companion paper will focus on the contemporary decoherence-based approaches to Everett. This paper instead treats the explicitly mentalistic Many Minds Interpreta- tion proposed by David Albert and Barry Loewer (Albert and Loewer 1988). In particular, we investigate what kind of supervenience of the mind on the body is implied by Albert and Loewer’s (...) Many Minds In- terpretation, and how the interpretation of the related ‘mindless hulks’ problem affects the issue of locality within this interpretation. (shrink)

This book examines in detail two of the fundamental questions raised by quantum mechanics. First, is the world indeterministic? Second, are there connections between spatially separated objects? In the first part, the author examines several interpretations, focusing on how each proposes to solve the measurement problem and on how each treats probability. In the second part, the relationship between probability (specifically determinism and indeterminism) and non-locality is examined, and it is argued that there is a non-trivial relationship between probability and (...) non-locality. The author then re-examines some of the interpretations of part one of the book in the light of this argument, and considers how they fare with regard to locality and Lorentz invariance. The book will appeal to anyone with an interest in the interpretation of quantum mechanics, including researchers in the philosophy of physics and theoretical physics, as well as graduate students in those fields. (shrink)

Neo-Confucian influence in early modern Japan was highly intellectual, indicating that Confucian ideals did not change the nature of Japanese norms of social lives. For early modern Japanese intellectuals, the conflict and contradiction between reality and ideals had always been a source of debate and inspiration. Within the theme of Neo-Confucian rites, the contradiction was highlighted owing to the fact that it included a guideline for authentic ancestral worship and religious policy. Once introduced within the Japanese circumstances of the day, (...) Confucian understanding on spirits and proper rites lead Japanese scholars to define what was legitimate worship in the format of state religion: it was necessary to authorize traditional Japanese worship toward domestic shrines. Within thepractical process of policy making, it must be noted that a keen interest toward local beliefs had emerged through the discussion. Arai Hakuseki (1657‐1725) reflects such political interest within his work ‘Kishinron’. In order to understand the impact of Japanese interpretation of Neo-Confucian ideals, it is essential to focus on the interrelationship between religious policy and interest toward local beliefs. (shrink)

The Measurement problem and Non-locality are classical problems in Quantum Mechanics and still unsolved in spite of the many proposed solutions. A new interpretation is proposed here, based on the idea that they are closely related problems. But it requires that we consider space and time not as objective mediums but as features of our representation of reality, as Kant explained more than two centuries ago.

One of the authors has recently propounded an SR model which shows, circumventing known no-go theorems, that an objective interpretation of quantum mechanics is possible. We consider here compound physical systems and show why the proofs of nonlocality of QM do not hold within the SR model, which is slightly simplified in this paper. We also discuss quantum measurement theory within this model, note that the objectification problem disappears since the measurement of any property simply reveals its unknown value, (...) and show that the projection postulate can be considered as an approximate law, valid FAPP. Finally, we provide an intuitive picture that justifies some unusual features of the SR model and proves its consistency. (shrink)

We show that the theory of the local structure of the enumeration degrees is computably isomorphic to the theory of first order arithmetic. We introduce a novel coding method, using the notion of a K-pair, to code a large class of countable relations.

This paper analyses the notion of ‘interpretation’, which is often tied to the semantic approach to logic, where it is used when referring to truth-value assignments, for instance. There are, however, other uses of the notion that raise interesting problems. These are the cases in which interpreting a logic is closely related to its justification for a given application. The paper aims to present an understanding of interpretations that supports the model-theoretic characterization of validity to the detriment of the (...) proof-theoretic one. This is done by making use of the hierarchy of ST-related logics. Finally, a localist conception of logic is defended as the natural view stemming from the model-theoretic approach. (shrink)

By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by ’t Hooft. We view these ontological states as the ones embedded with realism and compare them to the quantum states that represent superpositions, viewing the latter as mere information of the system they describe. Such a deterministic model puts forward conditions for the applicability of Bell’s inequality: the usual (...) inequality cannot be applied to the usual experiments. We build a Bell-like inequality that can be applied to the EPR scenario and show that this inequality is always satisfied by QM. In this way we show that QM can indeed have a local interpretation, and thus meet with the causal structure imposed by the Theory of Special Relativity in a satisfying way. (shrink)

In this brief paper, we argue about some epistemological positions about quantum non-locality.

In a two-channel interference experiment such as that considered in the preceding companion paper, a quantum may be localizable predominantly in one channel by a time-coincident experiment on a correlated quantum. The Copenhagen interpretation of quantum mechanics then requires a coincidence intensity prediction having the same reduced interference between channels as if the probability amplitude in the other channel had been attenuated by a filter. The quantum mechanical treatment of correlated systems originated by von Neumann does predict this reduced (...) interference, but avoids requiring a resulting direct locality violation by predicting that this reduced interference also occurs in a simple singles intensity observation. In contrast, de Broglie's locally causal interpretation of quantum mechanics requires that the experiment on the remote correlated system cannot change the amplitudes or phase relationship of coherent space-time wave propagating through the two channels, so that the full classical optics interference effect should be predicted for both singles and coincidence intensities. (shrink)

We construct a local \-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state \\rangle \) as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state \\rangle \) which is different from the prepared quantum state \\rangle \) and has an ontic status. The ontic state of a single particle (...) consists of two parts. First, a single particle ontic quantum state \|i\rangle \), where \\) is a 3-space wavepacket and \ is a spin eigenstate of the future measurement setting. Second, a particle position in 3-space \\), which evolves via a de Broglie–Bohm type guidance equation with the 3-space wavepacket \\) acting as a local pilot wave. The joint ontic quantum state \\rangle \) fixes the measurement outcomes deterministically whereas the prepared quantum state \\rangle \) determines the distribution of the \\rangle \)’s over an ensemble. Both \\rangle \) and \\rangle \) evolve via the Schrodinger equation. Our model exactly reproduces the Bell correlations for any pair of measurement settings. We also consider ‘non-equilibrium’ extensions of the model with an arbitrary distribution of hidden variables. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. We argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics. (shrink)

Interpretations that follow Everett's idea that the universal wave function contains a multiplicity of coexisting realities, usually claim to give a completely local account of quantum mechanics. That is, they claim to give an account that avoids both a non-local collapse of the wave function, and the action at a distance needed in hidden variable theories in order to reproduce the quantum mechanical violation of the Bell inequalities. In this paper, I sketch how these claims can be substantiated (...) in two renderings of Everett's ideas, namely the many-minds interpretation of Albert and Loewer, and versions of many-worlds interpretations that rely on the concepts of the theory of decoherence. (shrink)

The pragmatic framework developed by H.P. Grice in “Logic and Conversation” explains how a speaker can mean something more than, or different from, the conventional meaning of the sentence she utters. But it has been argued that the framework cannot give a similar explanation for cases where these pragmatic effects impact the understood content of an embedded clause, such as the antecedent of a conditional, a clausal disjunct, or the clausal complement of a verb. In this paper, I show that (...) such an explanation is available. One of the central arguments of the paper is that in a significant subset of cases, local pragmatic effects are a consequence of a global pragmatic requirement. In these cases, local pragmatic effects are a consequence of ‘acting locally’ to resolve a potential global pragmatic violation. These cases do not require us to posit application of pragmatic principles to the contents of embedded clauses. The account does, though, require the assumption that interpreters can identify and reason about the contents of unasserted sub-parts of sentences, an assumption that I motivate in section 3. Building on this, in section 4 of the paper, I argue that once we have recognized that interpreters can, and do, reason independently about the contents of non-asserted clauses, it becomes unproblematic to assume that in some cases, Gricean conversational principles do apply directly to these contents, providing an alternative route to account for local pragmatic effects. In revisiting the ideas of this paper in my response to the commentaries, I consider in more detail the revisions to Grice’s broader program that are necessitated by these moves, in particular acknowledging the problematicity of Grice’s notion of what is said. I argue that the starting point for Gricean reconstructions should instead be merely what is expressed, which carries no pragmatic commitments regarding what is speaker meant. (shrink)

It is a central aspect of our ordinary concept of time that history unfolds and events come into being. It is only natural to take this seriously. However, it is notoriously difficult to explain further what this `becoming' consists in, or even to show that the notion is consistent at all. In this article I first argue that the idea of a global temporal ordering, involving a succession of cosmic nows, is not indispensable for our concept of time. Our experience (...) does not support the existence of global simultaneity and arguments from modern physics further support the conclusion that time should not be seen as a succession of cosmic nows. Accordingly, I propose that if we want to make sense of becoming we should attempt to interpret it as something purely local. Second, I address the question of what this local becoming consists in. I maintain that processes of becoming are nothing but the successive happening of events, and that this happening of events consists entirely in the occurring of these events at their own spacetime locations. This leads to a consistent view of becoming, which is applicable even to rather pathological spacetimes. (shrink)

In response to Mandy Simons’ defence of a classical Gricean approach to pragmatic enrichment in terms of conversational implicature, I emphasize the following contrast. Conversational implicatures are generated by a global inference which uses as a premise the fact that the speaker has said that p, but only the triggering inference is global in cases of pragmatic enrichment. What generates the correct interpretation is a process of reconstrual, which locally maps the literal meaning of a constituent to a modulated (...) meaning and composes that meaning with that of the other constituents. That process is constrained by Gricean considerations but that is true of all pragmatic aspects of interpretation, whether pre-propositional or post-propositional. Just as indexical resolution, though pragmatic and constrained by Gricean considerations, does not fit the two-stage model through which Grice accounts for conversational implicatures, so pragmatic modulation can’t be accounted for in terms of that model despite the fact that, like conversational implicatures and unlike indexical resolution, modulation is pragmatically rather than semantically triggered. (shrink)

This paper tries to give some substance to local holism, a picture that seems to fit Wittgenstein’s analysis of the working of language. In the first part I state the well-known paradox of semantic holism, as discussed in philosophy of language: if meaning is holistic there is no possibility to share any meaning. In the second part I present the different answers to this paradox, from atomism to different forms of holism. In the third part I give a criticism (...) of the traditional interpretation of Wittgenstein as a supporter of global holism. As an alternative lecture I will suggest some lines of Wittgenstein's thought leading towards a definition of local holism. Eventually I will show connections with ideas developed in Multi Context theories in artificial intelligence, which help to show a possible direction of inquiry about restrictions on locality. (shrink)

In Re JB, a local authority, concerned with the risk the respondent posed to vulnerable women, successfully appealed against an order made in the Court of Protection that declared JB, an autistic man with impaired cognition, possessed capacity to consent to sexual relations. In this recent decision, the Court of Appeal has arguably reset the last 15 years of jurisprudence concerning P’s capacity to make decisions in regard to sexual relations. Previous case law focused on P’s ability to consent (...) to such relations, and whether P understood the information relevant to that decision. Notwithstanding the abundance of legal authority, including the recent appellate judgments of Hayden J in London Borough of Tower Hamlets v NB and AU [2019] EWCOP 27. and B v A Local Authority [2019] EWCA Civ 913. there was a lacuna in the existing law in relation to what information was relevant for the purposes of assessing the issue of capacity to consent to sexual relations. Judges have traditionally adopted a protectionist stance in understanding “the information relevant to the decision” under s3 of the Mental Capacity Act 2005, with an emphasis on whether P understood the risks of pregnancy and sexually transmitted diseases. However, the Court of Appeal in Re JB has broadened its interpretation of ‘relevant’ information to also include the ability to understand the importance of a partner’s consent to such relations. This is a welcome change to previous courts’ interpretations of the ‘nature’ of the sexual act, moving from an approach focused on the physical sexual mechanics to one which views the nature of sex as a mutually consensual engagement. However, a fundamental shift in how we view such cases is likely to have far-reaching consequences, particularly for local authorities and professionals seeking guidance in relation to their care planning. (shrink)

In this paper we provide a formal description of what it means to be in a local or partial information-state. Starting from the notion of locality in a relational structure, we define so-called adaptive gen- erated submodels. The latter are then shown to yield an adaptive logic wherein the derivability of Pφ is naturally interpreted as a core property of being in a state in which one holds the information that φ.

Of the unusual grammatical constructions which Statius employs for the sake of variety and novel effect, among the most remarkable is his use of the ablative case. There are striking instances at Th. 8. 157, Th. 10. 309, Ach. 1. 219, Ach. 2. 129; and W. C. Summers was led to say: ‘We see some traces in Valerius of the lax use of this case which became almost a disease with Statius, who employs it for almost any kind of idea.’ (...) There are three passages in Statius which have been misinterpreted or emended through the failure to recognize a use of the ablative to which he was especially prone—the local ablative where the poetic dative of ‘motion towards’ would seem more normal. I shall first list examples of this use in Statius where there is little or no doubt about interpretation or reading, and in the light of this accumulated evidence consider the three passages which are disputed. (shrink)

This paper is devoted to discuss a general tendency in contextualism which is known as "radical contextualism". In the first part I state the well known paradox of semantic holism, as discussed in philosophy of language: if meaning is holistic there is no possibility to share any meaning. In the second part I present the different answers to this paradox, from atomism to different forms of holism. In the third part I give a criticism of the traditional interpretation of (...) Wittgenstein as a supporter of global holism. I stress some similarities between Wittgenstein's thought and Multi Context theories in artificial inteligence. In the last part I give some argument against a rigid interpretation of "local holism": I claim the need to give restrictions to local holim and to develop a study of the connections between "default" properties and high level rules which are studied in Multi−Context theories. (shrink)

In this paper (a sequel to [4]) I put forward a "local" interpretation of mathematical concepts based on notions derived from category theory. The fundamental idea is to abandon the unique absolute universe of sets central to the orthodox set-theoretic account of the foundations of mathematics, replacing it by a plurality of local mathematical frameworks - elementary toposes - defined in category-theoretic terms.

The reality of physical properties is divided into two types: “relatively” and “absolutely” real. Concerning the reality of spatial observables, it is proposed to drop the concept of an absolute reality of spatial observables. The resulting relative reality then isnot the observer-dependent reality of the standard interpretation of quantum mechanics, but rather the reference frame-dependent reality implied by the principle of relativity. Within the frame of this relative reality, it is then shown that a local explanation for the (...) existence of EPR correlations can be found when two-valued discrete spatially directed observables (like the spin-1/2 components of electrons, or the polarization states of photons) are assumed. The new explanation is formally analogous to the standard explanation of classical correlations at a distance. Sufficient assumptions to obtain this result are the isotropy of space and the existence of two-valued discrete spatially directed observables. Thus, the possibility to find a both local and realistic explanation of correlations at a distance is extended to quantum variables violating Bell's inequality. (shrink)

Its interpretation, however, is as unsettled now as in the heroic days of Einstein and Bohr.This book focuses on quantum non-locality, the curious quantum ...

I will give a broad overview of what has become the standard paradigm in cosmology. I will describe the relational notion of time that is often used in cosmological calculations and discuss how the local nature of Einstein's equations allows us to translate this notion into statements about `initial' data. Classically this relates our local definition of time to a quasi-local region of a particular spatial slice, however incorporating quantum theory comes at the expense of losing this (...) locality entirely. This occurs due to the presence of two, apparently distinct, issues: Seemingly classical issues to do with the infinite spatial volume of the universe and Quantum field theory issues, which revolve around trying to apply renormalization in cosmology. Following the ‘cosmological principle’ - an extension of the ‘Copernicus principle’ - that physics at every point in our universe should look the same, we are lead to the modern view of cosmology. This procedure is reasonably well understood for an exactly homogeneous universe, however the inclusions of small perturbations over this homogeneity leads to many interpretational/ conceptual difficulties. For example, in an infinite universe perturbations can be arbitrarily close to homogeneous. To any observer, such a perturbation would appear to be a simple rescaling of the homogenous background and hence, physically, would not be considered an inhomogeneous perturbation at all. However, any attempt to choose the physically relevant scale at which perturbations should be considered homogeneous will break the cosmological principle i.e. it will make the resulting physics observer dependent. It amounts to `putting the perturbations in a box' and a delicate practical issue is that the universe is not static, hence the scale of the box will be time dependent. Thus what appears ‘physically homogeneous’ to an observer at one time will not appear so at another. This issue is brought to the forefront by considering the canonical version of the theory. The phase space formulation of General Relativity, just as for any other theory, contains the shadow of the underlying quantum theory. This means that, although the formulation is still classical, many of the subtleties that are present in the quantum theory are already apparent. In the cosmological context the infinite spatial volume renders almost all expressions formal or ill-defined. In order to proceed, we must restrict our attention to a cosmology that has some finite spatial extent, on which our relational notion of time is everywhere definable. In particular, this would constrain the permissible data outside our `observable universe'. This difficulty is an IR or large scale issues in cosmology, however in addition there are UV or short scale problems that need to be tackled. There are the usual problems of renormalization, which are further complicated by the fact that the universe is not static. In the cosmological setting this leads to new IR problems which again prevent one from taking the spatial extent of the universe to infinity. The physical relevance of this problem, the consequence for defining a time variable, and the distinction of homogeneous and inhomogeneous IR issues will be discussed. (shrink)

Bell's theorem is believed to establish that the quantum mechanical predictions do not generally admit a causal representation compatible with Einsten's principle of separability, thereby proving incompatibility between quantum mechanics and relativity. This interpretation is contested via two convergent approaches which lead to a sharp distinction between quantum nonseparability and violation of Einstein's theory of relativity.In a first approach we explicate from the quantum mechanical formalism a concept of “reflected dependence.” Founded on this concept, we produce a causal representation (...) of the quantum mechanical probability measure involved in Bell's proof, which is clearly separable in Einstein's sense, i.e., it does not involve supraluminal velocities, and nevertheless is “nonlocal” in Bell's sense. So Bell locality and Einstein separability aredistinct qualifications, and Bell nonlocality (or Bell nonseparability) and Einstein separability arenot incompatible. It is then proved explicitly that with respect to the mentioned representation Bell's derivation does not hold. So Bell's derivation does notestablish thatany Einstein-separable representation is incompatible with quantum mechanics. This first—negative—conclusion is asyntactic fact.The characteristics of the representation and of the reasoning involved in the mentioned counterexample to the usual interpretation of Bell's theorem suggest that the representation used—notwithstanding its ability to bring forth the specified syntactic fact—isnot factually true. Factual truth and syntactic properties also have to be radically distinguished in their turn. So, in a second approach, starting from de Broglie's initial relativistic model of a microsystem, a deeper, factually acceptable representation is constructed. The analyses leading to this second representation show that quantum mechanics does indeed involve basically a certain sort of nonseparability, called here de Broglie-Bohr quantum nonseparability. But the de Broglie-Bohr quantum nonseparability is shown to stem directly from the relativistic character of the considerations which led Louis de Broglie to the fundamental relation p = h/λ,thereby being essentially consistent with relativity. As to Einstein separability, it appears to be a still insufficiently specified conceptof which a future, improved specification, will probably be explicitly harmonizable with the de Broglie-Bohr quantum nonseparability.The ensemble of the conclusions obtained here brings forth a new concept of causality, a concept offolded, zigzag, reflexive causality, with respect to which the type of causality conceived of up to now appears as aparticular case of outstretched, one-way causality. The reflexive causality is found compatible with the results of Aspect's experiment, and it suggests new experiments.Considered globally, the conclusions obtained in the present work might convert the conceptual situation created by Bell's proof into a process of unification of quantum mechanics and relativity. (shrink)

This book concentrates on research done during the last twenty years on the philosophy of quantum mechanics. In particular, the author focuses on three major issues: whether quantum mechanics is an incomplete theory, whether it is non-local, and whether it can be interpreted realistically. Much of the book is concerned with distinguishing various senses in which these questions can be taken, and assessing the bewildering variety of answers philosophers and physicists have given up to now. The book is self-contained (...) in that it presents the necessary parts of the mathematical formalism of quantum mechanics and also covers other interpretative topics, such as the problem of measurement and the uncertainty relations. A considerable portion of the book is based on original arguments presented by the author in lectures and research papers over the past ten years. However, this material is integrated with a broad coverage of most of the recent research in the field, so as to provide a balanced introduction to the whole subject. (shrink)

There are two central themes that occupy the commentaries, and hence this response. The first is the character and role of what is said, both in my account, and in pragmatic theory in general. In response, I lay out in more detail the proposal from my original paper that the starting point for Gricean reasoning should be not what is said, but the pragmatically uncommitted what is expressed. As part of this argument, I restate and provide further arguments for my (...) claim that global and local pragmatic effects are continuous. The second central theme of the commentaries concerns the value of a Gricean account, which is not intended to model the psychological processes of interpretation. I respond to this concern in Section 5, ‘Pragmatics, psychology and processing’. (shrink)

Arguments are provided for the reality of the quantum vacuum fields. A polarization correlation experiment with two maximally entangled photons created by spontaneous parametric down-conversion is studied in the Weyl–Wigner formalism, that reproduces the quantum predictions. An interpretation is proposed in terms of stochastic processes assuming that the quantum vacuum fields are real. This proves that local realism is compatible with a violation of Bell inequalities, thus rebutting the claim that it has been refuted by experiments. Entanglement appears (...) as a correlation between fluctuations of a signal field and vacuum fields. (shrink)

Interpretive Political Science is the second of two volumes featuring a selection of key writings by R.A.W. Rhodes. Volume II looks forward and explores the 'interpretive turn' and its implications for the craft of political science, especially public administration, and draws together articles from 2005 onwards on the theme of 'the interpretive turn' in political science. Part I provides a summary statement of the interpretive approach, and Part II develops the theme of blurring genres and discusses a variety of research (...) methods common in the humanities, including: ethnographic fieldwork, life history, and focus groups. Part III demonstrates how the genres of thought and presentation found in the humanities can be used in political science. It presents four examples of such blurring 'at work' with studies of: applied anthropology and civil service reform; women's studies and government departments; and storytelling and local knowledge. The book concludes with a summary of what is edifying about an interpretive approach, and why this approach matters, and revisits some of the more common criticisms before indulging in plausible conjectures about the future of interpretivism. The author seeks new and interesting ways to explore governance, high politics, public policies, and the study of public administration in general. (shrink)

In this paper we study local induction w.r.t. Σ1‐formulas over the weak arithmetic. The local induction scheme, which was introduced in, says roughly this: for any virtual class that is progressive, i.e., is closed under zero and successor, and for any non‐empty virtual class that is definable by a Σ1‐formula without parameters, the intersection of and is non‐empty. In other words, we have, for all Σ1‐sentences S, that S implies, whenever is progressive. Since, in the weak context, we (...) have (at least) two definitions of Σ1, we obtain two minimal theories of local induction w.r.t. Σ1‐formulas, which we call Peano Corto and Peano Basso.In the paper we give careful definitions of Peano Corto and Peano Basso. We establish their naturalness both by giving a model theoretic characterization and by providing an equivalent formulation in terms of a sentential reflection scheme.The theories Peano Corto and Peano Basso occupy a salient place among the sequential theories on the boundary between weak and strong theories. They bring together a powerful collection of principles that is locally interpretable in. Moreover, they have an important role as examples of various phenomena in the metamathematics of arithmetical (and, more generally, sequential) theories. We illustrate this by studying their behavior w.r.t. interpretability, model interpretability and local interpretability. In many ways the theories are more like Peano arithmetic or Zermelo Fraenkel set theory, than like finitely axiomatized theories as Elementary Arithmetic, and. On the one hand, Peano Corto and Peano Basso are very weak: they are locally cut‐interpretable in. On the other hand, they behave as if they were strong: they are not contained in any consistent finitely axiomatized arithmetical theory, however strong. Moreover, they extend, the theory of parameter‐free Π1‐induction. (shrink)

For “natural enough” systems of ordinal notation we show that α times iterated local reflection schema over a sufficiently strong arithmetic T proves the same Π 1 0 -sentences as ω α times iterated consistency. A corollary is that the two hierarchies catch up modulo relative interpretability exactly at ε-numbers. We also derive the following more general “mixed” formulas estimating the consistency strength of iterated local reflection: for all ordinals α ⩾ 1 and all β, β ≡ Π (...) 1 0 T ω α · , α ≡ Π 1 0 T β + ω α . Here T α stands for α times iterated local reflection over T , T β stands for β times iterated consistency, and ≡ Π 1 0 denotes mutual Π 1 0 -conservativity. In an appendix to this paper we develop our notion of “natural enough” system of ordinal notation and show that such systems do exist for every recursive ordinal. (shrink)

A model for measurement in collapse-free nonrelativistic fermionic quantum field theory is presented. In addition to local propagation and effectively-local interactions, the model incorporates explicit representations of localized observers, thus extending an earlier model of entanglement generation in Everett quantum field theory (Rubin in Found. Phys. 32:1495–1523, 2002). Transformations of the field operators from the Heisenberg picture to the Deutsch-Hayden picture, involving fictitious auxiliary fields, establish the locality of the model. The model is applied to manifestly-local calculations (...) of the results of measurements, using a type of sudden approximation and in the limit of massive systems in narrow-wavepacket states. Detection of the presence of a spin-1/2 system in a given spin state by a freely-moving two-state observer illustrates the features of the model and the nonperturbative computational methodology. With the help of perturbation theory the model is applied to a calculation of the quintessential “nonlocal” quantum phenomenon, spin correlations in the Einstein-Podolsky-Rosen-Bohm experiment. (shrink)

Is it possible to approach quantum theory in a 'therapeutic' vein that sees its foundational problems as arising from mistaken conceptual presuppositions? The book explores the prospects for this project and, in doing so, discusses such fascinating issues as the nature of quantum states, explanation in quantum theory, and 'quantum non-locality'.

In the ninth book of his Ἀτθίς the Athenian historian and religious expert Philochorus related an omen about which he had himself been consulted in the late fourth centuryb.c.e.(FGrHist328 F 67).When this year was done and the next was beginning, there occurred on the Acropolis the following prodigy: a female dog, having entered the temple of Athena Polias and made its way into the Pandroseion, got up on the altar of Zeus Herkeios, which is under the olive tree, and lay (...) down. It is an ancestral custom among the Athenians that no dog go up on the Acropolis. Around the same time, a star was evident for a while even in the daytime sky, when the sun was out and the weather was clear. And when we were asked about what the portent and the phenomenon meant, we said that both predicted the return of the exiles and that this would happen not as a result of a political change but rather in the existingpoliteia. And this interpretation actually came to pass. (shrink)

The apparent nonlocality of quantum theory has been a persistent concern. Einstein et al. and Bell emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everett-inspired many worlds interpretation try to circumvent it. In this paper, we review Bell's "no-go" theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled (...) out by the experimentally confirmed entanglement correlations, we make clear that it is the conjunction of the three axioms that is ruled out by these correlations. We then show that by assuming local causality and no superdeterminism, we can give a direct proof of many worlds. The remainder of the paper searches for a consistent, local, formulation of many worlds. We show that prominent formulations whose ontology is given by the wave function violate local causality, and we critically evaluate claims in the literature to the contrary. We ultimately identify a local many worlds interpretation that replaces the wave function with a separable Lorentz-invariant wave-field. We conclude with discussions of the Born rule, and other interpretations of quantum mechanics. (shrink)

What is it to interpret the outputs of an opaque machine learning model? One approach is to develop interpretable machine learning techniques. These techniques aim to show how machine learning models function by providing either model-centric local or global explanations, which can be based on mechanistic interpretations (revealing the inner working mechanisms of models) or non-mechanistic approximations (showing input feature–output data relationships). In this paper, we draw on social philosophy to argue that interpreting machine learning outputs in certain normatively (...) salient domains could require appealing to a third type of explanation that we call “socio-structural” explanation. The relevance of this explanation type is motivated by the fact that machine learning models are not isolated entities but are embedded within and shaped by social structures. Socio-structural explanations aim to illustrate how social structures contribute to and partially explain the outputs of machine learning models. We demonstrate the importance of socio-structural explanations by examining a racially biased healthcare allocation algorithm. Our proposal highlights the need for transparency beyond model interpretability: understanding the outputs of machine learning systems could require a broader analysis that extends beyond the understanding of the machine learning model itself. (shrink)

We formulate a model of EPR experiments by including variables determining whether a photon will be detected or not. The resulting deterministic model satisfies Bell's original inequality even though it can agree exactly with the quantum mechanical predictions for the performed experiments. It violates variations of the inequality used in the interpretation of the experiments and deduced with the help of additional assumptions.

While much has been written about the uniquely Hawaiian take on the category “local” – usually in terms of resistance to colonization, the alternative or counterhegemonic – little has been written about “haole”, the trope that served to silhouette the “local” and has evolved in dialectical opposition to it. A term that emerged during the plantation era to represent working-class immigrant workers mostly from Asia, “local” is constructed by exclusion. It has evolved to represent solidarity against all (...) “external forces” controlling Hawai'i from without, such as land development, tourism and the military – all readily equated with haole, the visible sign of whiteness. The prevalence of the prescription “local vs. haole” in contemporary Hawai'i begs an inquiry into other interpretations that are being suppressed. This paper explores some suppressed histories, imaginings and subconscious aspects of identity in Hawai'i through the figure of the white person whose parents – and possibly great-great-great-grandparents – were born and raised in Hawai'i. (shrink)