We prove a uniqueness theorem showing that, subject to certain natural constraints, all 'no collapse' interpretations of quantum mechanics can be uniquely characterized and reduced to the choice of a particular preferred observable as determine (definite, sharp). We show how certain versions of the modal interpretation, Bohm's 'causal' interpretation, Bohr's complementarity interpretation, and the orthodox (Dirac-von Neumann) interpretation without the projection postulate can be recovered from the theorem. Bohr's complementarity and Einstein's realism appear as two quite different proposals (...) for selecting the preferred determinate observable--either settled pragmatically by what we choose to observe, or fixed once and for all, as the Einsteinian realist would require, in which case the preferred observable is a 'beable' in Bell's sense, as in Bohm's interpretation (where the preferred observable is position in configuration space). (shrink)

We show that the Bub-Clifton uniqueness theorem (1996) for 'no collapse' interpretations of quantum mechanics can be proved without the 'weak separability' assumption.

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

Proposed derivations of the Born rule for Everettian theory are controversial. I argue that they are unnecessary but may provide justification for a simplified version of the Principal Principle. It’s also unnecessary to replace Everett’s idea that a subject splits in measurement contexts with the idea that subjects have linear histories which partition Many worlds? Everett, quantum theory, and reality, Oxford University Press, Oxford, pp 181–205, 2010; Wallace in The emergent multiverse, Oxford University Press, Oxford, 2012, Chapter 7; Wilson in (...) Br J Philos Sci 64:709–737, 2013; The nature of contingency: quantum physics as modal realism, Oxford University Press, Oxford, forthcoming). Linear histories were introduced to provide a concept of pre-measurement uncertainty and I explain why pre-measurement uncertainty for splitting subjects is after all coherent, though not necessary because Everett’s original fission interpretation of branching can arguably be rendered coherent without it, via reference to Vaidman, Tappenden, Sebens and Carroll and McQueen and Vaidman. A deterministic and probabilistic quantum mechanics can be made intelligible by replacing the standard collapse postulate with a no-collapse postulate which identifies objective probability with relative branch weight, supplemented by the simplified Principal Principle and some revisionary metaphysics. (shrink)

Regarded for decades as a fallacy, intentionalist interpretation is beginning to attract a following among philosophers of art. Intentionalism is the doctrine that the actual intentions of artists are relevant to the interpretation of the artworks they create – just as actual intentions are relevant to the interpretation of the everyday words and deeds of other people. Although there are several forms of actual intentionalism, I defend the form known as modest actual intentionalism, which holds that the correct interpretation of (...) an artwork is compatible with the author's actual intention, which itself must be supported by the artwork. Looking at literary works specifically, I consider criticisms of actual intentionalism – for example, the contention that such a stance substitutes paraphrase for a reading of the text. In particular, I argue against hypothetical intentionalism, which maintains that the correct interpretation of an artwork is constrained by the best hypotheses of the artist's intentions. As I show, the methodology of this position is in fact designed to track the author's actual intentions, and furthermore, hypothetical intentionalism does not accurately depict existing interpretive practices. (shrink)

It has been shown that quantum mechanics in its orthodox interpretation violates four different formulations of causality principle endowed with empirical meaning. The present work aims to highlight how even a realistic non-standard interpretation of the theory conflicts with causality in its Cartesian formulation of the principle of the non-inferiority of causes over effects. Such an interpretation, which attributes some form of weak physical reality to the wave function (called empty wave, regarded as a zero-energy wave-like phenomenon), is a sort (...) of precursor of the more recent so-called wavefunction realism. We also discuss a more radical realistic interpretation according to which physical properties can also be assigned to non-metaphysical relative nothing, seen as the simple absence of a particle such as a photon, but not of its corresponding state (no-photon), which is considered real. By interpreting the wave function collapse as a consequence of an interaction with empty waves or of a detection of the no-photon, we will highlight how more real physical effects can derive from lower causes, including relative nothing. Finally, we will show how these interpretations, while violating Cartesian causality in its two variants, do not seem to affect the validity of the principle of a rational explanation that nothing can derive from (absolute) nothing, which does not seem satisfied by the orthodox interpretation. (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)

A recent no-go theorem gives an extension of the Wigner’s Friend argument that purports to prove the “Quantum theory cannot consistently describe the use of itself.” The argument is complex and thought provoking, but fails in a straightforward way if one treats QM as a statistical theory in the most fundamental sense, i.e. if one applies the so-called ensemble interpretation. This explanation is given here at an undergraduate level, which can be edifying for experts and students alike. A recent paper (...) has already shown that the no-go theorem is incorrect with regard to the de Broglie Bohm theory and misguided in some of its general claims. This paper’s contribution is three fold. It shows how the extended Wigner’s Friend argument fails in the ensemble interpretation. It also makes more evident how natural a consistent statistical treatment of the wave function is. In this way, the refutation of the argument is useful for bringing out the core statistical nature of QM. It, in addition, manifests the unnecessary complications and problems introduced by the collapse mechanism that is part of the Copenhagen interpretation. The paper uses the straightforwardness of the ensemble interpretation to make the no-go argument and its refutation more accessible. (shrink)

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

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)

Modal interpretations of quantum mechanics admit two kinds of state: physical states, which specify the values of observables on a system, and theoretical states, which specify a probability distribution over possible physical states. They appear to use this distinction to deny the projection postulate, claiming that collapse corresponds only to a change from discussing the theoretical state to discussing the physical state. I argue that modal interpretations should adopt a projection postulate at the level of the theoretical (...) state. However, other features of modal interpretations might render the projection postulate immune from the usual objections. (shrink)

Colloque international sur « Les adjectifs » Responsables : Georgette Dal, Jan Goes, Rafael Marín, Philip Miller, Fayssal Tayalati). Université de Lille 3, 13-15 septembre 2007. Programme téléchargeable en annexe Symposium « L’interprétation des fragments, I : recompositions antiquaires, usages esthétiques, enjeux philosophiques » Organisé dans le cadre du PICS Lille-Munich « L’interprétation entre logique et philologie ». Responsable du c...

Cécile Conduché, Les exemples grecs des Institutions grammaticales de Priscien, héritages et doctrines Thèse soutenue le 13 octobre 2012 à l’Université Lille 3 Composition du jury Jean-Christophe Jolivet, Professeur à l’Université de Lille 3 Guillaume Bonnet, Professeur à l’Université de Bourgogne Jean Schneider, Professeur à l’Université de Lyon 2 Marc Baratin, Professeur à l’Université de Lille 3, Directeur de thèse Gweltaz Guyomarc’h, Aux origines de la métaphysique : l’interprétation par ..

Reviews the book, Minding minds: Evolving a reflexive mind by interpreting others by Radu J. Bogdan. Drawing on philosophical, psychological, and evolutionary perspectives, Bogdan analyzes the main phylogenetic and ontogenetic stages through which primates’ abilities to interpret other minds evolved and gradually created the opportunities and resources for mental reflexivity. 2012 APA, all rights reserved).

Studien zum Entstehen der Philosophie Wittgensteins János Kristóf Nyíri. BEIM STERNENLICHT DER NICHTEXISTIERENDEN: ZUR IDEOLOGIEKRITISCHEN INTERPRETATION DES PLA- TONISIERENDEN ANTIPSYCHOLOGISMUS* ...

Reviews the book, Discovering existence with Husserl by Emmanuel Levinas, translated by Richard A. Cohen and Michael B. Smith. The work of Emmanuel Levinas represents one of the most innovative and influential expositions of twentieth-century phenomenology. His thought represents a radically new interpretation of the phenomenological project, the meaning of ethics, and the role of ontology and metaphysics in our discussion of the Other and the Good. 2012 APA, all rights reserved).

Reviews the book, Re-envisioning psychology: Moral dimensions of theory and practice by Frank C. Richardson, Blaine J. Fowers, and Charles B. Guignon . Not often in the discipline of psychology does a work of genuinely praiseworthy philosophical sophistication come along that also manages to avoid not only being overly narrow in its relevance but also avoids being filled with unintelligible and pseudo-intellectual jargon. This excellent text is an example of one such work. The authors divided their text into three major (...) sections beginning with a careful and ranging analysis of the ethical underpinnings of contemporary psychotherapy, followed by a timely and provocative discussion of individualism, social constructionism, and hermeneutics, and complete the volume with a preliminary exploration of the principle features of an interpretive psychology. 2012 APA, all rights reserved). (shrink)

Modal interpretations are hidden-variable, no-collapse interpretations of quantum mechanics that were designed to solve the measurement problem and reconcile this theory with relativity. Yet, as no-go theorems by Dickson and Clifton, Arntzenius and Myrvold demonstrate, current modal interpretations are incompatible with relativity. In the mainstream modal interpretations, properties of composite systems are generally unrelated to the properties of their subsystems. We propose holistic and relational interpretations of properties to explain this failure of property composition. (...) Based on these interpretations, we consider strategies for circumventing Myrvold's theorem, which are also effective against the other two theorems. (shrink)

Pack includes 2 titles from the popular Blackwell Philosophy Anthologies Series: Philosophy of Literature: Contemporary and Classic Readings - An Anthology Edited by Eileen John and Dominic McIver Lopes ISBN: 9781405112086 Essential readings in the philosophy of literature are brought together for the first time in this anthology. Contains forty-five substantial and carefully chosen essays and extracts Provides a balanced and coherent overview of developments in the field during the past thirty years, including influential work on fiction, interpretation, metaphor, literary (...) value, and the definition and ontology of literature Includes an additional historical section featuring generous selections of the writings of early pioneers such as Plato, Aristotle, Nietzsche, and Hume Serves as an ideal introduction to the philosophy of literature or the philosophy of art, as well as a handy compilation of contributions to the field by its leading figures Philosophy of Film and Motion Pictures: An Anthology Edited by Noël Carroll and Jinhee Choi ISBN: 9781405120272 Designed for classroom use, this authoritative anthology presents key selections from the best contemporary work in philosophy of film. The featured essays have been specially chosen for their clarity, philosophical depth, and consonance with the current move towards cognitive film theory Eight sections with introductions cover topics such as the nature of film, film as art, documentary cinema, narration and emotion in film, film criticism, and film's relation to knowledge and morality Issues addressed include the objectivity of documentary films, fear of movie monsters, and moral questions surrounding the viewing of pornography Replete with examples and discussion of moving pictures throughout. (shrink)

Testable predictions of quantum mechanics are invariant under time reversal. But the evolution of the quantum state in time is not so, neither in the collapse nor in the no-collapse interpretations of the theory. This is a fact that challenges any realistic interpretation of the quantum state. On the other hand, this fact raises no difficulty if we interpret the quantum state as a mere calculation device, bookkeeping past real quantum events.

Two of the main interpretative problems in quantum mechanics are the so-called measurement problem and the question of the compatibility of quantum mechanics with relativity theory. Modal interpretations of quantum mechanics were designed to solve both of these problems. They are no-collapse (typically) indeterministic interpretations of quantum mechanics that supplement the orthodox state description of physical systems by a set of possessed properties that is supposed to be rich enough to account for the classical-like behavior of macroscopic (...) systems, but sufficiently restricted so as to avoid the no-hidden-variables theorems. But, as recent no-go theorems suggest, current modal interpretations are incompatible with relativity. In this paper, we suggest a strategy for circumventing these theorems. We then show how this strategy could naturally be integrated in a relational version of the modal interpretation, where quantum-mechanical states assign relational rather than intrinsic properties. (shrink)

Chapter 1: An Introduction: The ‘Semantic Sting’ Argument Describes Dworkin’s theory as concerning the conditions of legal validity. “A legal system is a system of norms. Validity is a logical property of norms in a way akin to that in which truth is a logical property of propositions. A statement about the law is true if and only if the norm it purports to describe is a valid legal norm…It follows that there must be certain conditions which render certain norms, (...) but not others, legally valid. Hence it also follows that there can be two types of disagreement over the truth or falsehood of propositions about the law. People can disagree over the question ‘What are the conditions of legal validity?’, in which case their disagreement is a theoretical one. Or they can agree on the conditions of validity, and disagree as to whether or not those conditions actually obtain in a given case or not.” Argues that the best way to interpret Dworkin’s ‘semantic-sting argument’ is as a general argument against conventionalism in legal positivism. Summarizes the outcome of Dworkin’s argument as follows: “[I]f Dworkin is right about the legal reasoning of lawyers and judges, conventionalism would be self-defeating: if lawyers and judges recognize as legally binding not only those norms which are uncontroversially identifiable under the Rule of Recognition, that is, if what they recognize as binding is not only source-based law, then conventionalism turns out to be false on its own terms. In other words, either law is not what lawyers and judges think that it is, in which case law is not a matter of conventions, or – if it is what lawyers and judges think – conventionalism is false, as they do not see the law as purely a matter of conventions.” Dworkin’s theory, then, is a new conception of jurisprudence aiming to present itself as a rival to conventionalism. The book will be concerned with re-examining positivism in light of the interpretative challenge. Chapter 2: Meaning and Interpretation “[R]oughly, interpretation can be defined as an understanding or explanation of the meaning of an object.” Interpretation in this narrow sense is distinct from a less formal and broader use of interpretation that makes it equivalent to explanation. “Hence also, only those objects which are capable of bearing some meaning qualify as objects of interpretation.” [Why shouldn’t we think of interpretation as object-identification? This seems to be closer to what Dworkin has in mind.] Thus, a consideration of the philosophical work on meaning is appropriate. First, a consideration of Davidson on interpretation. The thesis is that Davidson’s “radical interpretation” can only account for sentence meaning and not for linguistic interpretation in general. Davidson cannot account for the non-rule-governed aspects of communication. “Semantics, as opposed to interpretation, concerns those aspects of communication which are rule or convention governed…but such rules are normally unavailable as reasons or justifications for an interpretation. On the contrary, interpretation is usually required because the issue is not determined by rules or conventions.” Interpretation, rather, is parasitic with understanding the meaning of an expression and not equivalent with it. As Dummett notes, any reflection on the meanings of words assumes prior knowledge of ordinary meanings. “This leads to the conclusion that understanding or explaining the meaning of an expression and interpreting it, are two conceptually separate things. It also indicates that seman ics can only be employed, if at all, to elucidate the concept of interpretation by way of contrast: interpretation concerns those aspects of communication which are under-determined by semantic rules or conventions.” Pragmatics, the study of problems posed by discrepancies between utterer’s meaning and sentence meaning, would seem to be closer to inquiry into interpretation. Both are concerned with understanding how meaning is possible where conventional rules leave off. Contemporary pragmatics, moreover, recognizes the logically indeterminate character of communicative inferences beyond conventional meaning and that the contextual conditions that account for the possibility cannot be realized in the semantic structure of the sentence. However, different criteria of success may be at work in pragmatics than interpretation. Pragmatics is concerned with how communication is achieved and thus the criteria of success would be grasping a speaker’s intentions. Many think, however, that communication is unimportant in certain spheres of communication, e.g. artistic interpretation, and that in these cases the aim of interpretation is not to uncover the actual artist’s intentions. What kind of meaning is interpretation aimed at then? It cannot be the meaning the object has for the interpreter. “Interpretation purports to be a statement about the object interpreted, not about the subject who offers the interpretation…it is crucial to remember that not everything we say about a work of art, or any other text, amounts to an interpretation of it. Only those aspects of a text which can shed light on its meaning form part of the text’s interpretation. What the text means for someone rarely entails anything about what the text means.” [This is puzzling to some extent for it remains somewhat ambiguous what it means to talk of subject-independent meaning.] Interpretive meaning attribution is, rather, counterfactual. “In general, I will suggest that the answer to this question consists in the fact that meaning is assigned by a counterfactual statement. Given that x is the meaning attributed to, for instance a text T, and x is not the literal meaning of T, nor is it the meaning of T intended by its author, then the attribution of meaning x to T can only be understood as the contention that on the basis of certain assumptions a certain fictitious or stipulated speaker would have meant x by expressing T.” Thus, on this account, interpretation, when it does not concern an actual speaker, turns out to be a kind of counterfactual intention attribution. Twofold point: “First, that interpretation is essentially a matter of attributing intentions, that is, in the pragmatics sense of ‘meaning’, namely, meaning that such-and-such by an act or expression. At the same time, interpretations need not be based on the intentions of actual authors; the meaning of an act or expression is understandable in terms of counterfactual intentions.” [Are we really restricted to understanding the coherence and integrity of meaning in such a way? Presumably the author is a kind of device for organizing meaning, much like Dworkin’s integrity, but need it take that format?] The logic of interpretation is typically reducible to intention attribution. [What role does the counterfactual author play in structuring meaning?] The criteria of interpretive success will depend upon the object, whether it is the real author or the counterfactual author. If the former, success will depend upon the retrieval of the author’s actual intentions. “Likewise, if the author is characterized in terms of some ideal representative of a certain genre, for instance, the presumptions which are taken to determine this c aracterization would provide the criteria of success for the particular interpretation offered.” [The criteria of success would seem, then, to be the principles, ideals, etc. that we attribute to the counterfactual author. These attributed qualities would be doing all the work – is the attribution of intention to the hypothetical author, then, really necessary at all?] [Does this account presuppose a weird dichotomy between what an object is and what it means? This dichotomy is different, if present at all, in Dworkin.] Chapter 3: Dworkin’s Theory of Interpretation and the Nature of Jurisprudence Three main insights of Dworkin’s theory of interpretation: “First, that interpretation strives to present its object in its best possible light. Second, that interpretation is essentially genre-dependent. And third, that there are certain constraints that determine the limits of possible interpretations of a given object.” Why the best light? Dworkin doesn’t really address this question in depth but claims that otherwise we are left with no way of justifying and choosing an interpretation or we are left with the author’s intention model, which we should reject. [Marmor doesn’t seem clear on what precisely it means to present something in its best light – seems to conflate it with most appealing light which, I take it, is different than what Dworkin has in mind.] “Dworkin is quite right to maintain that without having some views about the values inherent in the genre to which the text is taken to belong, no interpretation can take off the ground. The values we associate with the genre partly, but crucially, determine what would make sense to say about the text, what are the kinds of meaning we could ascribe to it.” There is no necessity for an interpretation to present an object in its best light with regards to the genre it is taken to be part of. Interpretations “could simply strive to present it in a certain light, perhaps better than some, worse than others, but in a way which highlights an aspect of the meaning of the text which may be worth paying attention to for some reason or another.” [What kind of reasons would count in choosing to present it in one light rather than another?] There is simply zero grounds for Dworkin’s assertion that we have no reason to pay attention to an interpretation that does not present it in its best light. Take a psychoanalytic interpretation of Hamlet, for example – not the best light, but a legitimate one. [This seems related to the next criticism – clearly Dworkin would have to loosen his insistence on the best, though not to detriment.] Moreover, especially with regards to art, it doesn’t appear possible to make an all things considered judgment about the best interpretation given the incommensurability of different values that are taken to inhere in a given genre. [Dworkin can respond here that we may have different available interpretations that could be justified with respect to the relevant value. Moreover, a lack of common denominator does not prevent any comparison whatsoever.] Constructive interpretation concerns social practices constituted by norms – it imposes a purpose or value rendering intelligible the normative character of the practice. There is a separate aspect of constructive interpretation that maintains that elements of the practice are sensitive to the point of the practice. It is important to note that different social practices will institutionalize themselves in different ways – thus, different practices will establish varying conditions on how the practice can be altered. The position of the positivists is that evaluative judgments concerning what the law should be are insufficient for determining what the law is given the nature of law’s institutionalization.&nb p; [This would seem to reside on a certain conception of law, i.e. an interpretation about where the value of law lies.] “[T]his being one of the main points of dispute between Dworkin and his positivist opponents, Dworkin cannot at this initial state presume law to be sensitive to its value in the manner that other, non-institutional practices might be, without incurring the charge of having assumed the very point at issue.” The upshot for Dworkin is that any explanation of a social practice such as law requires the same kind of reasoning as participation in that practice. This will be called the hermeneutic thesis. We can try to reconstruct a justification for this view based on the necessity of shared background assumptions – but this will not do since Dworkin’s claim is stronger: it contends that participants’ and theorists’ must “adopt one and the same normative point of view.” [The sense of normative here is unclear. It is true, though, that shared background assumptions do not imply viewing the law as valuable in any particular way, or at least it does not imply this in any strong sense.] Dworkin makes two distinct points with the hermeneutic thesis: “First, that the explanation of a social practice, like law or the arts, is essentially interpretative, and as such, necessarily value laden. Second, that the interpretation of such social practices, which Dworkin calls ‘argumentative’, is unique in the sense that the practice itself is an evaluative enterprise, and that therefore the interpreter of such a practice must form an evaluative judgment of her own about those values which are inherent in the practice that she purports to interpret.” [As stated, the first thesis is terribly ambiguous – for Dworkin, it clear implies a commitment to constructive interpretation. For Marmor, who accepts it, it is totally unclear what commitment he intends to make. He seems to mean simply that we have criteria for success concerning what counts as a successful explanation.] Mamor denies the second thesis. “What Dworkin seems to ignore here is that there is a crucial difference between forming a view about the values which are manifest in a social practice, like law, and actually having evaluative judgments about them.” [The problem, however, it that it is a contentious matter what values are part of the law – a theorist’s account of what values are constitutive of a particular legal system must rely on the kind of arguments which participants rely on. Of course, a theorist might simply note a debate about values and attempt to remain agnostic, but this will fail to be a full theoretical account of what law is!] Dworkin’s thesis seems to depend exclusively on his account of constructive interpretation. [This seems exactly right.] Chapter 4: Coherence, Holism, and Interpretation: The Epistemic Foundation of Dworkin’s Legal Theory Begins with discussion of Rawls’ reflective equilibrium. Sums up dual criticism as follows: “[T]he assumption that intuitions are independently true and the converse one, that their truth depends on fitting a coherent scheme, both seem to yield paradoxical results.” Dworkin, in his article “The Original Position”, claims that Rawls cannot commit himself to ethical realism. “[T]he natural model presupposes some form of ethical realism, while the constructive model does not. One important difficulty arising from an attempt to apply the natural model to Rawls is, that under the natural model, any theory which dopes not account for an intuition, at least for one which is held firmly, cannot be wholly satisfactory, just as scientific theory which does not account for certain observational data it is supposed to cover, would not be satisfactory in a familiar way.” Rawls, rather, is committed to a constructivist view of morality. Moreover, the reason we value coherence epistemically in moral theory is that it itself is a value of political morality – fairness requires consistency and publicity in the application of moral standards. Marmor notes the following problem with such a view: “[I]f coherence is justified, as it is here, with reference to certain moral values, that is, a specific conception of fairness, then we face the following problem: the presupposed values of fairness must themselves be based upon intuitive convictions, in which case the question of their truth cannot be ignored. If they are taken to be true…we are driven back to the perplexities of the natural model.” Discusses, helpfully, the Fish/Dworkin debate. The upshot is that Dworkin’s interpretive model is best off if it commits itself to a Quineian holism. However, this undermines his distinction between internal and external skepticism since holism must deny that moral judgments constitute a closed system. [This analysis seems exactly right.] Endorses Simmonds view that Dworkin’s theory does not meet the requirements of complexity he identifies as necessary to avoid vicious circularity in interpretive judgments of fit and identity. Coherence is doing the work through and through and therefore the interpretive theory of law is circular. [Will require further investigation, though it is unclear how coherence is doing any work in the pre-interpretive stage. At this stage, the judgments, if interpretive, seem to be derived from different sources. In any case, using coherence as a value seems to be highly suspect.] Why doesn’t Dworkin just reject Fish’s assumptions: because of his jurisprudence. “If legal texts can have a meaning that is not entirely dependent on a process of interpretation, then it is at least sometimes the case that the law can simply be understood, and applied, without the mediation of interpretation. And if that is the case, then the argument from interpretation against legal positivism collapses. It is no longer the case that every conclusion about what the law is, depends on evaluative considerations about what it ought to be.” Chapter 5: Semantics, Realism, and Natural Law Assessment of Michael Moore’s legal realism and its implications. [The final criticisms of Moore are not decisive.] Chapter 6: Constructive Identification and Razian Authority A consideration of Dworkin’s denial that the communication model of interpretation is appropriate for legal interpretation. Marmor argues that intentions do play a crucial role in the identification of legal norms in a way that is incompatible with Dworkin’s “coherence thesis”. Marmor takes Dworkin to be committed to the constructive identification thesis: that the identification of something as part of the legal, artistic, etc. genre can be done sufficiently by evaluative considerations. “Here, one must maintain that evaluative considerations are sufficient to determine whether something is a legal norm or a work of art”. [Fit, however, constrains possible evaluative considerations – thus evaluative considerations are not sufficient in themselves.] “Now the crucial point here is this: if you maintain the possibility of constructive identification in art, you must assume that works of art can be identified as such on the basis of certain features they happen to possess, features which contain no reference to any particular intention to create a work of art…unless we take intentions into account, how can we discriminate between the concept of an aesthetic artifact and the con ept of a work of art?” [It is unclear, and I think false, that constructive interpretation of anything requires identifying something irrespective of an artificers intentions. Those intentions may be relevant, dependent upon the genre under which we are trying to classify the object. Nothing, seemingly, about constructive interpretation in general excludes this possibility.] Marmor’s point is that it turns out to be impossible to identify art as art without reference to an artist’s intentions – especially given the state of contemporary art. [It is notable that Marmor’s response to counterexample implicitly depends upon a fully developed theory of aesthetics. His cursory comments on the matter of identifying art seem insufficient to say the least.] The rest of the chapter considers the incompatibility of Raz’s account of authority with constructive interpretation. The incompatibilities mentioned do not move beyond what Raz identifies in his article “Authority, Law and Morality”, but a defense of this notion of authority is defended in several [inconclusive] respects. [Raz and Marmor want to separate identification from content. This is not clearly a defensible separation.] Chapter 7: No Easy Cases? Chapter defends notion that there is a distinction between easy and hard cases in the positivist sense. Takes a Hartian approach and ultimately defends the distinction by associating it Wittgenstein’s conception of rule following. The point is that one need to look the purpose of rule in order to understand what the rule requires. Chapter 8: Legislative Intent and the Authority of Law Examines the following doctrine concerning the role of legislative intent in adjudication: “[F]irst, it would hold that laws, at least in certain cases, are enacted with relatively specific intentions, and that this is a matter of fact which is discernible through an ordinary fact-finding procedure. Second, that in certain cases the presence of such a fact, namely, that the law was enacted with a certain intention, provides judges with a reason to decide the legal dispute in accordance with the relevant legislative intent.” [It is important that for Marmor, interpretive strategies are only appropriate in hard cases. However, we should wonder what grounds positivism can offer for deciding a hard case in any manner which is not the morally best manner according to the judgment of the judge. There are no legal grounds, by definition, in hard cases and so what justificatory strategy would endorse any judicial decision except for the morally best one?] We can ascribe intentions to a legislative body, when this is possible at all, by taking the shared intentions of the majority, rather than some group intention, to be the significant intentions. Moreover, we should expect a good deal of consensus about intentions for otherwise it is hard to explain how legislative bodies are able to produce so much legislation. Discussion of kinds of intentions concludes as follows: “I have distinguished between three main types of intention that are potentially relevant from the legal point of view. Apart from the intentions that are manifest in the language of the law itself, legislators typically have further intentions in enacting a given law, and sometimes they would have certain intentions bearing on its proper application. I have also suggested that some of these further intentions may be essentially non-avowable, in which case they are rendered initially irrelevant. Finally, I have pointed out that considerations of consistency require that the legislator’s application intentions be taken into account only if, and to the extent that, they are in accord with his further intentions.” The manner in which intentionalism is to be justif ed relies on the distinction, Marmor maintains, between expert and mere collective action authority. “The point I wanted to make is strictly conditional: if, and only if, a certain law is justified on the basis of the expertise branch of the normal justification thesis, would it make sense to defer to the legislature’s intentions in the interpretation of the law, that is, to the extent that there is, in fact,; such an intention and it can clarify something that needs clarification.” Insofar as a legislature can be considered an expert on the matter requiring adjudication and interpretation should the body’s intention be taken into account. Chapter 9: Constitutional Interpretation Begins by laying out general necessary features of a constitution. Then Marmor moves on to consider general questions of constitutional legitimacy. First, he considers what grounds might be offered for the legitimacy of a constitution at all. He notes that the central question is what permits a single generation to bind future generations. He then examines four arguments to avoid this problem. The first is based on the moral legitimacy of the constitution; Marmor rejects this solution for the [truly dubious] reason that the constitution would make no practical difference because it would not supply reasons in addition to those provided by morality [but, presumably, the point is that these legally valid rules would be institutionally enshrined]. The second is based on the moral authority of the framers and Marmor rightly rejects this on the basis of the idealization of the framers it requires and less rightly on the basis that there cannot be moral authorities. Third is the “argument from interpretation” which claims that “as long as the particular content of the constitution is determined by its interpretation, and the authoritative interpretation at any time correctly instantiates the values which ought to be upheld in the community, the constitution would be morally legitimate”. The fourth is Raz’s which argues that a constitution is valid so long as its constraints are morally permissible because conventions of this type might aid the continuity of the legal system, i.e. it is important to have a convention of this type and the constitution is a kind of this type. Marmor appears to endorse these two approaches and concludes: “The conditions for the legitimacy of a constitution must comprise the following conditions. First, the values and principles enshrined in it must be morally permissible…Second, when certain choices are made in particular cases, they would be legitimate if they are either morally underdetermined, or else, morally correct…It follows from this that both arguments must assume that at least in those areas in which the constitution would make a moral difference, it can be interpreted to make the difference that it should, that is, according to the true moral principles that should apply to the particular case...the moral legitimacy of constitutions very much dependent on the practices of their interpretation. In other words, a great deal of the burden of moral legitimacy is shifted by these arguments to the application of the constitution, thus assuming that the constitution is legitimate only if the courts are likely to apply the constitution in a morally desirable way.” [This implies that the only significant value constitutions have is in providing a conventional practice where some such practice is required.] Moves on to argue that courts typically rely, and rightly so, on moral considerations when deciding constitutional issues because typically, in cases of the kind that reach the supreme or constitutional court, there is no law on the case. Much of this relies on his earlier discussion about the nature of interpretation in the law – that legal interpretation is always a matter of cha ging the law. (shrink)

Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We describe how the minimal modal interpretation closes a gap in this dynamical description, leading to a complete and consistent resolution to the measurement problem and an effective form of state collapse. Our interpretation also provides insight into the indivisible nature of measurement—the fact that you (...) can't stop a measurement part-way through and uncover the underlying 'ontic' dynamics of the system in question. Having discussed the hidden dynamics of a system's ontic state during measurement, we turn to more general forms of open-system dynamics and explore the extent to which the details of the underlying ontic behavior of a system can be described. We construct a space of ontic trajectories and describe obstructions to defining a probability measure on this space. (shrink)

Many works intended to introduce interpretive issues in quantum mechanics present John von Neumann as having a view in which measurement produces a physical collapse in the system being measured. In this paper I argue that such a reading of von Neumann is inconsistent with what von Neumann actually says. I show that much of what he says makes no sense on the physical collapse reading, but falls into place if we assume he does not have such a (...) view. I show that the physical collapse view is based on an understanding of ‘state’ which von Neumann does not share. Introduction The standard reading of von Neumann The standard reading of von Neumann and Chapter VI The Chapter VI argument The Chapter V argument The Chapters III and IV argument Conclusion. (shrink)

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory’s basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture (...) of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure—which we call subsystem space—that we believe merits further study. We conclude with a summary, a list of criteria for future work on quantum foundations, and further research directions. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text. (shrink)

In 1957, Feyerabend delivered a paper titled ‘On the Quantum-Theory of Measurement’ at the Colston Research Symposium in Bristol to sketch a completion of von Neumann's measurement scheme without collapse, using only unitary quantum dynamics and well-motivated statistical assumptions about macroscopic quantum systems. Feyerabend's paper has been recognised as an early contribution to quantum measurement, anticipating certain aspects of decoherence. Our paper reassesses the physical and philosophical content of Feyerabend's contribution, detailing the technical steps as well as its overall (...) philosophical motivations and consequences. Summarising our results, Feyerabend interpreted collapse as a positivist assumption in quantum mechanics leading to a strict distinction between the uninterpreted formalism of unitary evolution in quantum mechanics and the classically interpreted observational language describing post-measurement outcomes. Thus Feyerabend took the no-collapse completion of the von Neumann measurement scheme to show the dispensability of the positivist assumption, leading the way to a realistic interpretation of quantum theory. We note, however, that there are substantial problems with his account of measurement that bring into question its viability as a legitimate foil to the orthodox view. We further argue that his dissatisfaction with the von Neumann measurement scheme is indicative of early views on theoretical pluralism. (shrink)

The semantically ambiguous nature of the sign and aspects of non-classicality of elementary matter as described by quantum theory show remarkable coherent analogy. We focus on how the ambiguous nature of the image, text and art work bears functional resemblance to the dynamics of contextuality, entanglement, superposition, collapse and decoherence as these phenomena are known in quantum theory. These quantumlike properties in linguistic signs have previously been identified in formal descritions of e.g. concept combinations and mental lexicon representations and (...) have been reported on in the literature. In this approach the informationalized, communicated, mediatized conceptual configuration—of e.g. the art work—in the personal reflected mind behaves like a quantum state function in a higher dimensional complex space, in which it is time and again contextually collapsed and further cognitively entangled. The observer–consumer of signs becomes the empowered ‘produmer’ creating the cognitive outcome of the interaction, while loosing most of any ‘classical givenness’ of the sign. These quantum-like descriptions are now developed here in four example aesthetic signs; the installation Mist room by Ann Veronica Janssens, the installation Sections of a happy moment by David Claerbout, the photograph The Falling Man by Richard Drew and the documentary Huicholes. The Last Peyote Guardians by Vilchez and Stefani. Our present work develops further the use of a previously developed quantum model for concept representation in natural language. In our present approach of the aesthetic sign, we extend to individual—idiosyncratic—observer contexts instead of socially shared group contexts, and as such also include multiple idiosyncratic creation of meaning and experience. This irreducible superposition emerges as the core feature of the aesthetic sign and is most critically embedded in the ‘no-interpretation’ interpretation of the documentary signal. (shrink)

A two-body quantum correlation is calculated for a particle reflecting from a moving mirror. Correlated interference results when the incident and reflected particle substates and their associated mirror substates overlap. Using the Copenhagen interpretation of measurement, an asynchronous joint probability density, which is a function both of the different positions and different times at which the particle and mirror are measured, is derived assuming that no interaction occurs between each measurement. Measurement of the particle first, in the correlated interference region, (...) results in a splitting of the mirror substate into ones which have and have not reflected the particle. An analog of the interference from the Doppler effect for only measurements of the particle, in this two-body system, is shown to be a consequence of the asynchronous measurement. The simplification obtained for a microscopic particle reflecting from a mesoscopic or macroscopic mirror is used to illustrate asynchronous correlation interferometry. In this case, the small displacement between these mirror states can yield negligible environmental decoherence times. In addition, interference of these mirror states does not vanish in the limit of large mirror mass due to the small momentum exchange in reflecting a microscopic particle. (shrink)

On Jaakko Hintikka’s understanding of Aristotle’s modal thought, Aristotle is committed to a version of the Principle of Plenitude, which is the thesis that no genuine possibility will go unactualized in an infinity of time. If in fact Aristotle endorses the Principle of Plenitude, everything becomes necessary. Despite the strong evidence that Aristotle indeed accepts that Principle of Plenitude, there are key texts in which Aristotle seems to contradict it. On Hintikka’s final word on the matter, Aristotle either endorses the (...) Principle of Plenitude or Aristotle is simply inconsistent. Without challenging Hintikka’s interpretation of the relevant texts, I show how Aristotle may accept a form of the Principle of Plenitude that allows for genuine unactualized possibilities in the world. What allows me to reconcile the seemingly inconsistent data is to show how Aristotle is only committed to a de re version of the Principle of Plenitude. After I lay out my proposal, I show how it opens up new ways in which we might understand Aristotle’s attempt to reject fatalism in his De interpretatione 9. (shrink)

I briefly sketch Bohm's causal interpretation (BCI) and its solution to the measurement problem. Crucial to BCI's no-collapse account of both ideal and non-ideal measurement is the existence of particles in addition to wavefunctions. The particles in their role as the producers of the observable experimental outcomes render practical considerations, such as what observables can be reasonably measured or how to get rid of interference terms in non-ideal measurements, secondary to BCI's account of measurement. I then explain why it (...) is not easy for BCI to justify its statistical postulate. To successfully justify the postulate would be to solve the distribution problem. Two proposed deterministic solutions to this problem are only briefly set out and not discussed in detail. BCI can solve the measurement problem whether or not the distribution problem is solved. However, if the distribution problem is not solved, BCI cannot be shown to be empirically adequate. (shrink)

Most of the competent Nietzsche interpreters concede that there are two major strands of his thought that do not seem to sit comfortably with each other. The one strand affirms the primacy and irreducibility of interpretation, according to which the world admits of countless meanings with no extra-interpretive measure to decide among them. With this strand is associated Nietzsche’s so-called perspectivism, antifoundationalism, and genealogical method. The other strand calls for a “return to nature and naturalness”, enjoining us to “recognize” what (...) Nietzsche calls the “eternal original text homo natura ”. With this strand is associated Nietzsche’s doctrines of becoming and will to power. However, if there are no facts, only interpretations, direct appeal to the “facts” of nature as a claim to know unmediated reality in itself would be ruled out. Conversely, if the goal is to recognize nature just as it is in itself, then perforce all interpretations and perspectives would fall short of truth. Apparently, Nietzsche cannot have it both ways. Yet, apparently, neither can he have it just one way or the other. For simply to affirm that there are only interpretations would threaten to collapse into a self-defeating relativism; whereas simply to appeal to pure unmediated “facts ‘in themselves’” would contravene the very condition of such “facts” being known “in themselves,” since being known is being in relation. (shrink)

The GRW dynamics propose a novel, relevantly “observer”-independent replacement for orthodox “measurement”-induced collapse. Yet the tails problem shows that this dynamical innovation is not enough: a principled alternative to the orthodox account demands some corresponding ontological advancement as well. In fact, there are three rival fundamental ontologies on offer for the GRW dynamics. Debate about the relative merits of these candidates is a microcosm of broader disagreement about the role of ontology in our physical theorizing. According to imprimitivists, the (...) GRW dynamics directly describe (only) some (element’s) undulation in an unfamiliar high-dimensional physical field. Primitivists resist this GRW0 proposal on the grounds that it fails to secure comprehensible contact with our data about macroscopic objects in ordinary lowdimensional space-time. They expect an adequate fundamental ontology to include at least some spatiotemporally localized entities—intuitively, concrete constituents of our familiar macroscopic landscape. The most compelling case goes by way of distributional basing: minimally, primitivists expect a theory’s predictions immediately about spatiotemporal distributions of fundamental entities to provide a supervenience base for data about configurations of macroscopic objects. But while the background intuition is familiar, the distributional model is surprisingly subtle. Lack of clarity about its details generates serious confusion for both sides of our debate. (shrink)

Papers advocating a hidden-variable interpretation of quantum mechanics typically begin by emphasizing that John von Neumann’s no-go theorem does not apply to them. If authors are ontologically minded, their criticism also takes aim at his theory of measurement as expressed in his seminal 1932 book Mathematical Foundations of Quantum Mechanics Additionally, David Bohm and Basil Hiley have recently argued that “in so far as von Neumann effectively gave the quantum state a certain ontological significance, the net result was to produce (...) a confused and unsatisfactory ontology. This ontology is such that the collapse of the wave function must also have an ontological significance.”. (shrink)

A major problem facing no-collapse interpretations of quantum mechanics in the tradition of Everett is how to understand the probabilistic axiom of quantum mechanics (the Born rule) in the context of a deterministic theory in which every outcome of a measurement occurs. Deutsch claims to derive a decision-theoretic analogue of the Born rule from the non-probabilistic part of quantum mechanics and some non-probabilistic axioms of classical decision theory, and hence concludes that no probabilistic axiom is needed. I argue (...) that Deutsch’s derivation begs the question. (shrink)

In this ambitious work, Fred Weinstein confronts the obstacles that have increasingly frustrated our attempts to explain social and historical reality. Traditionally, we have relied on history and social theory to describe the ways people understand the world they live in. But the ordering explanations we have always used--derived from the classical social theories originally forged by Marx, Tocqueville, Weber, Durkheim, Freud--have collapsed. In the wake of this collapse or "fall," the rival claims of fiction, psychoanalysis, sociology, anthropology, and (...) history have created the dilemma of radical relativism, the prospect of multiple interpretations of any complex historical event. The basic strategy of social theory and the social sciences--the search for underlying unities--proves so inherently contradictory and has provided so little in the way of reliable knowledge of social and historical relationships that to many critics it seems no longer worth pursuing. Weinstein enters the debate by rejecting any search for underlying structural unities, dynamic or social, through which historians have attempted to find continuity with the past. He looks instead to ideological processes, to the construction of successive and changing versions of reality that mediate between the power of fantasy on the one side and the power of the social world on the other. He argues further that the need to use ideological constructs in this way accounts for the heterogeneous and changing content of social movements and for the persistent need people have always had for authoritative leaders, even in democratized societies. He suggests that people have historically been able to take a step away from leaders only by substituting the possession of objects such as property or money. This book is a breakthrough in poststructuralist theory that is sure to stimulate considerable discussion, especially about the shape of the social sciences and the future of historical interpretation. (shrink)

There has been a lot of interest over the last fifteen years or so in no-collapse interpretations of quantum mechanics. The Bohm interpretation of quantum mechanics has received several thorough accounts, perhaps most notably by Bohm himself.

Here I explore a novel no-collapse interpretation of quantum mechanics that combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.

This paper expands on, and provides a qualified defence of, Arthur Fine's selective interactions solution to the measurement problem. Fine's approach must be understood against the background of the insolubility proof of the quantum measurement. I first defend the proof as an appropriate formal representation of the quantum measurement problem. The nature of selective interactions, and more generally selections, is then clarified, and three arguments in their favour are offered. First, selections provide the only known solution to the measurement problem (...) that does not relinquish any of the explicit premises of the insolubility proofs. Second, unlike some no-collapse interpretations of quantum mechanics, selections suffer no difficulties with non-ideal measurements. Third, unlike most collapse interpretations, selections can be independently motivated by an appeal to quantum propensities. IntroductionThe problem of quantum measurement2.1 The ignorance interpretation of mixtures2.2 The eigenstate–eigenvalue link2.3 The quantum theory of measurementThe insolubility proof of the quantum measurement3.1 Some notation3.2 The transfer of probability condition (TPC)3.3 The occurrence of outcomes condition (OOC)A defence of the insolubility proof4.1 Stein's critique4.2 Ignorance is not required4.3 The problem of quantum measurement is an idealisationSelections5.1 Representing dispositional properties5.2 Selections solve the measurement problem5.3 Selections and ignoranceNon-ideal selections6.1 No-collapse interpretations and non-ideal measurements6.2 Exact and approximate measurements6.3 Selections for non-ideal interactions6.4 Approximate selections6.5 Implications for ignoranceSelective interactions test quantum propensities7.1 Equivalence classes as physical ‘aspects’: a critique7.2 Quantum dispositions7.3 Selections as a propensity modal interpretation7.4 A comparison with Popper's propensity interpretation. (shrink)

In 'How Many Lives Has Schrödinger's Cat?' David Lewis argues that the Everettian no-collapse interpretation of quantum mechanics is in a tangle when it comes to probabilities. This paper aims to show that the difficulties that Lewis raises are insubstantial. The Everettian metaphysics contains a coherent account of probability. Indeed it accounts for probability rather better than orthodox metaphysics does.

The aim of this article is twofold. Recently, Lewis has presented an argument, now known as the "counting anomaly", that the spontaneous localization approach to quantum mechanics, suggested by Ghirardi, Rimini, and Weber, implies that arithmetic does not apply to ordinary macroscopic objects. I will take this argument as the starting point for a discussion of the property structure of realist collapse interpretations of quantum mechanics in general. At the end of this I present a proof of the (...) fact that the composition principle, which holds true in standard quantum mechanics, fails in all realist collapse interpretations. On the basis of this result I reconsider the counting anomaly and show that what lies at the heart of the anomaly is the failure to appreciate the peculiarities of the property structure of such interpretations. Once this flaw is uncovered, the anomaly vanishes. (shrink)

In [15], [16] G. Kreisel introduced the no-counterexample interpretation (n.c.i.) of Peano arithmetic. In particular he proved, using a complicated ε-substitution method (due to W. Ackermann), that for every theorem A (A prenex) of first-order Peano arithmetic PA one can find ordinal recursive functionals Φ A of order type 0 which realize the Herbrand normal form A H of A. Subsequently more perspicuous proofs of this fact via functional interpretation (combined with normalization) and cut-elimination were found. These proofs however do (...) not carry out the no-counterexample interpretation as a local proof interpretation and don't respect the modus ponens on the level of the no-counterexample interpretation of formulas A and A → B. Closely related to this phenomenon is the fact that both proofs do not establish the condition (δ) and--at least not constructively-- (γ) which are part of the definition of an 'interpretation of a formal system' as formulated in [15]. In this paper we determine the complexity of the no-counterexample interpretation of the modus ponens rule for (i) PA-provable sentences, (ii) for arbitrary sentences A, B ∈ L(PA) uniformly in functionals satisfying the no-counterexample interpretation of (prenex normal forms of) A and A → B, and (iii) for arbitrary A, B ∈ L(PA) pointwise in given α( 0 ) -recursive functionals satisfying the no-counterexample interpretation of A and A → B. This yields in particular perspicuous proofs of new uniform versions of the conditions (γ), (δ). Finally we discuss a variant of the concept of an interpretation presented in [17] and show that it is incomparable with the concept studied in [15], [16]. In particular we show that the no-counterexample interpretation of PA n by α( n (ω))-recursive functionals (n ≥ 1) is an interpretation in the sense of [17] but not in the sense of [15] since it violates the condition (δ). (shrink)

Can we explain the laws of thermodynamics, in particular the irreversible increase of entropy, from the underlying quantum mechanical dynamics? Attempts based on classical dynamics have all failed. Albert (1994a,b; 2000) proposed a way to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wavefunction of Ghirardi, Rimini and Weber (1986). In this paper we propose an alternative way to explain thermodynamics within no-collapse interpretations of quantum mechanics. Our approach relies (...) on the standard quantum mechanical models of environmental decoherence of open systems, e.g. Joos and Zeh (1985) and Zurek and Paz (1994). (shrink)

We discuss a recent proposal by Albert (1994a; 1994b; 2000, ch. 7) to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wave function by Ghirardi, Rimini, and Weber (1986). We propose an alternative way to explain thermodynamics within no-collapse interpretations of quantum mechanics. Our approach relies on the standard quantum mechanical models of environmental decoherence of open systems (e.g., Joos and Zeh 1985; Zurek and Paz 1994). This paper presents (...) the two approaches and discusses their advantages. The problems faced by both approaches will be discussed in a sequel (Hemmo and Shenker 2003). (shrink)

The centerpiece of Jeffrey Bub's book Interpreting the Quantum World is a theorem (Bub and Clifton 1996) which correlates each member of a large class of no-collapse interpretations with some 'privileged observable'. In particular, the Bub-Clifton theorem determines the unique maximal sublattice L(R,e) of propositions such that (a) elements of L(R,e) can be simultaneously determinate in state e, (b) L(R,e) contains the spectral projections of the privileged observable R, and (c) L(R,e) is picked out by R and e (...) alone. In this paper, we explore the issue of maximal determinate sets of observables using the tools provided by the algebraic approach to quantum theory; and we call the resulting algebras of determinate observables, "maximal *beable* subalgebras". The capstone of our exploration is a generalized version of Bub and Clifton's theorem that applies to arbitrary (i.e., both mixed and pure) quantum states, to Hilbert spaces of arbitrary (i.e., both finite and infinite) dimension, and to arbitrary observables (including those with a continuous spectrum). Moreover, in the special case covered by the original Bub-Clifton theorem, our theorem reproduces their result under strictly weaker assumptions. This added level of generality permits us to treat several topics that were beyond the reach of the original Bub-Clifton result. In particular: (a) We show explicitly that a (non-dynamical) version of the Bohm theory can be obtained by granting privileged status to the position observable. (b) We show that Clifton's (1995) characterization of the Kochen-Dieks modal interpretation is a corollary of our theorem in the special case when the density operator is taken as the privileged observable. (c) We show that the 'uniqueness' demonstrated by Bub and Clifton is only guaranteed in certain special cases -- viz., when the quantum state is pure, or if the privileged observable is compatible with the density operator. We also use our results to articulate a solid mathematical foundation for certain tenets of the orthodox Copenhagen interpretation of quantum theory. For example, the uncertainty principle asserts that there are strict limits on the precision with which we can know, simultaneously, the position and momentum of a quantum-mechanical particle. However, the Copenhagen interpretation of this fact is not simply that a precision momentum measurement necessarily and uncontrollably disturbs the value of position, and vice-versa; but that position and momentum can never in reality be thought of as simultaneously determinate. We provide warrant for this stronger 'indeterminacy principle' by showing that there is no quantum state that assigns a sharp value to both position and momentum; and, a fortiori, that it is mathematically impossible to construct a beable algebra that contains both the position observable and the momentum observable. We also prove a generalized version of the Bub-Clifton theorem that applies to "singular" states (i.e., states that arise from non-countably-additive probability measures, such as Dirac delta functions). This result allows us to provide a mathematically rigorous reconstruction of Bohr's response to the original EPR argument -- which makes use of a singular state. In particular, we show that if the position of the first particle is privileged (e.g., as Bohr would do in a position measuring context), the position of the second particle acquires a definite value by virtue of lying in the corresponding maximal beable subalgebra. But then (by the indeterminacy principle) the momentum of the second particle is not a beable; and EPR's argument for the simultaneous reality of both position and momentum is undercut. (shrink)

In [15], [16] G. Kreisel introduced the no-counterexample interpretation (n.c.i.) of Peano arithmetic. In particular he proved, using a complicated ε-substitution method (due to W. Ackermann), that for every theoremA(Aprenex) of first-order Peano arithmeticPAone can find ordinal recursive functionalsof order type < ε0which realize the Herbrand normal formAHofA.Subsequently more perspicuous proofs of this fact via functional interpretation (combined with normalization) and cut-elimination were found. These proofs however do not carry out the no-counterexample interpretation as alocalproof interpretation and don't respect the (...) modus ponens on the level of the nocounterexample interpretation of formulasAandA → B. Closely related to this phenomenon is the fact that both proofs do not establish the condition (δ) and—at least not constructively—(γ) which are part of the definition of an ‘interpretation of a formal system’ as formulated in [15]. (shrink)

The aim of this paper is two-fold. Recently, Lewis has presented an argument, now known as the `counting anomaly', that the spontaneous localization approach to quantum mechanics, suggested by Ghirardi, Rimini, and Weber, implies that arithmetic does not apply to ordinary macroscopic objects. I will take this argument as the starting point for a discussion of the property structure of realist collapse interpretations of quantum mechanics in general. At the end of this I present a proof of the (...) fact that the composition principle, which holds true in Standard Quantum Mechanics, fails in all realist collapse interpretations. On the basis of this result I reconsider the counting anomaly and show that what lies at the heart of the anomaly is the failure to appreciate the peculiarities of the property structure of collapse interpretations. Once this flaw is uncovered, the anomaly vanishes. (shrink)

We discuss a recent proposal by Albert to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wave function of Ghirardi, Rimini and Weber. We propose an alternative way to explain thermodynamics within no-collapse interpretations of quantum mechanics. Our approach relies on the standard quantum mechanical models of environmental decoherence of open systems, \eg Joos and Zeh and Zurek and Paz. This paper presents the two approaches and discusses their advantages. (...) The problems they face will be discussed in a sequel. (shrink)