The theorist who denies the objective reality of non-relational temporal properties, or ‘A-series’ determinations, must explain our experience of the passage of time. D.H. Mellor, a prominent denier of the objective reality of temporal passage, draws, in part, on Kant in offering a theory according to which the experience of temporal passage is the result of the projection of change in belief. But Mellor has missed some important points Kant has to make about time-awareness. It turns out that Kant's (...) theory of time-awareness also involves projection – but for him, the projection of temporal passage is necessary to any coherent experience at all, and for this reason events in the world cannot be represented except as exhibiting real tensed change. Consequently we cannot intelligibly suppose the world we know to be without the passage of time. This fact would permit a modest transcendental argument the conclusion of which is that we are entitled to describe the world in terms of temporal passage. (shrink)
In this paper it is shown how a partial semantics for presuppositions can be given which is empirically more satisfactory than its predecessors, and how this semantics can be integrated with a technically sound, compositional grammar in the Montagovian fashion. Additionally, it is argued that the classical objection to partial accounts of presupposition projection, namely that they lack “flexibility,” is based on a misconception. Partial logics can give rise to flexible predictions without postulating any ad hoc ambiguities. Finally, it (...) is shown how the partial foundation can be combined with a dynamic system of common-ground maintenance to account for accommodation. (shrink)
Heim 1983 suggested that the analysis of presupposition projection requires that the classical notion of meanings as truth conditions be replaced with a dynamic notion of meanings as Context Change Potentials. But as several researchers (including Heim herself) later noted, the dynamic framework is insufficiently predictive: although it allows one to state that, say, the dynamic effect of F and G is to first update a Context Set C with F and then with G (i.e., C[F and G] = (...) C[F][G]), it fails to explain why there couldn’t be a ‘deviant’ conjunction and* which performed these operations in the opposite order (i.e., C[F and* G] = C[G][F]). We provide a formal introduction to a competing framework, the Transparency theory, which addresses this problem. Unlike dynamic semantics, our analysis is fully classical, i.e., bivalent and static. And it derives the projective behavior of connectives from their bivalent meaning and their syntax. We concentrate on the formal properties of a simple version of the theory, and we prove that (i) full equivalence with Heim’s results is guaranteed in the propositional case (Theorem 1), and that (ii) the equivalence can be extended to the quantificational case (for any generalized quantifiers), but only when certain conditions are met (Theorem 2). (shrink)
For a finite von Neumann algebra factor M, the projections form a modular ortholattice L(M). We show that the equational theory of L(M) coincides with that of some resp. all L(ℂ n × n ) and is decidable. In contrast, the uniform word problem for the variety generated by all L(ℂ n × n ) is shown to be undecidable.
The presupposition triggered by an expression E is generally satisfied by information that comes before rather than after E in the sentence or discourse. In Heim’s classic theory (1983), this left-right asymmetry is encoded in the lexical semantics of dynamic connectives and operators. But several recent analyses offer a more nuanced approach, in which presupposition satisfaction has two separate components: a general principle (which varies from theory to theory) specifies under what conditions a presupposition triggered by an expression E is (...) satisfied; and an ‘incremental’ component specifies that the principle must be checked on the basis of information that comes before E. Several researchers take this incremental component to be a processing bias, which can be overcome at some cost. If so, it should be possible, though costly, to satisfy presuppositions ‘symmetrically’, i.e. by taking into account linguistic material that comes both before and after the presupposition trigger. We test this claim with experimental means. Using inferential (and to some extent acceptability) tasks involving the anaphoric trigger aussi (‘too’) in French, we argue that symmetric readings are indeed possible (albeit degraded) in environments involving the connectives if, or, and unless. (shrink)
Simulationists have recently started to employ the term "empathy" when characterizing our most basic understanding of other minds. I agree that empathy is crucial, but I think it is being misconstrued by the simulationists. Using some ideas to be found in Scheler's classical discussion of empathy, I will argue for a different understanding of the notion. More specifically, I will argue that there are basic levels of interpersonal understanding - in particular the understanding of emotional expressions - that are not (...) explicable in terms of simulation-plus-projection routines. (shrink)
Writers on presupposition, and on the ‘‘projection problem’’ of determining the presuppositions of compound sentences from their component clauses, traditionally assign presuppositions to each clause in isolation. I argue that many presuppositional elements are anaphoric to previous discourse or contextual elements. In compound sentences, these can be other clauses of the sentence. We thus need a theory of presuppositional anaphora, analogous to the corresponding pronominal theory.
Nearly all philosophers agree that only true things can be known. One way to justify the truth condition in an analysis of knowledge is by appeal to the linguistic thesis that the word 'know' is factive. But does this principle reflect actual usage? Several examples in ordinary language seem to show that non-philosophers sometimes use 'know' in what appear to be non-factive ways, suggesting that the folk concept of knowledge is nonfactive. Presented here however, is a rival explanatory hypothesis for (...) these linguistic practices. The results of four experiments utilizing explicit paraphrasing tasks suggest that many seemingly non-factive uses of 'know' are better explained by a factive concept--together with a phenomenon known as protagonist projection--than by an ordinary concept that allows for knowledge under false belief. Thus it is argued that armchair philosophical orthodoxy regarding the factivity of knowledge withstands current empirical scrutiny. (shrink)
This paper criticizes the dominant approaches to presupposition projection and proposes an alternative. Both the update semantics of Heim and the discourse representation theory of van der Sandt have problems in explicating the presuppositions of disjunctions. Moreover, Heim's approach is committed to a conception of accommodation that founders on the problem of informative presuppositions, and van der Sandt's approach is committed to a conception of accommodation that generates over-interpretations of utterances. The present approach borrows Karttunen's idea that instead of (...) associating presuppositions with sentences, we should define the conditions that contexts must meet in order to satisfy-the-presuppositions-of a sentence. However, in place of Karttunen's conception of contexts in terms of common ground, the present theory substitutes a conception of contexts as objective entities that are independent of the attitudes of the interlocutors. Contexts, so conceived, may be defined as containing sets of relevant possibilities. This allows us to define the conditions under which a context satisfies-the-presuppositions-of a disjunction. (shrink)
Karttunen observed that, if the complement of an attitude sentence presupposes p, then that sentence as a whole presupposes that the attitude–holder believes p. I attempt to derive some representative instances of this generalization from suitable assumptions about the lexical semantics of attitude predicates. The enterprise is carried out in a framework of context change semantics, which incorporates Stalnaker's suggestion that presupposition projection results from the stepwise fashion in which information is updated in response to complex utterances. The empirical (...) focus is on predicates of desire and on the contribution of counterfactual mood. (shrink)
We define a notion of projective meaning which encompasses both classical presuppositions and phenomena which are usually regarded as non-presuppositional but which also display projection behavior—Horn’s assertorically inert entailments, conventional implicatures (both Grice’s and Potts’) and some conversational implicatures. We argue that the central feature of all projective meanings is that they are not-at-issue, defined as a relation to the question under discussion. Other properties differentiate various sub-classes of projective meanings, one of them the class of presuppositions according to (...) Stalnaker. This principled taxonomy predicts differences in behavior unexpected on other models among the various conventional triggers and conversational implicatures, while holding promise for a general, explanatory account of projection which applies to all the types of meanings considered. (shrink)
Abstract: In the 1980s, the analysis of presupposition projection contributed to a ‘dynamic turn’ in semantics: the classical notion of meanings as truth conditions was replaced with a dynamic notion of meanings as Context Change Potentials (Heim 1983). We argue that this move was misguided, and we offer an alternative in which presupposition projection follows from the combination of a fully classical semantics and a new pragmatic principle, which we call Be Articulate. This principle requires that a meaning (...) pp’ conceptualized as involving a pre-condition p (its ‘presupposition’) should be articulated as … (p and pp’) … (e.g. … it is raining and John knows it…) rather than as … pp’ …, unless the full conjunction is ruled out because the first or the second conjunct is semantically idle. In particular, … (p and pp’)… is infelicitous - and hence … pp’ … is acceptable - if one can determine as soon as p and is uttered that no matter how the sentence ends these words could be eliminated without affecting its contextual meaning. An equivalence theorem guarantees that this condition suffices to derive Heim’s results in almost all cases. Extensions of the condition lead to several new predictions, in particular concerning some ‘symmetric readings’ (e.g. If the bathroom is not hidden, this house has no bathroom), as well as presupposition projection in quantified structures, which displays a complex interaction between the nature of the trigger and the monotonicity of the quantifier. (shrink)
The present paper presents an anaphoric account of presupposition. It is argued that presuppositional expressions should not be seen as referring expressions, nor is presupposition to be explicated in terms of some non-standard logic. The notion of presupposition should not be relegated to a pragmatic theory either. Instead presuppositional expressions are claimed to be anaphoric expressions which have internal structure and semantic content. In fact they only differ from pronouns and other semantically less loaded anaphors in that they have more (...) descriptive content. It is this fact which enables them to create an antecedent in case discourse does not provide one. If their capacity to accommodate is taken into account they can be treated by basically the same mechanism which handles the resolution of pronouns. The theory is elaborated in the framework of discourse representation theory. It is shown that pragmatic factors interfere in the resolution of presuppositional anaphors. The resulting account can neither be classified as wholly semantic nor wholly pragmatic. Section 1 presents a survey of standing problems in the theory of presupposition projection and discusses the major competing approaches. An argumentation for a purely anaphoric account of presupposition is given in section 2. Section 3 presents a coding of presuppositional expressions in an extension of discourse representation theory. The final section is devoted to a discussion of the constraints which govern the resolution of presuppositional anaphors. (shrink)
Religion and the external world -- Projection, religion, and the external world -- The senses, reason and the imagination -- Realism, meaning and justification : the external world and religious belief -- Modality, projection and realism -- 'Our profound ignorance' : causal realism, and the failure to detect necessity -- Spreading the mind : projection, necessity and realism -- Into the labyrinth : persons, modality, and Hume's undoing -- Value, projection, and realism -- Gilding : (...) class='Hi'>projection, value and secondary qualities -- The gold : good, evil, belief and desire -- The golden : relational values, realism and a moral sense. (shrink)
My critical comments on Part I of P. J. E. Kail's Projection and Realism in Hume's Philosophy are divided into two parts. First, I challenge the exegetical details of Kail's take on Hume's important distinction between natural and philosophical relations. I show that Kail misreads Hume in a subtle fashion. If I am right, then much of the machinery that Kail puts into place for his main argument does different work in Hume than Kail thinks. Second, I offer a (...) brief criticism of Kail's argument for reading Hume "as a realist about the external world" (Kail, 67). The two parts are (loosely) tied together because it turns out that Kail and I disagree about how Hume thinks of philosophers' activity generally.One caveat: .. (shrink)
The main question of this paper is how to understand the notion of a truth-maker. In section 1, I show that the identification of truth-making with necessitation cannot capture the pretheoretic understanding of notions such as ‘x makes something true’. In section 2, I examine Barry Smith’s reaction to this problem: he defines truth-making as the combination of necessitation and projection. I focus on the formal part of Smith’s account, which is shown to yield undesired results. However, in section (...) 3, I present an alternative account of projection, which fares better and can fruitfully be employed to circumvent the problems raised in section 1. Unfortunately, the account still has to face some troublemakers, as I show in the final section. I conclude, therefore, with a pessimistic view on the project of defining truth-making via necessitation and projection. (shrink)
Hume talks of our ‚Äògilding and staining‚Äô natural objects, and of the mind's propensity to ‚Äòspread itself‚Äô on the world. This has led commentators to use the metaphor of ‚Äòprojection‚Äô in connection with his philosophy. This book spells out its meaning, the role it plays in Hume's work, and examines how, if at all, what sounds ‚Äòprojective‚Äô in Hume can be reconciled with what sounds ‚Äòrealist‚Äô. In addition to offering some original readings of Hume's central ideas on God and the (...) Self among other things, this book offers a detailed examination of the notion of projection and the problems it faces. (shrink)
Focusing on the mirror system and imitation, I examine the role of metaphor and projection in evolutionary neurolinguistics. I suggest that the key to language evolution in hominid might be an ability to project one's thoughts and feelings onto another agent or object, to see and feel things from another perspective, and to be able to empathize with another agent.
From Humean Supervenience to Humean Projection": This paper attempts to develop a projectivistic understanding of chance or objective probability or partial determination. It does so by critically examining David Lewis philosophy of probability and his defense of Humean Supervenience, building thereupon the constructive projectivistic alternative, which will basically be a suitable reinterpretation of de Finettis position. Any treatment of the topic must show how it extends to natural necessity or deterministic laws or full determination in perfect parallel. The paper (...) indicates at the end how this demand can be met. (shrink)
The goal of this paper is to offer a compositional semantics for subjunctive and indicative will conditionals, and to derive the projection properties of the types of conditionals we consider and in particular those of counterfactual conditionals. It is argued that subjunctive conditionals are "bare" conditional embedded under temporal and aspectural operators, which constrain the interpretation of the modal operators in the embedded conditional. Furthermore, it is argued that a theory of presupposition projection à la Heim together with (...) the present proposal about their logical form explains the projection facts. (shrink)
Although ‘glue semantics’ is the most extensively developed theory of semantic composition for LFG, it is not very well integrated into the LFG projection architecture, due to the absence of a simple and well-explained correspondence between glue-proofs and f-structures. In this paper I will show that we can improve this situation with two steps: (1) Replace the current quantificational formulations of glue (either Girard’s system F, or first order linear logic) with strictly propositional linear logic (the quantifier, unit and (...) exponential free version of either MILL or ILL, depending on whether or not tensors are used). (2) Reverse the direction of the standard σ-projection from f-structure to meaning, giving one going from the (atomic nodes of) the glue-proof to the f-structure, rather than from the f-structure to a ‘semantic projection’ which is itself somehow related to the glue-proof. As a side effect, the standard semantic projection of LFG glue semantics can be dispensed with. A result is that LFG sentence structures acquire a level composed of strictly binary trees, constructed out of nodes representing function application and lambda abstraction, with a significant resemblance to external and internal merge in the Minimalist Program. This increased resemblance between frameworks might assist in making useful comparisons. (shrink)
We carry out (formalize) the Karttunen-Stalnaker pragmatic account of presupposition projection within a state-of-the art version of dynamic epistemic logic. It turns out that the basic projection facts can all be derived from a Gricean maxim ‘be informative’. This sheds light on a recent controversy on the appropriateness of dynamic semantics as a tool for analysing presupposition.
When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, (...) similar to perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)
Understanding the pattern by which complex sentences inherit the presuppositions of their parts (presupposition projection) has been a major topic in formal pragmatics since the 1970s. Heim’s classic paper “On the Projection Problem for Presuppositions” (1983) proposed a replacement of truth-conditional semantics with a dynamic semantics that treats meanings as instructions to update the common ground. Heim’s system predicts the basic pattern of presupposition projection quite accurately. The classic objection to this program (including other versions of dynamic (...) semantics) is that the treatment of binary connectives is stipulative, and other, equally natural treatments fail to make the right predictions about presupposition projection. I give a variation on Heim’s system that is designed to escape this objection. I show that the most liberal possible version of this variant is equivalent to a strong-Kleene system in terms of its definedness conditions. (shrink)
This article responds to two criticisms by Professor Nani Ranken of the Principle of Moral Projection in business ethics. In the process it enlarges upon our understanding of the moral agenda of management and the corporation as a participant in ethical transactions.
This paper explores the status of the von Neumann-Luders state transition rule (the "projection postulate") within "real-logic" quantum logic. The entire discussion proceeds from a reading of the Luders rule according to which, although idealized in applying only to "minimally disturbing" measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effect that QL has an explanatory advantage over Copenhagen and other interpretations which relativize truth-value (...) assignments to experimental arrangements. Two versions of QL, the lattice-theoretic (LT) and partial-Boolean-algebra (PBA), are considered. It turns out that the projection postulate is intimately connected with the choice of conditional connective for QL. The effect of the projection postulate is obtained with the Sasaki conditional. However, this choice is found to require extra assumptions, on both the LT and PBA versions, which are either just as ad hoc as the projection postulate itself or indefensible from within the real-logic QL framework. (shrink)
The title of my book, Projection and Realism in Hume's Philosophy (Oxford: Clarendon Press, 2007), might mislead. One might protest, with some justification, that since neither "projection" nor "realism" is Hume's term and that both carry a severe threat of anachronism, discussing them in connection with Hume is misguided. Why might the readers of this journal wish to read such a work?Well, the first thing to note is that Hume's name has come to be associated with the metaphor (...) of projection, understood as having some kind of "non-realist" connotations, and, at the same time, he attracted readings that make him a "realist" of some sort or another in different areas.1 So, there seems to be some tension here. .. (shrink)
Goodpaster's principle of moral projection is intended to support a program of corporate moral improvement based on an analogy between persons and corporations. In this paper I try to show that the analogy breaks down at a crucial point — namely at the search for amotive for moral improvement. Further, the analogy may foster a tendency to suppose that corporations, like persons, have intrinsic value. I conclude that the analogy does more harm than good for the following reasons: (a) (...) it distracts from the crucial question, which is, how can we motivate people to shape the institutions in which they work into morally better ones? and (b) it may reinforce a morally dangerous tendency to serve corporations for their own sakes. (shrink)
Much of the recent discussion of problematic aspects of quantum-mechanical measurement centers around that feature of quantum theory which is called "the projection postulate." This is roughly the claim that a change of a certain sort occurs in the state of a physical system when a measurement is made on the system. In this paper an argument for the projection postulate due to von Neumann is considered. Attention is focused on trying to provide an understanding of the notion (...) of "the state of a physical system" which is compatible with the argument von Neumann offers. An attempt is made to formulate the argument in terms of an objectivistic interpretation of probability concepts. It is seen that such an interpretation does not provide a suitable way of understanding the argument. An attempt is made to illustrate the source of this failure in terms of a non-quantum-mechanical example. (shrink)
The purpose of this paper is to solve a serious problem for the projection postulate involving the time-energy uncertainty relation. The problem was recently raised by Teller, who believes that the problem is insoluble and, consequently, that the projection postulate should no longer be regarded as a serious focus for interpretive investigation.
The mother sacrificing herself while rescuing someone else's child is a red herring. Neither behaviorism nor cognitivism can explain it. Unlike behaviorism, however, the cognitive process of projection can explain cooperation in one-shot social dilemmas.
The phenomenon we now know as projection was first observed by Frege in his brief remarks about presupposition in “Sense and Reference.” Frege observes there that the assertion that Kepler died in misery gives rise to the implication that the name Kepler has a referent; but that so too does the assertion that Kepler did not die in misery. Here we have the source of the observation that if p is a presupposition of S, then p is implied by (...) (utterances of) S and by (utterances of) the negation of S. Since Frege, it has been observed that those implications which are shared by a sentence S and by its negation are also typically shared by a variety of other entailment-canceling embeddings of S: in questions, in the antecedents of conditionals, and under epistemic possibility modals. This observation has entered the canon in the form of the “family of sentences” test (Chierchia and McConnell-Ginet 2000). This test is 1 standardly used to demonstrate that some particular element of content projects. An application of the test is demonstrated below. (shrink)
This article explains why Bohr does not need to discuss the projection postulate or the "problem of measurement". Beginning with a thumbnail sketch of Bohr's general views (which should serve as an efficient introduction to Bohr for newcomers), it is argued that Bohr interprets the state function as giving a statistical summary of experimental outcomes. Against the objection that Bohr was too much a microrealist to endorse such an instrumentalist statistical interpretation it is suggested (...) that he rejected the issue of microrealism as not well formed. It is shown that on his statistical interpretation Bohr does not need the projection postulate or face the usual problem of measurement. (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)
Previous work has shown that the problem of measurement in quantum mechanics is not correctly seen as one of understanding some allegedly univocal process of measurement in nature which corresponds to the projection postulate. The present paper introduces a new perspective by showing that how we are to understand the nature of the change of quantum mechanical state on measurement depends very sensitively on the interpretation of the state function, and by showing how attention to this dependence can greatly (...) sharpen the problems and relations between them. In particular, the problems take a form resembling their traditional formulation only on an inexact value interpretation, according to which the state function attributes inexact values of quantities to systems. On other interpretations we can apply (with various drawbacks) the subensemble idea, according to which a discontinuous change of quantum mechanical description results on measurement simply because we need a new state function to describe a new object. (shrink)
This article provides a semantic analysis of Protagonist Projection, the phenomenon by which things are described from a point of view different from that of the speaker. Against what has been argued by some, the account vindicates the intuitive idea that Protagonist Projection does not give rise to counterexamples to factivity, and similar plausible principles. A pragmatics is sketched that explains the attitude attributions generated by Protagonist Projection. Further, the phenomenon is compared to Free Indirect Discourse, and (...) the proposed account is seen to preserve the relation between them. (shrink)
If we take the state function of quantum mechanics to describe belief states, arguments by Stairs and Friedman-Putnam show that the projection postulate may be justified as a kind of minimal change. But if the state function takes on a physical interpretation, it provides no more than what I call a fortuitous approximation of physical measurement processes, that is, an unsystematic form of approximation which should not be taken to correspond to some one univocal "measurement process" in nature. This (...) fact suggests that the projection postulate does not provide a proper locus for interpretive investigation. Readers will also find section 3's analysis of fortuitous approximations of independent interest and presented without the perils of quantum mechanics. (shrink)
Analysis of the Freudian interpretation of the Oedipus myth which functions as a paradigm case for the Oedipus complex reveals the neglect of certain essential details. Moreover, it appears that clinical material as presented by psychoanalysts in support of the Oedipus complex is strongly biased towards the acceptance of the hypothesis that the Oedipus complex is a universal phenomenon. In this article arguments are given that cast serious doubt on the validity of psychoanalytic theory. The author proposes a new interpretation (...) which explains the putative Oedipal conflict in the child as the projection of parental aggression on the child. (shrink)
I focus on the logic of the goggles experiment, which if it as watertight as Heyes argues, should clearly support ape theory of mind if positive, and clearly reject it if negative. This is not the case, since the experiment tests for only one kind of mindreading, “experience projection”: but it is an excellent test for this, given adequate controls.
I defend the projection postulate against two of Margenau's criticisms. One involves two types of nonideal measurements, measurements that disturb and measurements that annihilate. Such measurements cannot be characterized using the original version of the projection postulate. This is one of the most interesting and powerful objections to the projection postulate since most realistic measurements are nonideal, in Margenau's sense. I show that a straightforward generalization of the projection postulate is capable of handling the more realistic (...) kinds of measurements considered by Margenau. His other objection involves the EPR (Einstein-Podolsky-Rosen) situation. He suggests that there is a significant potential for violations of the no-superluminalsignals requirement of the special theory of relativity, if projections occur in this situation and others like it. He also suggests that what is paradoxical about this situation disappears if the projection postulate is rejected. I show that it is not possible to use measurements on pairs of spatially-separated systems whose states are entangled to transmit information superluminally, and generalize this result to include nonideal measurements. I also show that EPR's dilemma does not really depend on the projection postulate. (shrink)
The method of projection is applied to a relativistic field theory of fermions interacting with a nonlinear scalar field, specifically the Friedberg-Lee soliton model. Projection is effected by operating on a localized “bag” state with the translation operator exp (iP·Z), and integrating overZ. The resulting state is an eigenstate of zero momentum. The energy and the expectation value of other physical operators can be expressed as Gaussian moments of the Hamiltonian or the physical operator times powers of the (...) momentum operator taken with respect to the bag state. Renormalization in the one-loop approximation is discussed in detail for the boson sector, and briefly for the fermion sector. The method can be tested for convergence against nonexpansion techniques. The latter, however, cannot so easily handle distortion of the Bose modes or the distortion of the Dirac sea. (shrink)
The projection postulate, which prescribes “collapse of the state vector” upon measurement, is not an essential part of quantum mechanics. Rather it is only an optional discarding of certain branches of the state vector that are expected to be irrelevant for the purpose at hand. However, its use is hazardous, and there are examples of repeated measurements for which the conventional application of the projection postulate leads to incorrect results.
I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω and (...) the boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate. (shrink)
It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory doesnot present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical (...) theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given tomeasurement by the “projection postulate.” But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality ofone (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory. (shrink)