The ethical frameworks of consequentialism and formalism predict moral awareness and behavior in individuals, but current measures either do not treat these frameworks as independent or lack sufficient theoretical underpinnings and statistical dependability. This paper presents the development and validation of a new scale to measure consequentialism and formalism that is well grounded in prior research. The Ethical Standards of Judgement Questionnaire is validated via six studies. Measurement items are developed in the first three studies, which also confirm (...) the need to eliminate a unidimensional measure and evaluate these frameworks separately. The fourth study addresses discriminant validity and the two remaining studies provide insight into how consequentialism and formalism predict the degree to which behaviors are deemed acceptable by individuals in the context of consumer beliefs and religious beliefs. Suggested uses for the scale in both academia and organizations are presented. (shrink)

The ethical frameworks of consequentialism and formalism predict moral awareness and behavior in individuals, but current measures either do not treat these frameworks as independent or lack sufficient theoretical underpinnings and statistical dependability. This paper presents the development and validation of a new scale to measure consequentialism and formalism that is well grounded in prior research. The Ethical Standards of Judgement Questionnaire is validated via six studies. Measurement items are developed in the first three studies, which also confirm (...) the need to eliminate a unidimensional measure and evaluate these frameworks separately. The fourth study addresses discriminant validity and the two remaining studies provide insight into how consequentialism and formalism predict the degree to which behaviors are deemed acceptable by individuals in the context of consumer beliefs and religious beliefs. Suggested uses for the scale in both academia and organizations are presented. (shrink)

The key concept in Kant’s aesthetics is “aesthetic reflective judgment,” a critique of which is found in Part 1 of the Critique of the Power of Judgment (1790). It is a critique inasmuch as Kant unravels previous assumptions regarding aesthetic perception. For Kant, the comparative edge of a “judgment” implicates communicability, which in turn gives it a public face; yet “reflection” points to autonomy, and the “aesthetic” shifts the emphasis away from objective properties to the subjective response evoked by the (...) object. Contrary to the view he had inherited, Kant did not treat aesthetic judgments as confused perceptions or inferior cognitions, but rather put them in a category of their own. For Kant, aesthetic reflective judgments implicated not only the processes involved in understanding the empirical world but also the processes involved in ascribing ideas or meaning to experience (which go beyond what is given in perception/cognition). This “going beyond cognition” may have been referred to by Kant as non-cognitive, but it is conditioned on a way of cognizing the object. Kant describes the features of such judgments in the Analytic of the Beautiful before addressing their possibility in subtle ways throughout the Deduction of Pure Aesthetic Judgments. Kant’s critique gives rise to three apparent dichotomies: immediate intuition and prior learning; autonomy and communicability; and non-cognitive response and aesthetic ideas. An interpretation of Kant’s theory can be deemed correct to the degree that it succeeds in showing that the contradictions are only apparent. I will argue that the resulting positive account of Kant’s aesthetic theory offers an understanding of aesthetic reflective judgment that is quite different from the standard formalism that the critics of formalism usually target and by which they misrepresent Kant’s aesthetic theory. When I refer to Kant’s formalism, then, I mean something quite different by this than what is meant by “standard formalism.” The latter is the representation given Kant’s formalism by its contemporary critics and is the typical account of formalism found in the art theory and philosophy of art literature, as will be demonstrated. (shrink)

A decision by the Supreme Court of California in the case Conservatorship of Wendland, issued in August 2001, forces us once again to confront the all-too-common situation in which an individual has, on multiple occasions, expressed strongly held personal convictions about life-sustaining interventions but failed to incorporate those convictions into a formal advance directive. Many courts have recognized that lay citizens do not consistently resort to written legal formalities in their day-to-day lives, and reasonable accommodation must be made to this (...) fundamental fact about human nature. However, a small but apparently growing minority of courts adamantly insist on either formal written directives or prescience and prophetic precision on the part of the patient before a surrogate can direct the withdrawal of life-sustaining treatment. The chronology of cases that comprise this minority position in American medical jurisprudence raise important ethical issues. (shrink)

The guiding idea behind formalism is that mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess. This idea has some intuitive plausibility: consider the tyro toiling at multiplication tables or the student using a standard algorithm for differentiating or integrating a function. It also corresponds to some aspects of the (...) practice of advanced mathematicians in some periods—for example, the treatment of imaginary numbers for some time after Bombelli's introduction of them, and perhaps the attitude of some contemporary mathematicians towards the higher flights of set theory. Finally, it is often the position to which philosophically naïve respondents will gesture towards, when pestered by questions as to the nature of mathematics. (shrink)

A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a picture of an external reality. The new formalism, developed first for the single-particle case, has the advantage of generalizing immediately to quantum field theory and to the description of relativistic phenomena such as particle creation and annihilation.

Formalism in the philosophy of mathematics has taken a variety of forms and has been advocated for widely divergent reasons. In Sects. 1 and 2, I briefly introduce the major formalist doctrines of the late nineteenth and early twentieth centuries. These are what I call empirico-semantic formalism, game formalism and instrumental formalism. After describing these views, I note some basic points of similarity and difference between them. In the remainder of the paper, I turn my attention (...) to Hilbert’s instrumental formalism. My primary aim there will be to develop its formalist elements more fully. These are, in the main, its rejection of the axiom-centric focus of traditional model-construction approaches to consistency problems, its departure from the traditional understanding of the basic nature of proof and its distinctively descriptive or observational orientation with regard to the consistency problem for arithmetic. More specifically, I will highlight what I see as the salient points of connection between Hilbert’s formalist attitude and his finitist standard for the consistency proof for arithmetic. I will also note what I see as a significant tension between Hilbert’s observational approach to the consistency problem for arithmetic and his expressed hope that his solution of that problem would dispense with certain epistemological concerns regarding arithmetic once and for all. (shrink)

Professor Bennett's new book on Spinoza is a notably ambitious one. It i s ambitious in two ways. First, having worked on the book for twenty-five years, Bennett intends a treatment of Spinoza's Ethics at once comprehensive in scope and detailed in analysis. He tells us that his book “expounds and argues with Spinoza's Ethics, in the hope of drawing into the argument philosophers who have not previously brought Spinoza into their work as an energetic collaborator or antagonist”. Second, Bennett (...) claims to have written a book superior to other commentaries in that “The courtly deference which pretends that Spinoza is always or usually right, under some rescuing interpretation is one thing; it is quite another to look to him, as I have throughout this book, as a teacher, one who can help us to see things which we might not have seen for ourselves. This is showing him a deeper respect, but also holding him to a more demanding standard”. (shrink)

Given the collapse hypothesis (CH) of quantum measurement, EPR-type correlations along with the hypothesis of the impossibility of superluminal communication (ISC) have the effect of globalizing gross features of the quantum formalism making them universally true. In particular, these hypotheses imply that state transformations of density matrices must be linear and that evolution which preserves purity of states must also be linear. A gedanken experiment shows that Lorentz covariance along with the second law of thermodynamics imply a nonentropic version (...) of ISC. Partial results using quantum logic suggest, given ISC and a version of CH, a connection between Lorentz covariance and the covering law. These results show that standard quantum mechanics is structurally unstable, and suggest that viable relativistic alternatives must question CH. One may also speculate that some features of the Hilbert-space model of quantum mechanics have their origin in space time structure. (shrink)

We introduce a class of forcing notions, called forcing notions of type S, which contains among other Sacks forcing, Prikry-Silver forcing and their iterations and products with countable supports. We construct and investigate some formalism suitable for this forcing notions, which allows all standard tricks for iterations or products with countable supports of Sacks forcing. On the other hand it does not involve internal combinatorial structure of conditions of iterations or products. We prove that the class of forcing (...) notions of type S is closed under products and certain iterations with countable supports. (shrink)

The general properties of signals permit a nonaxiomatic reconstruction of the quantum “probability” formalism independent of the standard Copenhagen interpretation of quantum mechanics. Performance standards are specified for candidate clock, signaller, and reflector devices, and it is shown that the resulting formalism forces identification of a “probability”- or “intensity”-like structure as the absolute square of an amplitude, the relative phases of amplitudes appearing explicitly in the “probability” composition law. Inequalities are produced which on one interpretation reduce to (...) the Heisenberg relations, but it is pointed out that this reconstruction disqualifies position as an observable property of a signal. (shrink)

The mathematical formalism of quantum theory has been known for almost a century, but its physical foundation has remained elusive. In recent decades, many physicists have noted connections between quantum theory and information theory. In this study, we present a physical account of the derivation of quantum theory's mathematical formalism based on information considerations in physical systems. We postulate that quantum systems are physical systems with only one independent adjustable variable. Using this physical postulate along with the conservation (...) of the total probability, we derive the standard Hilbert space formalism of quantum theory, including the Born probability rule. Our complete derivation of quantum theory provides a clear and concise physical foundation for the mathematical formalism of quantum mechanics. (shrink)

We introduce a new “positive formalism” for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural and elegant, eliminates operationally irrelevant structure and opens the general boundary formulation to quantum information theory.

It is shown that a Clifford algebra formalism provides a unifying description of spin-0, -1/2, and-1 fields. Since the operators and operands are both expressed in terms of the same Clifford algebra, the formalism obtains some results which are considerably different from those of the standard formalisms for these fields. In particular, the conservation laws are obtained uniquely and unambiguously from the equations of motion in this formalism and do not suffer from the ambiguities and inconsistencies (...) of the standard methods. (shrink)

In standard quantum mechanics, a state vector \ may belong to infinitely many different orthogonal bases, as soon as the dimension N of the Hilbert space is at least three. On the other hand, a complete physical observable A is associated with a N-dimensional orthogonal basis of eigenvectors. In an idealized case, measuring A again and again will give repeatedly the same result, with the same eigenvalue. Let us call this repeatable result a modality \, and the corresponding eigenstate (...) \. A question is then: does \ give a complete description of \? The answer is obviously no, since \ does not specify the full observable A that allowed us to obtain \; hence the physical description given by \ is incomplete, as claimed by Einstein, Podolsky and Rosen in their famous article in 1935. Here we want to spell out this provocative statement, and in particular to answer the questions: if \ is an incomplete description of \, what does it describe? is it possible to obtain a complete description, maybe algebraic? Our conclusion is that the incompleteness of standard QM is due to its attempt to describe systems without contexts, whereas both are always required, even if they can be separated outside the measurement periods. (shrink)

Nonreflexive quantum mechanics is a formulation of quantum theory based on a non- classical logic termed nonreflexive logic. In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are non-individuals in some sense, and also to take into account the fact that they (...) may be absolutely indistinguishable. The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible. Here, we present the ideas of the development of nonreflexive quantum mechanics and discuss some philosophical motivations and consequences of it. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 44.4 (2006) 599-622 MuseSearchJournalsThis JournalContents[Access article in PDF]The Purposiveness of Form: A Reading of Kant's Aesthetic FormalismRachel ZuckertIn the "critique of aesthetic judgment," Kant claims that when we find an object beautiful, we are appreciating its "purposive form." Many of Kant's readers have found this claim one of his least interesting and most easily criticized claims about aesthetic experience. Detractors hold up his (...) aesthetics as a paradigmatic case of narrow formalism; 1 and even many admirers of Kant's aesthetics take Kant's claims about form to be problematic, but argue that they are inessential to his aesthetics (which includes more interesting, defensible claims). 2 Though these critics come to differing evaluations of Kant's aesthetics as a whole, they agree on two points. First, interpretively: that when Kant claims that it is the "form" of an object we find beautiful, he means that in aesthetic appreciation, we find certain spatial and/or temporal properties (such as proportion, line, shape) aesthetically pleasing—and that such properties are exclusively responsible for an object's beauty. Second, evaluatively: that Kant is wrong, at least about this.In this paper, I shall propose that we need not endorse either claim. I shall argue that one may interpret Kant's formalism as a claim that in aesthetic experience 3 [End Page 599] we appreciate the object as an individual, as comprising all (or indeterminately many) of its sensible properties as inextricably interrelated or unified to make the object what it is; in other words, we appreciate what has been called an object's 'individual form.' This reading, I shall suggest, allows us not only to understand Kant's aesthetics as intimately connected to his project in the Critique of Judgment (hereafter, CJ) as a whole, but also to see Kant's aesthetics, in general, as providing a richer, more plausible description of our aesthetic engagement with an object, or as less narrowly subjectivist than is frequently believed.I shall proceed by presenting Kant's claims about form, and the standard criticisms thereof, and then turn to defend this alternative reading. Before I do so, however, I wish to make some preliminary remarks about aesthetic formalism in general. Contemporary discussion of formalism often takes aesthetic formalism to be instantiated by the views of the twentieth-century art critics, Clive Bell and Roger Fry, 4 and Kant's formalism is often implicitly equated with theirs (or the kind of position attributed to them). I wish to resist that equation in this essay; to that end, I start here by giving a wider sense of what formalism might be, drawing especially on historical positions that were available to Kant. 5Broadly speaking, "formalism" is the view that, in aesthetic appreciation of an object (usually a work of art), we do and ought to pay attention not to the object's representational content, emotional expressiveness, historical, institutional, or social context (whether conditions for the production of the object or its effects), but only to its form. Formalism is characterized in some sense, then, by what it excludes, viz. considerations taken to be external to the object. But it does specify positively (if vaguely) that the form of an object is what makes it beautiful. 6'Form,' however, can mean a number of different things, all of which (in some sense) are the design or arrangement of an object's parts, often of its sensible properties. I wish to draw attention to three somewhat distinct ways in which one may understand such form or arrangement of properties, which I shall call 'property-formalism,' 'kind-formalism,' and 'whole-formalism.' Property-formalism is the view that the form of an object can be described in terms of a set of specific spatial or temporal properties that characterize the relations that hold among different parts of the object, and that these properties are responsible for the beauty of the object. Hogarth's view that the serpentine line is the most beautiful line, responsible... (shrink)

The traditional view regarding the philosophy of mathematics in the twentieth century is the dogma of three schools: Logicism, Intuitionism and Formalism. The problem with this dogma is not, at least not first and foremost, that it is wrong, but that it is biased and essentially incomplete. 'Biased' because it was formulated by one of the involved parties, namely the logical empiricists - if I see it right - in order to make their own position look more agreeable with (...) Intuitionism and Formalism. 'Essentially incomplete' because there was - and still exists - beside Frege's Logicism, Brouwer's Intuitionism and Hilbert's Formalism at least one further position, namely Husserl's phenomenological approach to the foundations of arithmetic, which is also philosophically interesting. In what follows, I want to do two things: First, I will show that the standard dogma regarding the foundations of mathematics is not only incomplete, but also inaccurate, misleading and basically wrong with respect to the three schools themselves. In doing this I hope to make room for Husserl and his phenomenological approach as a viable alternative in the foundations of arithmetic. Second, I will show how Husserl's phenomenological point of view is a position that fits exactly in between Frege's "logicism", properlyunderstood, and Hilbert's mature proof theory, in which his so called "formalism" turns out to be only a means to an end and not a goal in itself. (shrink)

In recent articles, Zangari (1994) and Karakostas (1997) observe that while an &unknown;-extended version of the proper orthochronous Lorentz group O + (1,3) exists for values of &unknown; not equal to zero, no similar &unknown;-extended version of its double covering group SL(2, C) exists (where &unknown;=1-2&unknown; R , with &unknown; R the non-standard simultaneity parameter of Reichenbach). Thus, they maintain, since SL(2, C) is essential in describing the rotational behaviour of half-integer spin fields, and since there is empirical evidence (...) for such behaviour, &unknown;-coordinate transformations for any value of &unknown;<>0 are ruled out empirically. In this article, I make two observations:(a)There is an isomorphism between even-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions of such spinor fields.(b)There is a 2-1 isomorphism between odd-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions for such spinor fields up to a sign. Evidence that the components of such fields do take unique values is not decisive in favour of the realist in the debate over the conventionality of simultaneity in so far as such fields do not play a role in clock synchrony experiments in general, and determinations of the one-way speed of light in particular.I claim that these observations are made clear when one considers the coordinate-independent 2-spinor formalism. They are less evident if one restricts oneself to earlier coordinate-dependent formalisms. I end by distinguishing these conclusions from those drawn by the critique of Zangari given by Gunn and Vetharaniam (1995). (shrink)

The belief that quantum mechanics does not admit a realistic interpretation is widespread. According to some scholars concerned with the foundations of QM all existing interpretations of this theory presuppose instead a form of realism which consists in assuming that QM deals with individual objects and their properties. We uphold in the present paper that the arguments supporting the contextuality and the nonlocality of QM are a significant clue to the implicit adoption of stronger forms of realism. If these kinds (...) of realism are substituted by a simpler and more intuitive semantic realism one can contrive a noncontextual and local interpretation of the formalism of QM. Moreover one can provide a model for such an interpretation in which local realism and QM do not conflict and some fundamental problems of the standard interpretation of QM are avoided. (shrink)

The presented enhanced version of Eriksen’s theorem defines an universal transform of the Foldy–Wouthuysen type and in any external static electromagnetic field reveals a discrete symmetry of Dirac’s equation, responsible for existence of a highly influential conserved quantum number—the charge index distinguishing two branches of DE spectrum. It launches the charge-index formalism obeying the charge-index conservation law. Via its unique ability to manipulate each spectrum branch independently, the CIF creates a perfect charge-symmetric architecture of Dirac’s quantum mechanics, which resolves (...) all the riddles of the standard DE theory. Besides the abstract CIF algebra, the paper discusses: the novel accurate charge-symmetric definition of the electric-current density; DE in the true-particle representation, where electrons and positrons coexist on equal footing; flawless “natural” scheme of second quantization; and new physical grounds for the Fermi–Dirac statistics. As a fundamental quantum law, the CICL originates from the kinetic-energy sign conservation and leads to a novel single-particle physics in strong-field situations. Prohibiting Klein’s tunneling in Klein’s zone via the CICL, the precise CIF algebra defines a new class of weakly singular DE solutions, strictly confined in the coordinate space and experiencing the total reflection from the potential barrier. (shrink)

We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to classical constraints, based on a question-and-answer procedure. The problem is posed from a particular batch of queries while the constraints are represented by the truth table of a set of Boolean functions. The Bayesian inference technique consists in assigning a probability distribution within a real-valued (...) probability space to the joint set of queries in order to satisfy the constraints. The initial query batch is not unique and alternative batches can be considered at will. They are enabled mechanically from the initial batch, quite simply by transcribing the probability space into an auxiliary Hilbert space. It turns out that this sole procedure leads to exactly rediscover the standard quantum information theory and thus provides an information-theoretic rationale to its technical rules. In this framework, the great challenges of quantum mechanics become simple platitudes: Why is the theory probabilistic? Why is the theory linear? Where does the Hilbert space come from? In addition, most of the paradoxes, such as uncertainty principle, entanglement, contextuality, nonsignaling correlation, measurement problem, etc., become straightforward features. In the end, our major conclusion is that quantum information is nothing but classical information processed by a mature form of Bayesian inference technique and, as such, consubstantial with Aristotelian logic. (shrink)

Alan Weir’s new book is, like Darwin’s Origin of Species, ‘one long argument’. The author has devised a new kind of have-it-both-ways philosophy of mathematics, supposed to allow him to say out of one side of his mouth that the integer 1,000,000 exists and even that the cardinal ℵω exists, while saying out of the other side of his mouth that no numbers exist at all, and the whole book is devoted to an exposition and defense of this new view. (...) The view is presented in the book in a way that can make it difficult for the reader to trace the main line of argument: with a great deal of apparatus, and with a great many digressions into subordinate issues. In what follows I will try to stick to what I take to be the essentials, even at the risk of oversimplifying some central but complicated issues, and at the cost of neglecting some interesting but peripheral ones.In chapter 1, the author introduces a distinction between what he calls ‘two aspects of meaning’ and dubs informational content and metaphysical content. Informational content is the aspect of meaning of primary interest to linguists, and the one of which speakers themselves are generally aware, at least upon reflection. Metaphysical content is supposed to be another aspect of meaning primarily of interest to philosophers. The basic idea is that if there are standards of correctness for assertions of a certain kind, then such an assertion may be called ‘true’ when those standards are met, even though the kind of correctness involved is not correctness in representing how the world is. What the world must be like in order for the utterance to be true is the metaphysical content of the assertion, but it need not be part of its …. (shrink)

When reassessing the role of Debreu’s axiomatic method ineconomics, one has to explain both its success and unpopularity; onehas to explain the “bright shadow” Debreu cast on the discipline:sheltering, threatening, and difficult to pin down. Debreu himself didnot expect to have such an influence. Before he received the Bank ofSweden Prize in 1983 he had never openly engaged with themethodology or politics of mathematical economics. When in severalspeeches he later rigorously distinguished mathematical form fromeconomic content and claimed this as the (...) virtue of mathematicaleconomics, he did both: he defended mathematical reasoning againstthe theoretical innovations since the 1970s and expressed remorse forhaving promised too much because it cannot support claims abouteconomic content. The analysis of this twofold role of Debreu’saxiomatic method raises issues of the social and political responsibilityof economists over and above standard epistemic issues. (shrink)

Some postulates are introduced to go from the classical Hamilton-Jacobi theory to the quantum one. We develop two approaches in order to calculate propagators, establishing the connection between them and showing the equivalence of this picture with more known ones such as the Schrödinger's and the Feynman's formalisms. Applications of the above-mentioned approaches to both the standard case of the harmonic oscillator and to the harmonic oscillator with time-dependent parameters are made.

Attempts to arrange all of classical mechanics upon a self-contained basis encounter difficulties due to "the lousy encyclopedia phenomenon": hard cases involving, e.g., billiard balls, often require that the standard treatments be abandoned in favor of conceptually different accounts. Worse yet, these chains of interdependence often travel in circular loops, where the practitioner is returned to formalisms that she had previously abandoned. However, behaviors of this sort are to be expected if classical doctrine is instead viewed as a "reduced (...) variable" covering of quantum mechanics, which is the point of view that this essay recommends. (shrink)

In the standard formalism of quantum gravity, black holes appear to form statistical distributions of quantum states. Now, however, we can present a theory that yields pure quantum states. It shows how particles entering a black hole can generate firewalls, which however can be removed, replacing them by the ‘footprints’ they produce in the out-going particles. This procedure can preserve the quantum information stored inside and around the black hole. We then focus on a subtle but unavoidable modification (...) of the topology of the Schwarzschild metric: antipodal identification of points on the horizon. If it is true that vacuum fluctuations include virtual black holes, then the structure of space-time is radically different from what is usually thought. (shrink)

Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No - that the status of individual continuous quantities is very different in quantum mechanics than in (...) classical mechanics. On the contrary, I shall show that the same subtle issues arise with respect to continuous quantities in classical and quantum mechanics; and that it is, after all, possible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics. (shrink)

I argue that quantum decoherence—understood as a dynamical process entailed by the standard formalism alone—carries us beyond conceptual aspects of non-relativistic quantum mechanics deemed insurmountable by many contributors to the recent quantum gravity and cosmology literature. These aspects include various incarnations of the measurement problem and of the quantum -to-classical puzzle. Not only can such problems be largely bypassed or dissolved without default to a particular interpretation, but theoretical work in relativistic arenas stands to gain substantial physical and (...) philosophical insight by incorporating decoherence phenomena. (shrink)

Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that (...) the Born probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation. (shrink)

Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that (...) the Born probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation. (shrink)

Hybrid logics are a principled generalization of both modal logics and description logics, a standard formalism for knowledge representation. In this paper we give the first constructive version of hybrid logic, thereby showing that it is possible to hybridize constructive modal logics. Alternative systems are discussed, but we fix on a reasonable and well-motivated version of intuitionistic hybrid logic and prove essential proof-theoretical results for a natural deduction formulation of it. Our natural deduction system is also extended with (...) additional inference rules corresponding to conditions on the accessibility relations expressed by so-called geometric theories. Thus, we give natural deduction systems in a uniform way for a wide class of constructive hybrid logics. This shows that constructive hybrid logics are a viable enterprise and opens up the way for future applications. (shrink)

Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain (...) kinds of 'time observables' to find a representation within quantum theory, including clock operators and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on reflection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack. (shrink)

This paper presents a substantivist construal of discourse ethics, which claims that we should see our engagement in public deliberation as expressing and elaborating a substantive commitment to basic moral ideas of solidarity, equality, and freedom. This view is different from Habermas's standard formalist defence of discourse ethics, which attempts to derive the principle of discursive moral justification from primarily non-moral presuppositions of rational argumentation as such. After explicating the difference between the substantivist and the formalist construal, I defend (...) the former by showing that it is not only intuitively compelling, but also particularly well equipped for addressing four important objections recently levelled against discourse ethics and its political applications. I conclude by pointing out some consequences of the previous discussion for the future of Critical Theory. (shrink)

A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced. In comparison with previous formulations, the formal aspect has been improved by the use of certain mathematical theories, such as the theory of equipped spaces, and group theory. The standard formalism is naturally obtained from the latter, starting from a central primitive concept: the Galilei group.

This article sets forth and discusses the Ithaca Interpretation of Quantum Mechanics. Section 1 presents the standard formalism of quantum mechanics and the measurement problem. Section 2 sketches Everett's interpretation as a preamble to IIQM. Section 3 sets out IIQM's central claim: it is possible to make sense of quantum mechanics by taking as the proper subject of physics the correlations among subsystems. Section 4 introduces a theorem of quantum mechanics, the SSC theorem, which supports this claim. Section (...) 5 contends that at least two problems exist with IIQM, and one serious objection against it. Section 6 discusses a strategy based on relational probabilities to go around the objection. /// Este artículo presenta y discute la Interpretación de la Mecánica Cuántica de Ithaca. La sección 1 expone el formalismo estándar de la mecánica cuántica y el problema de la medición. La sección 2 bosqueja la interpretación de Everett como preámbulo a la IIQM. La sección 3 plantea la tesis central de la IIQM: es posible dar sentido a la mecánica cuántica tomando como sujeto propio de la física las correlaciones entre subsistemas. La sección 4 expone el teorema SSC de la mecánica cuántica que sustenta esta tesis. En la sección 5 se sostiene que existen al menos dos problemas con la IIQM, y una seria objeción en su contra. Para sortear esta objeción, la sección 6 discute una estrategia basada en probabilidades relacionales. (shrink)

In this article I investigate several possibilities to define the concept of “temporal non-locality” within the standard framework of quantum theory. In particular, I analyze the notions of “temporally non-local states”, “temporally non-local events” and “temporally non-local observables”. The idea of temporally non-local events is already inherent in the standard formalism of quantum mechanics, and Basil Hiley recently defined an operator in order to measure the degree of such a temporal non-locality. The concept of temporally non-local states (...) enters as soon as “clock-representing states” are introduced in the context of special and general relativity. It is discussed in which way temporally non-local measurements may find an interesting application for experiments which test temporal versions of Bell inequalities. (shrink)

In this work we present a dynamical approach to quantum logics. By changing the standard formalism of quantum mechanics to allow non-Hermitian operators as generators of time evolution, we address the question of how can logics evolve in time. In this way, we describe formally how a non-Boolean algebra may become a Boolean one under certain conditions. We present some simple models which illustrate this transition and develop a new quantum logical formalism based in complex spectral resolutions, (...) a notion that we introduce in order to cope with the temporal aspect of the logical structure of quantum theory. (shrink)

Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown that the explanation does not make use of the full probability measure, but rather of a suitable set function deriving from it, which defines relative typicality between single-time cylinder sets. Such a set function can also be derived directly (...) from the standard quantum formalism, without the need of an underlying probability measure. The key concept for this derivation is the quantum typicality rule, which can be considered as a generalization of the Born rule. The result is a new formulation of quantum mechanics, in which particles follow definite trajectories, but which is based only on the standard formalism of quantum mechanics. (shrink)

Algebraic substantivalism, as an interpretation of general relativity formulated in the Einstein algebra formalism, avoids the hole argument against manifold substantivalism. In this essay, I argue that this claim is well-founded. I first identify the hole argument as an argument against a specific form of semantic realism with respect to spacetime. I then consider algebraic substantivalism as an alternative form of semantic realism. In between, I justify this alternative form by reviewing the Einstein algebra formalism and indicating the (...) extent to which it is expressively equivalent to the standard formalism of tensor analysis on differential manifolds. (shrink)

After a brief account of theway quantum theory deals with naturalprocesses, the crucial problem that such atheory meets, the measurement or, better, themacro-objectification problem is discussed.The embarrassing aspects of the occurrence ofentangled states involving macroscopic systemsare analyzed in details. The famous example ofSchroedinger's cat is presented and it ispointed out how the combined interplay of thesuperposition principle and the ensuingentanglement raises some serious difficultiesin working out a satisfactory quantum worldview, agreeing with our definiteperceptions. The orthodox solution to themacro-objectification problem, i.e. (...) thepostulate of wave packet reduction, isanalyzed and is proved to be inconsistent withthe assumption that the theory governes alsothe measurement process. After these premises,the rest of the paper is devoted to discuss arecent proposal of overcoming the difficultiesof the standard formalism by acceptingnonlinear and stochastic modifications of thequantum dynamics. The proposed theory is shownto agree with all known predictions of thestandard theory concerning microscopic systemsand to account, on the basis of a universaldynamics which is assumed to govern allnatural processes, for wave packet reductionin measurement processes and, more important,to eliminate all the difficulties concerningmacroscopic situations. Actually, the proposedtheory allows one to take consistently amacrorealistic position about natural processes and about our definite perceptions. (shrink)

Back in 1987 the physicist/theoretical biologist Walter Elsasser reviewed a range of philosophical issues at the foundation of organismal biology above the molecular level. Two of these are particularly relevant to quantifications of form: the concept of ordered heterogeneity and the principle of nonstructural memory, the truism that typically the forms of organisms substantially resemble the forms of their ancestors. This essay attempts to weave Elsasser’s principles together with morphometrics for one prominent data type, the representation of animal forms by (...) positions of landmark points. I introduce a new spectrum of pattern descriptors of the shape variation of landmark configurations, ranging from the most homogeneous through growth gradients and focal features to a model of totally disordered heterogeneity incompatible with the rhetoric of functional explanation. An investigation may end up reporting its findings by one of these descriptors or by several. These descriptors all derive from one shared diagrammatic device: a log–log plot of sample variance against one standard formalism of today’s geometric morphometrics, the bending energies of the principal warps that represent all the scales of variability around the sample average shape. The new descriptors, which I demonstrate over a variety of contemporary morphometric examples, may help build the bridge we urgently need between the arithmetic of today’s burgeoning image-based data resources and the rhetoric of biological explanations aligned with the principles of Elsasser along with an even earlier philosopher of biology, the Viennese visionary Hans Przibram. (shrink)

Theabstract variable binding calculus (VB-calculus) provides a formal frame-work encompassing such diverse variable-binding phenomena as lambda abstraction, Riemann integration, existential and universal quantification (in both classical and nonclassical logic), and various notions of generalized quantification that have been studied in abstract model theory. All axioms of the VB-calculus are in the form of equations, but like the lambda calculus it is not a true equational theory since substitution of terms for variables is restricted. A similar problem with the standard (...) formalism of the first-order predicate logic led to the development of the theory of cylindric and polyadic Boolean algebras. We take the same course here and introduce the variety of polyadic VB-algebras as a pure equational form of the VB-calculus. In one of the main results of the paper we show that every locally finite polyadic VB-algebra of infinite dimension is isomorphic to a functional polyadic VB-algebra that is obtained from a model of the VB-calculus by a natural coordinatization process. This theorem is a generalization of the functional representation theorem for polyadic Boolean algebras given by P. Halmos. As an application of this theorem we present a strong completeness theorem for the VB-calculus. More precisely, we prove that, for every VB-theory T that is obtained by adjoining new equations to the axioms of the VB-calculus, there exists a model D such that T s=t iff D s=t. This result specializes to a completeness theorem for a number of familiar systems that can be formalized as VB-calculi. For example, the lambda calculus, the classical first-order predicate calculus, the theory of the generalized quantifierexists uncountably many and a fragment of Riemann integration. (shrink)

The default theory of aesthetic value combines hedonism about aesthetic value with strict perceptual formalism about aesthetic value, holding the aesthetic value of an object to be the value it has in virtue of the pleasure it gives strictly in virtue of its perceptual properties. A standard theory of aesthetic value is any theory of aesthetic value that takes the default theory as its theoretical point of departure. This paper argues that standard theories fail because they theorize (...) from the default theory. (shrink)

One of the long-standing problems in particle physics is the covariant description of higher spin states. The standard formalism is based upon totally symmetric Lorentz invariant tensors of rank-K with Dirac spinor components, $\psi _{\mu _1 \cdots \mu _K } $ , which satisfy the Dirac equation for each space time index. In addition, one requires $\partial ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } = 0{\text{ }}and{\text{ }}\gamma ^{\mu _1 } \psi _{\mu _1 \cdots \mu (...) _K } = 0$ . The solution obtained this way (so called Rarita–Schwinger framework) describes “has–been” spin-(K+ $ - \frac{1}{2}$ ) particles in the rest frame and particles of indefinite (fuzzy) spin elsewhere. Problems occur when $\psi _{\mu _1 \cdots \mu _K } $ constrained this way are placed within an electromagnetic field. In this case, the energy of the spin-(K+ $ - \frac{1}{2}$ ) state becomes imaginary and it propagates acausally (Velo–Zwanziger problem). Here I consider two possible avenues for avoiding the above problems. First I make the case that specifically for baryon excitations there seems to be no urgency so far for a formalism that describes isolated higher-spin states as all the observed nucleon and Δ(1232) excitations (up to Δ(1600)) are exhausted by unconstrained ψ μ , $\psi _\mu ,\psi _{\mu _1 \cdots \mu _3 } {\text{ }}and{\text{ }}\psi _{\mu _1 \cdots \mu _5 } ,$ , structures which originate from rotational and vibrational excitations of an underlying quark–diquark string. Second, I show that the $\gamma ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } = 0$ constraint is a short-hand of a more general definition of the parity-singlet invariant subspace of the squared Pauli–Lubanski vector, W 2. I consider the simplest case of K=1 and construct the covariant projector onto that very state as $ - \frac{1}{3}(\frac{1}{{m^2 }}W^2 + \frac{3}{4})$ . I suggest to work in the sixteen dimensional vector space, Ψ, of the direct product of the four-vector, A μ , with the Dirac spinor, ψ, i.e., Ψ=A μ ⊗ψ, rather than keeping space-time and spinor indices separated and to consider $( - \frac{1}{3}(\frac{1}{{m^2 }}W^2 + \frac{3}{4}) - 1)\Psi = 0$ as the principal wave equation without invoking any further supplementary conditions. In gauging the equation minimally and, in calculating the determinant, one obtains the energy-momentum dispersion relation. The latter turned out to be well-behaved and free from pathologies, thus avoiding the classical Velo–Zwanziger problem. (shrink)