Morphogenesis is a key process in developmental biology. An important issue is the understanding of the generation of shape and cellular organisation in tissues. Despite of their great diversity, morphogenetic processes share common features. This work is an attempt to describe this diversity using the same formalism based on a cellular description. Tissue is seen as a multi-cellular system whose behaviour is the result of all constitutive cells dynamics. Morphogenesis is then considered as a spatiotemporal organization of cells activities. (...) We show how this formalism relies on Reaction–Diffusion/Positional Information approach and how it permits to generalize its modelling possibilities. Three quite different applications for concrete morphogenetic processes are presented. The first one is a model for epithelial invagination, the second is a model of cellular differentiation by local cell–cell signalling. The last example is the secondary radial growth of conifer trees. From the mathematical point of view, different modelling tools are used according to the specificity of each process. (shrink)

We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal (...) treatment introduced here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem. (shrink)

The structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom in interaction with a quantum electromagnetic field is investigated. Our main purpose is to rewrite the formalism in Zhu et al. and to deduce the general expressions of the Einstein A coefficients of an atom on an arbitrary stationary trajectory. The total rate of change of the energy and Einstein coefficients of the atom near a plate with finite temperature or (...) acceleration are also investigated. (shrink)

Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally (...) large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation. (shrink)

LEGO tells about not just LEGO architecture but architecture generally: its objects, its aesthetic properties, and how people judge them. To illustrate how thinking about LEGO can help people with such matters, this chapter considers some scenarios. These scenarios illustrate two very different ways of thinking about architecture. On the one hand, people might think architectural objects (more commonly, "works of architecture"), like buildings, bridges, and aqueducts, have forms that stand on their own, and which thereby do not depend on (...) historical, environmental, or any other contexts. On the other hand, they might think that architectural objects are best understood (maybe only understood) if they have one or more kinds of contextual information. From a different angle, some might see formalism as a better fit with original LEGO world design than with real‐world architectural design. Proponents of formalism take note of what makes architectural objects distinctive. (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.

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov}, \cite{Kryukov1} is further analyzed. The main subject here is a comparison of the ordinary and the string bases of eigenvectors of a linear operator as introduced in \cite{Kryukov}. It is shown that the string basis of eigenvectors is a natural generalization of its classical counterpart. It is also shown that the developed formalism forces us to consider any Hermitian operator with continuous spectrum as a restriction to a space of square (...) integrable functions of a self-adjoint operator defined on a space of generalized functions. In the formalism functional coordinate transformations preserving the norm of strings are now linear isometries rather than the unitary transformations. (shrink)

It is shown that the traditional formalism of equilibrium quantum statistical mechanics may fully be incorporated into a general macro-observable approach to quantum statistical mechanics recently proposed by the same author. (1,2) In particular, the partition functions which in the traditional approach are assumed to connect nonnormalized density operators with thermodynamic functions are reinterpreted as functions connecting so-called quantum mechanical effect operators with state parameters. It is argued that these functions although only part of a much richer internal structure (...) of the macro-observable are sufficient to cope with all problems one usually encounters in equilibrium quantum statistical mechanics. p]Denn eigentlich unternehmen wir umsonst, das Wesen eines Dinges auszudrücken. Wirkungen werden wir gewahr, und eine vollständige Geschichte dieser Wirkungen umfaßte wohl allenfalls das Wesen jenes Dinges.Johann W. v. Goethe Farbenlehre. (shrink)

We argue about a conceptual approach to quantum formalism. Starting from philosophical conjectures (Platonism, Idealism and Realism) as basic ontic elements (namely: math world, data world, and state of matter), we will analyze the quantum superposition principle. This analysis bring us to demonstrate that the basic assumptions affect in different ways:(a) the general problem of the information and computability about a system, (b) the nature of the math tool utilized and (c) the correspondent physical reality.

On a general level, this paper proposes a critical analysis of one of the attempts to make bridges between economics and moral and political philosophy. A priori, we may expect that formal methods may lead to clearer and more rigorous arguments, and may facilitate practical applications. However, this paper illustrates how precision is bought at the price of becoming tautological. Therefore, the statement that "it is already widely recognized that formal methods derived from economics can contribute to ethics" (Broome 1989: (...) ix) seems hasty. The paper is organized as follows: Section 2 discusses some philosophical background assumptions which underlie a decision theoretic argument in favour of utilitarianism. Section 3 recalls briefly John Harsanyi's decision theoretic arguments in favour of utilitarianism. It then focuses on the crucial assumption of separability in order to show that separability can always be saved as an assumption if one applies the strategy of dispersion. Section 4, finally, shows how the theorem may indeed reconcile the concern for equality and utilitarianism, at the price of becoming futile. (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)

It has often been remarked that Bohr's writings on the interpretation of quantum mechanics make scant reference to the mathematical formalism of quantum theory; and it has not infrequently been suggested that this is another symptom of the general vagueness, obscurity and perhaps even incoherence of Bohr's ideas. Recent years have seen a reappreciation of Bohr, however. In this article we broadly follow this "rehabilitation program". We offer what we think is a simple and coherent reading of Bohr's statements (...) about the interpretation of quantum mechanics, basing ourselves on primary sources and making use of and filling lacunas in|recent secondary literature. We argue that Bohr's views on quantum mechanics are more firmly connected to the structure of the quantum formalism than usually acknowledged, even though Bohr's explicit use of this formalism remains on a rather global and qualitative level. In our reading, Bohr's pronouncements on the meaning of quantum mechanics should first of all be seen as responses to concrete physical problems, rather than as expressions of a preconceived philosophical doctrine. In our final section we attempt a more detailed comparison with the formalism and conclude that Bohr's interpretation is not far removed from present-day non-collapse interpretations of quantum mechanics. (shrink)

On a general level, this paper proposes a critical analysis of one of the attempts to make bridges between economics and moral and political philosophy. A priori, we may expect that formal methods may lead to clearer and more rigorous arguments, and may facilitate practical applications. However, this paper illustrates how precision is bought at the price of becoming tautological. Therefore, the statement that "it is already widely recognized that formal methods derived from economics can contribute to ethics" seems hasty. (...) The paper is organized as follows: Section 2 discusses some philosophical background assumptions which underlie a decision theoretic argument in favour of utilitarianism. Section 3 recalls briefly John Harsanyi's decision theoretic arguments in favour of utilitarianism. It then focuses on the crucial assumption of separability in order to show that separability can always be saved as an assumption if one applies the strategy of dispersion. Section 4, finally, shows how the theorem may indeed reconcile the concern for equality and utilitarianism, at the price of becoming futile. (shrink)

The constraint formalism of classical mechanics is extended to field theories with gauge groups. Explicit examples of Klein-Gordon and Maxwell fields are presented. The symmetry properties of the Maxwell fields have the unexpcted feature in this formalism of forming a first-class algebra which is not Lie, a situation already encountered in the general theory of relativity.

In his remarkable paper Formalism 64, Robinson defends his eponymous position concerning the foundations of mathematics, as follows:Any mention of infinite totalities is literally meaningless.We should act as if infinite totalities really existed. Being the originator of Nonstandard Analysis, it stands to reason that Robinson would have often been faced with the opposing position that ‘some infinite totalities are more meaningful than others’, the textbook example being that of infinitesimals. For instance, Bishop and Connes have made such claims regarding (...) infinitesimals, and Nonstandard Analysis in general, going as far as calling the latter respectively a debasement of meaning and virtual, while accepting as meaningful other infinite totalities and the associated mathematical framework. We shall study the critique of Nonstandard Analysis by Bishop and Connes, and observe that these authors equate ‘meaning’ and ‘computational content’, though their interpretations of said content vary. As we will see, Bishop and Connes claim that the presence of ideal objects in Nonstandard Analysis yields the absence of meaning. We will debunk the Bishop–Connes critique by establishing the contrary, namely that the presence of ideal objects in Nonstandard Analysis yields the ubiquitous presence of computational content. In particular, infinitesimals provide an elegant shorthand for expressing computational content. To this end, we introduce a direct translation between a large class of theorems of Nonstandard Analysis and theorems rich in computational content, similar to the ‘reversals’ from the foundational program Reverse Mathematics. The latter also plays an important role in gauging the scope of this translation. (shrink)

Compares formalism and instrumentalism and evaluates their general claims. “Part of what is meant by formalism is this: The law provides sufficient basis for deciding any case that arises. There are no “gaps” within the law, and there is but one sound legal decision for each case.” The formalist also holds that law is traceable to an authoritative source. “…sound legal decisions can be justified as the conclusions of valid deductive syllogisms. Because law is believed to be complete (...) and univocal, all cases that arise can in principle be decided in this way. This is the formalistic model for legal justifications.” Moderate instrumentalism also accepts the notion that the law has sources and that past political events can determine what the law is for the future. However, they also maintain that the law has gaps. “Moderate instrumentalists and positivists alike embrace a source-based conception of the law as well as a formalistic model for legal justification; partly because of this combination, they reject the formalistic notion that law is complete and univocal. Instrumentalists, like positivists, emphasize that because the interpretation of authoritative legal texts and their application to cases are often controversial, reasonable arguments are often possible on both sides of a legal issue. Since there are no hard and fast rules for adjudicating such disputes, positivists conclude that law in such cases is indeterminate – not yet fully formed, needing judicial legislation. Instrumentalists most likely have a similar view of the law. They assume that law is determinate on an issue at a given time only if its identification and application are, roughly speaking, mechanical.” [Must keep in mind the distinction between determinate and conclusive.] “The instrumentalists make the decisive assumption that law is not determinate if it is controversial, for law is thought to be gappy and indeterminate only when reasonable legal arguments are possible on both sides of a legal question…This reasoning exposes a more fundamental assumption of formalism, instrumentalism, and positivism: Nondeductive reasoning is incapable of adequately establishing any conclusion.” This, though, is a radical thesis given that all scientific hypotheses are unproven deductively. [But it might be a claim restricted to legal reasoning. Moreover, it seems legitimate to wonder whether legal reasoning is really comparable to offering scientific hypotheses.] We should, however, reject the mechanistic model of legal and judicial reasoning that assumes a given major premise captured in authoritative legal texts that deductively produces conclusions in a situation to which a law applies. Take a law that requires some activity to be “economically efficient” but fails to specify economic efficiency. The text assumes that there is such a thing as economic efficiency, that some activities are so efficient and others not, that some judgments about economic efficiency are true and others false, and that the criteria of efficiency are determinable in principle. “[I]f there really are reasons for preferring one conception of economic efficiency to others in a given context, the assumption of the law in question would be true; if the court correctly identifies and applies that conception, it is simply carrying out its legal mandate. It would be faithful to the text, but it would not be limited to the four corners of the text and its literal implications.” Thus, a judge may employ non-mechanical reasoning in arriving at the meaning of legal requirements such as economic efficiency. Moral reasons are constitutive of the law. A judge must, in deciding the appropriate conc ption of economic efficiency, offer reasons for preferring that conception in the given context. (shrink)

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)

The traditional exposition of Kantian ethical theory in the business ethics literature is abstract, esoteric, and impractical compared to the more usable presentations of utilitarianism. This situation can be improved by identifying and describing the conceptual dimensions of formalistic ethical reasoning, as contained in the interplay between case and principle, with examples from the business/society literature.

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.

Beyond Formalism is Jay Rosenberg’s attempt to articulate his dissatisfactions with the Kripkean “revolution” in the philosophy of language and to propose an alternative to it. According to Rosenberg, even though a “surprisingly large number of philosophers simply adopted the Kripkean ideas, images, and idioms root and branch”, he has been “inarticulately irritated by Kripke’s views for almost twenty years”. Rosenberg claims that Kripke’s semantics for proper names and natural kind terms is a misguided attempt to apply results in (...) formal logic, in particular the semantics of modal logic, to natural language. In order to get “beyond formalism,” Rosenberg offers his own theory of nominal reference that is “for human beings.” Rosenberg’s “human” theory should be able to take account of the functioning of referring expressions in “contexts of individual understanding and interpersonal communication” —something Kripke’s theory cannot do, according to Rosenberg. Rosenberg’s book divides into criticism of Kripke’s ideas on naming and necessity, on the one hand, and adumbration of Rosenberg’s own theory for “human beings” on the other, supplemented by discussions of such topics as Kripke’s puzzle about belief and the role of formal logic in the philosophy of language. (shrink)

One can only look with favor upon the appearance of the English translation of this tremendously important work in the history of ethical theory in twentieth century European philosophy. We are also fortunate to have in Manfred Frings both the general editor of the German edition of the collected works of Scheler and a skillful translator of this significant work. In this work, Scheler hopes to mediate between Kant’s empty formalism and ethical relativism by developing an absolutistic ethics which (...) nonetheless does not focus on mere "duty" but on a definite moral "content". In the absence of an adjectival form for "content," Frings and Funk have decided to translate "die materiale Wertethik" by "non-formal ethics of values." Such an ethics centers on the absolute value of persons; thus the subtitle of the work: "A New Attempt toward the Foundation of an Ethical Personalism." Scheler’s method in this work is, as is well known, "phenomenological," i.e., concerned with intuiting the essence or absolute being of ethical values. There is a helpful bibliography, an index of names, and a detailed index of subjects.—J.D.C. (shrink)

Social network research is widely considered atheoretical. In contrast, in this article I argue that network analysis often mixes two distinct theoretical frameworks, creating a logically inconsistent foundation. Relationalism rejects essentialism and a priori categories and insists upon the intersubjectivity of experience and meaning as well as the importance of the content of interactions and their historical setting. Formalism is based on a structuralist interpretation of the theoretical works of Georg Simmel. Simmel laid out a neo-Kantian program of identifying (...) a priori categories of relational types and patterns that operate independently of cultural content or historical setting. Formalism and relationalism are internally consistent theoretical perspectives, but there are tensions between them. To pave the way for stronger middle-range theoretical development, I disaggregate the two approaches and highlight the contradictions that must be addressed or resolved for the construction of any general and inclusive theory. (shrink)

A current focus of legal debate is the proper role of the courts in the interpretation of statutes and the Constitution. Are judges to look solely to the naked language of an enactment, then logically deduce its application in simple syllogistic fashion, as legal formalists had purported to do? Or may the inquiry into meaning be informed by perhaps unbridled and unaccountable judicial notions of public policy, using legal realism to best promote the general welfare? Judge Posner considers the concepts (...) of formalism and realism to be meaningful and useful in common law reasoning but in interpretation to be useless and, worse, forbidden. He analogizes unclear "orders" from a legislature to garbled battlefield communications, and argues that the duty of the recipient of those orders (the judge) is to advance as best he can the enterprise set on foot by the superiors. Case studies elaborate this thesis. Judicial decisions interpreting fixed texts, Judge Posner concludes, can be neither logically correct or incorrect, philosophically sound or unsound, until the ultimate jurist, time, has adjudged their results. (shrink)

I defend extreme formalism about inorganic nature against arguments put forward by Glenn Parsons. I begin by laying out the general issue over aesthetic formalism, and I describe the position of extreme formalism about inorganic nature. I then reconsider -Ronald Hepburn's beach/seabed example. Next I discuss the notions of function in play in our thinking about inorganic nature. And lastly I consider Parsons's flooding river example. I conclude that extreme formalism about inorganic nature is safe from (...) Parsons's arguments. (shrink)

The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has (...) until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRW world, for example the number of collapses in a system during a chosen time interval. (shrink)

For about the last three decades, postmodernists have exposed the weaknesses of modernist formalism. Western modernist formalism effectively locates art’s meaning in its formal qualities. Clive Bell’s twentieth-century significant form aesthetic theory, Clement Greenberg and abstract art, and art educators’ preoccupation with design elements and principles typify this modernist tendency.1 In contrast, postmodernists generally insist that sociocultural context supplies art’s meaning. Within contemporary art education, postmodernist theory relies strongly on semiotics, neopragmatism, and social constructivist theories of culture; these (...) tend to reduce form to being an arbitrary vehicle for content supplied by cultural.. (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov} is reviewed. The results of \cite{Kryukov} are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving properties of various linear operators on Hilbert spaces are found. Any generalized solution of an arbitrary linear differential equation with constant coefficients is shown to be related to a regular solution by a (functional) coordinate transformation. The results also suggest a way of using generalized (...) functions to solve nonlinear problems on Hilbert spaces. (shrink)

Like moths attracted to a bright light, philosophers are drawn to glitz. So in discussing the notions of ‘gauge’, ‘gauge freedom’, and ‘gauge theories’, they have tended to focus on examples such as Yang–Mills theories and on the mathematical apparatus of fibre bundles. But while Yang–Mills theories are crucial to modern elementary particle physics, they are only a special case of a much broader class of gauge theories. And while the fibre bundle apparatus turned out, in retrospect, to be the (...) right formalism to illuminate the structure of Yang–Mills theories, the strength of this apparatus is also its weakness: the fibre bundle formalism is very flexible and general, and, as such, fibre bundles can be seen lurking under, over, and around every bush. What is needed is an explanation of what the relevant bundle structure is and how it arises, especially for theories that are not initially formulated in fibre bundle language. Here I will describe an approach that grows out of the conviction that, at least for theories that can be written in Lagrangian/Hamiltonian form, gauge freedom arises precisely when there are Lagrangian/Hamiltonian constraints of an appropriate character. This conviction is shared, if only tacitly, by that segment of the physics community that works on constrained Hamiltonian systems. (shrink)

This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. ;A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems---MN, NID, NCUM, N STCUM---are constructed in an increasing strength of the characterized nonmonotonic inference relation. In (...) these systems, two binary modal operators ⩾ and > are introduced in their syntax, and a ⊛ function lifted from the traditional * function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation "[phi], Gamma |∼ alpha", and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. ;A canonical form to read off generics is proposed: All generic sentences with subject-predicate structure can be re-written into their canonical form S . If S is a plural noun phrase, it can be further refined to be . Normal objects are selected based on the "meaning" of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. ;The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of L⩾,G -frames. Those benchmark examples of generic inferences are examined in the system G. (shrink)

In a series of recent papers, Professor Nick Zangwill has returned our attention to the merits of aesthetic formalism. In this paper, I seek to support formalism as an approach to understanding what counts as an aesthetic property by considering how this approach serves to illuminate identity conditions and critical assessment of a subset of allographic works of art I label “consumable”; these are works that exist as token art objects (as contrasted with art works) only within thetemporal (...) duration of their being reproduced and presented to their audiences. I look at three sorts of consumable art forms: food, theater plays, and dance. (shrink)

In this paper we try to convert the mathematician who calls himself, or herself, “a formalist” to a position we call “meth-odological pluralism”. We show how the actual practice of mathe-matics fits methodological pluralism better than formalism while preserving the attractive aspects of formalism of freedom and crea-tivity. Methodological pluralism is part of a larger, more general, pluralism, which is currently being developed as a position in the philosophy of mathematics in its own right.1 Having said that, henceforth, (...) in this paper, we abbreviate “methodological pluralism” with “pluralism”. (shrink)

The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has (...) until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 38.3 (2004) 19-35 [Access article in PDF] Moderate Formalism As a Theory of the Aesthetic Glenn Parsons Art history and art criticism explore, classify, and critique artworks from a number of perspectives. Their cultural, political, and moral significance are all of interest in this regard. This variety of perspectives notwithstanding, one way of considering artworks retains a central position for these disciplines. Despite (...) perennial shifting in conceptions of the purpose and nature of art, the aesthetic appreciation of art remains at the center of our practices for classifying and evaluating it. Without claiming that the aesthetic dimension of art is the only proper focus of its appreciation or that the aesthetic is a very clearly understood notion, we may say that some degree of contact with the aesthetic is what makes our consideration of an artwork an appreciation of it as art, rather than as historical artifact, manifestation of cultural ideology, and so on.In light of the central position of aesthetic appreciation in art history and criticism, an important concern regarding aesthetic education is what sort of knowledge, if any, is required for appropriate aesthetic appreciation of an artwork. Is knowledge of the historical context of an artwork required for appropriate aesthetic appreciation of it, or is its historical dimension a separate matter, perhaps worthy of appreciation in its own right but not relevant to the appreciation of the artistic achievement of the work? Virtually all modern theories of the aesthetic agree that in order to appreciate an artwork aesthetically, we need to perceive attentively certain of its perceptual properties, such as its shape and color. They differ, however, on whether such attentive perception is sufficient for appropriate aesthetic appreciation. On the one hand we have cognitivist views, which assert that, in addition to this sort of attentive perception, certain kinds of knowledge about the object of appreciation are required for appropriate aesthetic appreciation. On the other hand we have non-cognitivist views, which deny that such knowledge is necessary for appropriate aesthetic appreciation. According to the latter, the aesthetic qualities of an artwork, such as its gracefulness, [End Page 19] are formal in the sense that they depend only upon those perceptual properties, such as color, shape, and size, that constitute the "sensory surface" of the work.1 These properties, apparent to the attentive observer, are the only properties of the object to which one need attend in order to appreciate its gracefulness. Other properties of the painting, such as its depicting German peasants or having been rendered by a communist, are irrelevant to its aesthetic qualities, and knowledge about them is not required for its appropriate aesthetic appreciation. Today this non-cognitivist position is generally called formalism.2In the twentieth century, philosophical aesthetics largely rejected such views in favor of models of aesthetic appreciation with a richer cognitive element. This movement away from formalism has a number of dimensions, including the efforts of feminists to establish the aesthetic value of activist art, the desire to make sense of well-established practices of art appreciation, a growing awareness of the role that beliefs play in our aesthetic responses, the effort to do justice to the aesthetic character of the natural environment, and conceptual difficulties internal to formalism itself.3 Recently, however, some philosophers have revived the spirit, if not the letter, of formalism. Acknowledging widespread criticism of early formalists, such as Clive Bell, they concede that these theorists overstated the case when they claimed that all aesthetic qualities depend on nothing beyond the sensory surface of the object.4 The new formalists, in contrast, claim only that some aesthetic qualities are of this character. They call this doctrine moderate formalism, in contrast to the extreme formalism defended by earlier formalists.5By adopting this more modest position, moderate formalists can accommodate many of the criticisms that led to the decline of extreme formalism. However, if it turns out that only a handful of relatively unimportant aesthetic qualities are formal in nature, then moderate formalism would hardly make an impressively "formalist" theory of the... (shrink)

1. There is a sense in which, quite generally, with his logic Hegel can be considered the forerunner of many projects taken up by successive (non-classical) logics—and this despite the fact that He...

Coordinate form of tensor algebra on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear isometries. The unitary evolution and the non-unitary collapse processes are interpreted as isometric functional transformations. Several experiments are analyzed in the new context.

There are two ways interpreters have tended to understand the nature of the laws of Kant’s pure general logic. On the first, these laws are unconditional norms for how we ought to think, and will govern anything that counts as thinking. On the second, these laws are formal criteria for being a thought, and violating them makes a putative thought not a thought. These traditions are in tension, in so far as the first depends on the possibility of thoughts that (...) violate these laws, and the second makes violation impossible. In this essay I develop an interpretation of Kant’s pure general logic that overcomes this tension. It accounts for the possibility of logical mistakes, as the first tradition does, while still establishing the absolute impossibility of logical aliens, as the second tradition does. I then argue that the formalist insight that illogical exercises of the understanding are not alternative ways coherent thoughts could have been, but are mere confusions, is fundamental for achieving a proper understanding of the absolute normativity of the laws of pure general logic. (shrink)

This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a re-interpretation of "active" diffeomorphisms as "passive and metric-dependent" (...) dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (up to now unknown) connection to gauge transformations on-shell; understanding such connection also enlightens the real content of the Hole Argument or, better, dis-solves it together with its alleged "indeterminism"; 3) the utilization of the Bergmann-Komar "intrinsic pseudo-coordinates", defined as suitable functionals of the Weyl curvature scalars, as tools for a peculiar gauge-fixing to the super-hamiltonian and super-momentum constraints; 4) the consequent construction of a "physical atlas" of 4-coordinate systems for the 4-dimensional "mathematical" manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent "Dirac observables"). Such construction embodies the "physical individuation" of the points of space-time as "point-events", independently of the presence of matter, and associates a "non-commutative structure" to each gauge fixing or four-dimensional coordinate system; 5) a clarification of the multiple definition given by Peter Bergmann of the concept of "(Bergmann) observable" in general relativity. This clarification leads to the proposal of a "main conjecture" asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) "change" in the observable quantities of general relativity. 6) a clarification of the physical role of Dirac and gauge variables as their being related to "tidal-like" and "inertial-like" effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle, the Hamiltonian formalism allows to define notion of "force" in general relativity in a natural way; 7) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a "standard of space-time" more or less like atomic clocks define standards of time. We conclude that, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of "participating directly" in the individuation process, being involved in the determination of the Dirac observables. This circumstance leads naturally to a peculiar new kind of "structuralist" view of the general-relativistic concept of space-time, a view that embodies some elements of both the traditional "absolutist" and "relational" conceptions. In the end, space-time point-events maintain a "peculiar sort of objectivity". Some hints following from our approach for the quantum gravity programme are also given. (shrink)

A quantum physical projector is proposed for generally covariant theories which are derivable from a Lagrangian. The projector is the quantum analogue of the integral over the generators of finite one-parameter subgroups of the gauge symmetry transformations which are connected to the identity. Gauge variables are retained in this formalism, thus permitting the construction of spacetime area and volume operators in a tentative spacetime loop formulation of quantum general relativity.

We show that it is possible to generalize the Ursell–Mayer cluster formalism so that it may cover also the statistics of Internet websites. Our starting point is the introduction of an extra variable that is assumed to take account, as will be explained, of the nature of the Internet statistics. We then show, following the arguments in Mayer, that one may obtain a phase transition-like phenomena.

Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown (...) that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Fear of Formalism: Kant, Twain, and Cultural Studies in American LiteratureElizabeth Maddock Dillon (bio)I begin with what we might call a bipolar disturbance in literary criticism. Caught between the materialism of cultural studies and the formalism of philosophy, literary criticism is construed, on the one hand, as useless—struck dumb by its lack of purpose in the face of real politics and real bodies—and, on the other hand, (...) as singularly efficacious, the only tool through which to reveal the essentially discursive character of all forms of culture, including bodies and politics. While this rhetorical model of criticism is regularly posited as politically bankrupt, as having no purchase on the facticity of the world, the model of materialist cultural criticism is just as regularly unmasked as, at base, rhetorically constructed and thus guilty of concealing its own formalist dimensions. 1 This “disturbance,” as I’ve described it, tends to be acted out as a debilitating dialectic: caught between formalism and materialism, literary criticism is left without any ground to stand on. Yet this peculiar bipolarity within literary criticism is intimately linked to the strange status of literature itself. Language becomes recognizably literary at the moment it assumes a rhetorical or formal dimension rather than serving as the invisible conduit of mimetic representation. 2 Whence, evidently, the allure of formalism for literary criticism: form would seem to be exactly what demarcates the literary from the nonliterary, what defines the exclusive territory of literature. Yet formalism, as has been widely and persuasively argued, tends to turn literature into precisely the kind of artifact that means little in relation to the world and tends to obscure the worldly relations that inform the text and its production. Indeed, in the field of Cultural Studies—a field whose defining gesture is political engagement—“formalist” is a term whose meaning often comes to approximate “apolitical.” “Formalist,” fashioned as opprobium, speaks chidingly of hermeticism or more acerbically of the insidious erasures enacted by universalism.In contemporary criticism, formalism has thus come to occupy an important antipodal position which encompasses far more than the New Critical practices of the 1940s and ‘50s. In emphasizing the formal, intrinsic qualities of the literary work, New [End Page 46] Critics closeted the text away from the world and from the possibility of social action: their agenda has thus been construed as politically quietist and inherently conservative. 3 Yet the term “formalism,” used as a charge of conservatism, has been applied more broadly to poststructuralist criticism as well. Paul Lauter, for instance, uses the term “formalist” to describe deconstruction as an avatar of New Criticism: both emphasize textual relations to the exclusion of extratextual considerations. Poststructuralism, Lauter and others have argued, continues an aestheticization of literature which turns literary criticism over to an elitist and ultimately irrelevant “priesthood.” ‘“Formalist,’” writes Lauter, “suggests that the whole enterprise of literary theorizing subsists behind dense academic walls, where de Man speaks only to Heidegger, and Heidegger speaks only to God” [138]. While Lauter bases his analogy between poststructuralism and New Criticism on the charge of hermeticism as well as a lack of historical engagement, the notion of “form” as it appears in poststructuralism is nonetheless significantly different than the “form” that animated New Critical endeavors. Where New Critical “form” concerns specifically literary structures—irony, metaphor, tension, unity—the poststructural referent for these rhetorical terms is often the “form” of language or subjectivity itself. Accordingly, the meaning of “form” (and, indeed, “formalism”) undergoes a marked shift from specific rhetorical articulations to larger theoretical claims about language and identity.This second, broader articulation of form has been critiqued less for hermeticism or quietism than for its implied universalism—that is, for fashioning subjects and discursive forces in uniform shapes without regard for political and historical specificity. Stuart Hall, for example, whilst defining the practice of Cultural Studies, warns against theories of the subject (in this case psychoanalysis) that tend toward universalism: “The manner in which this ‘subject’ of culture is conceptualized is of a trans-historical and ‘universal’ character: it addresses the subject-in-general, not an historically-determinate social subject, or socially determinate particular language” [Hall 70]. On this reading, formalist theories of poststructuralism... (shrink)

We highlight methodological and theoretical limitations of the authors' Dirac formalism and suggest the von Neumann open systems approach as a resolution. The open systems framework is a generalization of classical probability and we hope it will allow cognitive scientists to extend quantum probability from perception, categorization, memory, decision making, and similarity judgments to phenomena in learning and development.