There is no unique way to generalize the mass operator 0 2 −p · p to curved spacetimes. The possible generalizations using either an analytic or an algebraic (group-theoretic) approach are discussed. We investigate in detail three possibilities: (i) the generalized D'Alembertian $$- \tilde \square = - (1/\sqrt { - g} )(\partial /\partial x^v )(\sqrt { - g} g^{\mu v} {\text{ }}\partial /\partial x^\mu$$ (ii) the operator ( $- (\tilde \square + \tfrac{1}{6}{\text{R)}}$ , which is conformally invariant in the massless (...) case, and (iii) an operator suggested by Meggs for Robertson-Walker spacetimes. A criterion for choosing among the different possibilities is proposed. It is used to eliminate the Meggs operator, but is not stringent enough to decide between the other two. (shrink)

While thinking philosophically we see problems in places where there are none. It is for philosophy to show that there are no problems.Those of us who are not colour blind have a happy command of colour concepts. We say of trees that they are green in spring, that they are the same colour as grass and a different colour from the sky. If we shine a torch with a red bulb upon a white surface, we say that the surface looks (...) pink although it is white. And if we suffer a bout of jaundice we claim that white things look yellowish to us, although they are not yellow, nor do they look yellow. We employ this tripartite distinction unworriedly and unthinkingly. But when, in doing philosophy, we are called upon to elucidate colour concepts it becomes evident that these elementary concepts present intricate problems to the philosophical understanding. It is extraordinarily difficult to obtain a proper surview of colour grammar, and the temptations of philosophical illusion are legion. We go wrong before the first step is even taken, and hence do not notice our errors, for they are implicit in every move we make. We multiply impossibilities seriatim, getting better, like the White Queen, with practice. We then either slide into scepticism, or alternatively exclude it on empirical grounds - appealing, as is so popular in American philosophical circles, to the wonders of science, in particular physics and neurophysiology, to keep the malin genie from the door. (shrink)

While thinking philosophically we see problems in places where there are none. It is for philosophy to show that there are no problems.Those of us who are not colour blind have a happy command of colour concepts. We say of trees that they are green in spring, that they are the same colour as grass and a different colour from the sky. If we shine a torch with a red bulb upon a white surface, we say that the surface looks (...) pink although it is white. And if we suffer a bout of jaundice we claim that white things look yellowish to us, although they are not yellow, nor do they look yellow. We employ this tripartite distinction unworriedly and unthinkingly. But when, in doing philosophy, we are called upon to elucidate colour concepts it becomes evident that these elementary concepts present intricate problems to the philosophical understanding. It is extraordinarily difficult to obtain a proper surview of colour grammar, and the temptations of philosophical illusion are legion. We go wrong before the first step is even taken, and hence do not notice our errors, for they are implicit in every move we make. We multiply impossibilities seriatim, getting better, like the White Queen, with practice. We then either slide into scepticism, or alternatively exclude it on empirical grounds - appealing, as is so popular in American philosophical circles, to the wonders of science, in particular physics and neurophysiology, to keep the malin genie from the door. (shrink)

Part I Introduction -/- Passion at a Distance (Don Howard) -/- Part II Philosophy, Methodology and History -/- Balancing Necessity and Fallibilism: Charles Sanders Peirce on the Status of Mathematics and its Intersection with the Inquiry into Nature (Ronald Anderson) -/- Newton’s Methodology (William Harper) -/- Whitehead’s Philosophy and Quantum Mechanics (QM): A Tribute to Abner Shimony (Shimon Malin) -/- Bohr and the Photon (John Stachel) -/- Part III Bell’s Theorem and Nonlocality A. Theory -/- Extending the Concept of an (...) “Element of Reality” to Work with Inefficient Detectors (Daniel M. Greenberger) -/- A General Proof of Nonlocality without Inequalities for Bipartite States (GianCarlo Ghirardi and Luca Marinatto) -/- On the Separability of Physical Systems (Jon P. Jarrett) -/- Bell Inequalities: Many Questions, a Few Answers (Nicolas Gisin) -/- B. Experiment -/- Do Experimental Violations of Bell Inequalities Require a Nonlocal Interpretation of Quantum Mechanics? II: Analysis a la Bell (Edward S. Fry, Xinmei Qu, and Marlan O. Scully) -/- The Physics of 2 = 1 + 1 (Yanhua Shih) -/- Part IV Probability, Uncertainty, and Stochastic Modifications of Quantum Mechanics -/- Interpretations of Probability in Quantum Mechanics: A Case of “Experimental Metaphysics” (Geoffrey Hellman) -/- “No Information Without Disturbance”: Quantum Limitations of Measurement (Paul Busch) -/- How Stands Collapse II (Philip Pearle) -/- Is There a Relation Between the Breakdown of the Superposition Principle and an Indeterminacy in the Structure of the Einsteinian Space-Time? (Andor Frenkel) -/- Indistinguishability or Stochastic Dependence? (D. Costantini and U. Garibaldi) -/- Part V Relativity -/- Plane Geometry in Spacetime (N. David Mermin) -/- The Transient nows (Steven F. Savitt) -/- Quantum in Gravity? (Michael Horne) -/- A Proposed Test of the Local Causality of Spacetime (Adrian Kent) -/- Quantum Gravity Computers: On the Theory of Computation with Indefinite Causal Structure (Lucien Hardy) -/- “Definability,” “Conventionality,” and Simultaneity in Einstein–Minkowski Space-Time (Howard Stein) -/- Part VI Concluding Words -/- Bistro Banter: A Dialogue with Abner Shimony and Lee Smolin -/- Unfinished Work: A Bequest (Abner Shimony) -/- Bibliography of Abner Shimony. (shrink)

Philosophy & Public Affairs, Volume 50, Issue 1, Page 6-49, Winter 2022.

Do the ethical features of an artwork bear on its aesthetic value? This movie endorses misogyny, that song is a civil rights anthem, the clay constituting this statue was extracted with underpaid labor—are facts like these the proper bases for aesthetic evaluation? I argue that this debate has suffered from a false presupposition: that if the answer is yes (for at least some such ethical features), such considerations feature as pro tanto contributions to an artwork's overall aesthetic value, i.e., as (...) merits or flaws which make something have more or less overall aesthetic value. As the case of ethically laden, aesthetic evaluation makes clear, however, good aesthetic judgement is irreducibly multi-dimensional, e.g., "the movie has an engaging soundtrack, tasteful camera work, and takes a misogynistically prurient perspective on its female lead.'' Such a "non-summative" judgement refuses to reduce those various dimensions of aesthetic value to a single aggregate aesthetic evaluation, like "it's a 6/10" or "it's a pretty good movie!" I defend both the modest claim that such non-summative evaluations are not mistaken and the extremist claim that summative (i.e., unidimensional) aesthetic evaluation is defective by considering other domains of normative assessment in which summing seems inappropriate, notably including evaluations of people's character. (shrink)

A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras, where * is a continuous t-norm. In this paper we investigate the structure of the (...) variety of basic hoops and some of its subvarieties. In particular we provide a complete description of the finite subdirectly irreducible basic hoops, and we show that the variety of basic hoops is generated as a quasivariety by its finite algebras. We extend these results to Hájek's BL-algebras, and we give an alternative proof of the fact that the variety of BL-algebras is generated by all algebras arising from continuous t-norms on [ 0,1] and their residua. The last part of the paper is devoted to the investigation of the subreducts of BL- algebras, of Gödel algebras and of product algebras. (shrink)

A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that ([ 0,1], *, 1) is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and ([ 0,1], *, →, 1) becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras ([ 0,1], *, →, 1), where (...) * is a continuous t-norm. In this paper we investigate the structure of the variety of basic hoops and some of its subvarieties. In particular we provide a complete description of the finite subdirectly irreducible basic hoops, and we show that the variety of basic hoops is generated as a quasivariety by its finite algebras. We extend these results to Hájek's BL-algebras, and we give an alternative proof of the fact that the variety of BL-algebras is generated by all algebras arising from continuous t-norms on [ 0,1] and their residua. The last part of the paper is devoted to the investigation of the subreducts of BL- algebras, of Gödel algebras and of product algebras. (shrink)

We show how in the hierarchies${F_\alpha }$of Fieldian truth sets, and Herzberger’s${H_\alpha }$revision sequence starting from any hypothesis for${F_0}$ that essentially each${H_\alpha }$ carries within it a history of the whole prior revision process.As applications we provide a precise representation for, and a calculation of the length of, possiblepath independent determinateness hierarchiesof Field’s construction with a binary conditional operator. We demonstrate the existence of generalized liar sentences, that can be considered as diagonalizing past the determinateness hierarchies definable in Field’s recent (...) models. The ‘defectiveness’ of such diagonal sentences necessarily cannot be classified by any of the determinateness predicates of the model. They are ‘ineffable liars’. We may consider them a response to the claim of Field that ‘the conditional can be used to show that the theory is not subject to “revenge problems”.’. (shrink)

We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.

We develop and apply a multi-dimensional conception of explanatory depth towards a comparative analysis of inflationary and bouncing paradigms in primordial cosmology. Our analysis builds on earlier work due to Azhar and Loeb (2021) that establishes initial condition fine-tuning as a dimension of explanatory depth relevant to debates in contemporary cosmology. We propose dynamical fine-tuning and autonomy as two further dimensions of depth in the context of problems with instability and trans-Planckian modes that afflict bouncing and inflationary approaches respectively. In (...) the context of the latter issue, we argue that the recently formulated trans-Planckian censorship conjecture leads to a trade-off for inflationary models between dynamical fine-tuning and autonomy. We conclude with the suggestion that explanatory preference with regard to the different dimensions of depth is best understood in terms of differing attitudes towards heuristics for future model building. (shrink)

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

Distributive, procedural, and interactional justice are constructs that are increasingly being recognized as important factors that affect individual perceptions in the workplace environment. This paper presents a theoretical perspective that suggests that justice is perceived through a subjective lens that consists of individualized beliefs and proposes that cultural attributes and demographic characteristics play an integral part in determining the perception of justice. The distinctions between these three constructs are presented in context with the core beliefs of individual employees – affected (...) by a multitude of perceptual and demographic factors that we briefly identify herein. Based on the theoretical perspective, an instrument that measures the constructs of justice as perceived by individuals was developed. With a focus on justice within the business setting, hypotheses about attitudes related to justice were tested. Survey results confirm that the three constructs of justice are distinct but correlated. Significant differences were found in the perceptions of African-American respondents with regard to procedural justice. Although the empirical findings do not support all the hypotheses, this research highlights the need for further development of measures to assess the perception of justice in business settings and at an applied level, underscores the importance of recognizing cultural attributes and demographic characteristics in understanding how justice is perceived. (shrink)

When I offered this title, I was engaging myself to investigate an apparent difference between two kinds of intentionality, in the hope that I should be able to find some firm logical criterion to distinguish them. I was less successful in this than I had hoped. I think I have gained a certain amount of insight into the logic and semantics of one kind of intentional context, largely due to the work I was doing while visiting the University of Pennsylvania (...) on Frege and on Michael Dummett’s monumental commentary on Frege. But as regards the other variety of intentionality I am still very much in the dark; so I am giving you thus far merely a progress report on that. (shrink)

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision operator ψ is similarly \Pi13 and which (...) is complete in Gödel’s universe of constructible sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points. (shrink)

We analyse the extent of possible computations following Hogarth ([2004]) conducted in Malament–Hogarth (MH) spacetimes, and Etesi and Németi ([2002]) in the special subclass containing rotating Kerr black holes. Hogarth ([1994]) had shown that any arithmetic statement could be resolved in a suitable MH spacetime. Etesi and Németi ([2002]) had shown that some relations on natural numbers that are neither universal nor co-universal, can be decided in Kerr spacetimes, and had asked specifically as to the extent of computational limits there. (...) The purpose of this note is to address this question, and further show that MH spacetimes can compute far beyond the arithmetic: effectively Borel statements (so hyperarithmetic in second-order number theory, or the structure of analysis) can likewise be resolved: Theorem A. If H is any hyperarithmetic predicate on integers, then there is an MH spacetime in which any query ? n H ? can be computed. In one sense this is best possible, as there is an upper bound to computational ability in any spacetime, which is thus a universal constant of that spacetime. Theorem C. Assuming the (modest and standard) requirement that spacetime manifolds be paracompact and Hausdorff, for any spacetime there will be a countable ordinal upper bound, , on the complexity of questions in the Borel hierarchy computable in it. Introduction 1.1 History and preliminaries Hyperarithmetic Computations in MH Spacetimes 2.1 Generalising SADn regions 2.2 The complexity of questions decidable in Kerr spacetimes An Upper Bound on Computational Complexity for Each Spacetime CiteULike Connotea Del.icio.us What's this? (shrink)

We show that Leitgeb’s dependence operator of Leitgeb is a \-operator and that this is best possible.

P S Wilson; Child-Centred Education, Journal of Philosophy of Education, Volume 3, Issue 1, 30 May 2006, Pages 105–126, https://doi.org/10.1111/j.1467-9752.1969.

The author clarifies the existential philosophy that is implicit in Kurt Goldstein's philosophy of organism (Goldstein, 1963; 1995). Situated in response to the growing trend that psychological phenomena are reducible to the nervous system, the author argues for the reverse: that the significance of nervous system activity can only be understood by viewing it as background to foreground performances. Like the organization of perception into meaningful figure-- ground Gestalts, the existential modes of embodiment, sociality, temporality, spatiality, and attunement are organized (...) together to accomplish foreground performances. It is only within this context that the activity of the nervous system may be understood as significant or insignificant. Speech is given as an example. The article concludes with a commentary on how the trend of reducing psychological phenomena to neurological phenomena has impaired our understanding of brain disorders and psychological disorders. (shrink)

In this paper I offer the term “potato ethics” to describe a particular professional rural health sensibility. I contrast this attitude with the sensibility behind urban professional ethics, which often focus on the narrow doctor–patient treatment relationship. The phrase appropriates a Swedish metaphor, the image of the potato as a humble side dish: plain, useful, versatile, and compatible with any main course. Potato ethics involves making oneself useful, being pragmatic, choosing to be like an invisible elf who prevents discontinuity rather (...) than a more visible observer of formal rules and assigned tasks. It also includes actively taking part in everyday disaster-prevention and fully recognizing the rural context as a vulnerable space. This intersectional argument, which emphasizes the ongoing, holistic responsibility of those involved in rural communities, draws on work from the domains of care ethics, relational ethics, pragmatic psychology, feminist ethics of embodiment, social location theory, and reflections on geographical narcissism. (shrink)

In this essay, P. Taylor Webb and Kalervo N. Gulson argue that educational policy is a spatial process and that implementation processes in particular produce crucial emergent geographies for policy research. Webb and Gulson describe how emergent geographies are produced when policy folds actors through senses and enactments of policy. The idea that policy is sensed and enacted is developed into the concept of a policy intension that extends approaches to spatial and, in particular, micropolitical analyses in policy research. Webb (...) and Gulson conclude by discussing cartographical methods that better map the geographies of subjectivity produced through policy intensions. (shrink)

We consider notions of truth and logical validity defined in various recent constructions of Hartry Field. We try to explicate his notion of determinate truth by clarifying the path-dependent hierarchies of his determinateness operator.