We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder (...) is then shown to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. (shrink)

Hermann von Helmholtz’s geometrical papers have been typically deemed to provide an implicitly group-theoretical analysis of space, as articulated later by Felix Klein, Sophus Lie, and Henri Poincaré. However, there is less agreement as to what properties exactly in such a view would pertain to space, as opposed to abstract mathematical structures, on the one hand, and empirical contents, on the other. According to Moritz Schlick, the puzzle can be resolved only by clearly distinguishing the empirical qualities of spatial perception (...) from those describable in terms of axiomatic geometry. This paper offers a partial defense of the group-theoretical reading of Helmholtz along the lines of Ernst Cassirer in the fourth volume of The Problem of Knowledge of 1940. In order to avoid the problem raised by Schlick, Cassirer relied on a Kantian view of space not so much as an object of geometry, but as a precondition for the possibility of measurement. Although the concept of group does not provide a description of space, the modern way to articulate the concept of space in terms of transformation groups reveals something about the structure and the transformation of spatial concepts in mathematical and natural sciences. (shrink)

The work is an attempt to transfer a structure from Euclidean plane (pure geometrical) under the physical observation limit (resolving power) to a physical space (observable space). The transformation from the mathematical space to physical space passes through the observation condition. The mathematical modelling is adopted. The project is based on two stapes: (1) Looking for a simple mathematical model satisfies the definition of Euclidian plane; (2)That model is examined against three observation resolution conditions (resolved, unresolved and partially resolved). (...) The simplest mechanical model satisfies the definition of Euclidian plane is a planetary gear. The interesting examination of the mechanical model is that is under partial resolution. That examination shows analogous equation for Euler’s formula. The derived complex formula contains the resolved (observable) quantities of the mechanical system and satisfies the linear wave equation. The interpretation of this complex formula is: it is a function related to the position vector of a point in the small wheel of the partially resolved planetary gear system. The function is in terms of the observable quantities only. The work shows the possibility of transformation from real to complex space. The work is purely classical but the result of the partial resolution shows a function similar to the Quantum mechanics wave function. (shrink)

Technology offers unique sets of opportunities, from human flourishing to civilization survival, but also challenges, from partial misuse to global apocalypse. Yet technology is shaped by the social environment in which it is developed and used, prompting questions about its desirable governance format. In this context, we look at governance challenges of large technical systems, specifically the peaceful use of high-power lasers in space, in order to propose a conceptual framework for legitimate global governance. Specifically, we adopt a context-based approach (...) to legitimacy to address the trade-offs between effectiveness (output legitimacy) and inclusivity (input legitimacy) in the governance of large technical systems. We show that distinguishing two basic phases of space laser policy which call for different legitimacy criteria helps balance out the trade-offs without sacrificing either effectiveness or inclusivity. Finally, we construe LTSs’ governance as a tool for creating globally networked spaces which may enable coordinated global democratic governance. (shrink)

In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied.

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite (...) to more definite states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

A historical review and philosophical look at the introduction of “negative probability” as well as “complex probability” is suggested. The generalization of “probability” is forced by mathematical models in physical or technical disciplines. Initially, they are involved only as an auxiliary tool to complement mathematical models to the completeness to corresponding operations. Rewards, they acquire ontological status, especially in quantum mechanics and its formulation as a natural information theory as “quantum information” after the experimental confirmation the phenomena of “entanglement”. Philosophical (...) interpretations appear. A generalization of them is suggested: ontologically, they correspond to a relevant generalization to the relation of a part and its whole where the whole is a subset of the part rather than vice versa. The structure of “vector space” is involved necessarily in order to differ the part “by itself” from it in relation to the whole as a projection within it. That difference is reflected in the new dimension of vector space both mathematically and conceptually. Then, “negative or complex probability” are interpreted as a quantity corresponding the generalized case where the part can be “bigger” than the whole, and it is represented only partly in general within the whole. (shrink)

This paper uses a partially ordered set of syntactic categories to accommodate optionality and licensing in natural language syntax. A complex but well-studied data set pertaining to the syntax of quantifier scope and negative polarity licensing in Hungarian is used to illustrate the proposal. The presentation is geared towards both linguists and logicians. The paper highlights that the main ideas can be implemented in different grammar formalisms, and discusses in detail an implementation where the partial ordering on categories (...) is given by the derivability relation of a calculus with residuated and Galois-connected unary operators. (shrink)

In this paper, I first examine the classification of mental derangements contained in Kant’s "Anthropology from a Pragmatic Point of View", in order to highlight the role played by imagination in their pathogenesis. Later, on the basis of this examination, I reflect on the origins of critical philosophy, which can be seen as an attempt to construct a control device for the imagination structured as a systematic, organic space.

Many approaches to quantum gravity -the theory that should account for quantum and gravitational phenomena under the same theoretical umbrella- seem to point at some form of spacetime emergence, i.e., the fact that spacetime is not a fundamental entity of our physical world. This tenet has sparked many philosophical discussions: from the so-called empirical incoherence problem to different accounts of emergence and mechanisms thereof. In this contribution, I focus on the partial order relation of causal set theory and argue that (...) causation can be characterized as an a-temporal constraint over the kinematic space defined by the theory. The relation constrains the growth of a new element/event with respect to the other elements/events of a given set. Therefrom, the flow of time emerges from the collection of the possible growths of the given set, where each possibility is characterized by a classical probability assigned by the dynamics of the theory. (shrink)

Igal Kvart A Coding Conception in Action-Directed-Pragmatics -/- I present formal Pragmatics for a domain in Pragmatics that I call Action-Directed Pragmatics, which focuses on the Pragmatic riddle of how implicit contents are conveyed and understood, by adopting a coding model, in which the speaker and addressee simulate each other iteratively in a deliberative context (an ‘action-pregnant’ one). The implicit content, conveyed by a speaker and decoded by her addressee, in such cases, consists in the specified steered-to action, plus modulations (...) on the action-polarity (pro or con) and the degree of the so-called Steering Thrust that accompanies such assertions and is conveyed by verbal locutions, intonation, and/or bodily and facial gestures. There are two main tasks to model (in a given setup and conversational context): First, how is the speaker, with a steered-to action in mind (and Steering Thrust), to select an assertion so as to (say) optimize the successful transmission and decoding of its implicit pragmatic content by her and her addressee? Second, how does the addressee, given an assertion by the speaker, decipher the implicit pragmatic content conveyed via it? Both will invoke pertinent information they have about each other and the setup/context in order to best encode and best decode the implicit pragmatic content. (This coding mechanism proposed here is not offered for the ubiquitous ‘frozen’, ‘trivial’ or ‘routinized’ pragmatic messages.) A prelude to this formal Pragmatics is a general formal Pragmatic account of Assertibility in contexts that are multi-normative (which is the common case). I focus here only on Epistemic/Semantic and Instrumental Norms. A linear representation of degrees of Overall Assertibility (i.e., taking into account various operative norms) will be an n-dimensional qualitative vector space with a function that computes them given different degrees of sub-normative Assertibility on each axis. (shrink)

I defend the extremist position that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The laws of physics are determined solely by the energy eigenspectrum of the Hamiltonian. The structure of our observed world, including space and fields living within it, should arise as a higher-level emergent description. I sketch how this might come about, although much work remains to be done.

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences. Theories carry with them their own ontology while the metaphysics may remain the same in the background. We follow a broadly Kantian tradition, distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Theories do not tell us how the noumenal world (...) is constituted but are conceptual constructs applying to models generated in the phenomenal world within limited contexts. -/- The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases characterising the oscillatory behaviour of quantum mechanical states. -/- The amplitude-dependent correlations (quantum entanglement) exist over and above the classical ones expressed in terms of probabilities. While the classical correlations are essentially local in nature, quantum correlations are shared globally in the process of environment-induced decoherence. The decoherence is an effectively random process that removes local correlations in the course of global sharing of entanglement—the removal being especially manifest in the case of systems that appear as classical ones. It is this aspect of the decoherence process that makes the so-called measurement postulate (one relating to wave function collapse) cohere with the rest of the principles of quantum theory where the latter implies a Schrodinger type time evolution of quantum mechanical systems. -/- The mathematical basis of the quantum correlations consists of the description of pure states of a system in terms of vectors in a linear vector space (a mixed state appears as an admixture of pure states with some probability distribution associated with it) and, in addition, the description of (pure) states of composite systems as vectors in the product space arising from the component sub-systems. -/- The crucial aspect of the decoherence process, of significance in the context of the apparent incompatibility of the measurement postulate with the unitary Schrodinger evolution, relates to the fact that it is almost instantaneous in the case of a classical object (one that is nevertheless amenable to a quantum description). Indeed, the decoherence time is, in all likelihood, of the order of the Planck scale, being driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining the finest details of the decoherence process since Planck scale physics remains an obscure terrain. -/- In other words, quantum theory is, to all intents and purposes, in the need of a radical revision, in keeping with the fact that all theories are defeasible and need revision as our domains of experience expand and get realigned in a complex manner. The context within which quantum theory (and quantum field theory too) is defined is set precisely by the Planck scale, across which a novel theoretical framework is likely to emerge. However, as in the case of theory revisions in general, that emerging theory will stand in an asymmetric relation of incommensurability with the present-day quantum theory, where the concepts of the latter will be comprehensible in terms of those of the former, but the converse will not hold. (shrink)

Abstract. The aim of this paper is to show that the topological interpretation of knowledge as an interior kernel operator K of a topological space (X, OX) comes along with a partially ordered family of belief modalities B that fit K in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB logic of knowledge and belief with the exception of the contentious axiom of negative introspection (NI). The new belief modalities B introduced in this (...) paper are defined with the help of the (dense) nuclei of the Heyting algebra OX of open subsets on the topological space (X, OX). In this way, the natural context for the belief operators B related to topological knowledge operator K is shown to be the Heyting algebra NUC(OX) of the nuclei of the Heyting algebra OX.1 More precisely, the dense nuclei of NUC(OX) can be used to define a variety of bimodal logics of knowledge operators K and belief operators B. The operators K and B are compatible with each other in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB system with the exception of the axiom (NI). Therefore, for (X, OX), one obtains a bounded, partially ordered family of belief operators B defined by the elements of NUC(OX). (shrink)

Accounts of Hobbes’s ‘system’ of sciences oscillate between two extremes. On one extreme, the system is portrayed as wholly axiomtic-deductive, with statecraft being deduced in an unbroken chain from the principles of logic and first philosophy. On the other, it is portrayed as rife with conceptual cracks and fissures, with Hobbes’s statements about its deductive structure amounting to mere window-dressing. This paper argues that a middle way is found by conceiving of Hobbes’s _Elements of Philosophy_ on the model of a (...) mixed-mathematical science, not the model provided by Euclid’s _Elements of Geometry_. I suggest that Hobbes is a test case for understanding early-modern system-construction more generally, as inspired by the structure of the applied mathematical sciences. This approach has the additional virtue of bolstering, in a novel way, the thesis that the transformation of philosophy in the long seventeenth century was heavily indebted to mathematics, a thesis that has increasingly come under attack in recent years. (shrink)

In this papers ,we use the control method of the maximal fractional integral and obtain the boundedness of higher order commutator generated by maximal Bochner-Riesz operator on Morrey space. Moreover , we get it's continuty from Morrey space to Lipschtz space and from Morrey space to BMO space.

Why do relationships of friendship and love support partiality, but not relationships of hatred or commitments of racism? Where does partiality end and why? I take the intuitive starting point that important cases of partiality are meaningful. I develop a view whereby meaning is understood in terms of transcending self-limitations in order to connect with things of external value. I then show how this view can be used to distinguish central cases of legitimate partiality from cases of illegitimate partiality and (...) how it puts pressure on the traditional way of thinking about partiality. (shrink)

‘Space does not exist fundamentally: it emerges from a more fundamental non-spatial structure.’ This intriguing claim appears in various research programs in contemporary physics. Philosophers of physics tend to believe that this claim entails either that spacetime does not exist, or that it is derivatively real. In this article, I introduce and defend a third metaphysical interpretation of the claim: reductionism about space. I argue that, as a result, there is no need to subscribe to fundamentality, layers of reality and (...) emergence in order to analyse the constitution of space by non-spatial entities. It follows that space constitution, if borne out, does not provide empirical evidence in favour of a stratified, Aristotelian in spirit, metaphysics. The view will be described in relation to two particular research programs in contemporary physics: wave function realism and loop quantum gravity. (shrink)

This paper provides a defence of the account of partial resemblances between properties according to which such resemblances are due to partial identities of constituent properties. It is argued, first of all, that the account is not only required by realists about universals à la Armstrong, but also useful (of course, in an appropriately re-formulated form) for those who prefer a nominalistic ontology for material objects. For this reason, the paper only briefly considers the problem of how to conceive of (...) the structural universals first posited by Armstrong in order to explain partial resemblances, and focuses instead on criticisms that have been levelled against the theory (by Pautz, Eddon, Denkel and Gibb) and that apply regardless of one’s preferred ontological framework. The partial identity account is defended from these objections and, in doing so, a hitherto quite neglected connection—between the debate about partial similarity as partial identity and that concerning ontological finitism versus infinitism—is looked at in some detail. (shrink)

A classic analytic approach to biological phenomena seeks to refine definitions until classes are sufficiently homogenous to support prediction and explanation, but this approach founders on cases where a single process produces objects with similar forms but heterogeneous behaviors. I introduce object spaces as a tool to tackle this challenging diversity of biological objects in terms of causal processes with well-defined formal properties. Object spaces have three primary components: (1) a combinatorial biological process such as protein synthesis that (...) generates objects with parts that are modular, independent, and organized according to an invariant syntax; (2) a notion of “distance” that relates the objects according to rules of change over time as found in nature or useful for algorithms; (3) mapping functions defined on the space that map its objects to other spaces or apply an evaluative criterion to measure an important quality, such as parsimony or biochemical function. Once defined, an object space can be used to represent and simulate the dynamics of phenomena on multiple scales; it can also be used as a tool for predicting higher-order properties of the objects, including stitching together series of causal processes. Object spaces are the basis for a strategy of theorizing, discovery, and analysis in biology: as heuristic idealizations of biology, they help us transform inchoate, intractable problems into articulated, well-structured ones. Developing an object space is a research strategy with a long, successful history under many other names, and it offers a unifying but not overreaching approach to biological theory. (shrink)

Partiality is the special concern that we display for ourselves and other people with whom we stand in some special personal relationship. It is a central theme in moral philosophy, both ancient and modern. Questions about the justification of partiality arise in the context of enquiry into several moral topics, including the good life and the role in it of our personal commitments; the demands of impartial morality, equality, and other moral ideals; and commonsense ideas about supererogation. This paper provides (...) an overview of the debate on the ethics of partiality through the lens of the domains of permissible and required partiality. After outlining the conceptual space, I first discuss agent-centred moral options that concern permissions not to do what would be impartially optimal. I then focus on required partiality, which concerns associative duties that go beyond our general duties to others and require us to give special priority to people who are close to us. I discuss some notable features of associative duties and the two main objections that have been raised against them: the Voluntarist and the Distributive objections. I then turn to the justification of partiality, focusing on underivative approaches and reasons-based frameworks. I discuss the reductionism and non-reductionism debate: the question whether partiality is derivative or fundamental. I survey arguments for ‘the big three’, according to which partiality is justified by appeal to the special value of either projects, personal relationships, or individuals. I conclude by discussing four newly emerging areas in the debate: normative transitions of various personal relationships, relationships with AI, epistemic partiality, and negative partiality, which concerns the negative analogue of our positive personal relationships. (shrink)

The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only (...) mathematical equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...) neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

Virtue theories can plausibly be argued to have important advantages over normative ethical theories which prescribe a strict impartialism in moral judgment, or which neglect people’s special roles and relationships. However, there are clear examples of both virtuous and vicious partiality in people’s moral judgments, and virtue theorists may struggle to adequately distinguish them, much as proponents of other normative ethical theories do. This paper first adapts the “expanding moral circle” concept and some literary examples to illustrate the difficulty of (...) adequately distinguishing virtuous from vicious partiality. Later sections aim to show how an adequate philosophical ethics will be able to both a) attribute virtue (and hence praiseworthiness) to agents whose actions may directly serve only their special interests, roles, or special relationships; and b) attribute vice (and hence censure) where an agent’s attitudes and/or actions mirror known personal biases (for instance, an egoistic attitude) or social biases (for instance, and ethnocentric attitude). This dual ability leaves space for much virtuous partiality, while also reflecting a “risk-aware” approach, recognizing the deleterious consequences of our human penchant for constructing and imbuing moral significance to oftentimes factitious us/them dichotomies. (shrink)

Recent scholarship has drawn attention to John Rawls’s concern with stability—a concern that, as Rawls himself notes, motivated Part III of A Theory of Justice and some of the more important changes of his political turn. For Rawls, the possibility of achieving ‘stability for the right reasons’ depends on citizens possessing sufficient moral motivation. I argue, however, that the moral psychology Rawls develops to show how such motivation would be cultivated and sustained does not cohere with his specific descriptions of (...) ‘pluralist ’ doctrines. Considering Rawls’s claims that ‘most’ citizens—both in contemporary liberal democracies and in the well-ordered society—possess such doctrines, this incompatibility threatens to undermine his stability arguments. Despite the enormous importance of pluralist doctrines and the potential difficulties they pose for Rawls’s project, remarkably little attention has been paid to them. By critically examining these difficulties, the article begins to address this oversight. (shrink)

We present a theory of human artistic experience and the neural mechanisms that mediate it. Any theory of art has to ideally have three components. The logic of art: whether there are universal rules or principles; The evolutionary rationale: why did these rules evolve and why do they have the form that they do; What is the brain circuitry involved? Our paper begins with a quest for artistic universals and proposes a list of ‘Eight laws of artistic experience’ -- a (...) set of heuristics that artists either consciously or unconsciously deploy to optimally titillate the visual areas of the brain. One of these principles is a psychological phenomenon called the peak shift effect: If a rat is rewarded for discriminating a rectangle from a square, it will respond even more vigorously to a rectangle that is longer and skinnier that the prototype. We suggest that this principle explains not only caricatures, but many other aspects of art. Example: An evocative sketch of a female nude may be one which selectively accentuates those feminine form-attributes that allow one to discriminate it from a male figure; a Boucher, a Van Gogh, or a Monet may be a caricature in ‘colour space’ rather than form space. Even abstract art may employ ‘supernormal’ stimuli to excite form areas in the brain more strongly than natural stimuli. Second, we suggest that grouping is a very basic principle. The different extrastriate visual areas may have evolved specifically to extract correlations in different domains , and discovering and linking multiple features into unitary clusters -- objects -- is facilitated and reinforced by direct connections from these areas to limbic structures. In general, when object-like entities are partially discerned at any stage in the visual hierarchy, messages are sent back to earlier stages to alert them to certain locations or features in order to look for additional evidence for the object . Finally, given constraints on allocation of attentional resources, art is most appealing if it produces heightened activity in a single dimension rather than redundant activation of multiple modules. This idea may help explain the effectiveness of outline drawings and sketches, the savant syndrome in autists, and the sudden emergence of artistic talent in fronto-temporal dementia. In addition to these three basic principles we propose five others, constituting a total of ‘eight laws of aesthetic experience’. (shrink)

I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the (...) cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson’s argument. (shrink)

Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones (...) in the logical representation of space and investigate current trends. In doing so, we do not only consider classical logic, but we indulge ourselves with modal logics. These present themselves naturally by providing simple axiomatizations of different geometries, topologies, space-time causality, and vector spaces. (shrink)

One of the advantages of my account in the essay “Instantiation as Partial Identity” was capturing the contingency of instantiation—something David Armstrong gave up in his experiment with a similar view. What made the contingency possible for me was my own non-standard account of identity, complete with the apparatus of counts and aspects. The need remains to lift some obscurity from the account in order to display its virtues to greater advantage. To that end, I propose to respond to those (...) who have grappled with it in print. There are various criticisms by commentators: that it is rendered absurd by the transitivity of identity, that it makes instantiation necessary instead of contingent, that it is unclear what counts are, that aspects are simply tropes, that my view does not capture multiple location, that I make an unclear reference to a theory of composition as identity, that the account suffers from problems with polyadicity, and that it is not a realist account of universals after all. I give responses to these objections. (shrink)

Objective. Conceptualization of the definition of space as a semantic unit of language consciousness. -/- Materials & Methods. A structural-ontological approach is used in the work, the methodology of which has been tested and applied in order to analyze the subject matter area of psychology, psycholinguistics and other social sciences, as well as in interdisciplinary studies of complex systems. Mathematical representations of space as a set of parallel series of events (Alexandrov) were used as the initial theoretical basis of the (...) structural-ontological analysis. In this case, understanding of an event was considered in the context of the definition adopted in computer science – a change in the object properties registered by the observer. -/- Results. The negative nature of space realizes itself in the subject-object structure, the components interaction of which is characterized by a change – a key property of the system under study. Observer’s registration of changes is accompanied by spatial focusing (situational concretization of the field of changes) and relating of its results with the field of potentially distinguishable changes (subjective knowledge about «changing world»). The indicated correlation performs the function of space identification in terms of recognizing its properties and their subjective significance, depending on the features of the observer`s motivational sphere. As a result, the correction of the actual affective dynamics of the observer is carried out, which structures the current perception of space according to principle of the semantic fractal. Fractalization is a formation of such a subjective perception of space, which supposes the establishment of semantic accordance between the situational field of changes, on the one hand, and the worldview, as well as the motivational characteristics of the observer, on the other. -/- Conclusions. Performed structural-ontological analysis of the system formed by the interaction of the perceptual function of the psyche and the semantic field of the language made it possible to conceptualize the space as a field of changes potentially distinguishable by the observer, structurally organized according to the principle of the semantic fractal. The compositional features of the fractalization process consist in fact that the semantic fractal of space is relevant to the product of the difference between the situational field of changes and the field of potentially distinguishable changes, adjusted by the current configuration of the observer`s value-needs hierarchy and reduced by his actual affective dynamics. (shrink)

The article fits into the debate regarding space, time and nature in dialogue with the world lived by subjects that build up themselves or are built as mythological heroes, source of speech and spacial concrete practices. It's a poorly explored field in Geography that recently approaches to the cultural dynamic debate, to the symbolic field and also to their spacialization processes. The aim is to discuss the possibility of understanding in the present time about the space organization processes related to (...) the society's previous moments, in a space/time dialectics which articulate the present and past times in a complex and non linear way. Methodologically, starting from a literature review about the theme, the present study was linked to the field and documental research about migration to the vicinal ways of Transamazônica Highway (BR-230 Highway), the creation of the "Centro Espírita União do Vegetal", a religion that arises in the Amazon and set up its headquarters in Brasília and the construction of Brasilia as a modern metropolis without a past. The conclusion points at the possibility of space/time nexuses linking the Myth of Nature to the Creation of Heroes, constantly appropriated and with new meanings, in order to support speeches and new actions dialectically throughout the Brazilian contemporaneous space. (shrink)

In her paper, “True Faith: Against Doxastic Partiality about Faith (in God and Religious Communities) and in Defense of Evidentialism,” Katherine Dormandy argues against the view that there is a partiality norm on faith. Dormandy establishes this by showing that partiality views can’t give the right responses to encounters with stubborn counter evidence. Either they (anti-epistemic-partiality views) recommend flouting the evidence altogether in order hold on to positive beliefs about the object of faith or they (epistemic-partiality views) lower the epistemic (...) standards in objectionable ways to alleviate the epistemic pressure imposed by the counterevidence. However, one cannot have praiseworthy faith when one refuses to really grapple with the evidence against the goodness of the faith’s object. So, partiality norms, far from constituting what makes for great faith, importantly stand in its way. Thus, we should reject any partiality norms on faith. We argue that cases of praiseworthy faith involve dispositions to confront the object of faith when presented with stubborn counter evidence against their goodness. Recognizing this enables us to endorse a partiality norm while avoiding Dormandy’s worries. We argue that dispositions to confront the object of faith presuppose positive beliefs about it, thus vindicating partiality. We further argue that the confrontation makes an epistemic demand of the object of faith: produce high confidence in whether it is still worth having faith in, thus carving out a central role for evidentialist norms. (shrink)

One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most of the propositions (...) which can be constructed from possible and impossible worlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (shrink)

Problem Statement. In modern conditions the reconstruction of self-developing socio-technological- ecological systems, which include man as its element, is actualized. The result of such a construction will be the management of the value of technogenic risk in its biological, social and civilizational forms. And the obvious consequence will be the transition of the development of biopolitical problems to a new, no longer international, but global-evolutionary level. The theory and practice of such a reconstruction can be designated by the category of (...) “Transbiolitics,” which implies the political institutionalization of “ecological re整ection. The article is a logical continuation of our previous publication devoted to the analysis of the transformation of the political process into the main factor of global evolution and the biopolitical transformation of the geopolitical landscape. The purpose of this paper is to create a general sketch of the con散guration of the main trends of the coevolutionary interaction of biological, sociocultural and techno-rationalist modules of the stable evolutionary strategy of the technogenic civilization in the space of bio- and geopolitical connotations of international relations. Based on a combination of methods of conceptual, discursive and political-anthropological analysis (in the context of transbiolitical paradigm) the content of the category “Transbiolitical Chronotope” is revealed: a geopolitically di䍕erentiated set of socio-cultural vectors of modern civilization evolution. In other words, the trans-biopolitical chronotope determines the direction of inclusive technological transformation of both cultural and ecological niche and the biosocial nature of man. The general conclusion/prognosis can be reduced to two theses. Firstly, transbiolitics, formed in a di䍕erentiated cultural-civilizational context, is currently being integrated into the general political process, partially replacing and partially intertwining with geopolitical doctrines in the sphere of international relations. Secondly, the growing con整ict of technological civilization with the cultural and ecological niche constructed by it through the turbulence of the geopolitical sphere of social life can bring the level of technological and civilizational risk to the existential boundary. (shrink)

We argue that a cognitive semantics has to take into account the possibly partial information that a cognitive agent has of the world. After discussing Gärdenfors's view of objects in conceptual spaces, we offer a number of viable treatments of partiality of information and we formalize them by means of alternative predicative logics. Our analysis shows that understanding the nature of simple predicative sentences is crucial for a cognitive semantics.

The extended mind thesis (EM) asserts that some cognitive processes are (partially) composed of actions consisting of the manipulation and exploitation of environmental structures. Might some processes at the root of social cognition have a similarly extended structure? In this paper, I argue that social cognition is fundamentally an interactive form of space management—the negotiation and management of ‘‘we-space”—and that some of the expressive actions involved in the negotiation and management of we-space (gesture, touch, facial and whole-body expressions) drive (...) basic processes of interpersonal understanding and thus do genuine social-cognitive work. Social interaction is a kind of extended social cognition, driven and at least partially constituted by environmental (non-neural) scaffolding. Challenging the Theory of Mind paradigm, I draw upon research from gesture studies, developmental psychology, and work on Moebius Syndrome to support this thesis. (shrink)

A central concept for information retrieval is that of similarity. Although an information retrieval system is expected to return a set of documents most relevant to the query word(s), it is often described as returning a set of documents most similar to the query. The authors argue that in order to reason with similarity we need to model the concept of discriminating power. They offer a simple topological notion called resolution space that provides a rich mathematical framework for reasoning with (...) limited discriminating power, avoiding the vagueness paradox. (shrink)

In the field theories in physics, any particular region of the presumed space-time continuum and all interactions between elementary objects therein can be objectively measured and/or accounted for mathematically. Since this does not apply to any of thefield theories, or any other neural theory, of consciousness, their explanatory power is limited. As discussed in detail herein, the matter is complicated further by the facts than any scientifically operational definition of consciousness is inevitably partial, and that the phenomenon has no spatial (...) dimensionality. Under the light of insights from research on meditation and expanded consciousness, chronic pain syndrome, healthy aging, and eudaimonic well being, we may conceive consciousness as a source of potential energy that has no clearly defined spatial dimensionality, but can produce significant changes in others and in the world, observable in terms of changes in time. It is argued that consciousness may have evolved to enable the human species to generate such changes in order to cope with unprecedented and/or unpredictable adversity. Such coping could, ultimately, include the conscious planning of our own extinction when survival on the planet is no longer an acceptable option. (shrink)

The objective of this essay is to provide the beginning of a principled classification of some of the ways space is intelligently used. Studies of planning have typically focused on the temporal ordering of action, leaving as unaddressed questions of where to lay down instruments, ingredients, work-in-progress, and the like. But, in having a body, we are spatially located creatures: we must always be facing some direction, have only certain objects in view, be within reach of certain others. How we (...) manage the spatial arrangement of items around us is not an afterthought: it is an integral part of the way we think, plan, and behave. The proposed classification has three main categories: spatial arrangements that simplify choice; spatial arrangements that simplify perception; and spatial dynamics that simplify internal computation. The data for such a classification is drawn from videos of cooking, assembly and packing, everyday observations in supermarkets, workshops and playrooms, and experimental studies of subjects playing Tetris, the computer game. This study, therefore, focuses on interactive processes in the medium and short term: on how agents set up their workplace for particular tasks, and how they continuously manage that workplace. (shrink)

How political opinions are spread on social media has been the subject of many academic researches recently, and rightly so. Social platforms give researchers a unique opportunity to understand how public discourses are perceived, owned and instrumentalized by the general public. This paper is instead focussing on the political discourses themselves, and how a specific machine learning technique - vector space models (VSMs) -, can be used to make systematic and more objective discourse analysis. Political footprints are vector-based (...) representation of a political discourse in which each vector represents a word, they are produced thanks to the training of the English lexicon on large corpora of text. This paper describes a simple implementation of political footprints, some heuristics on how to use them, and their application to four cases: the U.N. Kyoto Protocol and Paris Agreement, the 2008 and 2016 U.S. presidential elections. The reader will be given some reasons to believe that political footprints produce meaningful results, suggestions on how to improve them and validate the results. (shrink)

Moeser suggested participants default to linear ordering elements but they can be primed to impose either linear or partial ordering. This study seems problematic insofar as ‘greater than’ might be understood to incline participants to favor linear orderings. Recent follow-up studies strongly suggest participants do not default to linear ordering. It seems plausible, moreover, that the observed priming effect is far more pervasive than Moeser countenanced. The present work explores the extent to which priming for linear or partial orders conflicts (...) with the construction of linear or partial ordering lists. Our two experiments suggest friction between priming and task, and also show once the priming tasks are cleared of potentially confounding semantic content, participants perform equally with respect to constructing linear or partial orders under similar priming conditions. (shrink)

In this paper we have shown how the consideration of a chaotic mechanics supplies a redefinition of special-relativistic space-time. In particular chaotic time means no possibility of defining temporal ordering and implies a breakdown of causality. The new chaotic transformations among "undetermined" space-time coordinates are no more linear and homogeneous. The principles of inertia and of energy-impulse conservation are no longer well defined and in any case no more invariant.

We consider momentum operators on intrinsically curved manifolds. Given that the momentum operators are Killing vector fields whose integral curves are geodesics, it is shown that the corresponding manifold is either flat, or otherwise of compact type with positive constant sectional curvature and dimension equal to 1, 3 or 7. Explicit representations of momentum operators and the associated Casimir element will be discussed for the 3-sphere. It will be verified that the structure constants of the underlying Lie algebra are (...) proportional to 2ħ/R, where R is the curvature radius of the sphere. This results in a countable energy and momentum spectrum of freely moving particles. It is shown that the maximum resolution of the possible momenta is given by the de-Broglie wave length λ=πR, which is identical to the diameter of the manifold. The corresponding covariant position operators are defined in terms of geodesic normal coordinates and the associated commutator relations of position and momentum are established. (shrink)

Space is one of the most fundamental concepts over which scientific knowledge has been constructed. But it is also true that space concepts extrapolate by far the scientific domain, and permeate many other branches of human knowledge. Those are fascinating aspects that could di per se justify the compilation of a long bibliography. Another one is the passion for books. My interest in some physical, historical and philosophical problems concerning the concept of space in Physics, and its properties, can be (...) traced back to the early 1980. Since that time, I have being studying, with several collaborators, the influence of space dimensionality in different physical phenomena, like the Casimir Effect, neutron diffraction, Cosmic Microwave Background Radiation and the stability of Schrödinger’s and Dirac’s hydrogen atom in arbitrary number of dimensions, as well as epistemological aspects of the works of Kant, Ehrenfest an others on this particular subject. Meanwhile, I gave lectures about the History of the Concepts of Space in Physics at the Centro Brasileiro de Pesquisas Físicas (CBPF), at the Program of History of Sciences, Technics and Epistemology of the Federal University of Rio the Janeiro (UFRJ) and also at the Physics Institute of the State University of Rio de Janeiro (UERJ). As a consequence of both this interest and my love for books, I continuously bought books on space for my personal library which contains now quite one half of all the books quoted here. In 1996, Roberto Moreira and I published the Sources for the History of Space concepts in Physics: From 1845 to 1995 in the series Notas de Física of the CBPF (NF # 084/96), which is still available online. This was a first initiative to share our bibliography on space. At that time, it contained 1075 references, including 414 books entirely devoted to space, 380 articles in periodical journals and proceedings and 281 miscellaneous citations. After fifteen years, I decided to focus my attention here to collect what in my opinion are the 601 essential books which could be useful for anyone interested on learning about space. An important restriction is imposed here by language: only texts written in English, French, German, Italian, Spanish, Portuguese and Latin were considered. References are given in chronological order covering the period between 1739 and 2010. For each year, the books are listed in alphabetical order of authors’ name. An onomastic index is included at the end of the book. -/- Francisco Caruso Rio de Janeiro, October 2011 . (shrink)

A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture can be generalized (...) and interpreted in relation to the pseudo-Riemannian space of general relativity therefore allowing for both mathematical and philosophical interpretations of the force of gravitation due to the mismatch of choice and ordering and resulting into the “curving of information” (e.g. entanglement). Mathematically, that homeomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. Philosophically, the same homeomorphism implies transcendentalism once the philosophical category of the totality is defined formally. The fundamental concepts of “choice”, “ordering” and “information” unify physics, mathematics, and philosophy and should be related to their shared foundations. (shrink)

An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means the invariance to (...) choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. (shrink)

Kant's theory of transcendental ideas can be conceived as a sort of model theory for an empirical first-order object theory. The main features of Kant's theory of transcendental ideas (especially its antinomies and their solutions) can be recognized, in a modified way, in a religious discourse as exemplified in the dialogue of Jesus and the Samaritan woman (John 4). In this way, what is by Kant meant merely as regulative ideas obtains a sort of objective reality and becomes a religiously (...) founded metaphysics. A metaphysical theory of religious dialogue is formalized on the basis of an extended justification logic of evidence and wish agents. (shrink)