This paper starts with an intuitive notion of representational spaces, which is intended to provide an improved version of Kuhn's concept of paradigms. It then proceeds to study the following topics in terms of this new notion: incommensurability, paradigm change, explanation of anomalies, explanation of regularities, explanation of irregularities, and physical necessity. In the course of the investigation, "representational space" gets clarified and defined. It is envisaged that this new concept should throw light on many issues in (...) the philosophy of science. (shrink)

Real-world judgements and decisions often require choosing from an open-ended set of options which cannot be exhaustively considered before a choice is made. Recent work has found that the options people do consider tend to have particular features, such as high historical value. Here, we pursue the idea that option generation during decision making may reflect a more general mechanism for calling things to mind, by which relevant features in a context-appropriate representational space guide what comes to mind. (...) In this paper, we evaluate this proposal primarily based on what comes to mind in different familiar categories. We first introduce an empirical approach for deriving the space of features that people use to represent items in a particular category and for locating the category members that come to mind within that space. We show that in both familiar and ad hoc categories, a category member’s location along certain dimensions of the derived feature space predicts its likelihood of coming to mind. Next, we show that category members from these feature space locations come to mind by default in a way that is somewhat impervious to conscious control. We then demonstrate that the extent to which a given dimension is a predictor of what comes to mind within a category is related to how relevant that feature is for representing the category in question, using a novel measure of general feature relevance. Finally, we illustrate the usefulness of this framework in the context of a decision making task. We close with the proposal that people call category members to mind according to their location in representational space, specifically based on the predicted usefulness of considering category members with particular features. (shrink)

Life, but not as we know it -- Still life in nearly present time -- Driving and the city -- Movement-space -- Afterwords -- From born to made -- Spatialities of feeling -- But malice aforethought -- Turbulent passions.

During the last decades, many cognitive architectures (CAs) have been realized adopting different assumptions about the organization and the representation of their knowledge level. Some of them (e.g. SOAR [35]) adopt a classical symbolic approach, some (e.g. LEABRA[ 48]) are based on a purely connectionist model, while others (e.g. CLARION [59]) adopt a hybrid approach combining connectionist and symbolic representational levels. Additionally, some attempts (e.g. biSOAR) trying to extend the representational capacities of CAs by integrating diagrammatical representations and (...) reasoning are also available [34]. In this paper we propose a reflection on the role that Conceptual Spaces, a framework developed by Peter G¨ardenfors [24] more than fifteen years ago, can play in the current development of the Knowledge Level in Cognitive Systems and Architectures. In particular, we claim that Conceptual Spaces offer a lingua franca that allows to unify and generalize many aspects of the symbolic, sub-symbolic and diagrammatic approaches (by overcoming some of their typical problems) and to integrate them on a common ground. In doing so we extend and detail some of the arguments explored by G¨ardenfors [23] for defending the need of a conceptual, intermediate, representation level between the symbolic and the sub-symbolic one. In particular we focus on the advantages offered by Conceptual Spaces (w.r.t. symbolic and sub-symbolic approaches) in dealing with the problem of compositionality of representations based on typicality traits. Additionally, we argue that Conceptual Spaces could offer a unifying framework for interpreting many kinds of diagrammatic and analogical representations. As a consequence, their adoption could also favor the integration of diagrammatical representation and reasoning in CAs. (shrink)

Visual space can be distinguished from physical space. The first is found in visual experience, while the second is defined independently of perception. Theorists have wondered about the relation between the two. Some investigators have concluded that visual space is non-Euclidean, and that it does not have a single metric structure. Here it is argued that visual space exhibits contraction in all three dimensions with increasing distance from the observer, that experienced features of this contraction are (...) not the same as would be the experience of a perspective projection onto a fronto-parallel plane, and that such contraction is consistent with size constancy. These properties of visual space are different from those that would be predicted if spatial perception resulted from the successful solution of the inverse problem. They are consistent with the notion that optical constraints have been internalized. More generally, they are also consistent with the notion that visual spatial structures bear a resemblance relation to physical spatial structures. This notion supports a type of representational relation that is distinct from mere causal correspondence. The reticence of some philosophers and psychologists to discuss the structure of phenomenal space is diagnosed in terms of the simple materialism and the functionalism of the 1970s and 1980s. (shrink)

What is the role of language in constructing knowledge? In this article, we ask whether learning new relational language can create new ways of thinking. In Experiment 1, we taught English speakers to talk about time using new vertical linguistic metaphors, saying things like “breakfast is above dinner” or “breakfast is below dinner”. In Experiment 2, rather than teaching people new metaphors, we relied on the left–right representations of time that our American college student participants have already internalized through a (...) lifetime of visuospatial experience reading and writing text from left to right. In both experiments, we asked whether the representations are susceptible to verbal interference. We found that learning new metaphors created new space–time associations that could be detected in a nonlinguistic implicit association task; these newly learned representations were not susceptible to verbal interference; and with respect to both verbal and visual interference, representations newly learned from linguistic metaphor behaved just like those on the left–right axis that our participants had acquired through years of visuospatial experience. Taken together, these results suggest that learning new relational language can be a powerful tool in constructing new representations and expanding our cognitive repertoire. (shrink)

The posterior parietal cortex (PPC) is the most likely site where egocentric spatial relationships are represented in the brain. PPC cells receive visual, auditory, somaesthetic, and vestibular sensory inputs; oculomotor, head, limb, and body motor signals; and strong motivational projections from the limbic system. Their discharge increases not only when an animal moves towards a sensory target, but also when it directs its attention to it. PPC lesions have the opposite effect: sensory inattention and neglect. The PPC does not seem (...) to contain a “map” of the location of objects in space but a distributed neural network for transforming one set of sensory vectors into other sensory reference frames or into various motor coordinate systems. Which set of transformation rules is used probably depends on attention, which selectively enhances the synapses needed for making a particular sensory comparison or aiming a particular movement. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large – it is the space of applicable Turing machines. As a result, mappings that pivot on such attenuated regularities cannot, in general, be found by brute-force search. The class of problems that present such mappings we call the class of “type-2 problems.” Type-1 (...) problems, by contrast, present tractable problems of search insofar as the relevant regularities can be found by sampling the input data as originally coded. Type-2 problems, we suggest, present neither rare nor pathological cases. They are rife in biologically realistic settings and in domains ranging from simple animat behaviors to language acquisition. Not only are such problems rife – they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding biases so as to reduce specific type-2 problems to type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy – namely, the maximal exploitation of states of representation already achieved by prior, simpler learning so as to reduce the amount of subsequent computational search. Such exploitation both characterizes and helps make unitary sense of a diverse range of mechanisms. These include simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription”. In addition, the most distinctive features of human cognition – language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large type-2 problems. they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of (...) recoding biases so as to reduce specific type-2 problems to (tractable) type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general (not task-specific) strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy representational redescription language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

This article analyses the multimodal representations of public space in Chilean broadcast news reports on the figure of the hooded rioter and its alleged connections with the student movement. We seek to identify how space is constructed as a legitimation strategy in relation to the actors involved and the actions taking place across four different news broadcast pieces in the light of Multimodal Critical Discourse Analysis and Systemic Functional Linguistics. Results show that the multimodal representations of space (...) are crucial to identify and functionalize hooded rioters as belonging to the student movement. Actions are dependent on the spaces in which actors operate, restricting the occupation of certain spaces to specific actors. Thus, transgressive protest actions are to be contained to educational spaces and represented as naturalized vandalism, ignoring the students’/demonstrators’ motivations to recuperate/vindicate the public space. (shrink)

The dominating models of information processes have been based on symbolic representations of information and knowledge. During the last decades, a variety of non-symbolic models have been proposed as superior. The prime examples of models within the non-symbolic approach are neural networks. However, to a large extent they lack a higher-level theory of representation. In this paper, conceptual spaces are suggested as an appropriate framework for non- symbolic models. Conceptual spaces consist of a number of 'quality dimensions' that often are (...) derived from perceptual mechanisms. It will be outlined how conceptual spaces can represent various kind of information and how they can be used to describe concept learning. The connections to prototype theory will also be presented. (shrink)

The contribution deals with some key problems of cognitive science, whose plurality transcends the boundaries of the disciplines drawn by classical epistemology. In particular, it addresses the issues of mental images, spaces of representation, and the architecture of cognitive processes in vision theory. The thesis presented is that a proper treatment of vision within psychophysics entails an analysis of a series of interconnected spaces, objects and methodologies, from psychophysics to the many virtual realities of representation.

We show that metric spaces and continuous functions between them are domain representable using the category of Scott-Ershov domains. A notion of effectivity for metric spaces is thereby inherited from effective domain theory. It is shown that a separable metric space with an effective metric can be represented by an effective domain. For a class of spaces, including the Euclidean spaces, the usual notions of effectivity are obtained. The Banach fixed point theorem is a consequence of the least fixed (...) point theorem for domains. A notion of semieffective domains is introduced and used to give a new proof of Ceitin's theorem. (shrink)

We investigate ideals of the form {A⊆ω: Σn∈Axnis unconditionally convergent} where n∈ωis a sequence in a Polish group or in a Banach space. If an ideal onωcan be seen in this form for some sequence inX, then we say that it is representable inX.After numerous examples we show the following theorems: An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. An ideal is representable in a Banach space iff it is a nonpathological (...) analytic P-ideal.We focus on the family of ideals representable inc0. We characterize this property via the defining sequence of measures. We prove that the trace of the null ideal, Farah’s ideal, and Tsirelson ideals are not representable inc0, and that a tallFσP-ideal is representable inc0iff it is a summable ideal. Also, we provide an example of a peculiar ideal which is representable inℓ1but not in ℝ.Finally, we summarize some open problems of this topic. (shrink)

This article illustrates the ways in which visual representations construct the meanings of norms governing the spaces we commonly inhabit. I argue that norms regulating public spaces such as streets, parks, plazas, and beaches arise within the process of conceiving tourist representations of space that benefit hegemonic groups in society. My argument is empirically grounded on evidence from a case study on public space regulation in Acapulco, Mexico. By means of a semiotic analysis of tourist materials such as (...) maps and postcards, I show that images related to tourism represent urban space in a way that includes some elements and excludes others. By doing so, they portray a very specific image of the city and its public spaces. Because representations of space are performed upon the entire society, the imagery reproduced by tourist materials is part of the expectations that surround social actors’ actions. This is one of the mechanisms through which the tourism industry influences the regulation of public spaces. (shrink)

Religious Representation in Place brings together an interdisciplinary group of scholars from the Humanities and Sciences to broaden the understanding of how religious symbols and spatial studies interact. The essays consider the relevance of religion in the experience of space, a fundamental dimension of culture and human life.

A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result provides a (...) characterization of the projection lattices in operator algebras. (shrink)

b>: The problem of how physical systems, such as brains, come to represent themselves as subjects in an objective world is addressed. I develop an account of the requirements for this ability that draws on and refines work in a philosophical tradition that runs from Kant through Peter Strawson to Gareth Evans. The basic idea is that the ability to represent oneself as a subject in a world whose existence is independent of oneself involves the ability to represent space, (...) and in particular, to represent oneself as one object among others in an objective spatial realm. In parallel, I provide an account of how this ability, and the mechanisms that support it, are realized neurobiologically. This aspect of the article draws on, and refines, work done in the neurobiology and psychology of egocentric and allocentric spatial representation. (shrink)

We introduce and study several nonstandard representations of Banach-valued operators defined on the space of Bochner integrable functions. They will be less restrictive than the usual standard representation. In particular, without any hypothesis, we shall find a representation whose kernel belongs to a space of “extended Bochner integrable functions”, introduced by Zimmer by using Loeb measures.

We investigate the use of coalgebra to represent quantum systems, thus providing a basis for the use of coalgebraic methods in quantum information and computation. Coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. (...) We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics. (shrink)

We look at bimodal logics interpreted by cartesian products of topological spaces and discuss the validity of certain bimodal formulae in products of so-called cardinal spaces. This solves an open problem of van Benthem et al.

Most historians of science eagerly acknowledge that the early modern period witnessed a shift from a prevailing Aristotelian, spherical, centered conception of space to a prevailing Cartesian, rectilinear, oriented spatial framework. Indeed, this shift underlay many of the important advances for which the period is celebrated. However, historians have failed to engage the general conceptual shift, focusing instead on the particular explanatory developments that resulted. This historical lacuna can be attributed to a historiographical problem: the lack of an adequate (...) unit of analysis by which to investigate the conceptual change. Here, a philosophical argument is made for representations of space as an appropriate category of historical investigation, and methods of textual interrogation are suggested to this end. Finally, two examples, taken from Aristotle and Newton, demonstrate the feasibility and importance of this project. (shrink)

The libidinal economy could be exploited by both political movements and advertising campaigns in a pictorial space that is related to the social space at any historical moment. The arrangement of desires in a propaganda poster of the Chinese Cultural Revolution is, in light of political semiotics, the same as in a campaign poster in a consumer society today. The same libidinal economy is rooted in our political unconsciousness and remains to be the deep structure of our political (...) performance. A critical image analysis or a political semiotic critique of this libidinal economy that rules us in the Chinese Cultural Revolution and in consumer society today is necessary and urgent. (shrink)

Abstract:Unable to produce scales of one-to-one in places or spaces, people interact as they develop common representations, actions, and objects. In places, they can point to connect representations and objects. Places may be small spaces, but spaces can contain places and even more variations. Unable to name each variation, actors and analysts create abstractions. They might use a part to represent the whole, with miles of track for railroads, kilowatt-hours for electric power, and barrels of oil for energy. Some treat (...) their representations as hegemonic, even true. However, dealing with social and material variations, actors and analysts represent, build, maintain, and repair combinations of cultures, economies, governments, and materials. Thus, railroads and power systems, like other technologies and infrastructures, do not design, build, or repair themselves. To resolve problems, people with relevant skillsets interact in places to create common representations, actions, and objects tying themselves and others together in spaces. (shrink)

Extending a construction of Andreka, Givant, and Nemeti (2019), we construct some finite vector spaces and use them to build finite non-representable relation algebras. They are simple, measurable, and persistently finite, and they validate arbitrary finite sets of equations that are valid in the variety RRA of representable relation algebras. It follows that there is no finitely axiomatisable class of relation algebras that contains RRA and validates every equation that is both valid in RRA and preserved by completions of relation (...) algebras. Consequently, the variety generated by the completions of representable relation algebras is not finitely axiomatisable. This answers a question of Maddux (2018). (shrink)

Under shift, caused for example by eye movement, or by relative movement of the subject or object of perception, the cortical representation undergoes very large changes in “size” and “shape.” Space-variance of cortical representation rules out models that fundamentally require linear interpolation between shifted patterns (e.g., Edelman's model) or rigid shift of an invariant retinal stimulus corresponding to shift at the cortex (e.g., the shifter theory of van Essen). Recently, a computational solution of “quasi-shift” invariance for space-variant mappings (...) has been constructed (Bonmassar & Schwartz 1997a; 1997b). (shrink)

Social interaction and the constitution of mediated and nested space in the court of appeal -- Conclusion -- Concluding remarks: On becoming juridical -- Ways of spacing law and politics -- Becoming juridical -- Towards hybrid juridical spaces -- References -- Index.

Kant argued that the perceptual representations of space and time were templates for the perceived spatiotemporal ordering of objects, and common to all modalities. His idea is that these perceptual representations were specific to no modality, but prior to all—they are pre-modal, so to speak. In this paper, it is argued that active perception—purposeful interactive exploration of the environment by the senses—demands premodal representations of time and space.

Recognizing the centrality of representation in philosophy and social sciences as constitutive of knowledge concerning the interpretation of social reality, this article highlights on the need to e...

This article reviews experimental evidence for a specific sensorimotor function which can be dissociated from higher level representations of space. It attempts to delineate this function on the basis of results obtained by psychophysical experiments performed with brain damaged and healthy subjects. Eye and hand movement control exhibit automatic features, such that they are incompatible with conscious control. In addition, they rely on a reference frame different from the one used by conscious perception. Neuropsychological cases provide a strong support (...) for this specific motor representation of space, which can be spared in patients with lesions of primary sensory systems who have lost conscious perception of visual, tactile or proprioceptive stimuli. Observation of these patients also showed that their motor behavior can be ''attracted'' by a goal only under specific conditions, that is, when the response is immediate and when no cognitive representation of this goal is elaborated at the same time. Beyond the issue of the dissociation between an implicit motor representation and more cognitive processing of spatial information, the issue of the interaction between these two systems is thus a matter of interest. It is suggested that the conscious, cognitive representation of a stimulus can contaminate or override the short-lived motor representation, but no reciprocal influence seem to occur. The interaction observed in patients can also be investigated in normals. The literature provides examples of interaction between sensorimotor and cognitive framing of space, which confirm that immediate action is not mediated by the same system as delayed action, and that elaborating a categorial representation of the action goal prevents the expression of the short-lived sensorimotor representation. It is concluded that action can be controlled by a sensory system which is specialized for on-line processing of relevant goal characteristics. The temporal constraints of this system are such that it can affect the action before a full sensory analysis of this goal has been completed. The performance obtained on the basis of this spatial sensory processing suggests that short-lived motor representations may rather be considered as real ''presentation'' of the action world, which share its metric properties. (shrink)