Neuropsychological studies suggest the existence of lateralized networks that represent categorical and coordinate types of spatial information. In addition, studies with neural networks have shown that they encode more effectively categorical spatial judgments or coordinate spatial judgments, if their input is based, respectively, on units with relatively small, nonoverlapping receptive fields, as opposed to units with relatively large, overlapping receptive fields. These findings leave open the question of whether interactive processes between spatial detectors and types of (...) spatial relations can be modulated by spatial attention. We hypothesized that spreading the attention window to encompass an area that includes two objects promotes coordinate spatial relations, based on coarse coding by large, overlapping, receptive fields. In contrast, narrowing attention to encompass an area that includes only one of the objects benefits categorical spatial relations, by effectively parsing space. By use of a cueing procedure, the spatial attention window was manipulated to select regions of differing areas. As predicted, when the attention window was large, coordinate spatial transformations were noticed faster than categorical transformations; in contrast, when the attention window was relatively smaller, categorical spatial transformations were noticed faster than coordinate transformations. Another novel finding was that coordinate changes were noticed faster when cueing an area that included both objects as well as the empty space between them than when simultaneously cueing both areas including the objects while leaving the gap between them uncued. (shrink)

Spatial relations are central to geometrical thinking. With respect to the classical elementary geometry of Euclid’s Elements, a distinction between co-exact, or qualitative, and exact, or metric, spatial relations has recently been advanced as fundamental. We tested the universality of intuitions of these relations in a group of Senegalese and Dutch participants. Participants performed an odd-one-out task with stimuli that in all but one case display a particular spatial relation between geometric objects. As the (...) exact/co-exact distinction is closely related to Kosslyn’s categorical/coordinate distinction, a set of stimuli for testing all four types was used. Results suggest that intuitions of all spatial relations tested are universal. Yet, culture has an important effect on performance: Dutch participants outperformed Senegalese participants and stimulus layouts affect the categorical and coordinate processing in different ways for the two groups. Differences in level of education within the Senegalese participants did not affect performance. (shrink)

The thesis I wish to argue for in this article is that spatial relations such as occupying and being 1 km distant from are external. In the “Section 1” section, I shall introduce the distinction between external and internal relations and some other basic concepts in the ontology of relations. Afterwards, in the subsequent sections, I shall deal with different theories of space: substantivalism and relationism ; the spatial property theory ; super-substantivalism and super-relationism ; (...) and spatial essentialism. I shall demonstrate that, in all such theories, spatial relations need to be considered external. Otherwise, unacceptable consequences or spatial properties that are non-relational by mere façon de parler are in order. Finally, in the “Section 6” section, I shall briefly tackle length contraction in special relativity theory. (shrink)

The cognitive processing of spatial relations in Euclidean diagrams is central to the diagram-based geometric practice of Euclid's Elements. In this study, we investigate this processing through two dichotomies among spatial relations—metric vs topological and exact vs co-exact—introduced by Manders in his seminal epistemological analysis of Euclid's geometric practice. To this end, we carried out a two-part experiment where participants were asked to judge spatial relations in Euclidean diagrams in a visual half field task (...) design. In the first part, we tested whether the processing of metric vs topological relations yielded the same hemispheric specialization as the processing of coordinate vs categorical relations. In the second part, we investigated the specific performance patterns for the processing of five pairs of exact/co-exact relations, where stimuli for the co-exact relations were divided into three categories depending on their distance from the exact case. Regarding the processing of metric vs topological relations, hemispheric differences were found for only a few of the stimuli used, which may indicate that other processing mechanisms might be at play. Regarding the processing of exact vs co-exact relations, results show that the level of agreement among participants in judging co-exact relations decreases with the distance from the exact case, and this for the five pairs of exact/co-exact relations tested. The philosophical implications of these empirical findings for the epistemological analysis of Euclid's diagram-based geometric practice are spelled out and discussed. (shrink)

Immanent universals, being wholly present wherever they are instantiated, are capable of both multi-location and co-location. As a result, they can become involved in some bizarre situations, situations whose contradictory appearance cannot be dispelled by any of the relativizing maneuvers familiar to metaphysicials as solutions to the problem of change. Douglas Ehring takes this to be a fatal problem for immanent universals, but I do not. Although the old relativizing maneuvers don't solve the problem, I propose a new one that (...) does. I spend half the paper defending the proposed solution against objections, and in the course of this task I touch upon such topics as backward time travel and the distinction between universals and particulars. I close by putting forward -- merely as an option -- a new way to draw the distinction in question. (shrink)

According to strong immanent realism, proposed for instance by David M. Armstrong, universals are concrete, located in their instances. E.J. Lowe and Douglas Ehring have presented arguments to the effect that strong immanent realism is incoherent. Cody Gilmore has defended strong immanent realism against the charge of incoherence. Gilmore’s argument has thus far remained unanswered. We argue that Gilmore’s response to the charge of incoherence is an ad hoc move without support independent of strong immanent realism itself. We conclude that (...) strong immanent realism remains under the threat of incoherence posed by Lowe and Ehring. (shrink)

This paper presents a unified account of the meaning of the spatial relational terms right, left, in front of, behind, above and below. It claims that each term has three types of meanings, basic, deictic and intrinsic, and that the definitions of each type of meaning are identical in form for all six terms. Restrictions on the use of the terms, which are different for above and below than for the rest, are explained by a general constraint on all (...) uses of spatial relational terms, the framework vertical constraint. This constraint depends on the existence of a fourth type of meaning for above and below, one defined by the framework in which the related objects are located. It is argued that a theory centred on the framework vertical constraint is preferable to one centred on the principle of canonical orientation (Levelt, 1984). (shrink)

Este trabajo discute la teoría del espacio de Leibniz en el contexto de suconcepción metafísica según la cual las propiedades extrínsecas de unasubstancia se fundamentan, en últimas, en sus propiedades intrínsecas. Enparticular, el artículo sostiene que la teoría leibnizeana de las relacionesespaciales se compagina difícilmente con su principio de identidad, segúnel cual no hay diferencia cuantitativa que no sea a las vez una diferenciacualitativa. La propuesta es que la teoría de Leibniz cae presa del siguientedilema: o bien el espacio no (...) tiene partes, en cuyo caso la teoría no puedeexplicar cómo nos hacemos de la representación de espacio; o bien elespacio tiene partes, lo cual significa que puede haber diferencias que sonmeramente cuantitativas. (shrink)

We examine schoolchildren’s reasoning with spatial relations, such as ‘is to the left of’. Our aims are to obtain a more precise account of the effect of working memory on reasoning, a more detaile...

Journal Name: Cognitive Linguistics Issue: Ahead of print.

Three experiments investigated whether the similarity of relational structures influences the interpretation of spatial representations. Adults were shown diagrams of hand gestures paired with simple statements and asked to judge the meaning of new gestures. In Experiment 1 the gestures were paired with active declarative statements. In Experiment 2, the gestures were paired with conjunctive and disjunctive relations. Experiment 3 used statements similar to those used in Experiment 1, but eliminated the initial object‐to‐object mapping provided in Experiments 1 (...) and 2. In all three experiments, most participants chose an interpretation that set up a parallel relational structure between the gesture and its meaning: spatial elements were paired with conceptual elements and spatial relations were paired with conceptual relations. These results are consistent with the hypothesis that similarity of relational structures influences spatial reasoning, and have implications for analogical reasoning, diagrammatic reasoning, and language processing. (shrink)

Relational, operator, and predicate systems are distinguished on the basis that they correspond to the three possible pair-wise bracketings into two constituents of the three parts of a proposition: relation, subject, and object. It is asserted that the verbal propositional modality (left hemisphere) uses a predicate grammar, while the spatial-image operational modality (right hemisphere) uses an operator grammar. Verbal propositional memory has the capacity for extensive propositional embedding while spatial operational memory does not.

The remarkable growth in the application of information and communications technologies indicates a great shift toward a globally integrated society. The urban metropolises are turning into intersections of transit and migration of goods, capital, services, cultures, knowledge and especially people. Moreover the flow of bodies, information and money is changing the rules of what defines national territory, space and identity. Social realities with specific qualities are appearing, implying a new spatial correlation between the local and the global. International airports (...) and within emerging extraterritorial zones have become an important threshold controlling the flow of people in a free market economy. The airport border mutates into an abstract space permeating the physical territory of the airport and beyond. This abstract border space, within which mobile bodies operate, is created by a bureaucratic system of inclusion and exclusion particular to transition states. Transit zones at airports emerge because of a complex set of factors: border crossing as well as increasingly stringent security and safety regulations. The innumerable thresholds within these transit zones are points of congestion governed and increasingly supported by technological systems of identification. Within the transnation state, the movement of bodies is the constant subject of streaming and proceduralization. Increasingly, the conventional system of control based on face-to-face interaction between the controlling and the controlled is being replaced by the algorithmic precision of database logic. The paradigm of pattern matching ensures precise verification of the uniqueness of the body, in turn offering new potentials for permeability and flux. These different orders of legal and economic categorization create manifold sub-territories accessible to select groups of travellers. Nowadays, the airport is a transnation state spatialized through a new order of architecture, a manifestation of technology of abstract procedures of transition, inclusion and exclusion, adopting emergent patterns of socio-spatial mobility in a globalized network. (shrink)

The present paper focuses on the heuristic selection process preceding the actual transitive reasoning process. A part of the difficulty of transitive reasoning lies in the selection of the relevant problem aspects. Two experiments are presented using the paradigm introduced by Markovits, Dumas, and Malfait (1995), in which children were asked to make “higher than” inferences about arrays of coloured blocks. In order to discriminate between genuine transitive inference and a simple strategy of relative position, Markovits et al. interspersed white (...) blocks with the coloured blocks, such that the relative position strategy leads to erroneous responses. However, we argue that the white blocks cause confusion due to their ambiguity, which interferes with the heuristic selection process. Two methodological adaptations were introduced, which are hypothesised to facilitate the selection process and improve transitive reasoning: (1) the white blocks were replaced by coloured blocks, and (2) a less abstract context was added to the experimental design. The colour manipulation leads to a clear increase in the use of a transitive strategy by 9-year-old children; 8-year-old children mainly used the relative position strategy. When adding a context story, 9-year-old children used the transitive strategy regardless of the colour of the interspersed blocks. The overall performance of 8-year-olds improved slightly. These results are interpreted as support for a dual-process model of transitive reasoning. (shrink)

We present relational proof systems for the four groups of theories of spatial reasoning: contact relation algebras, Boolean algebras with a contact relation, lattice-based spatial theories, spatial theories based on a proximity relation.

Spatial visualization as a key variable in sex-related differences in mathematical problem solving and spatial aspects of geometry is traced to the 1960s. More recent relevant data are presented. The variability debate is traced to the latter part of the nineteenth century and an explanation for it is suggested. An idea is presented for further research to clarify sex-related brain laterality differences in solving spatial problems.

Spatial skills predict important life outcomes, such as mathematical achievement or entrance into Science, Technology, Engineering, and Mathematics disciplines. Children significantly vary in their spatial performance even before they enter formal schooling. One correlate of children's spatial performance is the spatial language they produce and hear from others, such as their parents. Because the emphasis has been on spatial language, less is known about the role of hand gestures in children's spatial development. Some children (...) are more likely to fall behind in their spatial skills than others. Children born premature constitute such a risk group. Here, we compared performance of term and preterm-born children on two non-verbal spatial tasks—mental transformation and block design. We also examined relations of children's performance on these tasks to parental spatial language and gesture input and their own production of spatial language and gesture during an independent puzzle play interaction. We found that while term and preterm-born children as a group did not differ in the mental transformation or block design performance, children varied widely in their performance within each group. The variability in mental transformation scores was predicted by both a subset of spatial words and all spatial gestures children produced. Children's spatial language and gesture were in turn related to their parents' spatial language and gesture. Parental spatial language and gesture had an indirect relation on children's mental transformation, but not block design, scores via children's spatial language, and gesture use. Overall, results highlight the unique contributions of speech and gesture in communicating spatial information and predicting children's spatial performance. (shrink)

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and connections to symbolic numbers remains in its infancy. The current research aims to further explore these similarities by investigating whether the magnitudes of nonsymbolic ratios are associated with space just as symbolic (...) numbers are. In two experiments, we found that responses were faster on the left for smaller nonsymbolic ratio magnitudes and faster on the right for larger nonsymbolic ratio magnitudes. These results further elucidate the nature of nonsymbolic ratio processing, extending the literature of spatial–numerical associations to nonsymbolic relative magnitudes. We discuss potential implications of these findings for theories of human magnitude processing in general and how this general processing relates to numerical processing. (shrink)

Although there exist advantages to group-living in comparison to a solitary lifestyle, costs and gains of group-living may be unequally distributed among group members. Predation risk, vigilance levels and food intake may be unevenly distributed across group spatial geometry and certain within-group spatial positions may be more or less advantageous depending on the spatial distribution of these factors. In species characterized with dominance hierarchy, high-ranking individuals are commonly observed in advantageous spatial position. However, in complex social (...) systems, individuals can develop affiliative relationships that may balance the effect of dominance relationships in individual's spatial distribution. The objective of the present study is to investigate how the group spatial distribution of a semi-free ranging colony of Mandrills relates to its social organization. Using spatial observations in an area surrounding the feeding zone, we tested the three following hypothesis: (1) does dominance hierarchy explain being observed in proximity or far from a food patch? (2) Do affiliative associations also explain being observed in proximity or far from a food patch? (3) Do the differences in rank in the group hierarchy explain being co-observed in proximity of a food patch? Our results showed that high-ranking individuals were more observed in proximity of the feeding zone while low-ranking individuals were more observed at the boundaries of the observation area. Furthermore, we observed that affiliative relationships were also associated with individual spatial distributions and explain more of the total variance of the spatial distribution in comparison with dominance hierarchy. Finally, we found that individuals observed at a same moment in proximity of the feeding zone were more likely to be distant in the hierarchy while controlling for maternal kinship, age and sex similarity. This study brings some elements about how affiliative networks and dominance hierarchy are related to spatial positions in primates. (shrink)

It’s often said that relational view of experience can’t provide an explanation of mode of presentation phenomena: the idea is that if experience is characterized merely as a relation to an object, then we can’t make sense of the idea that one and the same object can be given in perception in many different ways. I show that we can address this problem by looking at the causal structure in relational experience. Experience of an object is caused by experience of (...) particular properties it has, such as its color and location, and experience of the object is in turn a cause of experience of its properties as characteristics of that object. We can explain mode of presentation phenomena as a matter of there being different sets of properties that can cause perception of one and the same object. I discuss how experiments in vision science and computational models of vision can underwrite this way of finding the causal structure in experience, relationally conceived. I look at an alternative, internalist approach to mode of presentation phenomena, in terms of ‘mental paint’, and suggest that the internalist approach is simply incoherent. Finally, I point out that we have mode of presentation phenomena for the spatial aspects of vision, such as perception of spatial relations and spatial location, but that these phenomena resist analysis in any of the terms proposed so far.On a relational view, visual experience is a relation between the perceiver and the scene observed. It’s often said, quite wrongly, that relational views of experience cannot reckon with mode-of-presentation phenomena. I begin by explaining how a relational view of experience can make sense of the idea of the ‘way’ in which an object is given to the perceiver, in terms of the properties used to single out the object. I explain why relational views are to be preferred to approaches in terms of ‘mental paint’. I then sketch the problem posed by spatial perception. Spatial perception is peculiarly difficult to characterize on a relational view, because it’s difficult to characterize the way in which spatial locations and layouts are given to the subject. (shrink)

We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, (...) we find a certain kind of kinematical holographic relation in YSTA, which may be regarded as a primordial form of the holographic principle suggested so far in the framework of the present quantum theory that appears now in the contraction limit of YSTA, λ→0 and R→∞. (shrink)

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.

La thèse du présent article est que l’opposition factice entre James, repré- sentant supposé des « relations externes », d’une part, et Bradley, représen- tant supposé des « relations internes », d’autre part, est due à une mauvaise appréhension des thèses de ce dernier. Ce premier contresens conduit alors à manquer le propos même de James.

How does the human brain link relational concepts to perceptual experience? For example, a speaker may say “the cup to the left of the computer” to direct the listener's attention to one of two cups on a desk. We provide a neural dynamic account for both perceptual grounding, in which relational concepts enable the attentional selection of objects in the visual array, and for the generation of descriptions of the visual array using relational concepts. In the model, activation in neural (...) populations evolves dynamically under the influence of both inputs and strong interaction as formalized in dynamic field theory. Relational concepts are modeled as patterns of connectivity to perceptual representations. These generalize across the visual array through active coordinate transforms that center the representation of target objects in potential reference objects. How the model perceptually grounds or generates relational descriptions is probed in 104 simulations that systematically vary the spatial and movement relations employed, the number of feature dimensions used, and the number of matching and nonmatching objects. We explain how sequences of decisions emerge from the time‐ and state‐continuous neural dynamics, how relational hypotheses are generated and either accepted or rejected, followed by the selection of new objects or the generation of new relational hypotheses. Its neural realism distinguishes the model from information processing accounts, its capacity to autonomously generate sequences of processing steps distinguishes it from deep neural network accounts. The model points toward a neural dynamic theory of higher cognition. (shrink)

I argue that relations between non-collocated spatial entities, between non-identical topological spaces, and between non-identical basic building blocks of space, do not exist. If any spatially located entities are not at the same spatial location, or if any topological spaces or basic building blocks of space are non-identical, I will argue that there are no relations between or among them. The arguments I present are arguments that I have not seen in the literature.

Spatial cognitive abilities, including mental rotation and visuo-spatial working memory are correlated with mathematical performance, and several studies have shown that training of these abilities can enhance mathematical performance. Here, we investigated the behavioral and neural correlates of MR and vsWM training combined with number line training. Fifty-seven children, aged 6–7, performed 25 days of NL training combined with either vsWM or MR and participated in an Electroencephalography -session in school to measure resting state activity and steady-state visual (...) evoked potentials during a vsWM task before and after training. Fifty children, aged 6–7, received usual teaching and acted as a control group. Compared to the control group, both training groups improved on a combined measure of mathematics. Cognitive improvement was specific to the training. Significant pre-post changes in resting state-EEG, common to both training groups, were found for power as well as for coherence, with no significant differences in rs-EEG-changes between the vsWM and MR groups. Two of the common rs-EEG changes were correlated with mathematical improvement: an increase in coherence between the central frontal lobe and the right parietal lobe in frequencies ranging from 16 to 25 Hz, and an increase in coherence between the left frontal lobe and the right parietal lobe ranging from 23 to 25 Hz. These results indicate that changes in fronto-parietal coherence are related to an increase in mathematical performance, which thus might be a useful measure in further investigations of mathematical interventions in children. (shrink)