Prepositions name spatial relationships. But they are also used to convey abstract, non-spatial relationships —raising the question of how the abstract uses relate to the concrete spatial uses. Despite considerable success in delineating these relationships, no general account exists for the two most frequently extended prepositions: in and on. We test the proposal that what is preserved in abstract uses of these prepositions is the relative degree of control between the located object and the reference object. Across (...) four experiments, we find a continuum of greater figure control for on and greater ground control for in. These findings bear on accounts of semantic structure and language change, as well as on second language instruction. (shrink)

The target article undermines the existence of a shared unitary numerical format, illustrating a variety of representations. The / dichotomy does not capture their specific features. These representations are with respect to the sensory modality of the stimulus, and independent of its specific notation, with a main role of spatial codes, both related and unrelated to the mental number line.

I defend a reading of David Hume’s nominalism that he comes close to Keith Campbell's contemporary trope theory in the specific case of spatial properties. I argue that Hume's view should be construed as classifying spatial properties as Campbellian tropes (particular properties): abstract, particular, determinate and qualitatively simple properties. This has implications for reconstructing Hume's answer to the problem of universals. I argue that Hume’s account of objects resembling each other in respect of spatial properties is grounded (...) in the resemblance of tropes rather than in the resemblance of objects. (shrink)

There is mounting evidence that language comprehension involves the activation of mental imagery of the content of utterances (Barsalou, 1999;Bergen, Chang, & Narayan, 2004;Bergen, Narayan, & Feldman, 2003;Narayan, Bergen, & Weinberg, 2004;Richardson, Spivey, McRae, & Barsalou, 2003;Stanfield & Zwaan, 2001;Zwaan, Stanfield, & Yaxley, 2002). This imagery can have motor or perceptual content. Three main questions about the process remain under‐explored, however. First, are lexical associations with perception or motion sufficient to yield mental simulation, or is the integration of lexical semantics (...) into larger structures, like sentences, necessary? Second, what linguistic elements (e.g., verbs, nouns, etc.) trigger mental simulations? Third, how detailed are the visual simulations that are performed? A series of behavioral experiments address these questions, using a visual object categorization task to investigate whether up‐ or down‐related language selectively interferes with visual processing in the same part of the visual field (followingRichardson et al., 2003). The results demonstrate that either subject nouns or main verbs can trigger visual imagery, but only when used in literal sentences about real space—metaphorical language does not yield significant effects—which implies that it is the comprehension of the sentence as a whole and not simply lexical associations that yields imagery effects. These studies also show that the evoked imagery contains detail as to the part of the visual field where the described scene would take place. (shrink)

[Interactive and Immersive Practices; Critical Spatial Practices. The Augmented Reality of the Exhibition Space] The rise of installations, as well as immersive and interactive spaces, in both art and science museums has accustomed the public to heightened interactivity, leading to a better understanding of social, natural and scientific phenomena. These spatial systems have also paved the way for the production of innovative environments within exhibition design. This article aims to present a brief overview of the origins of immersive (...) and sensory practices at work in contemporary museums, and to evaluate the potential of these processes to generate critical thinking in the visitor. A concise description of the evolution of the operational and intellectual premise of these museums and their changing practices demonstrates the transformations that have occurred, their modalities, and their application in selected works, notably: The Weather Project by Olafur Eliasson presented at Tate Modern London; Diller + Scofidio’s media pavilion, Blur Building, in Yverdon-les-Bains in Switzerland; and the exhibition Sense of the City at the Canadian Centre for Architecture in Montreal. (shrink)

Despite the importance of mathematics in our educational systems little is known about how abstract mathematical thinking emerges. Under the uniting thread of mathematical development, we hope to connect researchers from various backgrounds to provide an integrated view of abstract mathematical cognition. Much progress has been made in the last 20 years on how numeracy is acquired. Experimental psychology has brought to light the fact that numerical cognition stems from spatial cognition. The findings from neuroimaging and single cell recording (...) experiments converge to show that numerical representations take place in the intraparietal sulcus. Further research has demonstrated that supplementary neural networks might be recruited to carry out subtasks; for example, the retrieval of arithmetic facts is done by the angular gyrus. Now that the neural networks in charge of basic mathematical cognition are identified, we can move onto the stage where we seek to understand how these basics skills are used to support the acquisition and use of abstract mathematical concepts. (shrink)

This article tackles the tricky problem of identifying metaphors in language that includes prepositions. We demonstrate how the Procedure for Identifying Metaphorical Scenes (PIMS) reflected and evoked by linguistic expressions in discourse, Johansson Falck & Okonski, accepted) can be used to identify metaphorical relations reflected in language. The scenes evoked correspond to conceptualizations that are directly attested by the specific linguistic constructions in the sentences under analysis. We present two studies that test the reliability of the procedure and the sensitivity (...) of the tool for prepositions. Results show that PIMS provides a simple procedure that increases both reliability and sensitivity for prepositional constructions. By focusing on the scenes evoked by linguistic constructions, the procedure highlights the contextual meanings of the constructions and the specific experiences that they code. (shrink)

ABSTRACT This article asks how social media changes and challenges critical agency through spatial, networked and embodied discourses? It argues that CDS has the potential to explore relations and contexts that go beyond the deliberative participatory, affective and exploitative conditions of social media. Employing a critical discursive reading of street artist Banksy’s mural of a Les Misérables-poster on the public wall across from the French embassy in London in 2016, we argue that social media is neither purely deliberative, affective, (...) nor exploitative. The illustrative case allows us to trace the intricate digital intertextual and interdiscursive relations between social media, public spaces and embodied politics offered in counter-discourse. Further, the case brings new light to the ability of CDS in combination with political discourse theory to underscore the political agency in social contexts. While critiques of the affective and exploitative conditions of social media have merit as critiques of hegemonic discourses, an affirmative response that emphasises the political agency in counter-discourses highlights the nuances of social media. This article argues that intersecting CDS with social media presents an opportunity to gain a complex understanding of how the political is played out in changing publics consisting of different mediated spaces, digital as well as non-digital. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:IntroductionSpatial, Environmental, and Ecocritical Approaches to Holocaust MemoryEmily-Rose Baker (bio), Michael Holden (bio), Diane Otosaka (bio), Sue Vice (bio), and Dominic Williams (bio)The successful implementation of genocide during the Holocaust depended on the spatial organisation of mass murder. From the concentrated ghettos and camps delimited by walls and barbed wire to the open fields and camouflaged forests where victims were shot en masse, Anne Kelly Knowles et al. (...) argue, specific locations, patterns of migration, deportation and evacuation, and other spatial elements such as scale, were all central to the Nazi regime's creation of a "comprehensive geography of oppression."1 This is hardly surprising given the biopolitical logics and colonial fantasies underpinning Lebensraum ('living space'), the territorial concept guiding the genocidal aims of the Third Reich, which designated zones of life as well as the inverse on the European continent. The Holocaust was also experienced spatially by its victims, who were forced to navigate new (and at times familiar) sites and landscapes as those of genocide, and whose testimonies in the aftermath of the event conjured these very places in detail.In recent years, the spaces of the Holocaust have been variously revisited, reconstructed, and reimagined within Holocaust studies scholarship. As a broader part of the 'spatial turn' in the humanities, Holocaust scholars have increasingly employed spatial perspectives of the event to deepen our understanding of the environments in which the Holocaust took place and the transformation of these spaces over time—particularly in the fields of history and social science.2 While drawing on diverse modes of spatialisation from interdisciplinary perspectives, contributions from these fields have tended to privilege methods we might describe as variously 'forensic,' including mapping, model-making, and investigations of material traces of the past.3 This work has resulted in many significant insights, not only into the [End Page 1] contexts and structures of Nazi genocide and the perpetrator imaginings of space, but also the experiences of victims and survivors.4Another significant body of work has attended to space and culture within Holocaust contexts. From early on in the postwar period, particular locations and buildings became identified with the Holocaust, such as the notorious entrance guard house at Auschwitz-Birkenau, which appears on countless book covers as well as within films and artworks. Engaging with spatial insights and methodologies from the perspective of cultural and memory studies, scholars have attested to the production and mnemonic significance of these and less well-known sites, as well as the symbolic spatial worlds and experiences to which they give rise. These include Paul Jaskot and Gavriel Rosenfeld, who have turned respectively to Holocaust and post-Holocaust architectures as commonly overlooked sites of history and memory. Drawing attention to the construction of Holocaust space, Jaskot shows how reading architecture 'as process' rather than static structures laden with symbolic meaning reveals unique histories of forced labor in which "the goals of the SS intersected with victims' experience."5 Rosenfeld demonstrates the ways in which spaces built in response to Nazi genocide after 1945 have been variously "imbued with Jewish significance" by their users and creators, resulting in the rise to prominence of Jewish-identified architects.6 Along similar lines, Michael Meng's work has explored the ways in which Jews and gentiles interact with ruined synagogues, cemeteries and Jewish districts as important remnants of pre-war Jewish life in the post-war period in German and Polish cities.7Studies such as those noted above have tended to focus on cities and public buildings, as well as state and civic policy. But as the spatial histories and geographies of the Holocaust have helped to show, extermination often took place in rural settings (mostly located in Central and Eastern Europe), such as the killing fields where Jews were shot en masse; the forests where victims hid and were hunted by Germans and local collaborators; or the open spaces of the dissolving Reich through which former concentration camp inmates were forced to march during the final year of the war—sites in which, owing to less contained spatial dynamics, violence played out differently.8These kinds of sites, which are sparsely documented and often simply thought of... (shrink)

Abstract:Given the distinctiveness of its urban and civic spaces and of the famously strong but also complex sense of civic identity among its populace, sixteenth century Venice is a prime case study for applying spatial thinking when imagining the deliberate construction of space and the relationship of inhabitants to that space; in particular, the relationship between those in power and those without power as indicative throughout the cityscape. The formation and development of central features of Venetian urban space and (...) identity, since maritime topography constrained its urban space, created an unusually cohesive sense of civic identity linked to mythic historical memory. Looking through an interdisciplinary lens, theories of space offer a conceptual framework for imagining how the Venetian cityscape was created and evolved into one of the most diverse and unique cityscapes in the sixteenth century. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Spatializing Culture: The Ethnography of Space and Place by Setha LowCarlos J. L. BalsasSpatializing Culture: The Ethnography of Space and Placeby setha low London: Routledge, 2017Spatializing Culture: The Ethnography of Space and Place adds clarity to our understanding of the value of ethnographic scholarship in the study of socio-economic, cultural, and developmental transformations. The book is a thorough review of two established conceptual frames of analysis—the social production (...) of space and the social construction of space—coupled with an in-depth discussion of four newer ways to make sense of the world around us: embodied space, language and discourse, emotion and affect, and translocal space. As the world is transformed by a myriad of forces and events occurring simultaneously, its complexity intensifies insurmountably and we require clear and robust concepts, theories, methods, and tools to not only interpret it, but above all to attempt to change it in ways that are more beneficial to our collective co-existence while enabling the flourishing of those most at risk.Readers of Spatializing Culture will find plentiful theoretical constructs, lineages, diverse viewpoints, examples, and overall opportunities for reflecting on how the (built) environment, spaces, and places have been changing mostly due to our behavior. Inspired by Foucault’s take on genealogy, in chapter 2, Setha Low traces the history of space and place according to distinct interpretative schools of thought ranging from philosophical and mathematical, French social theory, geographical, architectural, environmental psychology, to anthropological, and even archeological. Five Venn diagrams are utilized to illustrate the main conceptual relationships between space and place. Most of the book’s in-depth case studies were researched by the author with only a small number investigated and written up by fellow scholars, which Low utilizes in the book with gratitude. The interrelated thematic and distinct geographical scope of the cases is one of the book’s hallmarks. The illustrative case studies come from such faraway places as Latin America (San José, Costa Rica), Asia (Taipei, Taiwan), North America (New York City; Washington, D.C.; Philadelphia, Pennsylvania; and San [End Page 151] Antonio, Texas), Southern Europe (Smederevska Palanka, Serbia), and the Middle East (Beirut, Lebanon; Cairo, Egypt; and Tel Aviv, Israel).Spatializing Culture was first mentioned to me years ago by a former colleague at the University at Albany, SUNY. His ongoing work in Latin America, coupled with his ethnographic training and prior work in a region of the world also extensively examined by Low in other scholarly works, was likely the reason for bringing it up in a conversation about the latest developments in the field and potential research opportunities. I acquired the book when I was teaching Global Urbanism and Culture and International Urban Planning. I was pleasantly surprised with the book’s thorough conceptual lineage, historic characterizations, attention to detail, comprehensive ethnographic investigations, and implications for transforming reality as well as institutional processes. Spatializing Culture is a welcome addition to urban planning textbooks, which tend to be relatively less critical, are often covered with normative constructs and statistics, and are more institutional in their characterization of problems and recommendations for further action.For the most part, the ethnographic method is qualitative, participa-tory, detailed, and quite comprehensive in characterizing key variables as the researcher found them on the ground. This differs slightly from urban planning’s preoccupation with public policy, policy analysis, rules and regulations, institutionalized procedures, the public good, and overall positivist and rationalist concerns with documenting reality and helping to lead transformative planning processes, whether in the realm of land use, transportation, housing, economic development, infrastructure, or the environment. Although International Urban Planning was to be taught in a rather orthodox manner with recourse to understanding planning cultures, best practices, lessons learned, and implications for similar situations, the Global Urbanism and Culture course was slightly more aligned with the discussions put forward by Low. These included attention to postmodern ideals, the use of creativity in community planning, distinctions between popular and highbrow culture, and the building of iconic structures in contexts of urban regeneration and mega-event planning. As such, my students were somewhat already exposed to issues of embodied spaces and to ideas of... (shrink)

Based on architectural projects which interpret literature as program we discuss design reasoning when no routine models of problem solving apply. We address three aspects of formulation: defining the design charge so that it can be retrospectively stated independent of the actual proposal; defining a language of formal operations; and defining the intrinsic aims of design that are only intimated through the proposal itself. The coherence of the project is a function of the way in which formal properties interact, and (...) the way in which they sustain analogical or metaphorical relationships to text: how the patterns of subdivision, connection, differentiation, positioning, movement or perception associated with built space relate to textual figures, concepts, structure, or narrative. The possibility of constructing architectural meaning in this way implies an underlying model of space as a morphic language which works primarily through the constitution of generic and significant relationships rather than the combination of previously objectified elements. The gradual articulation of the design charge is mediated by a process of diagramming. Diagrams express as spatial constructions the conditions and concepts abstracted from text; also, they act as notations of constructive operations which are themselves spatial. Diagrams can be abstractive or pictorial, dense or discrete. They document two aspects of an integral process of reasoning: First, an exploration of how concepts, whether directly, analogically or metaphorically transferred from text to shape, may relate to produce a more complex idea; second, how formal properties co-vary and how an emergent design proposal engages and activates a field of formal possibility. (shrink)

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of (...) physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl’s ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Place and the "Spatial Turn" in Geography and in HistoryCharles W. J. WithersI. IntroductionA few years ago, British Telecom ran a newspaper advertisement in the British press about the benefits—and consequences—of advances in communications technology. Featuring a remote settlement in the north-west Highlands of Scotland, and with the clear implication that such "out-of-the-way places" were now connected to the wider world (as if they had not been before), (...) the advert proclaimed "Geography is History." What the advert signalled to as the "end" of geography in the sense of the social gradients associated with space and distance is what is known, variously, as "time-space convergence" and "time-space distanciation."1 The terms embrace not just the "collapse" of geographical space given technical advances (in travel time and in communications—consequences of what Castells calls "the information age" and "the network society"2), but also the idea that the modern world has become [End Page 637] more homogenized. One place is now much the same as another. Further, given the likelihood of such technical and cultural changes continuing into the future, geographical distinctiveness, evident in the particularity of place, would be a thing of the past: geography would indeed be history. There is, of course, much evidence to the contrary: that, in the face of "globalisation," questions of locality, sense of place and of identity in place matter now more than ever. Even, then, as Francis Fukuyama cautioned against the "death" of liberal democratic politics as The End of History,3 geography—that is, geography understood as questions to do with place, and questions to do with where you are in the world as part of questions about how you are and who you are in the world—has had considerably heightened significance and for some places and people more than others.4These notions of place—as a particular location, and the character or sense of place—are only part of the meanings associated with place in geographical and in historical work. Like space, its regular epistemic dancing partner in geographical ubiquity and metaphysical imprecision, place is a widespread yet complex term. What follows is historiographical in focus and, of necessity, partial in range. I offer a historiographical survey of the term place, principally but not alone within recent work in geography. In more detail, and with reference to one of the strong senses in which place is used, namely that of locale, "the local," or localness, I trace here the connections between place, space, and the idea of the local as evident in recent work in history and in geography, especially within the history and the geography of science. Particular attention is paid in this context to the distinctive features of what we may think of as the "spatial turn" in the history of science by looking at the idea of place and space in recent work in Enlightenment studies. My argument is three-fold. Notions of place and space, much debated by geographers, have been as central a concern for intellectual historians and historians of science as for philosophers and others, but they have been differently expressed. There is, I shall argue, value in looking at these different views in order to understand that whilst place is a commonplace term it is not agreed upon: working with imprecision has been both opportunity and restriction. In relation to work within the history of science and in Enlightenment studies, consideration of the so-called "spatial turn," of place [End Page 638] as social practice and of placing as a process in accounting for the uneven movement of ideas over space and time may help provide some precision and strengthen connections between geography and history.II. Place (In Geography): A Partial HistoriographyPlace is one of the most fundamental concepts in human geography. It is also one of the most problematic.5 Place, or small-scale regional space, features as a subdivision within the Classical tripartite division of cosmography (the earth in relation to other planetary bodies), geography (the earth as a whole) and chorography (parts of the earth or regional geography). So, too, does the distinction between chorography and chronology as... (shrink)

Abstract I develop the idea that there exists a special dimension of depth, or of scale. The depth dimension is physically real and extends from the bottom micro-level to the ultimate macro-level of the Universe. The depth dimension, or the scales axis, complements the standard three spatial dimensions. I discuss the tentative qualities of the depth dimension and the universal arrangement of matter along this dimension. I suggest that all matter in the Universe, at least in the present cosmological (...) epoch, is in joint downward motion along the depth dimension. The joint downward motion manifests itself in the universal contraction of matter. The opposite direction of motion, upward the dimension, would cause the expansion of matter. The contraction of matter is a primary factor, whereas the shrinking of space in the vicinity of matter is a derivative phenomenon. The observed expansion of the Universe is explained by the fact that celestial bodies become smaller due to matter contraction, while the overall space remains predominantly intact. Thus, relative to the contracting material bodies, the total span of cosmic space appears to be becoming vaster. I attempt to explain how the contraction of matter engenders the effect of universal gravity. I use over thirty animated and graphical color visualizations in the text to make the explanation of the proposed ideas more lucid. Content Type Journal Article Category Original Paper Pages 1-39 DOI 10.1007/s10516-011-9178-4 Authors A. Alyushin, Department of Philosophy, The Higher School of Economics, 20 Myasnitskaya Street, 101000 Moscow, Russia Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Abstract Antonio Gramsci?s philosophy of praxis is characterised by the spatialisation as well as historicisation of its analytical categories. These theoretical practices are deeply intertwined in his ?absolute historicism?. Highlighting the spatiality of Gramsci?s analysis not only enables us to recover the many geographical themes in his work but also provides a useful counterweight to the emphasis on the historical dimensions of his historicism. In addition to obvious references to Gramsci?s use of spatial metaphors and his discussion of the (...) Southern Question, it is shown that many of his key concepts are best interpreted from a spatio?temporal as well as social and material perspective. After introducing the concepts of space, place and scale, the essay shows that all three are relevant to Gramsci?s analyses of issues such as language, the historical significance of the Catholic Church, the role of intellectuals, cosmopolitanism, class and class struggle, Americanism and Fordism, the nature of the Italian state, the social bases of state power, Jacobinism, passive revolution and hegemony. The essay concludes that Gramsci?s interest in place, space and scale was not merely academic but had to do with his analysis of revolutionary conjunctures. (shrink)

This paper discusses attributively limited concrete objects such as disturbances (holes, folds, scratches etc), tropes, and attitudinal objects, which lack the sort of spatial location or part structures expected of them as concrete objects. The paper proposes an account in terms of (quasi-Fregean) abstraction, which has so far been applied only to abstract objects.

Aristotle’s philosophy of geometry is widely interpreted as a reaction against a Platonic realist conception of mathematics. Here I argue to the contrary that Aristotle is concerned primarily with the methodological question of how universal inferences are warranted by particular geometrical constructions. His answer hinges on the concept of abstraction, an operation of “taking away” certain features of material particulars that makes perspicuous universal relations among magnitudes. On my reading, abstraction is a diagrammatic procedure for Aristotle, and it (...) is through imagined variation of diagrams that one can universalize spatial inferences. In order to shift the discussion of Aristotle’s work on geometry from ontological to methodological questions, I argue in the first section that geometrical properties for Aristotle are necessary accidents of the particulars, canonically diagrams, in which they inhere. I then consider a line of research that shows how diagrams in ancient geometry are not illustrations of the textual proof but are in part constitutive of geometrical inference, an insight I claim can shed light on Aristotle’s philosophical project. Next I substantiate this assertion by giving an alternative interpretation of abstraction according to which it is a diagrammatic procedure that allows a part of a particular diagram to stand in for a universal. In the last section, I consider Aristotle’s account of mathematical cognition, arguing that there is evidence for the view that imagination is necessary both for the construction of figures, and for their presentation as abstractions subject to universal inference. (shrink)

Recent research suggests that people's understanding of the abstract domain of time is dependent on the more concrete domain of space. Boroditsky and Ramscar (2002) found that spatial context influences whether people see themselves as moving through time (ego-moving perspective) or as time moving towards them (time-moving perspective). Based on studies of the embodiment of affective experience, we examined whether affect might also influence which spatial metaphor of time people adopt. The results of Experiments 1 and 2 showed (...) that participants who imagined a negative event were more likely to report that the event was approaching them, whereas those who imagined a positive event were more likely to report that they were approaching the event. Experiments 3a and 3b showed that participants judge an event to be more positive if it is described from the ego-moving perspective than if it is described from the time-moving perspective. Results from these studies provide initial evidence that positive and negative events are associated with different spatial metaphors of time. (shrink)

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of (...) physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl’s ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl. (shrink)

Methodological innovations have a special status in disciplinary histories, because they can be widely adopted and anonymised. In the 1950s, this occurred to Georges Laplace’s innovative use of 3-dimensional metric Cartesian coordinate system to record the positions of archaeological objects. This paper proposes a conceptual and social history of this process, with a focus on its spatial context, the Pyrenean region (Spain, Basque Country, and France). Main results of this research based on archives, publications, and bibliometric data, include: 1) (...) a critical discussion of the notions concerning authorship of such methodological innovations; 2) a presentation of the lesser-known aspects of Laplace’s method, showing its contribution to the abstraction and formalisation of archaeological observations and data recording; and 3) the identification of an international Pyrenean intellectual lineage of innovation regarding stratigraphy and excavation methods, from the late 19th century to the early 21th century. (shrink)

Peano's axiomatizations of geometry are abstract and non-intuitive in character, whereas Peano stresses his appeal to concrete spatial intuition in the choice of the axioms. This poses the problem of understanding the interrelationship between abstraction and intuition in his geometrical works. In this article I argue that axiomatization is, for Peano, a methodology to restructure geometry and isolate its organizing principles. The restructuring produces a more abstract presentation of geometry, which does not contradict its intuitive content but only (...) puts it into a particular form. (shrink)

n the spatialized Prisoner’s Dilemma, players compete against their immediate neighbors and adopt a neighbor’s strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without opposition, (...) or will an equilibrium of some small number of strategies emerge? Here it is shown, for finite configurations of Prisoner’s Dilemma strategies embedded in a given infinite background, that such questions are formally undecidable: there is no algorithm or effective procedure which, given a specification of a finite configuration, will in all cases tell us whether that configuration will or will not result in progressive conquest by a single strategy when embedded in the given field. The proof introduces undecidability into decision theory in three steps: by (1) outlining a class of abstract machines with familiar undecidability results, by (2) modelling these machines within a particular family of cellular automata, carrying over undecidability results for these, and finally by (3) showing that spatial configurationns of Prisoner’s Dilemma strategies will take the form of such cellular automata. (shrink)

A critical re-examination of the history of the concepts of space (including spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlighting the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein “giving up the extensional continuum … is like to breathe in airless space”). On the other hand, Planck’s discovery of the atomization of action leads to the fundamental (...) recognition of an ontology of non-spatial, abstract entities (Quine) for the quantum level of reality (QT), as distinguished from the necessarily spatio-temporal, experimental revelations (measurements). The elementary quantum act (measured by Planck’s constant) has neither duration nor extension, and any genuinely quantum process literally does not belong in the Raum and time of our experience. As Heisenberg stresses: “Während also die klassische Physik ein objectives Geschehen in Raum and Zeit zum Gegenstand hat, für dessen Existenz seine Beobachtung völlig irrelevant war, behandelt die Quantentheorie Vorgänge, die sozusagen nur in den Momenten der Beobachtung als raumzeitliche Phänomene aufleuchten, und über die in der zwischenzeit anschaulische physikalische Aussagen sinloss sind”. An admittedly speculative, hazardous conjecture is then advanced concerning the relation of such quantum ontology with the role of the pre-phenomenal continuum (Husserl) in the perception of macroscopically distinguishable objects in the Raum and time of our experience. Although rather venturesome, it brings together important philosophical issues. Coherently with recent general results in works on the foundations of QT, it is assumed that the linearity of quantum dynamical evolution does not apply to the central nervous system of living beings at a certain level of the evolutionary ramification and at the pre-conscious stage of subjectivity. Accordingly, corresponding to the onset of a non-linear dynamic evolution, a ‘primary spatial’ reduction is ‘continually’ taking place, thereby constituting the neural precondition for the experience of distinguishable macroscopic objects in the continuous spatial extension. While preventing the theoretically possible quantum superpositions of macroscopic objects from being perceivable by living beings, the ‘primary reduction’ has no effect on the standard processes concerning quantum level entities involved in laboratory man-made experiments. In this connection, an experimental check which might falsify the conjecture is briefly discussed. The approach suggested here, if sound, leads to a naturalization of that part of Kant’s Transcendental Aesthetics than can survive the Euclidean catastrophe. According to such naturalized transcendentalism, “space can well be transcendental without the axioms being so”, in agreement with a well-known statement by Boltzman. Finally, as far as QT is concerned, the conjecture entails that a scheme for quantum measurement of the von Neumann type cannot even ‘leave the ground’, vindicating Bohr’s viewpoint. A quantum theory of measurement, in a proper sense, turns out to be unnecessary and in fact impossible. (shrink)

In the spatialized Prisoner's Dilemma, players compete against their immediate neighbors and adopt a neighbor's strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without opposition, (...) or will an equilibrium of some small number of strategies emerge? Here it is shown, for finite configurations of Prisoner's Dilemma strategies embedded in a given infinite background, that such questions are formally undecidable: there is no algorithm or effective procedure which, given a specification of a finite configuration, will in all cases tell us whether that configuration will or will not result in progressive conquest by a single strategy when embedded in the given field. The proof introduces undecidability into decision theory in three steps: by (1) outlining a class of abstract machines with familiar undecidability results, by (2) modelling these machines within a particular family of cellular automata, carrying over undecidability results for these, and finally by (3) showing that spatial configurations of Prisoner's Dilemma strategies will take the form of such cellular automata. (shrink)

The present paper aims to contribute to the substantivalism versus relationalism debate and to defend general relativity (GR) against pseudoscientific attacks in a novel, especially inclusive way. This work was initially motivated by the desire to establish the incompatibility of any ether theories with accelerated cosmic expansion and inflation (motto: where would a hypothetical medium supposedly come from so fast?). The failure of this program is of interest for emergent GR concepts in high energy particle physics. However, it becomes increasingly (...) important to guard scientific results against their misrepresentation by fundamentally anti-scientific agendas. We therefore argue that although it is not known whether the perceived space-time is fundamental (rather than a condensed state or a particular membrane), in a fundamental theory, space-time must be abstract relational: fundamental space-time is the consistent spatial-temporal arrangement of events. To pursue its own goals, this work should be accessible to a wide audience: physicists, philosophers of science, those being tempted by anti-relativity theories, but also those who vigorously defend some orthodox relativity that is not actually supported by GR. It must thus be extensive in order to satisfy the different parties’ desire to have included and understood their respective positions. (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)

The more carefully we look, the more impressive the repertoire of infant concepts seems to be. Across a wide range of tasks, infants seem to be using concepts corresponding to surprisingly high-level and abstract categories and relations. It is tempting to try to explain these abilities in terms of a core capacity in spatial cognition that emerges very early in development and then gets extended beyond reasoning about direct spatial arrays and events. Although such a spatial cognitive (...) capacity may indeed form one valuable basis for later cognitive growth, it seems unlikely that it can be the sole or even primary explanation for either the impressive conceptual capacities of infants or the ways in which concepts develop. (shrink)

Conceptual realism acknowledges the existence of abstract objects: theoretical realism acknowledges the existence of non-observable objects; whereas classical realism acknowledges the existence of observable objects. Similarly, temporal realism accepts the existence of future and past events along with present ones, and spatial realism accepts the events which occur there (else-where) as well as those that occur here. We dealt earlier with the three former kinds of realism and their opposites: nominalism, instrumentalism and (ontological) idealism [2]. This paper contains an (...) examination of the two latter forms of realism: temporal and spatial, and their counterparts: temporal and spatial irrealisms. Analogies and connections between these standpoints will be the focus of the paper. (shrink)

This contribution takes as its point of departure the spatial turn in law and the notion of spatial justice. It traces the term ‘spatial justice’ as introduced through the Spatial Planning and Land Use Management Act and it looks at the underlying view of space that has influenced the spatial turn in law. It furthermore investigates the ways in which the spatial turn in law has been influenced by the thinking of Henri Lefebvre, who (...) relies on a Leibnizian conception of space. Lastly the link between Leibniz and legal positivism is considered in order to reach the final conclusion in the form of a caution against merely adding the language of spatial justice to an approach to space that remains caught up in abstract space. This will only further entrench existing fault lines in society. For this conclusion the work of Roger Berkowitz is central. Berkowitz argues convincingly that the work of Leibniz was central in the development of legal positivism, despite Leibniz in general being considered as a natural law thinker. The same applies to spatial justice theory, where the work of Leibniz is central: it may present the possibilities of another law – the law as it ought to be. The law conceptualised as ‘ought’ instead of ‘is’ would promote reconciliation. Alternatively, spatial justice can simply present the law as it ‘is’ and reconfirm and deepen the chasms in our world. (shrink)

Words, languages, symphonies, fictional characters, games, and recipes are plausibly abstract artifacts— entities that have no spatial location and that are deliberately brought into existence as a result of creative acts. Many accept that composition is unrestricted: for every plurality of material objects, there is a material object that is the sum of those objects. These two views may seem entirely unrelated. I will argue that the most influential argument against restricted composition—the vagueness argument—doubles as an argument that there (...) can be no abstract artifacts. There is no way to resist the vagueness argument against abstract artifacts that does not also undermine the vagueness argument against restricted composition. (shrink)

L’objectif de cet article est de montrer que la réflexion engagée par Jules Vuillemin sur les structures algébriques dans les années 1960 lui permettra de dégager une conception structurale de l’abstraction, dont il tirera une compréhension nomologique de l’objectivité. Ces deux concepts seront alors convoqués bien des années plus tard pour proposer une construction de l’espace représentatif, que Vuillemin conçoit comme une réfutation de l’idéalisme matériel de Berkeley. La possibilité de retracer la genèse de nos notions spatiales et de (...) leur garantir une certaine objectivité serait ainsi rendue possible par un emprunt aux méthodes de l’algèbre moderne, conformément à l’esprit de La Philosophie de l’algèbre. (shrink)

In the present essay I address the apparently problematic status of epistemology in F.W.J. Schelling’s work. Given the overblown emphasis on Schelling’s anti-Kantianism, there would seem to be little hope in articulating anything like a theory of knowledge in Schelling’s thought. For the sake of brevity I emphasize knowledge’s spatial and navigational functions in Schelling’s texts. For Schelling, the navigational is that which locates, and constructively constrains, the capacity of the subject to synthesize. This is accomplished, I argue, via (...) a spatialized reading of Schelling’s concept of intellectual intuition. While this form of intuition initially resembles that of Fichte’s, Schelling transforms the term, using it in tandem with construction, in order to maintain both the sensory immediacy, yet abstract form, of intuition as the initial means a knowing subject, immersed in the activities of nature, comes to recognize its own capacities and begins to form claims about the world. (shrink)

Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but second, (...) that if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

Previous research has linked the concept of number and other ordinal series to space via a spatially oriented mental number line. In addition, it has been shown that in visual scene recognition and production, speakers of a language with a left-to-right orthography respond faster to and tend to draw images in which the agent of an action is located to the left of the patient. In this study, we aim to bridge these two lines of research by employing a novel (...) method that measures the spatial bias produced by transitive sentences that use a wide variety of abstract and concrete verbs. Across four experiments, participants read sentences and then responded to probe words appearing on either the left or right sides of the screen. Probe words consisted of agents, patients, other words in the sentence, or newly encountered words. We found consistent lateral biases to responding to agents and patients, which appears to be independent of order of mention in the sentence but which does reflect a correspondence between position in the sentence and role in the causal sequence of the action. Our results also show that this spatial bias is driven by the use of the hands in two different ways: The left hand shows a greater sensitivity to the spatial effect than the right hand, and vocal responses produce no spatial effect. (shrink)

ABSTRACT This essay will explore the constitution of a transcendental theory of space through an examination of the notion of spatial synthesis in the works of Husserl, Paliard, and Deleuze. First, we shall explore the constitution of the sensorial fields in Husserl’s phenomenology. In Husserlian terms, space is not originally an empty form that can eventually be filled with a certain empirical content. Accordingly, the philosopher claims that spatiality is a consequence of the immanent synthesis of sensations. Then, we (...) will move on to Jacques Paliard’s psychology of perception, where we will find both aesthetic and noetic synthesis as transcendental conditions for the perception of space. Lastly, we will explore Deleuze’s theory of intensive space, specifically the concept of depth developed in a dialogue with Paliard. This comparative analysis shows that purely intensive fields of individuation are a transcendental a priori for the perception of an extensive space. (shrink)

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of (...) models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, whose satisfaction is parametrised by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided. (shrink)

How do we understand time and other entities we can neither touch nor see? One possibility is that we tap into our concrete, experiential knowledge, including our understanding of physical space and motion, to make sense of abstract domains such as time. To examine how pervasive an aspect of cognition this is, we investigated whether thought about a nonliteral type of motion called fictive motion (FM; as in The road runs along the coast) can influence thought about time. Our results (...) suggest that FM uses the same structures evoked in understanding literal motion, and that these literal aspects of FM influence temporal reasoning. (shrink)

To date, few studies have focused on mapping the mechanisms underlying children’s skills in science. This study investigated to what extent logical reasoning, spatial processing, and working memory, tapped at age 9-10-years, are predictive of physics skills at age 12-13-years. The study used a sample of 81 children (37 girls). Measures of mathematics and reading were also included in the study. Multiple regression analysis showed that spatial processing, and verbal working memory accounted for a similar amount of unique (...) variance (4.5–4.6%) while logical reasoning accounted for 5.7% variance. Physics is a multivariate discipline that draws upon numerous cognitive resources. Logical reasoning ability is a key component in order for children to learn about abstract physics facts, concepts, theories, and applying complex scientific methods. Spatial processing is important as it may sub-serve the assembly of diverse sources of visual-spatial information into a spatial-schematic image. The working memory system provides a flexible and efficient mental workspace that can supervise, coordinate, and execute processes involved in physics problem solving. (shrink)

Speakers perform manual gestures in the physical space nearest them, called gesture space. We used a controlled elicitation task to explore whether speakers use gesture space in a consistent way and whether they use space in a contrastive way when talking about abstract referents. Participants answered two questions designed to elicit contrastive, abstract discourse. We investigated manual gesture behavior. Gesture hand, location on the horizontal axis, and referent in corresponding speech were coded. We also coded contrast in speech. Participants’ overall (...) tendency to use the same hand = 13.12, p =.001, 95% CI [.31,.43], d = 2.53) and same location = 7.47, p =.001, 95% CI [.27,.47], d = 1.69) when referring to an entity was higher than expected frequency. When comparing pairs of gestures produced with contrastive speech to pairs of gestures produced with non-contrastive speech, we found a greater tendency to produce gestures with different hands for contrastive speech: = 4.19, p =.001, 95% CI [.27,.82], d = 1.42). We did not find associations between dominant side and positive concepts or between left, center, and right space and past, present, and future, respectively, as predicted by previous studies. Taken together, our findings suggest that speakers do produce spatially consistent and contrastive gestures for abstract as well as concrete referents. They may be using spatial resources to assist with abstract thinking, and/or to help interlocutors with reference tracking. Our findings also highlight the complexity of predicting gesture hand and location, which appears to be the outcome of many competing variables. (shrink)

The present study used masked repetition priming to examine whether face representations can be accessed without attention. Two experiments using a face recognition task presented masked repetition and control primes in spatially unattended locations prior to target onset. Experiment 1 used the same images as primes and as targets and Experiment 2 used different images of the same individual as primes and targets. Repetition priming was observed across both experiments regardless of whether spatial attention was cued to the location (...) of the prime. Priming occurred for both famous and non-famous targets in Experiment 1 but was only reliable for famous targets in Experiment 2, suggesting that priming in Experiment 1 indexed access to view-specific representations whereas priming in Experiment 2 indexed access to view-invariant, abstract representations. Overall, the results indicate that subliminal access to abstract face representations does not rely on attention. (shrink)

Abstract:Since 31 October 2018, Extinction Rebellion has advocated in numerous examples of civil disobedience across the UK in an attempt to call for further action to address climate change. Following this example, similar activism has also been seen across Europe and North America. Such activism falls within the context of climate justice (the framing of climate change as an ethical and political issue); given the disproportionate impacts that climate change has on the most vulnerable people in society, e.g., low-income communities, (...) women, and future generations. What is noticeable about Extinction Rebellion is its ability to place climate change on the social agenda, a task that has proven difficult in the age of denialism, skepticism, false-balance media reporting, and far-right politics. With reference to recent examples of civil disobedience and protests in 2019, this paper evaluates how climate justice movements, specifically Extinction Rebellion, change meanings of urban landscapes into becoming more contested places and disrupt the consciousness of everyday routines toward sustainability. This disruption and contested nature is brought about through changing the sociocultural dynamics of urban landscapes during, and after, such protests. The meanings of urban landscapes thus change from being viewed as purely sites of materialist consumption to sites of initial resistance against business-as-usual approaches to climate change leading to changes in policy. Through substantial public engagement with the narrative of climate justice, civil disobedience protests, and urban art, it is clear that urban areas “held” for a number of successive days have started to be perceived differently. This article concludes with implications for subsequent spatial disruption and civil disobedience advocating for stronger climate policy. (shrink)

Abstract:Atmosphere in architecture acts as a communication tool between the space and its experiencers. This tool has the potential of being detached from the physical environment and conveyed by memories and imagination, which may augment the physical environment in a poetic way. This paper aims to demonstrate this potential by utilizing the technique of comparative reading using unmanipulated photographs of physical space, computer- generated film/images of the same space, and a spatial narration/text, all in the context of Japanese architecture. (...) By viewing this context from a lens focused on the intersection of aesthetics, phenomenology, and architecture, the study points out the possibility of utilizing atmosphere as a tool to convey ideas and augment the aesthetic experience through different techniques of representation. In this way, it highlights the importance of the narrative quality of spatial atmosphere in architectural design, and its potential as a transposable spatial identity. (shrink)