Representing part–whole relations in conceptual spaces

In this paper, we propose a cognitive semantic approach to represent part–whole relations. We base our proposal on the theory of conceptual spaces, focusing on prototypical structures in part–whole relations. Prototypical structures are not accounted for in traditional mereological formalisms. In our account, parts and wholes are represented in distinct conceptual spaces; parts are joined to form wholes in a structure space. The structure space allows systematic similarity judgments between wholes, taking into consideration shared parts and their configurations. A point in the structure space denotes a particular part structure; regions in the space represent different general types of part structures. We argue that the structural space can represent prototype effects: structural types are formed around typical arrangements of parts. We also show how structure space captures the variations in part structure of a given concept across different domains. In addition, we discuss how some taxonomies of part–whole relations can be understood within our framework.     

Partial Monotonic Protothetics

This paper has four parts. In the first part, I present Leniewski's protothetics and the complete system provided for that logic by Henkin. The second part presents a generalized notion of partial functions in propositional type theory. In the third part, these partial functions are used to define partial interpretations for protothetics. Finally, I present in the fourth part a complete system for partial protothetics. Completeness is proved by Henkin's method [4] using saturated sets instead of maximally saturated sets. This technique provides a canonical representation of a partial semantic space and it is suggested that this space can be interpreted as an epistemic state of a non-omniscient agent.     

Some open problems in the philosophy of space and time

This article is concerned to formulate some open problems in the philosophy of space and time that require methods characteristic of mathematical traditions in the foundations of geometry for their solution. In formulating the problems an effort has been made to fuse the separate traditions of the foundations of physics on the one hand and the foundations of geometry on the other. The first part of the paper deals with two classical problems in the geometry of space, that of giving operationalism an exact foundation in the case of the measurement of spatial relations, and that of providing an adequate theory of approximation and error in a geometrical setting. The second part is concerned with physical space and space-time and deals mainly with topics concerning the axiomatic theory of bodies, the operational foundations of special relativity and the conceptual foundations of elementary physics.     

The spatial intersection of minds

Spatial formats of information are ubiquitous in the cognitive and neural sciences. There are neural uses of space in the topographic maps found throughout cortex. There are metaphorical uses of space in cognitive linguistics, physical uses of space in ecological psychology, and mathematical uses of space in dynamical systems theory. These varied informational uses of space each provide a single contiguous medium through which cognitive processes can be shared across subsystems. As we further develop our understanding of how the human mind processes information in real time, the continuous sharing and cascading of information patterns between brain areas can be extended to a sharing and cascading of information between multiple brains and bodies to produce coordinated behavior. Essentially, the way you and the people around you negotiate your shared space affects the way you think, because space is a fundamental part of how you think. It is via space that the mental processes of one mind can form an intersection with the mental processes of another mind.     

The effect of limb crossing and limb congruency on multisensory integration in peripersonal space for the upper and lower extremities

The present study investigated how multisensory integration in peripersonal space is modulated by limb posture (i.e. whether the limbs are crossed or uncrossed) and limb congruency (i.e. whether the observed body part matches the actual position of one’s limb). This was done separately for the upper limbs (Experiment 1) and the lower limbs (Experiment 2). The crossmodal congruency task was used to measure peripersonal space integration for the hands and the feet. It was found that the peripersonal space representation for the hands but not for the feet is dynamically updated based on both limb posture and limb congruency. Together these findings show how dynamic cues from vision, proprioception, and touch are integrated in peripersonal limb space and highlight fundamental differences in the way in which peripersonal space is represented for the upper and lower extremity.     

Embodied perception of reachable space: how do we manage threatening objects?

This study aimed at determining whether the size of reachable space is affected by the level of danger of some everyday manipulable objects. Two possibilities are examined: Dangerous objects affect the size of reachable space because of long-term semantic knowledge of their potential hurtful value or the on-line relation between objects’ dangerous attributes and the body. The experimental paradigm combined the danger value (dangerous/not dangerous) and the orientation of objects (e.g. pointing away from/towards the perceiver). Reachability judgments measured the size of peripersonal space, and perception of objects’ danger was estimated through questionnaires. Results revealed that, whatever the estimated level of objects’ danger, the extent of peripersonal space was reduced when the threatening part of dangerous objects was oriented towards participants, not when oriented away. This suggests that the characteristics of the here and now body-objects interaction are crucial in affecting the boundary of peripersonal space.     

A theory of magnitude: common cortical metrics of time, space and quantity

Research into the perception of space, time and quantity has generated three separate literatures. That number can be represented spatially is, of course, well accepted and forms a basis for research into spatial aspects of numerical processing. Links between number and time or between space and time, on the other hand, are rarely discussed and the shared properties of all three systems have not been considered. I propose here that time, space and quantity are part of a generalized magnitude system. I outline A Theory Of Magnitude (ATOM) as a conceptually new framework within which to re-interpret the cortical processing of these elements of the environment.     

Embodied perception of reachable space: how do we manage threatening objects?

This study aimed at determining whether the size of reachable space is affected by the level of danger of some everyday manipulable objects. Two possibilities are examined: Dangerous objects affect the size of reachable space because of long-term semantic knowledge of their potential hurtful value or the on-line relation between objects' dangerous attributes and the body. The experimental paradigm combined the danger value (dangerous/not dangerous) and the orientation of objects (e.g. pointing away from/towards the perceiver). Reachability judgments measured the size of peripersonal space, and perception of objects' danger was estimated through questionnaires. Results revealed that, whatever the estimated level of objects' danger, the extent of peripersonal space was reduced when the threatening part of dangerous objects was oriented towards participants, not when oriented away. This suggests that the characteristics of the here and now body-objects interaction are crucial in affecting the boundary of peripersonal space.     

Invasions of personal space and helping: Mediating effects of invader's apparent need

A field experiment was conducted to examine the influence of invasions of personal space and invader's apparent need upon subsequent helping. On the basis of previous research, it was predicted that helping would be inhibited by invasions of personal space when the invader's apparent need for assistance was low, but would actually be facilitated by such intrusions when his/her apparent need for assistance was high. Results offered support for both of these predictions. Additional findings suggested that these differential effects of invasions of personal space may have stemmed, at least in part, from the induction of contrasting affective reactions among subjects under conditions of low and high apparent need.     

Relations between multidimensional scaling and three-mode factor analysis

A combination is achieved of two lines of psychometric interest: a) multidimensional scaling and b) factor analysis. This is accomplished with the use of three-mode factor analysis of scalar product matrices, one for each subject. Two of the modes are the groups of objects scaled and the third mode is the sample of subjects. Results are an object space, a person space, and a system for changing weights given to dimensions and of angles between dimensions in the object space for individuals located at different places in the person space. The development is illustrated with data from an adjective similarity study.Supported in part by the Personnel and Training Branch of the Office of Naval Research under Contract Number 00014-67-A-0305-0003. A number of very helpful comments were made by an anonymous editorial reviewer forPsychometrika.During 1970–71 at the L. L. Thurstone Psychometric Laboratory, University of North Carolina.     

Multiple 3-D interpretations in a classic stereokinetic effect

It is known that a flat ellipse rotating in the frontoparallel plane sooner or later appears as a rigid circular disc tilting in 3-D space. An experiment is reported in which prolonged exposure to the same flat pattern produces a second previously unnoticed 3-D percept: an elongated egg slanted in 3-D space, which points towards the observer and the end parts of which describe a circular trajectory in the frontal plane. It is shown that the achievement of this alternative percept is not affected by the particular shape of the ellipse, although the time needed to reach it increases with an ellipse with a 2:3 axis ratio.     

The Holy See: The Individual and the Group-Intersubjective Meetings

The analytic group is a space where powerful meetings between the various selves of its members occur. These meetings have the potential to facilitate processes of mutual recognition and the development of multiple selves, on one hand, but may also lead to collapse of the potential space and experiences of destruction, on the other. Group and individual processes of recognition and destruction may be dramatic and require special coping on the part of the leader (mainly in situations of impasse), or they may be more subtle, almost unnoticeable. Both in the case of the big dramas and in the case of the little dramas, the possibility for surrender, for movement toward unfamiliar areas within one or more of the participants, is what furthers the group's development. In the current paper, I apply intersubjective concepts to group work and, more precisely, propose a way of looking at how the group and the group leader can act to expand the intersubjective space in order to enable processes of destruction and recognition to coexist without the potential space collapsing.     

Husserl on Geometry and Spatial Representation

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.     

The Drexel Disk: Hypertext-based instructional software as a tool for the exploration of a constrained knowledge space

In this paper, an example of multi-functional, transportable instructional software is described. The software provides the user with a constrained knowledge space and the necessary tool to explore it. Relying heavily on graphics and hypertext linkages, the software is easy to use; it is distributed throughout the university as part of a solution to the problems of training and supporting microcomputer users.     

F. A. Trendelenburg and the Neglected Alternative

Despite his impressive influence on nineteenth-century philosophy, F. A. Trendelenburg's own philosophy has been largely ignored. However, among Kant scholars, Trendelenburg has always been remembered for his feud with Kuno Fischer over the subjectivity of space and time in Kant's philosophy. The topic of the dispute, now frequently referred to as the ‘Neglected Alternative’ objection, has become a prominent issue in contemporary discussions and interpretations of Kant's view of space and time. The Neglected Alternative contends that Kant unjustifiably moves from the claim that we have a priori intuitions of space and time to the sceptical conclusion that space and time are exclusively subjective. Most current discussions trace the objection back to Trendelenburg and often use him to motivate the objection. However, to date Trendelenburg's actual arguments and reasons for rejecting the Kantian view of space and time have not been sufficiently uncovered; my goal here is to fill this lacuna. By better understanding what Trendelenburg actually argued, we will be in a better position to assess whether the Neglected Alternative objection against Kant is successful. But in addition, Trendelenburg's own system is of independent philosophical interest, and my work here will shed light on one part of it.     

Against Matricide: Rethinking Subjectivity and the Maternal Body

In this article I critically re‐examine Julia Kristeva's view that becoming a speaking subject requires psychical matricide: violent separation from the maternal body. I propose an alternative, non‐matricidal conception of subjectivity, in part by drawing out anti‐matricidal strands in Kristeva's own thought, including her view that early mother–child relations are triangular. Whereas she understands this triangle in terms of a first imaginary father, I re‐interpret this triangle using Donald Winnicott's idea of potential space and Jessica Benjamin's idea of an intersubjective space of thirdness. I argue that this space provides a maternal third term: a relation of connection and difference between two, a relation that inherits the affective, mobile, generative qualities of the maternal body as the infant (according to Kristeva) imagines it. This connecting space allows both mothers and children to emerge as subjects in their own right. I then suggest that potential‐maternal space expands into language, so that language intrinsically allows the possibility of a speaking position of connection with the mother. Entrance into language need not entail separation or matricide: the problem is not language as such but the particular way that speech and logos have been defined historically.     

Space, Time and Documents in a Refrigerated Warehouse

In a refrigerated warehouse, workers organize distribution and exchange of frozen seafood by the spatial and temporal arrangement of loads. Using videotapes of workers' activities and interviews, this paper investigates how workers organize space, time and artifacts in the activity of frozen seafood distribution and exchange, and how organized space, time and artifacts systematize workers' multiple courses of actions and give direction to them. Particular attention is paid to how the workers use artifacts such as various documents and computers as part of their practices, because the activity of distribution and exchange in this workplace is regarded as the activity of organizing space and time with various artifacts in multiple contexts. Through the analysis of situated literacy of using artifacts, it was shown that the activity of using artifacts is always embedded in multiple contexts. At the same time, diverse artifacts organize multiple contexts of work. Thus, there is the reflexive interaction between the artifacts and the contexts.     

The EPR-Experiment and Free Process Theory

As part of the ‘creation-discovery’ interpretation of quantum mechanics Diederik Aerts presented a setting with macroscopical coincidence experiments designed to exhibit significant conceptual analogies between portions of stuff and quantum compound entities in a singlet state in Einstein—Podolsky—Rosen/Bell-experiments (EPR-experiments). One important claim of the creation-discovery view is that the singlet state describes an entity that does not have a definite position in space and thus ‘does not exist in space’. ‘Free Process Theory’ is a recent proposal by Johanna Seibt of an integrated ontology, i.e., of an ontology suitable for the interpretation of theories of the macrophysical and microphysical domain (quantum field theory). The framework of free process theory allows us to show systematically the relevant analogies and disanalogies between Aerts' experiment and EPR-experiments. From free process ontology it also follows quite naturally that the quantum compound entity described by the singlet state ‘does not exist in space.’