Because culture plays a role in determining the aesthetic merit of a work of art, intrinsically similar works can have different aesthetic merit when assessed in different cultures. This paper argues that a form of aesthetic hedonism is best placed to account for this relativity of aesthetic value. This form of hedonism is based on a functional account of aesthetic pleasure, according to which it motivates and enables mental engagement with artworks, and an account of pleasure-learning, in which it reinforces (...) the appreciation of culture specific ways of engaging with art. (shrink)

When I act on something, three kinds of idea (or representation) come into play. First, I have a non-visual representation of my goals. Second, I have a visual description of the kind of thing that I must act upon in order to satisfy my goals. Finally, I have an egocentric position locator that enables my body to interact with the object. It is argued here that these ideas are distinct. It is also argued that the egocentric position locator functions in (...) the same way as a demonstrative, and that the involvement of such demonstratives in visual content negates naive realism. (This is a nearly final draft of a paper that is to be published in Raftopoulos and Machamer (eds), Perception, Realism, and the Problem of Reference (forthcoming from Cambridge UP. It is a shorter revised version of "Visual Reference", posted earlier.). (shrink)

Higher animals need to identify and track material objects because they depend on interactions with them for nutrition, reproduction, and social interaction. This paper investigates the perception of material objects. It argues, first, that material objects are tagged, in all five external senses, as bearers of the features detected by them. This happens through a perceptual process, here entitled Generalized Completion, which creates the appearance of objects that have properties that transcend the activation of sensory receptors. The paper shows, secondly, (...) that material objects are privileged subjects for perceived motion and interaction. That is, they are perceived as subjects for these properties while their parts seem to be subjects only derivatively. Material objects are the only perceptual subjects that are both multisensory and privileged. (shrink)

In this Handbook entry, I review how colour similarity spaces are constructed, first for physical sources of colour and secondly for colour as it is perceptually experienced. The unique hues are features of one of the latter constructions, due initially to Hering and formalized in the Swedish Natural Colour System. I review the evidence for a physiological basis for the unique hues. Finally, I argue that Tye's realist approach to the unique hues is a mistake.

This chapter contains section titles: Introduction: Russell's Natural Kinds Is Biological Homeostasis Historical? Intrinsic Properties Redux Population Structure Conclusion: Are Species Duplicable?

In “Two Ways of Thinking About Fitness and Natural Selection” (Matthen and Ariew [2002]; henceforth “Two Ways”), we asked how one should think of the relationship between the various factors invoked to explain evolutionary change – selection, drift, genetic constraints, and so on. We suggested that these factors are not related to one another as “forces” are in classical mechanics. We think it incoherent, for instance, to think of natural selection and drift as separate and opposed “forces” in evolutionary (...) change – that it makes sense to say, for instance, that selection contributed 80% to the actual evolutionary history of the human eye, and drift only 20%. We proposed instead a statistical view of the Theory of Evolution, a view in which fitness is not a cause of evolution, but rather a measure of growth. We also argued for a “hierarchical realization model” for thinking about the relationship between evolutionary factors such as those mentioned above, and suggested that in a “fully specified model”, as we call it below, there is no distinction between natural selection and evolution. (shrink)

Homeostatic Property Cluster (HPC) theory suggests that species and other biological taxa consist of organisms that share certain similarities. HPC theory acknowledges the existence of Darwinian variation within biological taxa. The claim is that “homeostatic mechanisms” acting on the members of such taxa nonetheless ensure a significant cluster of similarities. The HPC theorist’s focus on individual similarities is inadequate to account for stable polymorphism within taxa, and fails properly to capture their historical nature. A better approach is to treat distributions (...) of traits in species populations as irreducible facts, explained in terms of selection pressures, genealogy, and other evolutionary factors. We call this view Population Structure Theory (PST). PST accommodates the view, implicit in biological systematics, that species are identified by reference to particular historical populations. (shrink)

Seeing, Doing, and Knowing is an original and comprehensive philosophical treatment of sense perception as it is currently investigated by cognitive neuroscientists. Its central theme is the task-oriented specialization of sensory systems across the biological domain. Sensory systems are automatic sorting machines; they engage in a process of classification. Human vision sorts and orders external objects in terms of a specialized, proprietary scheme of categories - colours, shapes, speeds and directions of movement, etc. This 'Sensory Classification Thesis' implies that sensation (...) is not a naturally caused image from which an organism must infer the state of the world beyond; it is more like an internal communication, a signal concerning the state of the world issued by a sensory system, in accordance with internal conventions, for the use of an organism's other systems. This is why sensory states are both easily understood and persuasive.Sensory classification schemes are purpose-built to serve the knowledge-gathering and pragmatic needs of particular types of organisms. They are specialized: a bee or a bird does not see exactly what a human does. The Sensory Classification Thesis helps clarify this specialization in perceptual content and supports a new form of realism about the deliverances of sensation: 'Pluralistic Realism' is based on the idea that sensory systems coevolve with an organism's other systems; they are not simply moulded to the external world. The last part of the book deals with reference in vision. Cognitive scientists now believe that vision guides the limbs by means of a subsystem that links up with the objects of physical manipulation in ways that bypass sensory categories. In a novel extension of this theory, Matthen argues that 'motion-guiding vision' is integrated with sensory classification in conscious vision. This accounts for the quasi-demonstrative form of visual states: 'This particular object is red', and so on. He uses this idea to cast new light on the nature of perceptual objects, pictorial representation, and the visual representation of space. (shrink)

Aesthetic preferences and practices vary widely between individuals and between cultures. How should aesthetics proceed if we take this fact of aesthetic diversity, rather than the presumption of aesthetic universality, as our starting point? How should we theorize the cultural origins and cultural basis of aesthetic diversity? How should we think about the value and normativity of aesthetic diversity? In an effort to model what the turn toward diversity might look like in aesthetic inquiry, each author defends a different account (...) of aesthetic diversity, and they engage in a collective dialogue about these issues. (shrink)

How do fitness and natural selection relate to other evolutionary factors like architectural constraint, mode of reproduction, and drift? In one way of thinking, drawn from Newtonian dynamics, fitness is one force driving evolutionary change and added to other factors. In another, drawn from statistical thermodynamics, it is a statistical trend that manifests itself in natural selection histories. It is argued that the first model is incoherent, the second appropriate; a hierarchical realization model is proposed as a basis for a (...) statistical treatment. It emerges that natural selection does not cause evolution; it just is evolution. The theory incorporates relations of statistical correlation, but not the kind of causation found in fundamental physical processes. (shrink)

This volume is about the many ways we perceive. Contributors explore the nature of the individual senses, how and what they tell us about the world, and how they interrelate. They consider how the senses extract perceptual content from receptoral information. They consider what kinds of objects we perceive and whether multiple senses ever perceive a single event. They consider how many senses we have, what makes one sense distinct from another, and whether and why distinguishing senses may be useful. (...) They consider the extent to which the senses act in concert, rather than as discrete modalities, and whether this influence is epistemically pernicious, neutral, or beneficial. They explore both the familiar five sense modalities and other candidate sense modalities, including a sense for flavour, inner senses (e.g., a sense for pain), and various senses that may result from using sensory substitution devices. Contributors often represent competing views, and the methods they deploy sometimes differ from one essay to the next—with some drawing upon the sciences and engineering and others relying upon conceptual analysis. All contributors agree, nonetheless, that traditional theorizing about the senses is hampered by a neglect of the senses other than vision, and by the misconception that vision is a passive receptacle for an image thrown by a lens. And many contributors believe that it is unduly restrictive to think of perception as a collation of contents provided by individual sense modalities; they think that to understand perception properly, we need to build into our accounts the idea that the senses work together. The ambition of the volume is to begin to develop better paradigms for understanding the senses, and thereby to move toward a better understanding of perception. (shrink)

This paper presents a new account of aesthetic pleasure, according to which it is a distinct psychological structure marked by a characteristic self-reinforcing motivation. Pleasure figures in the appreciation of an object in two ways: In the short run, when we are in contact with particular artefacts on particular occasions, aesthetic pleasure motivates engagement and keeps it running smoothly—it may do this despite the fact that the object we engagement is aversive in some ways. Over longer periods, it plays a (...) critical role in shaping how we engage with objects to get this kind of pleasure from them. This account is yoked to a broadly functional understanding of art: it is not the nature of the object that makes it art, but the nature of the response that it is designed to elicit. The view does not, however, rest on individual psychology alone, as some other functional accounts do. Crucially, it is argued that shared cultural context is a key determinant of the pleasure we derive from aesthetic artefacts. The pleasure of art is always communal and communicative. (shrink)

Perceptions "present" objects as red, as round, etc.-- in general as possessing some property. This is the "perceptual content" of the title, And the article attempts to answer the following question: what is a materialistically adequate basis for assigning content to what are, after all, neurophysiological states of biological organisms? The thesis is that a state is a perception that presents its object as "F" if the "biological function" of the state is to detect the presence of objects that are (...) "F". The theory contrasts with causal/informational theories, and with internalist theories, for example those which assign content on the basis of introspected feel. Its advantages are that it permits perceptual error while at the same time allowing content to be expressed in terms of external properties. The argument of the paper is illustrated throughout by examples from biology and computational psychology. (shrink)

Philosophers and scientists have long speculated about the nature of color. Atomists such as Democritus thought color to be "conventional," not real; Galileo and other key figures of the Scientific Revolution thought that it was an erroneous projection of our own sensations onto external objects. More recently, philosophers have enriched the debate about color by aligning the most advanced color science with the most sophisticated methods of analytical philosophy. In this volume, leading scientists and philosophers examine new problems with new (...) analytic tools, considering such topics as the psychophysical measurement of color and its implications, the nature of color experience in both normal color-perceivers and the color blind, and questions that arise from what we now know about the neural processing of color information, color consciousness, and color language. Taken together, these papers point toward a complete restructuring of current orthodoxy concerning color experience and how it relates to objective reality. Kuehni, Jameson, Mausfeld, and Niederee discuss how the traditional framework of a three-dimensional color space and basic color terms is far too simple to capture the complexities of color experience. Clark and MacLeod discuss the difficulties of a materialist account of color experience. Churchland, Cohen, Matthen, and Westphal offer competing accounts of color ontology. Finally, Broackes and Byrne and Hilbert discuss the phenomenology of color blindness. Contributors: Justin Broackes, Alex Byrne, Paul M. Churchland, Austen Clark, Jonathan Cohen, David R. Hilbert, Kimberly A. Jameson, Rolf Kuehni, Don I.A. MacLeod, Mohan Matthen, Rainer Mausfeld, Richard Niederée, Jonathan Westphal The hardcover edition does not include a dust jacket. (shrink)

The Introduction discusses determinables and similarity spaces and ties together the contributions to Color Ontology and Color Science.

Memory seems intuitively to consist in the preservation of some proposition (in the case of semantic memory) or sensory image (in the case of episodic memory). However, this intuition faces fatal difficulties. Semantic memory has to be updated to reflect the passage of time: it is not just preservation. And episodic memory can occur in a format (the observer perspective) in which the remembered image is different from the original sensory image. These difficulties indicate that memory cannot be preserved content. (...) It is proposed that what is preserved in memory isan underlying "trace", and that in every act of remembering, memorial content is reconstructed from the preserved trace. (shrink)

We have argued elsewhere that: (A) Natural selection is not a cause of evolution. (B) A resolution-of-forces (or vector addition) model does not provide us with a proper understanding of how natural selection combines with other evolutionary influences. These propositions have come in for criticism recently, and here we clarify and defend them. We do so within the broad framework of our own “hierarchical realization model” of how evolutionary influences combine.

How many senses do humans possess? Five external senses, as most cultures have it—sight, hearing, touch, smell, and taste? Should proprioception, kinaesthesia, thirst, and pain be included, under the rubric bodily sense? What about the perception of time and the sense of number? Such questions reduce to two. 1. How do we distinguish a sense from other sorts of information-receiving faculties? 2. By what principle do we distinguish the senses? Aristotle discussed these questions in the De Anima. H. P. Grice (...) revived them in 1967. More recently, they have taken on fresh interest as a result of a collection of essays edited by Fiona Macpherson. This entry reviews some approaches to these questions and advances some new ideas for the reader’s consideration. It proposes that the senses constitute an integrated learning system, membership in which answers question 1. It also proposes that the modalities can be distinguished from one another in two ways, by the means of information pick-up and by the kinds of activity that a perceiver undertakes to make use of them. (shrink)

A hitherto neglected form of explanation is explored, especially its role in population genetics. “Statistically abstractive explanation” (SA explanation) mandates the suppression of factors probabilistically relevant to an explanandum when these factors are extraneous to the theoretical project being pursued. When these factors are suppressed, the explanandum is rendered uncertain. But this uncertainty traces to the theoretically constrained character of SA explanation, not to any real indeterminacy. Random genetic drift is an artifact of such uncertainty, and it is therefore wrong (...) to reify it as a cause of evolution or as a process in its own right. *Received July 2009. †To contact the author, please write to: Department of Philosophy, University of Toronto, 170 St. George St., Toronto, ON M5R 2M8, Canada; e‐mail: mohan.matthen@utoronto.ca. (shrink)

What is color? What is color vision? Most philosophers answer by reference to humans: to human color qualia, or to the environmental properties or "quality spaces" perceived by humans. It is argued, with reference to empirical findings concerning comparative color vision and the evolution of color vision, that all such attempts are mistaken. An adequate definition of color vision must eschew reference to its outputs in the human cognition and refer only to inputs: color vision consists in the use of (...) wavelength discrimination in the construction of visual representations. A color quality is one that is generated from such processing. (shrink)

What colour does a white wall look in the pinkish light of the late afternoon? Philosophers disagree: they hold variously that it looks pink, white, both, and no colour at all. A new approach is offered. After reviewing the dispute, a reinterpretation of perceptual constancy is offered. In accordance with this reinterpretation, it is argued that perceptual features such as color must always be predicated of perceptual objects. Thus, it might be that in pinkish light, the wall looks white and (...) the light looks pink. The paper concludes by discussing some criteria for object identification in perceptual states. (shrink)

Two questions are addressed in this paper. First, what is it to see? I argue that it is veridical experience of things outside the perceiver brought about by looking. Second, what is it to see a material object? I argue that it is experience of an occupant of a spatial region that is a logical subject for other visual features, able to move to another spatial region, to change intrinsically, and to interact with other material objects. I show how this (...) theory is different from the idea that object-seeing is merely the visual segregation of a region of the visual field. Finally, I argue that we do not object-see objects reflected in mirrors, surfaces of back-lit objects, and depictions of objects. (shrink)

Molyneux's Question (MQ) concerns whether a newly sighted man would recognize/distinguish a sphere and a cube by vision, assuming he could previously do this by touch. We argue that (MQ) splits into questions about (a) shared representations of space in different perceptual systems, and about (b) shared ways of constructing higher dimensional spatiotemporal features from information about lower dimensional ones, most of the technical difficulty centring on (b). So understood, MQ resists any monolithic answer: everything depends on the constraints faced (...) by particular perceptual systems in extracting features of higher dimensionality from those of lower. Each individual question of this type is empirical and must be investigated separately. We present several variations on MQ based on different levels of dimensional integration—some of these are familiar, some novel adaptations of problems known elsewhere, and some completely novel. Organizing these cases in this way is useful because it unifies a set of disparate questions about intermodal transfer that have held philosophical and psychological interest, suggests a new range of questions of the same type, sheds light on similarities and differences between members of the family, and allows us to formulate a much-augmented set of principles and questions concerning the intermodal transfer of spatiotemporal organization. (shrink)

Perception has been for philosophers in the last few decades an area of compelling interest and intense investigation. Developments in contemporary cognitive science and neuroscience has thrown up new information about the brain and new conceptions of how sensory information is processed and used. These new conceptions offer philosophers opportunities for reconceptualising the senses--what they tell us, how we use them, and the nature of the knowledge they give us. Today, the philosophy of perception resonates with ideas that had not (...) even been articulated in the 1970s and 1980s. This Handbook is a survey by leading philosophical thinkers of contemporary issues and new thinking in philosophy of perception. It includes sections on the history of the subject, introductions to contemporary issues in the epistemology, ontology and aesthetics of perception, treatments of the individual sense modalities and of the things we perceive by means of them, and a consideration of how perceptual information is integrated and consolidated. New analytic tools and applications to other areas of philosophy are discussed in depth. Each of the entries is written by a leading expert, some collaborating with younger figures; each seeks to introduce the reader to a broad range of issues. All contain new ideas on the topics covered; together they demonstrate the vigour and innovative zeal of a young field. (shrink)

The sense of touch provides us knowledge of two kinds of events. Tactile sensation (T) makes us aware of events on or just below the skin; haptic perception (H) gives us knowledge of things outside the body with which we are in contact. This paper argues that T and H are distinct experiences, and not (as some have argued) different aspects of the same touch-experience. In other words, T ≠ H. Moreover, H does not supervene on T. Secondly: In T, (...) we are aware of immanent, phenomenal qualities; in H, we come to know of transcendent qualities in things that exist independently of ourselves. Finally: T is non-spatial; it is indexed by parts of the body, but not by position in space. H, by contrast, is spatial. This brings to mind Kant’s contention that things are presented as existing objectively when they are represented spatially. (shrink)

This paper defends two theses about sensory objects. The more general thesis is that directly sensed objects are those delivered by sub-personal processes. It is shown how this thesis runs counter to perceptual atomism, the view that wholes are always sensed indirectly, through their parts. The more specific thesis is that while the direct objects of audition are all composed of sounds, these direct objects are not all sounds—here, a composite auditory object is a temporal sequence of sounds (whereas a (...) composite visual object is a spatial composite). Many composite objects are directly heard in the sense just mentioned. There is a great variety of such composite auditory objects—melodies, harmonies, sequences of phonemes, individual voices, meaning-carrying sounds, and so on. This diversity of auditory objects has an important application to aesthetics. Perceivers do not naturally or easily attend simultaneously to auditory objects that overlap in time. Yet, aesthetic appreciation depends on such an allocation of attention to overlapping objects. (shrink)

This collection of 25 essays by leading researchers provides an overview of the state of the field.

We perceive in many ways. But several dubious presuppositions about the senses mask this diversity of perception. Philosophers, scientists, and engineers alike too often presuppose that the senses (vision, audition, etc.) are independent sources of information, perception being a sum of these independent contributions. We too often presuppose that we can generalize from vision to other senses. We too often presuppose that vision itself is best understood as a passive receptacle for an image thrown by a lens. In this essay (...) we illustrate how reflection on results from the cognitive sciences undermine these (and many other) traditional presuppositions. Our illustration situates the remaining essays in the volume, Perception and its Modalities, which further extend the case against various traditional presuppositions, and offer alternatives ways to understand the senses and their role in perception. While many of the essays in this volume represent competing views and draw on different fields, from conceptual analysis to engineering, most contributors believe that to understand perception properly, we need to treat as foundational the idea that the senses work together. From that agreement, new paradigms for theorizing about perception begin to emerge. (shrink)

Food has savour: a collection of properties (including appearance, aroma, mouth-feel) connected with the pleasure (or displeasure) of eating. After explaining this concept, and outlining a theory of aesthetic pleasure, I argue that, like paradigm examples of art, savour can be assessed relative to a culturally determined set of norms. Also like paradigm examples of art, the assessment of savour has no objective basis in the absence of such cultural norms. My argument in this paper is part of a larger (...) project in which I develop an account of the pleasure of art. It is a virtue (I claim) of my approach that it permits a much greater diversity of artforms than traditional philosophical aesthetics is inclined to allow. This includes food. (shrink)

The paper argues that material objects are the primary referents of visual states -- not places, as Austen Clark would have it in his A Theory of Sentience.

Art is universal across cultures. Yet, it is biologically expensive because of the energy expended and reduced vigilance. Why do humans make and contemplate it? This paper advances a thesis about the psychological origins of perceptual art. First, it delineates the aspects of art that need explaining: not just why it is attractive, but why fine execution and form—which have to do with how the attraction is achieved—matter over and above attractiveness. Second, it states certain constraints: we need to explain (...) pleasure in contemplation, not value extracted from the object by activities other than contemplation. The theory is that aesthetic pleasure is a motivation for learning skills. Two forms of pleasure are postulated. The first accompanies the spontaneous activity necessary for learning a more or less universal basic level of skill. The second accompanies highly skilled activity. This second kind of pleasure is specific to art as such. (shrink)

Argues for a category of “cognitive feelings”, which are representationally significant, but are not part of the content of the states they accompany. The feeling of pastness in episodic memory, of familiarity (missing in Capgras syndrome), and of motivation (that accompanies desire) are examples. The feeling of presence that accompanies normal visual states is due to such a cognitive feeling; the “two visual systems” are partially responsible for this feeling.

The author investigates greek ontologies that apparently rely on a conflation of "binary" (x is f) and "monadic" (x is) uses of 'is'. He uses Aristotelian and other texts to support his proposal that these ontologies are explained by the Greeks using two alternative semantic analyses for 'x is F'. The first views it as asserting a relation between x and F, the second as asserting that a "predicative complex" exists, where a predicative complex is a complex consisting of x (...) and F. The article concludes by indicating some uses for the novel concept of predicative complex in aristotelian interpretation. (shrink)

I can be wrong about things I seem to perceive; the conditions might lead me to be mistaken about them. Since I can't rule out the possibility that the conditions are misleading, I can't be sure that I am perceiving this thing in my hand correctly. But suppose that I am able to examine it actively—handling it, looking closer, shining a light on it, and so on. Then, my level of uncertainty goes down; in the limit it is eliminated entirely. (...) Of course, I might be mistaken because I am a brain in a vat, or because some other sceptical scenario obtains. But sceptical scenarios apply not just to this thing in my hand, but to everything all at once. Define "empirical certainty" as the absence of the kind of doubt that spreads to all empirical states of affairs. Sensory exploration, or active examination, can in principle lead to empirical certainty. (shrink)

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

The senses present their content in the form of images, three-dimensional arrays of located sense features. Peacocke’s “scenario content” is one attempt to capture image content; here, a richer notion is presented, sensory images include located objects and features predicated of them. It is argued that our grasp of the meaning of these images implies that they have propositional content. Two problems concerning image content are explored. The first is that even on an enriched conception, image content has certain expressive (...) limitations. In particular, it cannot express absolute location and time (as opposed to spatiotemporal relations) or logical complexity. Yet, perceptual experience does seem to express certain absolute locations—namely, here and now. How can it do so? Secondly, image content cannot exhaust the significance of perceptual states. This is proved by noting that perception, memory, and anticipation can have the same image content. Yet they have different significance. These problems show that some of the significance of sensory states comes from outside the image. (shrink)

This is the editors' Introduction to a special issue of the journal, Multisensory Research. European philosophers of the modern period found multisensory perception to be impossible because they thought that perceptual ideas are defined by how they are experienced. Under this conception, the individual modalities are determinables of ideas—just as colour is a determinable that embraces red and blue, so also the visual is a determinable that embraces colour and (visually experienced) shape. Since no idea is experienced as, for example, (...) both visual and auditory, there can be no such thing as audiovisual perception. This conception of modality is not directly contested, but a variety of perceptual phenomena are listed that could raise interesting questions if treated as multimodal in origin. (shrink)

Molyneux asked whether a newly sighted person could distinguish a sphere from a cube by sight alone, given that she was antecedently able to do so by touch. This, we contend, is a question about general ideas. To answer it, we must ask (a) whether spatial locations identified by touch can be identified also by sight, and (b) whether the integration of spatial locations into an idea of shape persists through changes of modality. Posed this way, Molyneux’s Question goes substantially (...) beyond question (a), about spatial locations, alone; for a positive answer to (a) leaves open whether a perceiver might cross-identify locations, but not be able to identify the shapes that collections of locations comprise. We further emphasize that MQ targets general ideas so as to distinguish it from corresponding questions about experiences of shape and about the property of tangible (vs. visual) shape. After proposing a generalized formulation of MQ, we extend earlier work (“Many Molyneux Questions,” Australasian Journal of Philosophy 2020) by showing that MQ does not admit a single answer across the board. Some integrative data-processes transfer across modalities; others do not. Seeing where and how such transfer succeeds and fails in individual cases has much to offer to our understanding of perception and its modalities. (shrink)

Cognitive definitions cannot accommodate fear as it occurs in species incapable of sophisticated cognition. Some think that fear must, therefore, be noncognitive. This paper explores another option, arguably more in line with evolutionary theory: that like other "biological universals" fear admits of variation across and within species. A paradigm case of such universals is species: it is argued that they can be defined by ostension in the manner of Putnam and Kripke without implying that they must have an invariable essence. (...) Emotions can be defined in this way too, in principle, but the theoretical understanding of homology necessary to do so is lacking at present. (shrink)