In the last posting I spoke of the ‘phenomenal space’ of subjective being and how the facts of our embodiment bring with them an intuitive understanding of space. This space has particular characteristics that flow from the nature of our embodiment and from the environment in which that embodiment comes together. What I would like to indicate here is that we also live in other, complementary spaces which also inform how we construct thought and meaning.
In the appendix to his book on relativity theory (2003) the physicist David Bohm addressed some of the issues around perception that come out of some of the idea in that book. Part of this concerns the relationship between perception and space and how the ability to occupy different positions in space changes the nature of perception and the objects that such perception embraces. He gives the example of seeing an ellipse, perhaps the ellipse formed by looking at the top of a coffee cup as it is held in the hand prior to drinking from it. Even though the visual image presented to the organ of sense, the eye, is this ellipse it is not seen as such. Perception seamlessly interprets the top of the cup as circular, even though we at no point see this circle in its most essential form (if we did we would have a lapful of coffee). The process at work here is that the visual sensorimotor system responsible for engaging with the top of the cup is not stationary, fixing its gaze unswervingly on this object. Instead it is an eye in motion (even if that motion is relatively slight) and each motion of eye, head, hand, and arm changes the orientation of the cup to our eye and simultaneously changes the shape of the ellipse in lockstep with this motion. Extrapolating from this constantly changing but systematically related data the perception of the top of the cup is made up not from a single viewpointed image but of this extrapolation, the circle we rarely see. This process points up an understanding of space in which it is not only egocentrically oriented around the axis of the unmoving situated body. The space that Bohm indicates is one in which our ability to move and to quite literally see things from different angles is taken into account. In this space there is no inevitable perspectivalism, and the railway tracks which lead off toward the horizon are seen as the parallel lines that they surely are. This is the scientific method in miniature, in which the evidence of the senses are peer reviewed by those same senses but from other places and at other times.
There is also another space, perhaps an extension of the last, which arises from our being in a world shared by other beings with similar senses. The space that I occupy is also entertained by you and by others, and the number of eyes which look out onto this space multiply accordingly. Experiencing this space involves social processes and the sharing of sense through interpersonal and extrapersonal means. This is the kind of sense which one gains from learning and becoming informed. It is common sense because it is held in common, available not only to one individual through the intuitive sense of their subjective embodiment but to anyone who cares to learn. The common sense alluded to here, whilst it may offer a viewpoint on the universe which seems, to some at least, arbitrary, gyratory, and lacking the privilege of centeredness, is also a sense which places our eyes everywhere and gives us what Thomas Nagel (1986) paradoxically referred to as ‘the view from nowhere’. In the vast incomprehensibility of space there is not a single place anywhere that one cannot conceive oneself as occupying and the totality of one’s image of the universe is a collation of all these possible viewing positions.
It seems likely, therefore, that we are creatures who simultaneously inhabit not one space but several. There is the space of subjectivity and self-centeredness, in which the world radiates out from one’s body, diminishing with distance in both size and importance until it disappears over the horizon, and there is the space of experience which presents the world to us in the different ways available to mobile animals; And then there is the space of objectivity, in which we occupy all the centres of the universe at once and the peripheral horizon disappears. The first space is our birthright; the product of our animal embodiment and our embeddedness in the environment. The second we earn through motion and exploration. The third is our New Found Land; the result of the gradual enlightenment of our species and the vision admitted by that light.
When Primack and Adams (2006) draw attention to the potential for existential anomie afforded by the internalization of Newtons’s impersonal space, they are reminding us that such learning is not only the acquisition of rational, disembodied facts. They recognize that the images we hold of space, on the grandest scale possible, are also constructive of the fabric of our understanding. The intuition that comes with subjective embodiment is joined by other intuitions, which may at times be at odds with the first. Each of these spaces is at work in our cognition, and each is active in our intuitions. Each appears, unbidden and often invisible, in the poetics of our language, and each space is used to contain the ideas and objects of our experience, the stuff of meaning and thought.
BOHM, D. & NICHOL, L. (2003) The essential David Bohm, London, Routledge.
NAGEL, T. (1986) The view from nowhere, New York, OUP.
PRIMACK, J. R. & ABRAMS, N. E. (2006) The view from the centre of the universe, London, Fourth Estate.
In the last entry I began to unpack what kinds of variables mark out the category of those entities we think of as ‘objects’, including such aspects as size, shape, substance, weight, etc. What I want to move onto here is a discussion of the overall category of ‘objects’ as a whole.
Until recently it was widely assumed to be the case that our ability to understand our perceptions, concepts, and experiences in terms of distinctions between types was modeled on what are sometimes called ‘classical’ categories. That is, experiences could be grouped together according to whatever necessary and sufficient conditions served to define that category. So, for example an even number is a category of integer in which the necessary condition is that it be wholly divisible by two. This is not a sufficient condition however as we must also require that this division leaves no remainder or involves no fraction. We can say therefore, that any number that we generate, providing these conditions are met, is a member of the category of even numbers. Any number which does not meet these conditions cannot be placed in this category. These conditions define the terms of what it means to say that any number is even.
It should be evident from this that classical categorization, in setting up clear definitions based on necessary and sufficient conditions, establishes a form in which any entity, a number in this case, is either a member or not a member of such a category. There are no liminal cases, no fuzzy boundaries, and no irregularities. This clarity is, indeed, the strength of such a method, and classical categorization underpins much taxonomy and typing, as well as Aristotelian logic and the Law of the Excluded Middle, and is the default method of categorization employed within most (disembodied) systems of organization from the separate branches on Diderot and D’Alembert’s tree of knowledge to the Dewey Decimal system in our libraries. As a means of structuring information such that it is impersonal and apparently rational it is stunningly effective; the only drawback is that, when it comes to understanding how categories are constructed within human cognition and human epistemology, it is woefully inadequate.
The major studies into human systems of categorization were initially carried out by Eleanor Rosch (1973, 1983), although this work has been significantly advanced by George Lakoff (1990). Rosch’s work consisted of a series of survey-type experiments in which subjects were offered lists of items in a particular category, say birds, and were invited to put a number next to each item indicating to what extent it was felt to belong to the category. On the face of it this experiment should be nonsensical. If we do use systems of categorization based on definitions formed out of necessary and sufficient conditions then we should simply compare each item on the list to our definition and either say it meets the conditions and is, in this case, a bird, or say that the conditions are not met and it isn’t. The idea of placing different birds along a numerical scale of how ‘birdlike’ they are should be meaningless. This is not what Rosch found however. Subjects given this task found it intuitively obvious that some birds were indeed better representatives of the category than others and were able to allocate a number to quantify this level of membership. Perhaps unsurprisingly, those examples which were given the highest ‘mark’ for birdness were blackbirds, robins, and sparrows, whilst the low scorers were penguins, ostriches, and emus. This finding has been interpreted to suggest that whilst in certain specific practices we do indeed use classical categories; in scientific avian taxonomy for example, in practice we do not classify according to definition but according to prototype. In cognitive terms, and therefore in terms of our intuitive epistemology, we form categories around central prototypical examples, with other members of that category radiating outward and becoming less and less typical the further out they go.
It might be tempting to suspect that, in choosing birds as a category, Rosch singled out a particularly difficult set to define and distinguish, and that more self-evidently logical categories would not show these effects of prototypicality. However, this experiment has been repeated with other sets including furniture (Rosch, 1983) and numbers. Sharon Lee Armstrong and colleagues (1983) found that the category EVEN NUMBERS exhibits typicality effects: participants in their experiments consistently rated certain member of the category including ‘2’, ‘4’, ‘6’, and ‘8’, as ‘better’ examples of the category than, say, ‘98’ or ’10,002’. We can say from this therefore, that the categories we use to organise our cognition significantly centre on such prototypes and have a radial structure with a fuzzy boundary.
To return to the concept of ‘object’ which began this section of writing, and to begin to apply this revised concept of what a category is, we might say that, whilst a prototypical material object might exhibit the features outlined by Stockwell above, our understanding of the general category of objects is likely to extend outward from this point to include less typical examples. It is also inevitable that there will be no clear line dividing those experiences or perceptions which we think of as ‘objects’ from those which we do not.
A glance around the room or out of the window will confirm the truth of that inevitability. I am looking at the chair across from where I am typing these words, and it seems to fulfill most of the criteria that Stockwell draws up. It can be regarded as a self-contained object in its own right, and that right is asserted by the affordances that it offers as a device for sitting on. It has well-defined edges separating it from the rest of the environment, at least from where I am sitting. For the period of time that I am looking at it, and that it occupies the centre of my attention, it is better focused and possibly brighter than the rest of the room (although I would not say it was attractive, and now that I am no longer looking in that direction but am instead watching these words march across the screen it has merged into the background.) Despite these intrusions of subjectivity into my individual identification of that chair I would still regard it as prototypical and undoubtedly deserving of its secure status as a card-carrying member of the category of objects, and you would probably share that regard.
Looking around I can also take in the vase of flowers on the mantelpiece, and have to admit to an uncertainty as to the status of this object, or rather, to the sense of a slight delay in my willingness to acknowledge this collection, this arrangement, this floral contrivance as a single object. For the briefest of moments I waver between seeing each flower in its own inalienable objective right and seeing the whole kit and caboodle. What’s more, if I allow myself I can even feel a sense of vertiginous escalation as each flower explodes into petals, sepals, stems, stamens, pistels, ovule, filaments, and anthers before a memory of holding the bunch as a totality in my hand and placing them in that vase returns their wholeness. The hand-shaped affordance asserts itself as confirmation of the-bunch-of-flowers as a prototypical member of this basic level category ‘a bunch of flowers’, and now I am gripping them, conceptually, as an object again. I am forced to admit, however, that as an object its self-containedness is less solid than the chair, the edges separating one part from another when there should not even be any parts at all blur and grow transparent. Parts break away, emerge to become new figures, then re-enter the gestalt. The brightness shimmers unsteadily, growing and shrinking in space and the time of memory. Outside my window there are clouds in the sky, and under the clouds is the rain that falls on my garden, and on the grass, and last weeks grass is in the compost heap, and next week’s is under the ground. Each word is separate from every other word and the white space between the words is glowing from the LCD screen on my laptop.
The category of objects, then, and indeed the ontology of objects, is not (only) one of clearly delineated, unitary, stationary, permanent, and unchanging solids. The space of objects is graduated from such prototypical solidity at its heart through increasingly fragmentary, filamentary, and fungible forms, and there is no delineated latitude at which the objective ends and that-which-is-not-the-object begins.
If this is an approximation of the cognitive ontology of objects, then I will want to argue that it is also the structure of our understanding of the metaphor in which we conceive of KNOWLEDGE AS OBJECTS. Objects of thought may be rationally identified as involving clearly defined stable facts easily distinguishable from the ground of their context and from the space of our own looking, but the phenomenally-derived experience of it may be more complex and variable than that. What I hope to show is that objectivity blurs imperceptibly into subjectivity and the solid nuggets of data melt and volatilise into the airy light of wisdom and spirit. The functioning of our cognition requires that, just as there is no category of entities called ‘objects’ that can be unequivocally identified and separated from non-objects, so there is no category of knowledge which is simply ‘objective’, and which is wholly removed from contact and consanquinity with the body of the subjective.
Armstrong, S. L., L. Gleitman, et al. (1983). “What some concepts might not be.” Cognition 13: 263-308.
Lakoff, G. (1990). Women, fire, and dangerous things : what categories reveal about the mind. Chicago, University of Chicago Press.
Rosch, E. H. (1973). “Natural categories.” Cognitive Psychology 4: 328-350.
Rosch, E. H. (1983). “Prototype Classification and Logical Classification: The Two Systems”. New Trends in Conceptual Representation: Challenges to Piaget’s Theory? E. K. Scholnick. Hillsdale, Lawrence Erlbaum Associates:73-86.