In the history of modern philosophy, the concepts - and we will need to return to the word 'concept' again for clarification - of space and time emerged early as a central part of that process by which the human mind organizes sensations, and as a central topic of conflict between philosophers.
In a famous disagreement between Gottfried Wilhelm Leibniz (1646-1716) and Isaac Newton (1642–1727), two basic views were set forth. Samuel Clarke (1675–1729) joined the discussion on Newton's side, and letters between Clarke and Leibniz are the primary text for this matter (Leibniz almost certainly never met Clarke or Newton in person). Norman Kemp Smith outlines their positions:
(a) The view propounded by Newton, and defended by Clarke, is that space has an existence in and of itself, independent alike of the mind which apprehends it and of the objects with which it is filled. (b) The view held by Leibniz is that space is an empirical concept abstracted from our confused sense-experience of the relations of real things.
The argumentation produced by both sides is sophisticated and brilliant. Ultimately, however, the question was a stalemate until Kant proposed a third view. Immanuel Kant (1724-1804) hoped to split the difference between Leibniz and Newton, glean the best of both, and discard the worst of both. Kant argued that space and time were part of the mind, but not abstracted from experience; rather space and time were part of the mechanism which makes experience possible.
With Leibniz, then, Kant refused to make space and time a physical reality in the way in which rocks and oceans are physical realities; with Newton, Kant gave space and time an unshakeable basis, so much so that they could serve as the a priori foundation for mathematics and geometry.
Since the time of Kant, a number of physicists and philosophers have wrestled with, refined, and produced variants of, these explanations of space and time. The long list would include Einstein and Hawking. Orlin Ottman Fletcher, at Furman University, hopes to make progress by distinguishing types of space and time. If there are different types of space, and different types of time, then we need not trouble ourselves seeking definitions and explanations which would apply to all time and space; this would allow us to steer clear of some of the problems and paradoxes on which others have foundered. He writes:
We distinguish between Perceptual space-experience and that which is purely Ideational. Their essential differences will appear in the course of this discussion. We treat perceptual space first.
Fletcher bases his notion of 'perceptual space' on the phenomenon of distinctness between objects and on the phenomenon of the extension of bodies - which is to say, he bases his notion of perceptual space on phenomena, not on any thing in itself.
The book, inkstand, and ben which are on my desk are seen to be distinct objects; each of them is apart from, or "out of," the others. As I lay my hand on the door-knob in the dark, the knob is felt to be "out from" the surface of the door. Similarly each of the corners of one of the covers of the book is perceived to be apart from the other corners. In like manner we apprehend that parts of other material objects on the desk are experienced as "out from" me. We do not perceive sensible objects otherwise than in a relation of "outness" to one another and to ourselves. So also portions of the over of a book or of a patch of light are seen to be "out from" one another. In a word, all sensible individuals are perceived to be in a relation of "outness" to one another and to the perceiver. In perceiving sensible objects, we always relate them in respect of position; and the objective reality which yields experience of mutual "outness," is the position-relation of the objects perceived. To say that the inkstand and the pen are "out from" each other, is to say that they are in distinct positions, and that we have related them in respect of those positions.
He turns from discussing the perceived distinctness of objects - their occupying of mutually exclusive spaces - to the extension of bodies in space. Note that he is restricting his discussion to perception, and has not yet addressed any metaphysical or a priori considerations.
When we look at a patch of light, the cover of a book, or the top of a desk, we not only have a consciousness of the apartness of portions of the whole, but we also have an experience of "spread-outness," or extensity. Taking all the many positions on the surface together, the whole appear extended. This is true likewise of the perceptions of objects which are not in contact with one another. You see two colored spots at a sensible remove from each other. The whole which you thus perceive is two spots related in position, and it has an aspect of "extendedness." The element of extensity is your experience arises in your perception of the position-relation of the spots. This is evident from the fact that the extensity of the whole is dependent upon the relative positions of the spots. Suppose these spots are colored counters. If you give them positions nearer each other, the extensity is lessened; if you move them farther apart, the extensity is increased. When a sheet of paper is folded, the more widely separated portions are brought nearer to one another, and what we then perceive appears to be less extended than the unfolded sheet. In a word, the aspect of extensity varies with variation of the position-relation of the objects. The position-relation of perceived objects is the objective reality which yields experience of extensity.
Fletcher's text thus far is experiential, and bears some similarity to Leibniz. He goes on to posit that extension is not the primary feature of "perceptual space" but rather that position-relation is.
We have found that perceptual space-experience comes of the perception of sensible objects, and that it has two characteristics: the mutual "outness" of the objects, and the extensity aspect of the whole. We have also learned that it is the perceived position-relation of objects which gives us experience of the mutual "outness" of objects and of extensity. From this it would follow that perceptual space is essentially the perceived position-relation of objects. This, however, differs fundamentally from the common conception of space, which is that space is extensity. This common conception of space is so fixed in thought that we restate considerations already presented. Every whole is many particulars in one. The surface of this sheet is for perception many distinguishable portions of a whole; and it is because we relate distinguishable portions to one another in respect of their positions, that the sheet appears to be extended. When I have experience of the book, the inkstand, and the pen in one perception, it is the position-relation of these objects that gives the aspect of extensity to the whole which I perceive. Spatial experience is, therefore, not primarily experience of extensity; it is experience of the position-relation of objects. The objects whose perception yields this consciousness are necessarily presented together in experience. You cannot relate the positions of three colored spots unless all three are present in your thought at the same time. Including this fact in our description of spatial experience, we would say that it is primarily experience of the position-relation of co-existent objects. Space, as a category, is the position-relation of objects, abstracted from the objects. There is, of course, no perceptual experience of space thus abstracted; for space does not exist by itself, it is a relation. Neither is there experience of extensity by itself; for extensity is an aspect of a perceived whole in which there are sensible particulars, — as the book and the pen, or distinguishable portions of a surface, — and it does not exist apart from sensible particulars. We conclude, then, that perceptual space is the perceived position-relation of co-existent sensible objects, the perception of this relation giving an aspect of eztensity to the whole of what is perceived.
Having posited position-relation as the basis of space, Fletcher then goes on to deal with indexical terms. Indexicals seem to refer necessarily to a conscious perceiver, to the knowing subject.
You reach out and touch a wall, you see a tree toward your right, you hear a bell sounding behind you. The position of each of these objects is related by you to your own position; and you express this relation in the terms, "before," "to the right," "behind." Other terms definitive of like spatial experience are in frequent use — as "here," "there," "above," "below," etc. They define the position of objects and are terms of direction. Such definition of position-relation is present in all developed spatial experience. If we deal efficiently with objects, we must apprehend where they are with respect to ourselves. This definition of space-perception also makes experience available for intersubjective intercourse. If I should say, "The book is on the upper shelf of the case which is at the left of the door as you enter the study," you would understand me and would easily locate the book. The examples given show that, in perceptual space-experience, direction is determined with reference to the position of the subject. The wall is before you, the tree is at your right, the bell is behind you, the book-case is at your left as you enter the room. In general, in perceptual space, the direction is determined by relating the position of the object to the position of the subject.
Having dealt at length with "perceptual space," Fletcher goes on to consider what he calls "conceptual space," which seems to be his version of the a priori concept or intuition of space. Kant argues that space is not, and cannot be, a concept, but is rather an intuition; Kant sees space as prior to concepts, and as making concepts possible. Whether Fletcher will follow Kant in this remains to be seen.
Our discussion has led us to conclude that perceptual space, the space of sense-experience, is the perceived position-relation of sensible objects and the resultant extensity aspect of the perceived whole. As the extension element of the perception is an aspect of what is perceived, it cannot exist by itself. We cannot image extension apart from sensible objects. Conceptual space is extension abstracted from objects; it is mere extensity. According to this conception, space is whether objects are or not. As thus conceived, space has a sort of thinghood ; it is treated as an entity and is virtually regarded as a receptacle for material objects. We easily think of space as an infinite emptiness within which is all that is material. This mode of thought has even found a place in Philosophy; we often say that all sensible objects are in space. But we must not so regard the objective reality corresponding to our perceptual experience; for our perceptions and our images have a spatial character because of the perceived and imaged objects. Conceptual space is not the same with perceptual space. Perceptual space is a relation and a resultant aspect; conceptual space is this aspect, conceived as existing by itself. It is a product of reflection; and, although it is related to perceptual space, it differs significantly from the latter.
Continuing to think nearer to Leibniz than to Newton, Fletcher posits conceptual space as something abstracted from perceptual space, and perceptual space as something existing only relative to objects. Yet, if he give space so weak a foundation, how can geometry, which he seems to see as arising from the intuition of space, have a basis, much less a certain basis?
But, if conceptual space, the space of mathematics, differs so greatly from the space of sense-experience, are the conclusions of mathematics valid for the world which we know through sense-experience? Are they valid for the real external world? Although mathematics conceives space as extensity abstracted from perceived objects, nevertheless it sets ideal objects in this extensity when it reasons respecting space. The ideal objects are the mathematical point, line, surface, and solid. Having set these in space, it discusses position-relations. The point, being without extension, is pure position. It takes the place of the subject in perceptual space; and direction and distance are determined from the point. Its line, surface, and solid are constituted ideally of positions which arc external to one another. The science of geometry is the science of related positions. From this we conclude (1) that, although mathematics conceives space as extensity abstracted from objects, it is wont in its reasoning to give this extensity concreteness by setting ideal objects within space; and (2) that mathematical reasonings respecting space are discussions concerning position-relations. In both these particulars, it puts itself at one with perceptual space. The conclusions logically deduced by such reasoning are true for related positions and are, therefore, true for the position-relations of objects. By so much as they are valid for spatial relations in general, they are valid for the spatial relations of the universe.
Having set forth his views on space and time, Fletcher explains why he rejects the Kantian view, and what he takes the Kantian view to be:
Kant's refusal to regard space and time as categories came of his sharp and overwrought distinction between "sense" and "thought." He himself recognizes that there is no spatial or temporal perception apart from the activity of the understanding; from this it follows that the space and time elements enter cognitive experience through the judging activity of the mind. He was not wholly consistent, then, in refusing to list space and time with the categories. It is also evident that he gave the categories an external, or merely mechanical, relation to the material of knowledge; for he has the material of knowledge ordered in keeping with these forms. The forms are imposed upon the material; they are not an expression of the nature of the material itself. He limited the categories to the province of sense-experience. He could not do otherwise; for the understanding, in his system, only deals with material which is furnished by the senses. As a consequence, Kant's doctrine of the categories leaves them unrelated to the moral order and to judgments of value and purpose. Having limited cognitive experience to the phenomenal world, a world formally constituted by the mind out of sensuous material, he was obliged to assign the moral order and judgments of value and purpose to a realm beyond experience. His refusal to recognize space and time as categories, the extreme subjectivity of his conception of the categories, and their inapplicability (as conceived by him) to the moral order and to judgments of value and purpose, lead us to conclude that his doctrine is inadequate.
The question left, then, is this: are Fletcher's criticisms of Kant strong enough to cause us to abandon Kant? Is Fletcher's description of space and time strong enough to make us embrace it instead? Does Fletcher's version of space and time avoid the pitfalls which he attributes to Kant's version?
