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he more accurately expresses it by saying that they need (exigent) it. This is a technical term which he elsewhere uses to express the relation of the possible to the actual. The possible “needs” the actual, not in the sense that it necessarily requires existence, but in the sense that when the actual gives it existence, it is the logical basis of the actual,—the actual, on the other hand, being its real complement. The passivity of the monad is therefore at once the logical basis and the possibility of the impenetrability of matter. It is owing to the passivity of the monad that it does not adequately reflect (that it is not transparent to, so to speak) the activities of other monads. In its irresponsiveness, it fails to mirror them in itself. It may be said, therefore, to be impenetrable to them. They in turn, so far as they are passive, are impenetrable to it. Now the impenetrable is, ex vi terminis, that which excludes, and that which excludes, not in virtue of its active elasticity, but in virtue of its mere inertia, its dead weight, as it were, of resistance. But mutual exclusion of this passive sort constitutes that which is extended. Extension is the abstract quality of this concrete subject. Such, in effect, is the deduction which Leibniz gives of body, or physical matter, from matter as metaphysical; of matter as sensible or phenomenal, from matter as ideal or as intelligible.
If we put together what has been said, it is clear that material phenomena (bodies, corpora, in Leibniz’s phrase) simply repeat in another sphere the properties of the spiritual monad. There is a complete parallelism between every property, each to each, and this necessarily; for every property of “body” is in logical dependence upon, and a phenomenalization of, some spiritual or ideal quality. Motion is the source of all the dynamic qualities of body, and motion is the reflection of Force, that force which is Life. But this force in all finite forms is conditioned by a passive, unreceptive, unresponsive factor; and this must also have its correlate in “body.” This correlate is primarily impenetrability, and secondarily extension. Thus it is that concrete body always manifests motion, indeed, but upon a background of extension, and against inertia. It never has free play; had it an unrestrained field of activity, extension would disappear, and spatial motion would vanish into ideal energy. On the other hand, were the essence of matter found in resistance or impenetrability, it would be wholly inert; it would be a monotone of extension, without variety of form or cohesion. As Leibniz puts it with reference to Locke, “body” implies motion, or impetuosity, resistance, and cohesion. Motion is the active principle, resistance the passive; while cohesion, with its various grades of completeness, which produce form, size, and solidity, is the result of their union.
Leibniz, like Plato, has an intermediary between the rational and the sensible; and as Plato found that it was mathematical relations that mediate between the permanent and unified Ideas and the changing manifold objects, so Leibniz found that the relations of space and time form the natural transition from the sphere of monads to the world of bodies. As Plato found that it was the possibility of applying mathematical considerations to the world of images that showed the participation of Ideas in them, and constituted such reality as they had, so Leibniz found that space and time formed the element of order and regularity among sense phenomena, and thus brought them into kinship with the monads and made them subjects of science. It is implied in what is here said that Leibniz distinguished between space and time on the one hand, and duration and extension on the other. This distinction, which Leibniz draws repeatedly and with great care, has been generally overlooked by his commentators. But it is evident that this leaves Leibniz in a bad plight. Mathematics, in its various forms, is the science of spatial and temporal relations. But if these are identical with the forms of duration and extension, they are purely phenomenal and sensible. The science of them, according to the Leibnizian distinction between the absolutely real and the phenomenally real, would be then a science of the confused, the imperfect, and the transitory; in fact, no science at all. But mathematics, on the contrary, is to Leibniz the type of demonstrative, conclusive science. Space and time are, in his own words, “innate ideas,” and the entire science of them is the drawing out of the content of these innate—that is, rational, distinct, and eternal—ideas. But extension and duration are sensible experiences; not rational, but phenomenal; not distinct, but confused; not eternal, but evanescent. We may be sure that this contradiction would not escape Leibniz, although it has many of his critics and historians.
It is true, however, that he occasionally uses the terms as synonymous; but this where the distinction between them has no bearing on the argument in hand, and where the context determines in what sense the term is used. The distinction which he actually makes, and to which he keeps when space and time are the subject of discussion, is that extension and duration are qualities or predicates of objects and events, while space and time are relations, or orders of existence. Extension and duration are, as he says, the immensity, the mass, the continuation, the repetition, of some underlying subject. But space and time are the measure of the mass, the rule or law of the continuation, the order or mode of the repetition. Thus immediately after the passage already quoted, in which he says that extension in body is the diffusion of materiality, just as whiteness is the diffusion of a property of milk, he goes on to say “that extension is to space as duration to time. Duration and extension are attributes of things; but space and time are to be considered, as it were, outside of things, and as serving to measure them.” Still more definitely he says: “Many confound the immensity or extent of things with the space by means of which this extent is defined. Space is not the extension of body, any more than duration is its time. Things keep their extension, not always their space. Everything has its own extent and duration; but it does not have a time of its own, nor keep for its own a space.” Or, as he expresses the latter idea elsewhere, space is like number, in the sense that it is indifferent to spatial things, just as number is indifferent to res numerata. Just as the number five is not a quality or possession of any object, or group of objects, but expresses an order or relation among them, so a given space is not the property of a thing, but expresses the order of its parts to one another. But extension, on the other hand, is a property of the given objects. While extension, therefore, must always belong to some actual thing, space, as a relation, is as applicable to possible things as to actual existences; so that Leibniz sometimes says that time and space “express possibilities.” They are that which makes it possible for a definite and coherent order of experiences to exist. They determine existence in some of its relations, and as such are logically prior to any given forms of existence; while extent and duration are always qualities of some given form of existence, and hence logically derivative. Since time and space “characterize possibilities” as well as actualities, it follows as a matter of course “that they are of the nature of eternal truths, which relate equally to the possible and to the existing.” Being an eternal truth, space must have its place in that which is simply the active unity of all eternal truths,—the mind of God. “Its truth and reality are based upon God. It is an order whose source is God.” Since God is purus actus, he is the immediate, the efficient source only of that which partakes in some degree of his own nature, or is rational; and here is another clear point of distinction between space and extension, between time and duration.
But we must ask more in detail regarding their nature. Admitting that they are relations, ideal and prior to particular experiences, the question must be asked, What sort of relations are they; how are they connected with the purely spiritual on one hand, and with the phenomenal on the other? Leibniz’s most extended answers to these questions are given in his controversy with Clarke. The latter took much the same position regarding the nature of space (though not, indeed, concerning the origin of its idea) as Locke, and the arguments which Leibniz uses against him he might also have used, for the most part, against Locke. Locke and Clarke both conceived of space and time as wholly without intrinsic relation to objects and events. It is especially against this position that Leibniz argues, holding that space and time are simply orders or relations of objects and events, that space exists only where objects are existing, and that it is the order of their co-existence, or of their possible co-existence; while time exists only as events are occurring, and is the relation of their succession. Clarke, on the other hand, speaks of the universe of objects as bounded by and moving about in an empty space, and says that time existed before God created the finite world, so that the world came into a time already there to receive its on-goings, just as it fell into a space already there to receive its co-existences.
To get at the ideas of Leibniz, therefore, we