Science and the modern world

by Alfred North Whitehead

An abstractive hierarchy is called ‘finite’ if it stops at a finite grade of complexity. It is called ‘infinite’ if it includes members belonging respectively to all degrees of complexity.

It is to be noted that the base of an abstractive hierarchy may contain any number of members, finite or infinite. Further, the infinity of the number of the members of the base has nothing to do with the question as to whether the hierarchy be finite or infinite.

A finite abstractive hierarchy will, by definition, possess a grade of maximum complexity. It is characteristic of this grade that a member of it is a component of no other eternal object belonging to any grade of the hierarchy. Also it is evident that this grade of maximum complexity must possess only one member; for otherwise the condition of connexity would not be satisfied. Conversely any complex eternal object defines a finite abstractive hierarchy to be discovered by a process of analysis. This complex eternal object from which we start will be called the ‘vertex’ of the abstractive hierarchy: it is the sole member of the grade of maximum complexity. In the first stage of the analysis we obtain the components of the vertex. These components may be of varying complexity; but there must be among them at least one member whose complexity is of a grade one lower than that of the vertex. A grade which is one lower than that of a given eternal object will be called the ‘proximate grade’ for that object. We take then those components of the vertex which belong to its proximate grade; and as the second stage we analyse them into their components. Among these components there must be some belonging to the proximate grade for the objects thus analysed. Add to them the components of the vertex which also belong to this grade of ‘second proximation’ from the vertex; and, at the third stage analyse as before. We thus find objects belonging to the grade of third proximation from the vertex; and we add to them the components belonging to this grade, which have been left over from the preceding stages of the analysis. We proceed in this way through successive stages, till we reach the grade of simple objects. This grade forms the base of the hierarchy.

It is to be noted that in dealing with hierarchies we are entirely within the realm of possibility. Accordingly the eternal objects are devoid of real togetherness: they remain within their ‘isolation.’

The logical instrument which Aristotle used for the analysis of actual fact into more abstract elements was that of classification into species and genera. This instrument has its overwhelmingly important application for science in its preparatory stages. But its use in metaphysical description distorts the true vision of the metaphysical situation. The use of the term ‘universal’ is intimately connected with this Aristotelian analysis: the term has been broadened of late; but still it suggests that classificatory analysis. For this reason I have avoided it.

In any actual occasion α, there will be a group g of simple eternal objects which are ingredient in that group in the most concrete mode. This complete ingredience in an occasion, so as to yield the most complete fusion of individual essence with other eternal objects in the formation of the individual emergent occasion, is evidently of its own kind and cannot be defined in terms of anything else. But it has a peculiar characteristic which necessarily attaches to it. This characteristic is that there is an infinite abstractive hierarchy based upon g which is such that all its members are equally involved in this complete inclusion in α.

The existence of such an infinite abstractive hierarchy is what is meant by the statement that it is impossible to complete the description of an actual occasion by means of concepts. I will call this infinite abstractive hierarchy which is associated with α ‘the associated hierarchy of α.’ It is also what is meant by the notion of the connectedness of an actual occasion. This connectedness of an occasion is necessary for its synthetic unity and for its intelligibility. There is a connected hierarchy of concepts applicable to the occasion, including concepts of all degrees of complexity. Also in the actual occasion, the individual essences of the eternal objects involved in these complex concepts achieve an aesthetic synthesis, productive of the occasion as an experience for its own sake. This associated hierarchy is the shape, or pattern, or form, of the occasion in so far as the occasion is constituted of what enters into its full realisation.

Some confusion of thought has been caused by the fact that abstraction from possibility runs in the opposite direction to an abstraction from actuality, so far as degree of abstractness is concerned. For evidently in describing an actual occasion α, we are nearer to the total concrete fact when we describe α by predicating of it some member of its associated hierarchy, which is of a high grade of complexity. We have then said more about α. Thus, with a high grade of complexity we gain in approach to the full concreteness of α, and with a low grade we lose in this approach. Accordingly the simple eternal objects represent the extreme of abstraction from an actual occasion; whereas simple eternal objects represent the minimum of abstraction from the realm of possibility. It will, I think, be found that, when a high degree of abstraction is spoken of, abstraction from the realm of possibility is what is usually meant—in other words, an elaborate logical construction.

So far I have merely been considering an actual occasion on the side of its full concreteness. It is this side of the occasion in virtue of which it is an event in nature. But a natural event, in this sense of the term, is only an abstraction from a complete actual occasion. A complete occasion includes that which in cognitive experience takes the form of memory, anticipation, imagination, and thought. These elements in an experient occasion are also modes of inclusion of complex eternal objects in the synthetic prehension, as elements in the emergent value. They differ from the concreteness of full inclusion. In a sense this difference is inexplicable; for each mode of inclusion is of its own kind, not to be explained in terms of anything else. But there is a common difference which discriminates these modes of inclusion from the full concrete ingression which has been discussed. This differentia is abruptness. By ‘abruptness’ I mean that what is remembered, or anticipated, or imagined, or thought, is exhausted by a finite complex concept. In each case there is one finite eternal object prehended within the occasion as the vertex of a finite hierarchy. This breaking off from an actual illimitability is what in any occasion marks off that which is termed mental from that which belongs to the physical event to which the mental functioning is referred.

In general there seems to be some loss of vividness in the apprehension of the eternal objects concerned: for example, Hume speaks of ‘faint copies.’ But this faintness seems to be a very unsafe ground for differentiation. Often things realised in thought are more vivid than the same things in inattentive physical experience. But the things apprehended as mental are always subject to the condition that we come to a stop when we attempt to explore ever higher grades of complexity in their realised relationships. We always find that we have thought of just this—whatever it may be—and of no more. There is a limitation which breaks off the finite concept from the higher grades of illimitable complexity.