, i.e. in other words
may be part of
. The concepts of time and of space in the main, though not entirely, arise from the empirically determined properties of this relation of extension. It is evident from the universal and uniform application of the spatio-temporal concepts that they must arise from the utilisation of the simplest characteristics without which no datum of knowledge would be recognised as an event belonging to the order of nature. Extension is a relation of this type. It is a property so simple that we hardly recognise it as such—it of course is so. Thus the event which is the passage of the car is part of the whole life of the street. Also the passage of a wheel is part of the event which is the passage of the car. Similarly the event which is the continued existence of the house extends over the event which is the continued existence of a brick of the house, and the existence of the house during one day extends over its existence during one specified second of that day.
18.2 Every element of space or of time (as conceived in science) is an abstract entity formed out of this relation of extension (in association at certain stages with the relation of cogredience) by means of a determinate logical procedure (the method of extensive abstraction). The importance of this procedure depends on certain properties of extension which are laws of nature depending on empirical verification. There is, so far as I know, no reason why they should be so, except that they are. These laws will be stated in the succeeding parts so far as is necessary to exemplify the definitions which are there given and to show that these definitions really indicate the familiar spatial and temporal entities which are utilised by science in precise and determinate ways. Many of the laws can be logically proved when the rest are assumed. But the proofs will not be given here, as our aim is to investigate the structure of the ideas which we apply to nature and the fundamental laws of nature which determine their importance, and not to investigate the deductive science which issues from them.
18.3 The various elements of time and space are formed by the repeated applications of the method of extensive abstraction. It is a method which in its sphere achieves the same object as does the differential calculus in the region of numerical calculation, namely it converts a process of approximation into an instrument of exact thought. The method is merely the systematisation of the instinctive procedure of habitual experience. The approximate procedure of ordinary life is to seek simplicity of relations among events by the consideration of events sufficiently restricted in extension both as to space and as to time; the events are then 'small enough.' The procedure of the method of extensive abstraction is to formulate the law by which the approximation is achieved and can be indefinitely continued. The complete series is then defined and we have a 'route of approximation.' These routes of approximation according to the variation of the details of their formation are the points of instantaneous space (here called 'event-particles'), linear segments (straight or curved) between event-particles (here called 'routes'), the moments of time (each of which is all instantaneous nature), and the volumes incident in moments. Such elements are the exactly determined concepts on which the whole fabric of science rests.
18.4 The parts of an event are the set of events (excluding itself) which the given event extends over. It is a mistake to conceive an event as the mere logical sum of its parts. In the first place if we do so, we are necessarily driven back to conceive of more fundamental entities, not events, which would not have the mere abstract logical character which (on this supposition) events would then have. Secondly, the parts of an event are not merely one set of non-overlapping events exhausting the given event. They are the whole complex of events contained in that event; for example, if
