The Concept of Nature — the Tarner Lectures, 1920

I will call such a set of durations an ' abstractive set ' of durations. It is evident that an abstractive set as we pass along it converges to the ideal of all nature with no temporal extension, namely, to the ideal of all nature at an instant. But this ideal is in fact the ideal of a nonentity. What the abstractive set is in fact doing is to guide thought to the consideration of the progressive simplicity of natural relations as we progressively diminish the temporal extension of the duration considered. Now the whole point of the procedure is that the quantitative expressions of these natural properties do converge to limits though the abstractive set does not converge to any limiting duration. The laws relating these quantitative limits are the laws of nature ' at an instant,' although in truth there is no nature at an instant and there is only the abstractive set. Thus an abstractive set is effectively the entity meant when we consider an instant of time without temporal extension. It subserves all the necessary purposes of giving a definite meaning to the concept of the properties of nature at an instant. I fully agree that this concept is fundamental in the expression of physical science. Thep. 62 difficulty is to express our meaning in terms of the immediate deliverances of sense-awareness, and I offer the above explanation as a complete solution of the problem.

In this explanation a moment is the set of natural properties reached by a route of approximation. An abstractive series is a route of approximation. There are different routes of approximation to the same limiting set of the properties of nature. In other words there are different abstractive sets which are to be regarded as routes of approximation to the same moment. Accordingly there is a certain amount of technical detail necessary in explaining the relations of such abstractive sets with the same convergence and in guarding against possible exceptional cases. Such details are not suitable for exposition in these lectures, and I have dealt with them fully elsewhere^.

It is more convenient for technical purposes to look on a moment as being the class of all abstractive sets of durations with the same convergence. With this definition (provided that we can successfully explain what we mean by the 'same convergence' apart from a detailed knowledge of the set of natural properties arrived at by approximation) a moment is merely a class of sets of durations whose relations of extension in respect to each other have certain definite peculiarities. We may term these connexions of the component durations the 'extrinsic' properties of a moment; the ' intrinsic ' properties of the moment are the properties of nature arrived at as a limit as we proceed along any one of its abstractive sets. These are the properties of nature 'at that moment,' or 'at that instant.'

1 Cf . An Enquiry concerning the Principles of Natural Knowledge,
Cambridge University Press, 1919.

Ill] TIME 6;

The durations which enter into the composition o a moment all belong to one family. Thus there is on* family of moments corresponding to one family o durations. Also if we take two moments of the samt family, among the durations which enter into the com position of one moment the smaller durations ar( completely separated from the smaller durations whicl enter into the composition of the other moment. Thui the two moments in their intrinsic properties mus exhibit the limits of completely different states of nature In this sense the two moments are completely separated I will call two moments of the same family 'parallel.'

Corresponding to each duration there are tw( moments of the associated family of moments whicl are the boundary moments of that duration, t 'boundary moment' of a duration can be defined ii this way. There are durations of the same family as th( given duration which overlap it but are not containe( in it. Consider an abstractive set of such durations Such a set defines a moment which is just as mucl without the duration as within it. Such a moment is ; boundary moment of the duration. Also we call upoi our sense-awareness of the passage of nature to inforn us that there are two such boundary moments, namel; the earlier one and the later one. We will call them th( initial and the final boundaries.

There are also moments of the same family such tha the shorter durations in their composition are entirely separated from the given duration. Such moments wil be said to lie ' outside' the given duration. Again othe moments of the family are such that the shorter dura tions in their composition are parts of the given dura tion. Such moments are said to lie 'within' the givei

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duration or to ' inhere ' in it. The whole family of parallel moments is accounted for in this way by reference to any given duration of the associated family of durations. Namely, there are moments of the family which lie without the given duration, there are the two moments which are the boundary moments of the given duration, and the moments which lie within the given duration. Furthermore any two moments of the same family are the boundary moments of some one duration of the associated family of durations.

It is now possible to define the serial relation of temporal order among the moments of a family. For let A and C be any two moments of the family, these moments are the boundary moments of one duration d of the associated family, and any moment B which lies within the duration d will be said to lie between the moments A and C. Thus the three-termed relation of ' lying-between ' as relating three moments A, B, and C is completely defined. Also our knowledge of the passage of nature assures us that this relation distributes the moments of the family into a serial order. I abstain from enumerating the definite properties which secure this result, I have enumerated them in my recently published book^ to which I have already referred. Furthermore the passage of nature enables us to know that one direction along the series corresponds to passage into the future and the other direction corresponds to retrogression towards the past.

Such an ordered series of moments is what we mean by time defined as a series. Each element of the series exhibits an instantaneous state of nature. Evidently this serial time is the result of an intellectual process of

^ Cf . Enquiry,p. 65 abstraction. What I have done is to give precise definitions of the procedure by which the abstraction is effected. This procedure is merely a particular case of the general method which in my book I name the 'method of extensive abstraction.' This serial time is evidently not the very passage of nature itself. It exhibits some of the natural properties which flow from it. The state of nature ' at a moment ' has evidently lost this ultimate quality of passage. Also the temporal series of moments only retains it as an extrinsic relation of entities and not as the outcome of the essential being of the terms of the series.

Nothing has yet been said as to the measurement of time. Such measurement does not follow from the mere serial property of time; it requires a theory of congruence which will be considered in a later lecture.