CHAPTER III
TIME
The two previous lectures of this course have been mainly critical. In the present lecture I propose to enter upon a survey of the kinds of ent.i.ties which are posited for knowledge in sense-awareness. My purpose is to investigate the sorts of relations which these ent.i.ties of various kinds can bear to each other. A cla.s.sification of natural ent.i.ties is the beginning of natural philosophy. To-day we commence with the consideration of Time.
In the first place there is posited for us a general fact: namely, something is going on; there is an occurrence for definition.
This general fact at once yields for our apprehension two factors, which I will name, the "discerned" and the "discernible." The discerned is comprised of those elements of the general fact which are discriminated with their own individual peculiarities. It is the field directly perceived. But the ent.i.ties of this field have relations to other ent.i.ties which are not particularly discriminated in this individual way. These other ent.i.ties are known merely as the relata in relation to the ent.i.ties of the discerned field. Such an ent.i.ty is merely a "something" which has such-and-such definite relations to some definite ent.i.ty or ent.i.ties in the discerned field. As being thus related, they are--owing to the particular character of these relations--known as elements of the general fact which is going on. But we are not aware of them except as ent.i.ties fulfilling the functions of relata in these relations.
Thus the complete general fact, posited as occurring, comprises both sets of ent.i.ties, namely the ent.i.ties perceived in their own individuality and other ent.i.ties merely apprehended as relata without further definition. This complete general fact is the discernible and it comprises the discerned. The discernible is all nature as disclosed in that sense-awareness, and extends beyond and comprises all of nature as actually discriminated or discerned in that sense-awareness. The discerning or discrimination of nature is a peculiar awareness of special factors in nature in respect to their peculiar characters. But the factors in nature of which we have this peculiar sense-awareness are known as not comprising all the factors which together form the whole complex of related ent.i.ties within the general fact there for discernment. This peculiarity of knowledge is what I call its unexhaustive character. This character may be metaphorically described by the statement that nature as perceived always has a ragged edge. For example, there is a world beyond the room to which our sight is confined known to us as completing the s.p.a.ce-relations of the ent.i.ties discerned within the room. The junction of the interior world of the room with the exterior world beyond is never sharp. Sounds and subtler factors disclosed in sense-awareness float in from the outside. Every type of sense has its own set of discriminated ent.i.ties which are known to be relata in relation with ent.i.ties not discriminated by that sense. For example we see something which we do not touch and we touch something which we do not see, and we have a general sense of the s.p.a.ce-relations between the ent.i.ty disclosed in sight and the ent.i.ty disclosed in touch.
Thus in the first place each of these two ent.i.ties is known as a relatum in a general system of s.p.a.ce-relations and in the second place the particular mutual relation of these two ent.i.ties as related to each other in this general system is determined. But the general system of s.p.a.ce-relations relating the ent.i.ty discriminated by sight with that discriminated by sight is not dependent on the peculiar character of the other ent.i.ty as reported by the alternative sense. For example, the s.p.a.ce-relations of the thing seen would have necessitated an ent.i.ty as a relatum in the place of the thing touched even although certain elements of its character had not been disclosed by touch. Thus apart from the touch an ent.i.ty with a certain specific relation to the thing seen would have been disclosed by sense-awareness but not otherwise discriminated in respect to its individual character. An ent.i.ty merely known as spatially related to some discerned ent.i.ty is what we mean by the bare idea of "place." The concept of place marks the disclosure in sense-awareness of ent.i.ties in nature known merely by their spatial relations to discerned ent.i.ties. It is the disclosure of the discernible by means of its relations to the discerned.
This disclosure of an ent.i.ty as a relatum without further specific discrimination of quality is the basis of our concept of significance.
In the above example the thing seen was significant, in that it disclosed its spatial relations to other ent.i.ties not necessarily otherwise entering into consciousness. Thus significance is relatedness, but it is relatedness with the emphasis on one end only of the relation.
For the sake of simplicity I have confined the argument to spatial relations; but the same considerations apply to temporal relations. The concept of "period of time" marks the disclosure in sense-awareness of ent.i.ties in nature known merely by their temporal relations to discerned ent.i.ties. Still further, this separation of the ideas of s.p.a.ce and time has merely been adopted for the sake of gaining simplicity of exposition by conformity to current language. What we discern is the specific character of a place through a period of time. This is what I mean by an "event." We discern some specific character of an event. But in discerning an event we are also aware of its significance as a relatum in the structure of events. This structure of events is the complex of events as related by the two relations of extension and cogredience. The most simple expression of the properties of this structure are to be found in our spatial and temporal relations. A discerned event is known as related in this structure to other events whose specific characters are otherwise not disclosed in that immediate awareness except so far as that they are relata within the structure.
The disclosure in sense-awareness of the structure of events cla.s.sifies events into those which are discerned in respect to some further individual character and those which are not otherwise disclosed except as elements of the structure. These signified events must include events in the remote past as well as events in the future. We are aware of these as the far off periods of unbounded time. But there is another cla.s.sification of events which is also inherent in sense-awareness.
These are the events which share the immediacy of the immediately present discerned events. These are the events whose characters together with those of the discerned events comprise all nature present for discernment. They form the complete general fact which is all nature now present as disclosed in that sense-awareness. It is in this second cla.s.sification of events that the differentiation of s.p.a.ce from time takes its origin. The germ of s.p.a.ce is to be found in the mutual relations of events within the immediate general fact which is all nature now discernible, namely within the one event which is the totality of present nature. The relations of other events to this totality of nature form the texture of time.
The unity of this general present fact is expressed by the concept of simultaneity. The general fact is the whole simultaneous occurrence of nature which is now for sense-awareness. This general fact is what I have called the discernible. But in future I will call it a "duration,"
meaning thereby a certain whole of nature which is limited only by the property of being a simultaneity. Further in obedience to the principle of comprising within nature the whole terminus of sense-awareness, simultaneity must not be conceived as an irrelevant mental concept imposed upon nature. Our sense-awareness posits for immediate discernment a certain whole, here called a "duration"; thus a duration is a definite natural ent.i.ty. A duration is discriminated as a complex of partial events, and the natural ent.i.ties which are components of this complex are thereby said to be "simultaneous with this duration." Also in a derivative sense they are simultaneous with each other in respect to this duration. Thus simultaneity is a definite natural relation. The word "duration" is perhaps unfortunate in so far as it suggests a mere abstract stretch of time. This is not what I mean. A duration is a concrete slab of nature limited by simultaneity which is an essential factor disclosed in sense-awareness.
Nature is a process. As in the case of everything directly exhibited in sense-awareness, there can be no explanation of this characteristic of nature. All that can be done is to use language which may speculatively demonstrate it, and also to express the relation of this factor in nature to other factors.
It is an exhibition of the process of nature that each duration happens and pa.s.ses. The process of nature can also be termed the pa.s.sage of nature. I definitely refrain at this stage from using the word "time,"
since the measurable time of science and of civilised life generally merely exhibits some aspects of the more fundamental fact of the pa.s.sage of nature. I believe that in this doctrine I am in full accord with Bergson, though he uses "time" for the fundamental fact which I call the "pa.s.sage of nature." Also the pa.s.sage of nature is exhibited equally in spatial transition as well as in temporal transition. It is in virtue of its pa.s.sage that nature is always moving on. It is involved in the meaning of this property of "moving on" that not only is any act of sense-awareness just that act and no other, but the terminus of each act is also unique and is the terminus of no other act. Sense-awareness seizes its only chance and presents for knowledge something which is for it alone.
There are two senses in which the terminus of sense-awareness is unique.
It is unique for the sense-awareness of an individual mind and it is unique for the sense-awareness of all minds which are operating under natural conditions. There is an important distinction between the two cases. (i) For one mind not only is the discerned component of the general fact exhibited in any act of sense-awareness distinct from the discerned component of the general fact exhibited in any other act of sense-awareness of that mind, but the two corresponding durations which are respectively related by simultaneity to the two discerned components are necessarily distinct. This is an exhibition of the temporal pa.s.sage of nature; namely, one duration has pa.s.sed into the other. Thus not only is the pa.s.sage of nature an essential character of nature in its _role_ of the terminus of sense-awareness, but it is also essential for sense-awareness in itself. It is this truth which makes time appear to extend beyond nature. But what extends beyond nature to mind is not the serial and measurable time, which exhibits merely the character of pa.s.sage in nature, but the quality of pa.s.sage itself which is in no way measurable except so far as it obtains in nature. That is to say, "pa.s.sage" is not measurable except as it occurs in nature in connexion with extension. In pa.s.sage we reach a connexion of nature with the ultimate metaphysical reality. The quality of pa.s.sage in durations is a particular exhibition in nature of a quality which extends beyond nature. For example pa.s.sage is a quality not only of nature, which is the thing known, but also of sense-awareness which is the procedure of knowing. Durations have all the reality that nature has, though what that may be we need not now determine. The measurableness of time is derivative from the properties of durations. So also is the serial character of time. We shall find that there are in nature competing serial time-systems derived from different families of durations. These are a peculiarity of the character of pa.s.sage as it is found in nature.
This character has the reality of nature, but we must not necessarily transfer natural time to extra-natural ent.i.ties. (ii) For two minds, the discerned components of the general facts exhibited in their respective acts of sense-awareness must be different. For each mind, in its awareness of nature is aware of a certain complex of related natural ent.i.ties in their relations to the living body as a focus. But the a.s.sociated durations may be identical. Here we are touching on that character of the pa.s.sage nature which issues in the spatial relations of simultaneous bodies. This possible ident.i.ty of the durations in the case of the sense-awareness of distinct minds is what binds into one nature the private experiences of sentient beings. We are here considering the spatial side of the pa.s.sage of nature. Pa.s.sage in this aspect of it also seems to extend beyond nature to mind.
It is important to distinguish simultaneity from instantaneousness. I lay no stress on the mere current usage of the two terms. There are two concepts which I want to distinguish, and one I call simultaneity and the other instantaneousness. I hope that the words are judiciously chosen; but it really does not matter so long as I succeed in explaining my meaning. Simultaneity is the property of a group of natural elements which in some sense are components of a duration. A duration can be all nature present as the immediate fact posited by sense-awareness. A duration retains within itself the pa.s.sage of nature. There are within it antecedents and consequents which are also durations which may be the complete specious presents of quicker consciousnesses. In other words a duration retains temporal thickness. Any concept of all nature as immediately known is always a concept of some duration though it may be enlarged in its temporal thickness beyond the possible specious present of any being known to us as existing within nature. Thus simultaneity is an ultimate factor in nature, immediate for sense-awareness.
Instantaneousness is a complex logical concept of a procedure in thought by which constructed logical ent.i.ties are produced for the sake of the simple expression in thought of properties of nature. Instantaneousness is the concept of all nature at an instant, where an instant is conceived as deprived of all temporal extension. For example we conceive of the distribution of matter in s.p.a.ce at an instant. This is a very useful concept in science especially in applied mathematics; but it is a very complex idea so far as concerns its connexions with the immediate facts of sense-awareness. There is no such thing as nature at an instant posited by sense-awareness. What sense-awareness delivers over for knowledge is nature through a period. Accordingly nature at an instant, since it is not itself a natural ent.i.ty, must be defined in terms of genuine natural ent.i.ties. Unless we do so, our science, which employs the concept of instantaneous nature, must abandon all claim to be founded upon observation.
I will use the term "moment" to mean "all nature at an instant." A moment, in the sense in which the term is here used, has no temporal extension, and is in this respect to be contrasted with a duration which has such extension. What is directly yielded to our knowledge by sense-awareness is a duration. Accordingly we have now to explain how moments are derived from durations, and also to explain the purpose served by their introduction.
A moment is a limit to which we approach as we confine attention to durations of minimum extension. Natural relations among the ingredients of a duration gain in complexity as we consider durations of increasing temporal extension. Accordingly there is an approach to ideal simplicity as we approach an ideal diminution of extension.
The word "limit" has a precise signification in the logic of number and even in the logic of non-numerical one-dimensional series. As used here it is so far a mere metaphor, and it is necessary to explain directly the concept which it is meant to indicate.
Durations can have the two-termed relational property of extending one over the other. Thus the duration which is all nature during a certain minute extends over the duration which is all nature during the 30th second of that minute. This relation of "extending over"--"extension" as I shall call it--is a fundamental natural relation whose field comprises more than durations. It is a relation which two limited events can have to each other. Furthermore as holding between durations the relation appears to refer to the purely temporal extension. I shall however maintain that the same relation of extension lies at the base both of temporal and spatial extension. This discussion can be postponed; and for the present we are simply concerned with the relation of extension as it occurs in its temporal aspect for the limited field of durations.
The concept of extension exhibits in thought one side of the ultimate pa.s.sage of nature. This relation holds because of the special character which pa.s.sage a.s.sumes in nature; it is the relation which in the case of durations expresses the properties of "pa.s.sing over." Thus the duration which was one definite minute pa.s.sed over the duration which was its 30th second. The duration of the 30th second was part of the duration of the minute. I shall use the terms "whole" and "part" exclusively in this sense, that the "part" is an event which is extended over by the other event which is the "whole." Thus in my nomenclature "whole" and "part"
refer exclusively to this fundamental relation of extension; and accordingly in this technical usage only events can be either wholes or parts.
The continuity of nature arises from extension. Every event extends over other events, and every event is extended over by other events. Thus in the special case of durations which are now the only events directly under consideration, every duration is part of other durations; and every duration has other durations which are parts of it. Accordingly there are no maximum durations and no minimum durations. Thus there is no atomic structure of durations, and the perfect definition of a duration, so as to mark out its individuality and distinguish it from highly a.n.a.logous durations over which it is pa.s.sing, or which are pa.s.sing over it, is an arbitrary postulate of thought. Sense-awareness posits durations as factors in nature but does not clearly enable thought to use it as distinguishing the separate individualities of the ent.i.ties of an allied group of slightly differing durations. This is one instance of the indeterminateness of sense-awareness. Exactness is an ideal of thought, and is only realised in experience by the selection of a route of approximation.
The absence of maximum and minimum durations does not exhaust the properties of nature which make up its continuity. The pa.s.sage of nature involves the existence of a family of durations. When two durations belong to the same family either one contains the other, or they overlap each other in a subordinate duration without either containing the other; or they are completely separate. The excluded case is that of durations overlapping in finite events but not containing a third duration as a common part.
It is evident that the relation of extension is transitive; namely as applied to durations, if duration A is part of duration B, and duration B is part of duration C, then A is part of C. Thus the first two cases may be combined into one and we can say that two durations which belong to the same family _either_ are such that there are durations which are parts of both _or_ are completely separate.
Furthermore the converse of this proposition holds; namely, if two durations have other durations which are parts of both _or_ if the two durations are completely separate, then they belong to the same family.
The further characteristics of the continuity of nature--so far as durations are concerned--which has not yet been formulated arises in connexion with a family of durations. It can be stated in this way: There are durations which contain as parts any two durations of the same family. For example a week contains as parts any two of its days. It is evident that a containing duration satisfies the conditions for belonging to the same family as the two contained durations.
We are now prepared to proceed to the definition of a moment of time.
Consider a set of durations all taken from the same family. Let it have the following properties: (i) of any two members of the set one contains the other as a part, and (ii) there is no duration which is a common part of every member of the set.
Now the relation of whole and part is asymmetrical; and by this I mean that if A is part of B, then B is not part of A. Also we have already noted that the relation is transitive. Accordingly we can easily see that the durations of any set with the properties just enumerated must be arranged in a one-dimensional serial order in which as we descend the series we progressively reach durations of smaller and smaller temporal extension. The series may start with any arbitrarily a.s.sumed duration of any temporal extension, but in descending the series the temporal extension progressively contracts and the successive durations are packed one within the other like the nest of boxes of a Chinese toy. But the set differs from the toy in this particular: the toy has a smallest box which forms the end box of its series; but the set of durations can have no smallest duration nor can it converge towards a duration as its limit. For the parts either of the end duration or of the limit would be parts of all the durations of the set and thus the second condition for the set would be violated.
I will call such a set of durations an "abstractive set" of durations.
It is evident that an abstractive set as we pa.s.s 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 nonent.i.ty. 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 quant.i.tative expressions of these natural properties do converge to limits though the abstractive set does not converge to any limiting duration. The laws relating these quant.i.tative 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 ent.i.ty 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. The 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[5].
[5] Cf. _An Enquiry concerning the Principles of Natural Knowledge_, Cambridge University Press, 1919.
It is more convenient for technical purposes to look on a moment as being the cla.s.s 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 cla.s.s 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."
The durations which enter into the composition of a moment all belong to one family. Thus there is one family of moments corresponding to one family of durations. Also if we take two moments of the same family, among the durations which enter into the composition of one moment the smaller durations are completely separated from the smaller durations which enter into the composition of the other moment. Thus the two moments in their intrinsic properties must 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 two moments of the a.s.sociated family of moments which are the boundary moments of that duration. A "boundary moment" of a duration can be defined in this way. There are durations of the same family as the given duration which overlap it but are not contained in it. Consider an abstractive set of such durations.
Such a set defines a moment which is just as much without the duration as within it. Such a moment is a boundary moment of the duration. Also we call upon our sense-awareness of the pa.s.sage of nature to inform us that there are two such boundary moments, namely the earlier one and the later one. We will call them the initial and the final boundaries.
There are also moments of the same family such that the shorter durations in their composition are entirely separated from the given duration. Such moments will be said to lie "outside" the given duration.
Again other moments of the family are such that the shorter durations in their composition are parts of the given duration. Such moments are said to lie "within" the given 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 a.s.sociated 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 a.s.sociated 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 a.s.sociated 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 pa.s.sage of nature a.s.sures 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[6] to which I have already referred. Furthermore the pa.s.sage of nature enables us to know that one direction along the series corresponds to pa.s.sage into the future and the other direction corresponds to retrogression towards the past.
[6] Cf. _Enquiry_.
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 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 pa.s.sage 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 pa.s.sage. Also the temporal series of moments only retains it as an extrinsic relation of ent.i.ties 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.
In estimating the adequacy of this definition of the temporal series as a formulation of experience it is necessary to discriminate between the crude deliverance of sense-awareness and our intellectual theories. The lapse of time is a measurable serial quant.i.ty. The whole of scientific theory depends on this a.s.sumption and any theory of time which fails to provide such a measurable series stands self-condemned as unable to account for the most salient fact in experience. Our difficulties only begin when we ask what it is that is measured. It is evidently something so fundamental in experience that we can hardly stand back from it and hold it apart so as to view it in its own proportions.
We have first to make up our minds whether time is to be found in nature or nature is to be found in time. The difficulty of the latter alternative--namely of making time prior to nature--is that time then becomes a metaphysical enigma. What sort of ent.i.ties are its instants or its periods? The dissociation of time from events discloses to our immediate inspection that the attempt to set up time as an independent terminus for knowledge is like the effort to find substance in a shadow.
There is time because there are happenings, and apart from happenings there is nothing.