Part 9 (1/2)
This, together with its necessity for the statement of causal laws, seems to be the source of the entirely erroneous feeling that matter is more ”real” than sense-data.
Consider for example the infinite divisibility of matter. In looking at a given thing and approaching it, one sense-datum will become several, and each of these will again divide. Thus _one_ appearance may represent _many_ things, and to this process there seems no end.
Hence in the limit, when we approach indefinitely near to the thing there will be an indefinite number of units of matter corresponding to what, at a finite distance, is only one appearance. This is how infinite divisibility arises.
The whole causal efficacy of a thing resides in its matter. This is in some sense an empirical fact, but it would be hard to state it precisely, because ”causal efficacy” is difficult to define.
What can be known empirically about the matter of a thing is only approximate, because we cannot get to know the appearances of the thing from very small distances, and cannot accurately infer the limit of these appearances. But it _is_ inferred _approximately_ by means of the appearances we can observe. It then turns out that these appearances can be exhibited by physics as a function of the matter in our immediate neighbourhood; e.g. the visual appearance of a distant object is a function of the light-waves that reach the eyes.
This leads to confusions of thought, but offers no real difficulty.
One appearance, of a visible object for example, is not sufficient to determine its other simultaneous appearances, although it goes a certain distance towards determining them. The determination of the hidden structure of a thing, so far as it is possible at all, can only be effected by means of elaborate dynamical inferences.
X. TIME[30]
It seems that the one all-embracing time is a construction, like the one all-embracing s.p.a.ce. Physics itself has become conscious of this fact through the discussions connected with relativity.
Between two perspectives which both belong to one person's experience, there will be a direct time-relation of before and after. This suggests a way of dividing history in the same sort of way as it is divided by different experiences, but without introducing experience or anything mental: we may define a ”biography” as everything that is (directly) earlier or later than, or simultaneous with, a given ”sensibile.” This will give a series of perspectives, which _might_ all form parts of one person's experience, though it is not necessary that all or any of them should actually do so. By this means, the history of the world is divided into a number of mutually exclusive biographies.
We have now to correlate the times in the different biographies. The natural thing would be to say that the appearances of a given (momentary) thing in two different perspectives belonging to different biographies are to be taken as simultaneous; but this is not convenient. Suppose _A_ shouts to _B_, and _B_ replies as soon as he hears _A's_ shout. Then between _A's_ hearing of his own shout and his hearing of _B's_ there is an interval; thus if we made _A's_ and _B's_ hearing of the same shout exactly simultaneous with each other, we should have events exactly simultaneous with a given event but not with each other. To obviate this, we a.s.sume a ”velocity of sound.”
That is, we a.s.sume that the time when _B_ hears _A's_ shout is half-way between the time when _A_ hears his own shout and the time when he hears _B's_. In this way the correlation is effected.
What has been said about sound applies of course equally to light. The general principle is that the appearances, in different perspectives, which are to be grouped together as const.i.tuting what a certain thing is at a certain moment, are not to be all regarded as being at that moment. On the contrary they spread outward from the thing with various velocities according to the nature of the appearances. Since no _direct_ means exist of correlating the time in one biography with the time in another, this temporal grouping of the appearances belonging to a given thing at a given moment is in part conventional.
Its motive is partly to secure the verification of such maxims as that events which are exactly simultaneous with the same event are exactly simultaneous with one another, partly to secure convenience in the formulation of causal laws.
XI. THE PERSISTENCE OF THINGS AND MATTER
Apart from any of the fluctuating hypotheses of physics, three main problems arise in connecting the world of physics with the world of sense, namely:
1. the construction of a single s.p.a.ce; 2. the construction of a single time; 3. the construction of permanent things or matter.
We have already considered the first and second of these problems; it remains to consider the third.
We have seen how correlated appearances in different perspectives are combined to form one ”thing” at one moment in the all-embracing time of physics. We have now to consider how appearances at different times are combined as belonging to one ”thing,” and how we arrive at the persistent ”matter” of physics. The a.s.sumption of permanent substance, which technically underlies the procedure of physics, cannot of course be regarded as metaphysically legitimate: just as the one thing simultaneously seen by many people is a construction, so the one thing seen at different times by the same or different people must be a construction, being in fact nothing but a certain grouping of certain ”sensibilia.”
We have seen that the momentary state of a ”thing” is an a.s.semblage of ”sensibilia,” in different perspectives, not all simultaneous in the one constructed time, but spreading out from ”the place where the thing is” with velocities depending upon the nature of the ”sensibilia.” The time _at_ which the ”thing” is in this state is the lower limit of the times at which these appearances occur. We have now to consider what leads us to speak of another set of appearances as belonging to the same ”thing” at a different time.
For this purpose, we may, at least to begin with, confine ourselves within a single biography. If we can always say when two ”sensibilia”
in a given biography are appearances of one thing, then, since we have seen how to connect ”sensibilia” in different biographies as appearances of the same momentary state of a thing, we shall have all that is necessary for the complete construction of the history of a thing.
It is to be observed, to begin with, that the ident.i.ty of a thing for common sense is not always correlated with the ident.i.ty of matter for physics. A human body is one persisting thing for common sense, but for physics its matter is constantly changing. We may say, broadly, that the common-sense conception is based upon continuity in appearances at the ordinary distances of sense-data, while the physical conception is based upon the continuity of appearances at very small distances from the thing. It is probable that the common-sense conception is not capable of complete precision. Let us therefore concentrate our attention upon the conception of the persistence of matter in physics.
The first characteristic of two appearances of the same piece of matter at different times is _continuity_. The two appearances must be connected by a series of intermediaries, which, if time and s.p.a.ce form compact series, must themselves form a compact series. The colour of the leaves is different in autumn from what it is in summer; but we believe that the change occurs gradually, and that, if the colours are different at two given times, there are intermediate times at which the colours are intermediate between those at the given times.
But there are two considerations that are important as regards continuity.
First, it is largely hypothetical. We do not observe any one thing continuously, and it is merely a hypothesis to a.s.sume that, while we are not observing it, it pa.s.ses through conditions intermediate between those in which it is perceived. During uninterrupted observation, it is true, continuity is nearly verified; but even here, when motions are very rapid, as in the case of explosions, the continuity is not actually capable of direct verification. Thus we can only say that the sense-data are found to _permit_ a hypothetical complement of ”sensibilia” such as will preserve continuity, and that therefore there _may_ be such a complement. Since, however, we have already made such use of hypothetical ”sensibilia,” we will let this point pa.s.s, and admit such ”sensibilia” as are required to preserve continuity.
Secondly, continuity is not a sufficient criterion of material ident.i.ty. It is true that in many cases, such as rocks, mountains, tables, chairs, etc., where the appearances change slowly, continuity is sufficient, but in other cases, such as the parts of an approximately h.o.m.ogeneous fluid, it fails us utterly. We can travel by sensibly continuous gradations from any one drop of the sea at any one time to any other drop at any other time. We infer the motions of sea-water from the effects of the current, but they cannot be inferred from direct sensible observation together with the a.s.sumption of continuity.
The characteristic required in addition to continuity is conformity with the laws of dynamics. Starting from what common sense regards as persistent things, and making only such modifications as from time to time seem reasonable, we arrive at a.s.semblages of ”sensibilia” which are found to obey certain simple laws, namely those of dynamics. By regarding ”sensibilia” at different times as belonging to the same piece of matter, we are able to define _motion_, which presupposes the a.s.sumption or construction of something persisting throughout the time of the motion. The motions which are regarded as occurring, during a period in which all the ”sensibilia” and the times of their appearance are given, will be different according to the manner in which we combine ”sensibilia” at different times as belonging to the same piece of matter. Thus even when the whole history of the world is given in every particular, the question what motions take place is still to a certain extent arbitrary even after the a.s.sumption of continuity. Experience shows that it is possible to determine motions in such a way as to satisfy the laws of dynamics, and that this determination, roughly and on the whole, is fairly in agreement with the common-sense opinions about persistent things. This determination, therefore, is adopted, and leads to a criterion by which we can determine, sometimes practically, sometimes only theoretically, whether two appearances at different times are to be regarded as belonging to the same piece of matter. The persistence of all matter throughout all time can, I imagine, be secured by definition.