Algunas observaciones acerca de las relaciones temporales

Abstract

The argument about the possibility of a reductio of the concept of time to that of the relation of succession has been opposed by philosophers like Mc Taggart according to whom it is necessary to divide the temporal flux into three parts: past, present and future; and such a distinction can not be reduced to the series based on the relation of succession.
In the present paper we go beyond that point and we attempt to show that both series: 1-earlier-later and 2-past-future, require, to make sense, a more complex relational structure.
In our view, the main difficulty in these approaches lies in the fact that neither of them provides an adequate definition of ‘instant’. If we attempt to give to this notion the dimensional thickness which corresponds to it, we are led to the statement that an instant p belongs and does not belong to class T, which implies the infinite subdivision of the instant p, in consequence it will never be possible to provide instant p with an exhaustive placement in the temporal flux. When a definition of ‘instant’ as punctual and dimensionless be given, we are led to the paradox of not being able to explain how a succession of instants is a duration.
A characterization of temporal relations which provides a definition of ‘instant’ not liable to these difficulties will have to take into account the function fulfilled by something which does not change in the constant temporal flux with respect to the changes. If this “permanent” is not somehow witness of change, that is to say, if is not provided with a sufficiently loose concept of identity to accept that something is x and nevertheless it changes from t to t′, it will not fulfill its function. We imply that this “permanent” should be a temporal subject (an a-temporal subject would probably have a more rigid concept of identity).
In fact, if the permanence of Egypt’s pyramids were sufficient to realize that trees turn periodically over new leaves, would not be necessary the presence of a subjective permanence such as that we are asking for. A non-testimonial permanence, in the sense described, does not have, in fact, temporal cycles: the concept of instant as well as that of present becomes extended, in a way; we mean that the present of the pyramids extends itself from a non easily identifiable date in the dynasty of the Ramessides to our own time, where the event of a fall of a plaster is the only interruption of such monotony. It is evident that such permanence neither can grasp cycles nor can tell us anything about change.
What is the position of our postulate of the “temporal subject” in connection with these questions?
The events belonging to the set of relation of succession gather themselves and belong to a set which can be actualized, that is to say, that they enter into a past.
The present is configurated by those events which are included in an actual perception as simultaneous. It may be argued whether or not it is possible to include in this present a minimal instance of succession; since this problem will take us beyond the scope of the present work we shall not consider it here.
In connection with the concept of future, we understand that this notion is only possible as a function of cycles from which the temporal subjects infer their continuation. Returning to our example of the pyramid, the concept of ‘morning’ does not make sense because it is not related to the event night in a way in which these events are related in a temporal subject. Anticipating a possible misinterpretation of the present paper we state that we are not concerned with the problem of whether those events occur and occur successively, but only with the fact that such relationship is not meaningful for the pyramid. According to us it is only meaningful in a case of a temporal subject.