212 IV, STRUCTURAL FACTORS IN A LANGUAGES |
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1933, We do not make any metaphysical assertions about 'time' and we should not be surprised to find that statements involving 'years' are generally propositions, but that statements involving 'time' often are not. It is necessary not to forget this to appreciate fully what follows.
The theory of infinity will clear away a troublesome stumbling-block. We will use the expression 'infinite numbers of years', remembering the definition of 'infinite number/ and what was said about the
unit-process which we call a year. We have seen in an example above that if only a hundred individuals attend a lecture, and all 'by chance' have their names begin with M, such an event happens, on an average, only once in an inconceivably large number of years, represented by a number with a hundred figures. If we would ask how many times an occurrence would happen, we would have to state the period in years for which we ask the how many. It is easy to see that in infinite numbers of years, this humanly extremely rare occurrence would happen precisely infinite numbers of times, or, in other words, 'just as often', this last statement being from a non-anthropomorphic point of view. An event that appears, from our human, limited, anthropomorphic point of view, as 'rare', or as 'chance', when transposed from the level of finite process, arrays., to that of infinite processes, arrays., is as 'regular', as much a 'law', involving 'order', as anything else. It is the old primitive s.r to suppose that man is the only measure of things.Here the reader might say that infinite numberj of years is a rather large assumption to be accepted so easily. This objection is indeed serious, but a method which can dispose of it is given later on. At this stage, it is sufficient to say that, on the one hand, this problem is connected with the semantic disturbance, called identification (objectifica-tion of 'time'), which afflicts the majority of us, excepting a few younger einsteinists; and that, on the other hand, it involves the structurally reformulated law of the 'conservation of energy', 'entropy',.
Before parting with the problem of infinity, let me say a word about the notion of 'continuity', which is fundamental in mathematics. Mathematical continuity is a structural characteristic connected with ordered series. The difficulties originated in the fact that a 'continuous' series must have infinite numberj of terms between any two terms. Accordingly, these difficulties are concerned with infinity. That mathematicians need some kind of continuity is evident from the example of two intersecting lines. If the lines have gaps, as, for instance, there would be the possibility that two gaps would coincide, and the two lines not intersect; although in a plane the first line would pass to the other side of the second line. At present, we have two kinds of 'con- |
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