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Quelques précisions sur la méthode des potentiels-vie et ses notions fondamentales. (En réponse aux critiques du Prof. Wilhelm Winkler)

Liebmann Hersch
Revue de l'Institut International de Statistique / Review of the International Statistical Institute
Vol. 12, No. 1/4 (1944), pp. 23-35
DOI: 10.2307/1401069
Stable URL: http://www.jstor.org/stable/1401069
Page Count: 13
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Quelques précisions sur la méthode des potentiels-vie et ses notions fondamentales. (En réponse aux critiques du Prof. Wilhelm Winkler)
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Abstract

The writer thanks Prof. Winkler in the first place for his remarks, and with gratitude takes notice of his conclusion according to which the study of the life potentials of a population "offers an interesting enrichment of our demographic knowledge", as well as of his agreement in principle as regards the various developments which the idea of life potential implies. As to Prof. Winkler's criticisms, the writer examines them one by one, either to make the corrections which seem necessary to him, or to reject them as the product of a misunderstanding. Here is a summary: Prof. Winkler's criticisms are of two kinds: the first category refers to the form writer has used in his studies on life potentials; the other category relating to the essence itself of these papers. To the first belongs, to begin with, the question of the algebraic symbols used by writer. The latter agrees that in principle it would be desirable to indicate each notion by the initial letter of the corresponding latin term; but as in this way, different notions would often be indicated by the same letter, there are also other considerations to be taken into account. So he endorses the wish expressed by Prof. Winkler that the International Statistical Institute may put the problem of the uniformity of the symbols to be used in the statistical analysis of social phenomena on the agenda of one of the next Meetings. The question of the use of the infinitesimal calculus in statistics belongs to the same category of remarks. According to writer its use is justified, whenever it is indispensable; in the future, with the spreading of the knowledge of higher mathematics, it will also be justified, whenever it only offers a simplification of the elementary calculus. However, at the present moment, writer thinks, and with him a number of eminent statisticians, that it is preferable to work in those cases with the help of elementary mathematics, even if the calculations should be more complicated and longer, in order not to limit without necessity the circle of readers for whom the study is meant. Those who are familiar with the infinitesimal calculus will moreover be able to transform without any difficulty the formulae with elementary bases into integral formulae, and thus save certain intermediate developments, as Prof. Winkler has done in his article, and as did at the time, in writer's Seminary, his pupil M. J. Stachel (cf. Annex). As regards the category of essential remarks made by Prof. Winkler, part of them are meant to point out mistakes in the deduction of certain formulae given by writer; other remarks refer to some of the fundamental notions of the method of life potentials. Writer shows that the so-called mistakes do in no way weaken his deductions, since they are only inaccuracies within the limits of the degree of approximation admitted implicitly, or even explicitly by writer, or resulting from a misunderstanding by the critic. Among the fundamental notions, Prof. Winkler rejects entirely that of the average life potential per head of the population, and with it the notion of generalised expectation of life, on the presumption that an average taken from a heterogeneous mass only has sense, if this heterogeniety is of a political or social character, but not of a natural one. Writer shows the inconsistency of such a conception, and in accordance with the ideas which he das developed before in this Revue, emphasizes that the interest of such averages, whether they refer to natural or to social phenomena, lies in their synthetic character; for they give us the resultant of the multitude of the real factors which act on the phenomena under consideration, included the particular structure of the mass in which the phenomena have been observed. These averages, frequently used in statistics, give a reduced representation (on an individual scale, per 1000 inhabitants, etc.) of the sum from which they are derived; they are interesting in so far as the sum itself is interesting. As the sum of the life potentials of the entire population offers a great interest, the average life potential of a population is interesting in its turn. It permits comparisons between the vitality of populations, very different in number, as noticed in reality under the combined action of their particular age composition, and of their survival (or mortality) at various ages. By way of illustration writer gives in a note data which have been compiled in his Seminary, concerning the total average life potential, and the average female life potential for the age of procreation (15 to 49 years) in eight European countries, from which results among other things that for France the first coefficient was about 1930 7.1 years, and the second 2.6 years lower than for the Netherlands. In addition, the generalised expectation of life does not only involve more extensive magnitudes, but also more restrictive and better defined ones than the traditional notion of expectation of life (e.g. the expectation of life of a man of twenty for working age or for the age of retiring, the expectation of life of a female newly born for the age of procreation, and so on). The other observations made by Prof. Winkler give writer an opportunity to stress the following points: 1. The traditional demographic method deals with past realities, the method of life potentials deals with probable realities. 2. The method of life potentials characterises a given demographic situation in showing the subsequent developments which this situation implies, but it goes without saying that on account of the intervention of new factors, the real future may be very different from what results from the mere given demographic situation. 3. The method of life potentials is not meant to replace the traditional method, but should be used together with it, showing other aspects of demographic reality, especially its potential side, the vitality which a population bears potentially in itself. For more details writer refers to his study: "De la démographie actuelle à la démographie potentielle". Finally, in an Annex, writer reproduces with some observations, the extract of an exposition which has been established in his statistical Seminary, and which reduces the principal formulae of writer's first paper to one general formula in the form of a double integral.

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