MATEMATICA ŞI MECANICA ÎN ŞTIINŢELE SOCIALE. (Romanian)

Mathematics and Mechanics in the Social Sciences. (English)

The present study is based on a conference delivered by N. Ghiulea at the Sociology Seminar at the Jassy University on the occasion of the publication of Spiru Haret's work, Mecanique sociale (Social Mechanics, 1910). The study makes a synthetic presentation of the most relevant theories on how to apply quantitative methods to the investigation of social phenomena that have been up to then debated upon in the national and world literature in the field. In opposition to those who believe that mechanics is part of mathematics due to the fact that both sciences operate with numerical values, the author deems that the two disciplines have distinct subjects of research, as mathematics is the science of pure quantity, while mechanics is the science of motion in general. In addition, the methods used by the two sciences are essentially different: whereas the mathematical method involves complex logical reasoning, the mechanistic method is a system of reasoning that enables to determine the movement accompanying a phenomenon by knowing the forces that generate the movement and the circumstances in which the respective phenomenon is manifested. The mathematical method can be used whenever the constitutive elements of the phenomenon enable the employment of its reasoning, while the mechanistic method can be used when certain forces determine a movement or equilibrium between the respective elements. Focusing on the field of social sciences, the author asserts that the mathematical method can be applied to the disciplines that relate only to quantities, characterized by a static view on the phenomena - finances, statistics, insurances; the mechanistic method is useful to the disciplines governed by forces and motion, characterized by a dynamic view on the social phenomena - economics and sociology. The former group of sciences, namely those characterized by a static view on the social phenomena, is more briefly approached because mathematics has anyway played a leading part in their creation as they are essentially quantitative, and nobody has ever doubted the role and significance of the mathematical method in these sciences. Having a dual way of envisaging and approaching phenomena - its quantitative elements "favor" a static, mathematical approach, while the components "in motion" point to a dynamic, mechanistic approach - the science of economics enjoys a special attention from the part of the author. He states that the quantitative nature of the economic elements has compelled the economists who wished to give an accurate scientific form to political economy to employ the mathematical method. Nevertheless, reservations have been and are still expressed at the attempts at applying mathematics to the study of economic phenomena in spite of the fact that the mathematical method has already proved its efficiency. More fruitful have been the attempts of the economists who, understanding the deep nature of economic realities, have systematically employed mechanistic methods in their research. In the economic thought, the "mechanistic" approach has a long standing tradition. From its earliest stages, the vocabulary of mechanics has been most successfully used in this field. The notions peculiar to mechanics, such as: equilibrium, stability, elasticity, expansion, pressure, dilatation, contraction, flux, reflux, force, movement, resistance, action and reaction, distribution, friction, etc. have already been adopted by the classics of economics, Adam Smith, for instance, who "used terms and expressions from the field of mechanics in his works". As far as economics is concerned, the presence of real forces and movements in society has been put into evidence by many sociologists-economists. According to the author, Irving Fisher and Vilfredo Pareto are the most illustrative names associated with laying the scientific foundation of the importance and value of applying the mechanistic method in economics, who elaborated the mechanistic view on economic reality. In spite of the fact that he did not elaborate a comprehensive economic theory, I. Fisher was the first representative of mechanistic interpretation in economics who rigorously applied mechanistic methods to solve seminal economic problems. Although he did not deal thoroughly with dynamic questions of pure economics, he did nevertheless pay enough attention to economic dynamics. In his turn, V. Pareto's mathematical approach to production and exchange endowed economics with a strong mechanistic character. His system, whose basic features were described by N. Ghiulea, was the most comprehensive system of mathematical economics, but in his case as well "static" prevailed over "dynamic" economics, which made it incomplete. The example of "economic mechanics" was followed by sociology, certain representatives of the science tried to determine the criteria for applying the mechanistic methods to the research in the field, namely to lay de foundation of a social mechanics. The core principles of mechanics, being so general, were thus extended to the study of social phenomena and movements. Asserted as early as Antiquity, when the principle of attraction and rejection was considered the foundation of social life, mechanistic sociology found its earliest "modern" expressions in the theories of J. Fr. Herbart, A. Quetelet, H. C. Carey, H. Spencer, and Ch. Mismer. But the true measure of mechanistic sociology was revealed in the works of Lester Ward - who defined for the first time sociology as "social mechanics" with its two subfields: social statics (studying social equilibrium) and social dynamics (studying social transformation, social progress) - and Léon Winiarski - the author of the first scientific system of social mechanics presented in his work Essai sur la mécanique sociale. The system was built according to the model of rational mechanics. It was based on the principle of universal attraction as the social system is but a "material system in which molecules are held together by the forces of attraction and repulsion", an "aggregate of individuals-molecules" forever in motion, in which the constitutive elements move closer or farther away from one another. The aggregate is constantly subject to the action of several forces none other than man's needs and wishes that aim at procuring maximum pleasure for the individual and the society. All social forces are born form various combinations between twofundamental forces that move the individual: egoism and altruism, which "can be seen as playing the same part as attraction and repulsion in a certain material or cosmic system". In this system, social functions and structures were the subject of statics, while the study of movements was the object of dynamics. In this context, the author also mentions a Romanian contribution to the field, namely the attempt of the mathematician Spiru Haret to elaborate a social mechanics as revealed in the work Mécanique sociale, whose publication has been the starting point of N. Ghiulea's paper. He is extremely critical towards the social mechanics conceived by S. Haret, which he regards as a "rigid application of rational mechanics to sociology". N. Ghiulea has a clear-cut perspective on the role and use or the quantitative method in social sciences in general, and in sociology in particular. In his opinion, the natural path of any positive science is the evolution from a qualitative and descriptive to a quantitative and causal stage. Like any other social science, sociology is a positive science because its object is the study of a reality, as social phenomena are real phenomena, social movements and regularities are natural movements and regularities, and its limitations are the natural limitations of our own knowledge like in the case of any other positive science. Consequently, sociology must have all the features of a positive science: it must be experimental, deductive, it must always expect confirmation or information of its deductions from experience, and lastly to evolve towards the quantitative and causal stage. Of course, it doesn't mean that if mechanics is the science of quantity, sociology, which must aspire to the status of quantitative science, is meant to make up a chapter of mathematics like algebra or geometry. This would be nonsense, chiefly because all positive sciences, even those that have reached the quantitative stage, preserve their distinct character of natural sciences. On the other hand, nobody should imagine that a formal, purely mathematical science could be able to encompass the entire highly complex field of sociology. There are many phenomena, many connections between phenomena in the field of sociology that could never be described in terms of mathematical formulae. In conclusion, sociology has to preserve its character of special science and only borrow the mathematical method whenever is possible and profitable. A science cannot progress but by itself. Not much is gained by comparing phenomena of different sciences, by making more or less valid analogies, or by borrowing alien methods. For that reason, the mathematical method should not be overrated. Mathematics cannot play other part in sociology than being a high judgment tool, a complex logical instrument untainted by human errors, a technique of research complementary to other methods. As concerns the mechanistic method, N. Ghiulea believes that it is called to play a significant part in social sciences, but he also emphasizes that, because of the complex social realities, social movements cannot be investigated by means of rational mechanics, which is not appropriate for such an approach, because it is restricted to the analysis of local movements and therefore is not enough even for the "world of physical phenomena". "Social mechanics will be a complex mechanics, with all-encompasing principles, with wide applications, whose pale image one may distinguish in thermodynamics". Giving up any forced comparison or analogy, the science of social movements should be conceived as a distinct science, a social mechanics that should study the nature and importance of social movements with its own methods. This is the only path to be followed by sociology in its evolution in order to become a deductive, quantitative and causal, distinct and clear-cut science. [ABSTRACT FROM AUTHOR]

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