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The Transition of Quality into Quantity

Prepared by the Leningrad Institute of Philosophy under the Direction of 
M. Shirokov 1941 

To attain to concrete knowledge we must not ascribe everything in the world to quality or to quantity but must explain the mutual connection and mutual transitions of the qualitative and quantitative definitenesses in every process. As Lenin showed, the dialectical law that connects quantity with quality is only an example, a partial case of a more general principle which he formulated as follows: “Not only is there unity of opposites, but there are transitions of every definition, quality, trait, aspect, property into each other (into their opposites).” In this formulation it is easy to recognize the concretization and development of this same unity and the mutual-penetration of opposites. The relation of quantity and quality is mutual, “each side passes over into each other.”

In actuality there is no such thing as quantity in general. There exists only the quantity of a determined quality. A mere number in itself says nothing to us about a thing until we know what this thing is and from what aspect and how it was measured. Two tons of iron and two motor-cars are by no means equal although for the purpose of mathematical operations which are abstracted from concrete things two is unconditionally equal to two. Number unaccompanied by a knowledge of quality conveys nothings But that which is dear to all in any example taken from life is by no means so evident to scientists and upholders of pure mathematics with their complex theoretical constructions.
It is by no means by chance that only at a determined stage of knowledge of qualities can every science put the question of the quantitative aspect of the processes it is studying. We saw above that chemistry could disclose the fruitfulness of the qualitative approach to elements only when these elements themselves were to a certain degree known and distinguished from each other. But as soon as the means of measuring chemical processes were discovered, chemists who had formerly been indifferent to quantity turned the quantitative approach into an absolute. In the majority of works on the history of chemistry everything that was done before this change of attitude is treated with the greatest contempt. Before Lavoisier people never dreamed about quantitative definiteness; if only they had done so two or three centuries earlier the history of chemistry would have been very different. That is the attitude and it is injudicious. Anyhow it is quite clear that by becoming worshippers of pure quantity chemists were cutting down the trunk by which they were climbing up. Contempt of quality became an obstacle to the future development of knowledge; it deprived the quantitative method of its necessary qualitative basis. The study of the quantitative aspect of things is in direct dependence on the depth and accuracy of the knowledge of their qualities. The physics of recent times was able to widen the application of mathematics, as it has done, only by accurately distinguishing between the qualitative uniqueness of the elements of matter and energy – atoms, electrons, quantum, etc. But at the same time owing to an unfortunate lapse into a metaphysical point of view on the part of bourgeois scientists this “great success of science, its discovery of the homogeneous and simple elements of matter, whose laws of motion are subject to formulae, caused matter to be forgotten by the mathematicians.” Lenin, Materialism and Empirio-Criticism, chap. v, sec. 8.

Except by ignoring the material and its qualities, it is impossible to turn the application of mathematics into a basic method of investigation. Mathematical calculations and formulae play in the actual study of an object a subordinate role, because they must always be secondary to the known quality of the thing. By turning mathematics into a basis of knowledge we adopt a procedure that leads only to a barren play of figures that mean nothing, a sophistry that enables us to prove anything however absurd. This secondary importance of mathematics is specially stressed in the difference of the role which it plays in the various sciences. The more simple the qualities that are being studied by this or that science, and the more apparent and external the relations between the elements of the process, and furthermore the greater the consequent ease with which these elements can be distinguished from each other, the wider is the scope of mathematical application.

Mathematics studies quantity, i.e. external definiteness. Mathematical operations presuppose a certain stability and independence of those things whose number and measurement is required. And the less their stability and independence are, the more complex are those mathematical operations which are needed for the study of the quantitative definiteness.

It is very easy and quite necessary to apply mathematical calculations to machines, which work according to a definite, exactly established pattern, whose separate parts have been made and assembled in a purely external fashion. But try to submit the life of an organism to the mathematical analysis and you will see that the fluidity and continuous mutual connectedness of vital processes convert your calculations into an empty play with mathematical symbols.

In astronomy and physics the application of mathematics has from ancient times held a very important place. Chemistry from Lavoisier’s time has studied quantitative relations, but the application of mathematics was limited to simple arithmetical processes. Only in recent times on a basis of studying the deeper aspects of chemical processes has the field of mathematical calculations in chemistry been extended But in one way or another the application of mathematics in this science occupies a place distinct in principle from its place in physics; it plays here a far more subordinate role. Chemical processes are more complex and the complete connection of their different aspects has been expressed in a much clearer manner than is possible by mathematical means.

Even more subordinate and restricted is the role of mathematics in the biological and still more in the social sciences.

Marx made use of mathematical formulae, but he never substituted them for an investigation of the quality of economic processes. On the contrary, these formulae served him only as an auxiliary means of illustration and for a more accurate expression of basic economic ideas.

Quantitative definiteness is just as essential in social development as in anything else, but among social phenomena the connection of quantity and quality is markedly more complex and close and therefore the abstract and complex formulae of modern mathematics, which have been devised for the solution of physico-mechanical and technical problems, are less applicable for dealing with the quantitative side of social processes. That is why the philosophy of pure mathematics is especially artificial in the realm of social sciences.

In bourgeois political economy and sociology mathematics emerges very often as the tool of plain political charlatanism.

One of the favourite methods of bourgeois scientists is the calculation of the average magnitude of a collection of different items. For example, if they want to know whether the standard of living of the peasantry is improving or not, they find out and add up the incomes of all the peasant economic units, and so work out the average income of a peasant’s farm. They compare such magnitudes for different years and demonstrate that capitalism in small-scale agriculture is not developing. It is easy to show that the root of this false conclusion lies in a wrong approach to the unit under consideration.

It is supposed that by uniting together into a unit the workers and the master farmers and thus arriving at an average income-budget it is possible to demonstrate a condition of ‘moderate satisfaction’ and of a ‘moderate net income.’ But the average is quite fictitious. It merely covers up the utter poverty of the mass of lower peasantry” (Lenin).

Figures obtained like that only obscure and confuse the picture of the actual position of the countryside.
“Instead of a study of the types of peasant economy (the day-labourer, the middle peasant, the big landowner) they study, with the ardour of lovers, endless columns of figures as if it were their aim to astound the world with their arithmetical zeal” (Lenin).
This empty “play with ciphers” this “arithmetical zeal” expresses the definite class setting of those who like to underestimate the development of kulakism in the countryside…. It is not without significance that critics of Soviet policy made considerable use of this method when they openly voiced the interests of the kulaks. Statistics play a great part in science and in practice, but in order correctly to make use of numerical data we must proceed from the qualitative differences of the enumerated phenomena.

As we have seen in all the material we have been analysing, the only way to knowledge is first carefully to study quality, then quantity, and finally to restudy quality on the basis of all the data. The dialectical way of knowledge is a reflection of the law of objective development. In the development of material actuality quality and quantity are inseparable. They presuppose and penetrate each other and their unity is expressed in continual mutual transitions. Not only does quantity go over into quality, but also the reverse – quality goes over into quantity, the quality of a process defines the line, the character and the tempo of its quantitative changes.

Let us return to concrete facts. In the transition from small-scale production to capitalist manufacture there took place at first the union of many tradesmen within one workshop. “The workshop of the guild master only widens its dimensions.... At first there is only a quantitative difference” (Marx).

However, at a determined stage quantity goes over into quality – the joint work of many workmen in a capitalist undertaking is qualitatively distinct from small-scale craft. And this new quality creates a new quantity. The cooperation of many persons, the fusion of many separate forces into one common force creates – as Marx puts it – a new “force,” which is essentially distinct from the summation of the particular forces that compose it. Whence does this new force appear, wherein lies the source of the magnification of the productivity of work? Quite evidently in that new quality which belongs to large-scale production. The new quality has created a new quantity, quality has gone over into quantity.

We see this same dialectical transition in the example of our collective farms.
The simple concentrations of the peasants’ implements within the collective farms has had an effect not contemplated on the basis of our earlier experience. How was this effect manifested? In the fact that the transition to collective-farming methods gave an increase of the area under crops of from 30 per cent to 40 per cent and even 50 per cent. How do we explain this astounding result? By the fact that the peasants, who were powerless under the conditions of individualistic work, have been converted into a very great power by the concentration of their implements and by uniting into collective farms.” Stalin, on the question of agrarian policy in U.S.S.R.
Metaphysicians separate quantity and quality, whereas in vital developments these categories are all the time making transitions into each other. Opportunists on the question of the transition of quality into quantity, as in everything else, take up a metaphysical view-point. Both the counter-revolutionary, Trotsky, and the Right-opportunists united themselves in defence of the theory of the declining curve of our economic growth. They asserted that with the transition from the restoration period to the period of reconstruction* the tempo of the development of industry would be continually lowered and would at last fall to the “normal” rate of increase, namely, that at which industry in capitalist countries develops. We have seen how drastically actual experience has treated this theory. Our tempo is determined by the qualitative advantages of planned socialist economy; the course of the qualitative changes of socialist production cannot fail to be different in principle from the growth of capitalism. The methodological root of the theory of the declining curve lies in the negation of the dialectical transition of quality into quantity.

* Restoration period – reconstruction period. From the end of the “war communism” period, during which foreign intervention had to be faced, down to the beginning of the Five Year Plan the national economy was undergoing restoration assisted by the New Economic Policy. The Five Year Plan initiates the period of socialist reconstruction.

A correct understanding of this transition plays a big role in the practical tasks of constructing a socialist economic order. In addressing the directors of Soviet industrial undertakings Stalin has pointed out a number of cases where the plan of developing industry has been unfulfilled because of inability to understand what new systems of working are possible under socialist construction. In his slogan of mastering technique in his Six Conditions* he showed the actual way to fulfil the quantitative indices of our plans, the way to achieve a Bolshevist tempo in socialist construction. Our successes have created a qualitatively new state of affairs; the new position demands a new quality of work, a new quality of direction, a qualitatively new approach to the organization of work on production, to the training of specialists, to the function of the old type of specialists, to the sources of accumulation in industry, etc. The way to raise the tempo is to master this new quality of work.

* Six Conditions. See Note on Section II, Chapter III.

Meanwhile, certain metaphysicians and simple-minded directors think that the whole matter can be settled by a clamour about tempo, by simple, mechanical administrative pressure, by a campaign successfully conducted to the end of the month or quarter, etc. Nothing is obtained by such an approach except the exchange of practical work for cheap and empty exhortations. Anxiety over high tempo if it is not based on a concrete study of the quality of the given production, if it is not based on a thoughtful and serious organization of the business side of production, is abstract, empty and impotent, like the numerical conjurings of mystics, like the “arithmetical zeal” of the bourgeois economists.

We repeat, the key to actual Bolshevik tempo lies in that change of the quality of work which is to be brought about by fulfilling the six conditions of Stalin, by studying the qualitatively unique conditions and possibilities of every branch of production, by showing a creative initiative in the organization of every qualitatively unique matter. “Write what resolutions you will, swear by what words you like, if you do not master the technique, the economics, the finances of the works, the mine, the factory – all will be fruitless.” Stalin, speech on the mastery of technique.

Stalin in his masterly and profound treatment of the question of the tempo of socialist construction, has over and over again showed the great importance of the dialectical materialist method in the proletarian revolution. Directors must learn the dialectic of Marx, Engels, Lenin and Stalin, for without dialectic Bolshevik direction is impossible. And so in the reverse transition, in the transition of quality into quantity, we have approached from a new side the unity of quantity and quality, thus making concrete once again the unity of opposites. The problem of knowledge is not limited by the disclosure of the quality of a thing, just as it is not exhausted by the establishing of its quantitative characteristic – the point of the matter is in the transition of quality and quantity into each other. Only by disclosing the peculiarity of the transition in every phenomenon do we know an object in its self-movement, in its vital and concrete development.

The resolution of the contradictions between quality and its particular level in the evolutionary process, its degree of development, is at the same time an intensification of that contradiction, which reveals the final limit of the quality and leads to a new leap. The higher the degree of the development of the given quality, the more clearly is its limitation revealed, the more clearly the premises and tendencies of the new emerge in it, tendencies which cannot develop within its confines and are preparing the leap to the new quality. The overcoming of the remnants of the old in the new, the unfolding of a given quality as a whole, single system are at the same time a process “of dividing the unity into its mutually-exclusive opposites” and the intensification of the conflict between them. The more capitalism is developed, the more strongly are revealed the contradictions between the socializing of work and private ownership, between the proletariat and the bourgeoisie, between the “changeableness” of capitalism and its “stability.” The highest stage of the development of a quality, which it reaches in its evolution, is at the same time the highest stage of the intensification of its contradictions, is its limit, its end. The highest stage of capitalist development – imperialism – is, at the same time, its last stage, the eve of the leap to socialism.

By examining quality first of all in its emergence and then in the process of its evolutionary development, as a transition of quality into quantity, we showed that this quantitative change is at the same time the preparation for the transition to a new quality. In our investigation we returned to the transition of quantity into quality. And this circle expresses the continuous course of development. Development can never stop still; in the birth of a quality there is already included the seed of its decay, the decay of the one is the inevitable beginning of the new and so on, endlessly.

We are evolving into communism, but the attainment of our aim by no means excludes its further development.
Utterly false is the usual bourgeois representation that socialism is something dead, frozen, given once and for all; it is a fact that only from socialism will begin the advance in every realm of social and personal life – an advance that will be a rapid, genuine, real mass advance, in which first the majority of the population and later the whole population will take part.” Lenin, State and Revolution, chap. 5, section iv.
As Marx said, the transition to communism will end the pre-history of human society and will begin its real history. We do not yet know through what qualitatively unique stages this future historic process will go, but we are assured that communism will never in any way be a system of sleep and stagnation.

The double, mutually contradictory transition of quality into quantity expresses the eternal cycle of development in which matter, through the ceaseless emergence and annihilation of the forms of its movement, keeps on reproducing itself in ever new movement and in ever new qualities.
Matter moves in an eternal cycle in which every particular form of the existence of matter – be it the sun or a nebula, a particular animal or biological process, a chemical combination or decomposition – is equally in transition, and in which there is nothing permanent except eternally moving matter and the laws of its movement and change.” Engels, Dialectic of Nature.
It is impossible to understand actuality with any degree of fullness, it is impossible to understand an object in its self-movement, until you disclose in it the cycle, the connection of its beginning and end.

The law of transition of quantity into quality and its converse show us the way to the understanding of this connection, to the study of the cycle of emergence and annihilation in all the phenomena of nature and society.
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