p It has long been known that a natural science is converted into an exact study of nature through measurement. Progress is also impossible in applied science without measurement. The idea of the leading role of measurement in physics has been established in scientific thought since the days of Galileo. The whole history of natural science and philosophy witnesses to the mounting significance of mensuration in the development of human culture and scientific understanding. The thinkers of antiquity, and Leonardo da Vinci, Descartes, Newton, Leibniz, Lomonosov, Kant, Hegel, Gauss, Helmholtz, Mendeleev, Einstein, and Bohr made a profound analysis of fundamental aspects of the problems arising, developing the theory of mensuration and its logical foundation. Light was thrown on the methodological and epistemological foundations of this theory from the standpoint of dialectical materialism in the work of the classics of MarxismLeninism. This was first done by Karl Marx in Capital on the material of political economy, and in other works; the whole course of Marx’s ideas about measurement, as Engels noted,; had] a direct] bearing on mensuration in science.^^1^^

p So one cannot agree with those authors who—in this case either knowingly or unwittingly ignoring the history of science and philosophy—do not see any broad theoretical problems in the idea of measurement. Measurement cannot 257 be reduced to the simple procedure of ’look and see’, recording the readings of a measuring device. In this respect Lebesgue is^certainly right when, speaking about the measurement of geometric quantities, he draws attention to the fact that though ’a geometrical measurement begins physically..., it is only achieved metaphysically’.^^2^^

p This statement is valid not simply to the measurement of geometric quantities: ‘metaphysics’, or rather theoretical thinking, cannot be banished from the measurement either of geometrical or of any other quantities. Indeed, it is impossible, in particular, in measurement, to avoid the concept of infinity (with which, for example, the concept of absolutely accurate measurement is conjugate), and infinity cannot be studied in a visualised, empirical manner.

p Let us note in addition that no physical theory that reflects objective reality can ignore the need to link its mathematical apparatus up with the readings of the experimental devices. How is the passage made in physics from mathematical abstractions to the ‘observed’ in experiment, and from the observed experimental data to the equations of theory? Analysis of this question leads to most important philosophical problems specially connected with the development of modern, non-classical physics, which usually deals with objects and phenomena not directly perceivable, understanding of which does not fit into the schemes of classical theories.^^3^^ On the other hand, problems of determining physical principles on the basis of measuring observable properties, and the transition from the principles of the theory to the measured properties, had already been posed by classical physics.

p Mensuration thus unites the formulas (the mathematical part) of theory with the ‘visualisation’ (the ‘visualisable’ part). Problems of the accuracy of one theory or another cannot be solved independently of measurement. Mensuration also belongs, of course, to the crossroads, so to say, of the ideas of discontinuity and continuity in the cognition of nature. This list alone is sufficient (analysis of the related problems is also our concern) to conclude that the philosophical status of mensuration is still very, very far from crude obviousness.

p What, then, is mensuration? If we bear its definition in mind we can justifiably say that it is a cognitive process 258 in which information is obtained through experiment on the numerical value of a measured quantity. This definition, like definitions of this kind in general, is necessary for everyday use.^^4^^ On the other hand, it is necessary, in order to get a quite complete scientific understanding of mensuration, to analyse its manifold real forms in their interconnection. The act of measurement itself usually implies the following elements as constituents of mensuration: (1) the object of measurement, i.e. the measured quantity; (2) the unit of measurement, i.e. the quantity with which the measured quantity is compared; (3) the observer, i.e. the subject making the measurement, and also the measuring instruments; (4) the methods by means of which the measurement is made and (5) the result of the measurement of the quantity. Some of these elements, which can be distinguished relatively clearly when we are dealing with an individual completed measurement made by an observer, may drop out when the measurement procedure is continuous and is included in the general system of operation of an automatic device. The observer may then not be directly involved in the measurement, since the information produced by the devices recording the measurement results is processed directly by the automatic device itself, which uses it to generate commands for its own working units.

p Do the possibility and fact of automatic measurement mean that mensuration itself, in ?ome cases at least, is ceasing to be a cognitive process? One meets such statements in the literature.^^8^^ One cannot, however, agree with them. Any automatic device, no matter how ‘perfect’ it seems, is essentially an artificially constructed organ of labour or organ of man’s cognition, and it would be only a physical system outside its relation to and peculiar connection with man (which connection expands his field of activity, including cognition). This circumstance also answers the question posed.

p Let us note, finally, that any accurate measurement is impossible outside application of the laws governing the measured quantities, and is based on definite theoretical premises.

These remarks outline the context of the exposition that follows. It does not in the least claim to be a complete analysis of the problems of measurement.