Ralph Dumain: "The Autodidact Project": "Idealised & Real Objects" by V. A. Lektorsky

IDEALISED AND REAL OBJECTS

V. A. Lektorsky

The interrelation of theory and its objects poses yet another problem, one that we have not touched on so far. Implementation of theoretical cognition involves the adoption of a whole series of idealisations, i.e., of assumptions or suppositions which essentially do not correspond and even sometimes contradict what can be directly observed.

For instance, the abstraction of actual infinity that was widely used in classical mathematics is based on the assumption that we can count the entire natural number series, although that is clearly impossible in experience. In constructing his geometry, Euclid assumed that any section of a straight line, however short or long it might be, may be divided into two with the aid of ruler and dividers. In classical physics, it is assumed that we can measure velocity at any given point of the path, that is, that we can measure instantaneous velocity.

The laws formulated in scientific theory also refer to certain ideal cases. Therefore their employment for the description of actual experience and for predicting future empirical facts is only possible if a whole series of additional factors are taken into account, those which are ignored by theory revealing the law "in pure form". Inasmuch as it is impossible to consider all these factors theoretically, there will always be a kind of gap between the flow of empirical events predicted by the given theory and that which we directly observe in experience, although this gap becomes smaller and smaller as science develops. Lenin pointed out the role of idealising assumptions in Marx's development of the scientific theory of political economy: “‘Concretely impossible’ is not only realisation as put forward by Marx, but also land rent as put forward by him, and average profit, and the equality between wages and the value of labour‑power, and much more besides. But the impossibility of something being realised in a pure form is not a refutation.” [54]

Idealisation means not only adoption of some assumptions in formulating theoretical laws but also in constructing idealised objects. The "material point", a concept widely used in classical mechanics, is an example of such an idealised object. It is assumed that such an object, which exists in time and space, has mass (as all real bodies) and at the same time it has no extension. that is, coincides in fact with the mathematical point in this respect. Another example of an idealised object is "incompressible liquid" studied in hydrodynamics. Clearly, idealised objects have no real referents; they are constructions of theoretical thinking (sometimes called "intratheoretical", distinct from "extratheoretical" objects, that is, those which exist independently of theory). The question naturally arises, what is the reason for such fictitious objects?

Constructing idealised objects is a way of formulating idealised assumptions and a method for establishing, "in a pure form", certain dependences expressed in theoretical laws. For example, if a real body moves under the action of a force applied to its centre of gravity, the motion of that centre does not depend on either the geometrical form of the body or the distribution of mass in it but only on the overall quantity of mass. The centre of gravity moves as if the entire mass were concentrated in it, i.e., like the idealised object known as "material point". Establishing with the aid of the idealised object the dependences obtaining in the motion of bodies under the impact of a force applied to the centre of gravity, we get a key to the whole of the complex system of dependences existing in the diverse cases of real mechanical motions.

What is the nature of the dependences formulated in a theory on the basis of a number of idealising assumptions? Should they be regarded as mere subjective "simplifications" or "schematisations" of actual empirical situations (this interpretation of the idealisation procedure is not at all rare)?

It appears that idealisation cannot be reduced to "simplification" of that which is given in experience. In idealisation one not only ignores certain factors given in experience but also formulates in some cases assumptions which cannot be realised in experience. Idealisation can therefore serve to establish essential, objective and real dependences, for revealing various connections "in pure form" is exactly the discovery of actual substantive relations which do not directly coincide with dependences characterising the phenomenon and registered in experience. However, one may accept that a theory formulating definite dependences in a system of scientific laws reflects objective, real substantive relations, while believing at the same time that all theoretical objects constructed with the aid of theory have no real referents, that is, are idealised, fictitious objects playing a purely auxiliary role in formulating definite dependences. It will have to be recognised in this case that only those objects are real that are fixed at the pre‑scientific level, that is, through ordinary perception and in terms of everyday language. Those who hold this view argue that knowledge of any theoretical object is always introduced through a number of idealisations. That means that the object itself is always an idealisation, that is to say it has no real referent leading "intratheoretical" existence, so to speak. [55]

Let us note, however, that the knowledge, recorded in ordinary perception, about objects the reality of which does not occasion any doubts, also implies a whole series of assumptions and hypotheses; we considered this point in the previous section. True, the assumptions on which perception is founded, as distinct from the idealisations used in science, are implemented in the sense experience itself and are therefore not even consciously realised, as a rule. It is important in any case that, far from excluding the possibility of correlating knowledge and real objects, adopting a number of assumptions and suppositions is a necessary condition of such correlation. Where there are no definite assumptions, it is impossible to separate a real object from a subjective illusion. Let us note further that dependences formulated by science "in pure form" (their establishment naturally assumes the adoption of a number of idealisations) need not necessarily have only "theoretical objects" as referents, that is, objects the knowledge of which is only possible at the theoretical level. They may also be objects fixed in ordinary experience, the reality of which causes no doubts. For instance, Marx's Capital establishes the laws of the capitalist mode of production "in pure form" treating exclusively of real objects—commodities, men, their activity, machines, etc. Of course, the objects themselves are considered from a definite standpoint carefully formulated in theoretical assumptions, the elaboration of the theoretical system involving consistent analysis of those factors that had to be ignored at the initial stage (the famous method of ascending from the abstract to the concrete). [56] Let us note, finally, that science does not at all identify theoretical objects with idealised ones. That means that at least some of the objects the knowledge of which is introduced at the theoretical level are accepted as existing objectively and really: molecules, atoms, electrons, positrons, virtual particles, events in the four‑dimensional spatio‑temporal continuum, the field, quarks, etc. This point is extremely important, for the very distinction between idealised and non‑idealised objects, that is, real ones, is only possible and meaningful if we know which objects are real and what their characteristics are.

This knowledge is specified not only extra‑theoretically (e.g., with the aid of ordinary perception). The scientific theory itself introduces notions of such actually existing objects which may not coincide with the objects fixed in ordinary, pre‑scientific experience or may even be non‑observable (actually or in principle). Importantly, the assumption concerning the existence of a number of real objects the knowledge of which is specified only at the theoretical level is usually connected with formulating the so‑called nucleus of a research programme which serves as a foundation for subsequent development of a series of scientific theories; it determines to a considerable degree the heuristic possibilities of the given programme. Idealised theoretical objects are constructed only relative to real ones; they thus lack certain characteristics of real objects or, on the contrary, possess properties impossible in real objects. [57] It follows from this, among other things, that idealised objects may be idealisations not only of the real objects which are given at the extratheoretical or even extra‑scientific level (as a rule, the actual prototypes of idealised objects are interpreted in exactly this way), but also of the real objects knowledge of which can only be acquired theoretically. It is essential at the same time that the objects which are assumed at the given stage of the development of science to be actually existing, may be either rejected as completely fictitious in the course of changes in scientific conceptions (that was the destiny, e.g., of such a theoretical object of classical physics as ether) or relegated to the status of idealised objects (the atoms of classical physics as compared to the actual atoms with which modem physics deals).

If the structure of theory should be considered purely formally, without regard for its various meaningful layers, and if the meaning of the theoretical system should be reduced to a set of prescriptions for measurement operations, the difference disappears, of course, between idealised and real theoretical objects: all objects specified at the theoretical level will seem mere auxiliary constructs.

However, we shall try to demonstrate that the content aspect, the referential meaning of theoretical constructions cannot be ignored.

The procedure usually referred to in logic and the methodology of science as idealisation includes in actual fact a number of different procedures. Along with idealisation proper, aimed at establishing the substantive dependences of the processes under study, and thus permitting to study a definite system of connections "in pure form", procedures are usually included here which are not in actual fact idealisations but might more precisely be referred to as "simplifications". The latter are widely used for convenience of calculations (e.g., representing the electron orbit as circular, application of geometrical optics as a convenient simplification for purely practical purposes, etc.). It appears that the reduction of the entire range of devices used in constructing knowledge about theoretical objects to idealisation only greatly impedes the analysis of the nature and structure of scientific theory.

Thus the application of the idealisation procedure as a necessary element of constructing a scientific theory does not eliminate the possibility of studying such real objects the knowledge of which is obtained only at the theoretical level.

Finally, let us consider yet another argument used in contemporary Western literature on "the philosophy of science": the assertion of the impossibility of obtaining adequate knowledge about real objects studied at the theoretical level.

We are dealing here with representing theoretical statements as an ensemble of the so‑called Ramsay propositions. For this, the given theory must first be axiomatised and then a conjunction formed of all the axioms of the given theory and of the "correspondence rules" linking theoretical terms with those of observation. This conjunction may tentatively be represented as — —p— — —q— — — . . ., where p and q are theoretical terms and dashes signify those propositions of the given conjunction of which p and q are terms. Then p and q are replaced in this conjunction by the variables connected with the existential quantifier. As a result, the so‑called Ramsay propositions are obtained: (∃ f ) (∃ g). . . (— — —f — — —g— — —. . .). On the content plane, the Ramsay method of eliminating terms pertaining to theoretical objects may be illustrated as follows. If, for instance, the theory originally contained the assertion that there exist atoms with such and such characteristics, and that the processes in which they participate are associated in such and such a manner with what is observed in experience, after eliminating the terms pertaining to the theoretical objects by means of the Ramsay propositions, we shall obtain the proposition that, if there exist certain non‑observable objects (of indefinite nature) connected in a definite manner with what is observed in experience. we shall empirically state such and such facts. It is easy to show that after the terms pertaining to theoretical objects are eliminated by the Ramsay propositions, the theory will yield the same observation propositions as were yielded by the original axiomatised theory. This is taken as proof that a theory rewritten in Ramsay propositions has the same content as the original version of the theory. But the new variant of the theory does not contain direct knowledge of the theoretical objects. They appear as something unknown, as an x which, though recognised as existing, is not an immediate object of knowledge. Grover Maxwell, mentioned above, infers from this that theoretically fixed real objects, as distinct from empirical ones, may only be cognized in an oblique, symbolic way, that is, knowledge of these objects cannot be regarded as adequate. [58]

It is easy to show, though, that this conclusion is untenable. Let us point out, first of all, the inadequacy of presenting the very structure of the theory in this case. We have already commented on the unjustifiability of presenting a theory in terms of an axiomatised calculus which is given a meaningful interpretation exclusively in terms of "correspondence rules" linking theoretical terms with those of observation. In actual fact, science describes experimental data in theoretical terms, and "purely" observational non‑theoretical terms are not employed in the production of scientific knowledge. For this reason "correspondence rules" in their positivist interpretation are non‑existent, strictly speaking. It is therefore impossible to outline the potential empirical applications of this theory (through the mediation of other, "auxiliary" theories, as a rule) beforehand: they are not fixed, and are discovered gradually, along with the elaboration of the given and other theories. It is therefore difficult to compare two theories (or two versions of a given theory) in terms of the possibilities of their application in experience. Yet even if we accept that the presentation of the structure of a theory used in the above argument about the elimination of theoretical terms is justifiable, the very possibility of rewriting the theory in terms of the Ramsay propositions arises only when this theory has already been formulated. It is easy to see that if the task was, from the outset, to construct a theory in which the terms pertaining to theoretical objects were eliminated according to Ramsay's rules, we could hardly have a single theoretical system. The assertions regarding the connections in which theoretical objects are included are determined by the meaning, the content ascribed to these objects. If the nature of the theoretical objects is unknown to us (and rewriting a theory in terms of the Ramsay propositions compels us to recognise precisely that), it is not clear why these x's, the existence of which we postulate according to the Ramsay rules, must be connected by such and such relations. Rewriting a theory in terms of the Ramsay propositions looks like a clever trick which does not express real connections between theoretical assertions and which itself only becomes possible on the basis of the unfolding of the content of the theory, assuming as it does a knowledge of the meaningful dependences between theoretical objects. The possibility of obtaining knowledge about certain real objects only on the theoretical level does not at all make this knowledge inadequate or defective. It may be assumed that the experimental observability of the object facilitates acquisition of knowledge about it, but this fact has no direct relevance to the substantive meaningful characteristic of this knowledge. The fact that a non‑observable object becomes observable (which sometimes happens, as we pointed out above) does not prove that our previous knowledge of this object was "symbolic" and that only now does it become genuine. On the contrary, the justifiability and adequacy of knowledge obtained at the theoretical level is here confirmed.

Of course, many essentially non‑observable objects with which theory is concerned radically differ in their characteristics from ordinary observed bodies. (For instance, the particles differing in their position in space but identical in the rest of their properties, are regarded as identical m quantum mechanics.) However, the fundamental difference between objects of different types does not follow from their observability or nonobservability but from their different real nature, for it is the latter that determines the possibility or impossibility of their observation.

In conclusion, let us touch on some general points.

In pre‑Marxian philosophy, it was usual to interpret knowledge of real objects (strictly speaking, knowledge can only relate to real objects, for otherwise it is not knowledge but something else) as something more or less immediately given. Our analysis of some methodological problems involved in the study of the structure and content of scientific knowledge proceeded from the fundamental propositions of Marxist philosophy about the dialectically mediated nature of any knowledge. We have endeavoured to show that the existence of definite assumptions does not at all exclude the possibility of relating knowledge to an object existing in reality, independently of an act of cognition; on the contrary, the characteristics of real objects can only be established on the basis of a number of premises, assumptions, hypotheses, etc. (of course, on condition hat these assumptions and hypotheses are in one way or another justified in practice, however complicated the justification might be).

Marxist‑Leninist philosophy emphasises the genetic and functional dependence of cognition on practical activity with objects directed at transformation of natural and social reality. It is also pointed out that cognition differs essentially from practical activity on a number of vital points. Cognition is also a definite form of the subject's activity, but this activity is aimed, at any level and in any form, at revealing the substantive content of a system of real objects. The subject's activity is only possible in the framework of definite assumptions about the content of these objects and cannot therefore be viewed as simple constructing or creation of a certain ensemble of artificial structures without real referents. In this case, cognition can deal with real objects even if they are not in principle given in experience. Cognition is an activity of a special kind which assumes the use of definite referential meanings, object‑hypotheses, norms, etc., and aims at reconstructing a system of substantive relations between real objects. The operations included in cognitive activity, both experimental ones and the operations of measurement, have meaning only in the context of definite assumptions about the real nature of the objects studied.

Notes

54 V. I. Lenin, "To A. N. Potresov", Collected Works, Vol. 34, Moscow, 1977, p. 34. [—> main text]

55 See e.g. B. S. Gryaznov, "Theory and Its World", B. S. Gryaznov et al., Theory and Its Object, Moscow, 1973, pp. 5‑38. [—> main text]

56 On Marx's method in Capital see M. M. Rozental, The Dialectics of Marx's "Capital", Moscow, 1967; V. P. Kuzmin, The Systems Principle in Marx's Theory and Methodology, Moscow, 1976; The History of Marxist Dialectics from the Origin of Marxism to the Leninist Stage (ed. by M. M. Rozental), Moscow, 1971, (all in Russian); E. V. Ilyenkov, The Dialectics of the Abstract and the Concrete in Marx`s "Capital", Progress Publishers, Moscow, 1982. [—> main text]

57 Dudley Shapere formulates the following features inherent in the real objects with which scientific theoretical thinking is concerned and which are absent in the idealised objects:

(1) If object A exists really, it can interact with other real objects, in particular macroscopic ones (which is not true of idealised objects);

(2) To say that "A exists" implies that A may have properties which have not yet been discovered;

(3) A real object A may be ascribed properties which it does not actually have, but which may subsequently come to light (it would obviously be meaningless to refer the features formulated in points (2) and (3) to idealised objects);

(4) If A actually exists, there may be different and even competing theories about it (as is actually the case with the electron); A thus acquires what amounts to a theory‑transcendent status.

See D. Shapere, "Notes toward a Post‑Positivistic Interpretation of Science", The Legacy of Logical Positivism, ed. by P. Achinstein and S. F. Barker, Baltimore, 1969, pp. 155, 156.

Also: D. Shapere, "Scientific Theories and Their Domains", The Structure of Scientific Theories, pp. 567‑569. We shall point out in this connection, that the so‑called abstract objects studied in mathematics (numbers, sets, functions etc.) express certain relations between real objects and not real objects existing in space and time. [—> main text]

58 G. Maxwell, "Theories, Perception, and Structural Realism”, The Nature and Function of Scientific Theories, University of Pittsburgh Press, 1970, pp. 3‑34. [—> main text]

Lektorsky, V.A. [Lektorskii, V. A.]; translated by Sergei Syrovatkin. Subject, Object, Cognition (Moscow: Progress Publishers, 1984), Part 2, Chapter 2.2, pp. 166-173, 272.

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