on some interpretation of the marxist methodology

BERICHT

On Some Interpretation of the Marxist Methodology

L E S Z E K N O W A K

Summary

The peculiarity of Marx's investigation method is the use of idealization, i. e. idealizing assumptions are introduced, the laws, being in force under these assumptions, are being established, and then these assumptions are being removed with the simultaneous modifi- cation of the law. This method has not been recognized in the contemporary methodology because it assumes the essentialist vision of reality while contemporary methodology developed from the phenomenalism which negates the differentiation between essence and experience.

Much is said in the marxist literature about the methodology employed and advised by the makers of marxism. It is also thought that their methodology is right and original, and that it differs from all other methodologies of science that we know today. It is also true that not many non-marxists would like to point out that the marxists are wrong in saying that. The latter fact should put those who believe that marxism has something to say in philosophy of science on guard: if someone says something important others usually are bound to protest. But who is bound to protest hearing that Marx employed deduction and induction, synthesis, and analysis as well, a historical method -- but a logical one, too, dia- chronic explanation -- but a synchronic one, too, etc. etc. ? And if all this is expressed in a vague manner, if all this is not a justification of Marx's scientific practice, but a claim lost in a jungle of quotations?

I t can be supposed t h a t the books of the marxists who present the Marxian methodology are often committing the sin of ecclecicism. The methodology of the author of Caflital is presented as an aggregate of trivial or vague principles of a cognitive conduct, for the authors describe only what Marx says on various topics. To make it short -- they do not view Marx's works as an object of investigation which has to be exfllained in order to find out what is inside them; instead, they view them as a Scripture which has to beflresented to the world. But the marxist methodology is not ~bresented in the writing~ of the classics, it is employed in them. Hence, it cannot be quoted, it should be reconstructed in the same way a physicist reconstructs the principles of nature. With the latter view in mind it becomes clear that there is no single unfallible way of finding out what the marxist methodology claims. Hypotheses only can be pres-

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142 Leszek N o w a k

ented and they ought to be possibly well justified with the instances from the scientific investigations of the classics and from their methodological comments.

This would constitute the first step. I t will be demonstrated how the makers of Marxism conducted their research on economy, sociology and history. The problem arises whether the methodological rules they employed -- more or less consciously -- are really interesting from the viewpoint of a scientific method as defined by numerous contemporary methodological schools. If it turns out that they conducted their research in a different way than they should have done according to these schools, then a valid argument that there is indeed the marxist methodology shall be obtained, and it will be clear that the marxist methodology is not the marxists' wishful thinking. This would constitute the second step. The third one would include an at tempt at what the classics did not do, an at tempt at the construction of a systematic theory of science, (it should present an approach which differs from the other contemporary approach- es). It is obvious that the theory can be constructed in a number of ways on the basis of the writings which the classics left behind. Therefore it would be just one possible interpretation of the marxist methodology and it would be capable of rivalry when faced with another interpretation in one way only: by explaining as much from the traditional ideas of the classics and from the inquiry in numerous branches of modern science as possible.

1. T H E ; R E C O N S T R U C T I O N O F " C A P I T A L " : T H E M E T H O D O F I D E A L I Z A T I O N

a. Case study: the theory of value

Let us consider a typical theorem of Marx in Ca~ital, the law of value. I t says that the prices of commodities are formed with respect to their value (the amount of socially indispensable time to produce these commodities). That holds under certain conditions. One of the formulations of the law of value has it that : "if supply and demand are balanced, the market prices of commodities correspond to their values, determined by respective amounts of work which is indispensable for their production" (Marx, 1, p. 141). Therefore the formula:

(1) P = f (V)

where P is a price, V -- value, f -- dependence of linear type, holds only if the assumption (2) also holds:

(2) F ----- (D - - S) = 0

where F stands for changes in demand (D) and supply (S). We shall now present the Marxian statements in their complete form:

(3) if x is a commodity (T) and the changes (F) of demand (D) and supply (S) of x are equal to zero, then the price (P) of the commodity x

On Some Interpretation of the Marxist Methodology 143

depends in a linear way on the value (V) of this commodity (linear dependence -- f) .

Nevertheless, the condition (2) which postulates and ideal balance of supply and demand is not the only assumption which guarantees that the formula (1) holds true. Of the numerous assumptions of the same kind (cf. Nowak, I, 2, 3) we shall mention another one: "foreign commerce just replaces home products with the articles of another utility or natural form, but it does not infringe on the value relations ( . . . ) . Accounting for foreign commerce ( . . . ) can only obscure tha matter. Therefore it can be completely delected" (Marx, 2, vol. II, p. 500). Marx then assumes that :

(4) W = 0

where W is a commercial exchange with foreign countries. A more complete reconstruction of the law of value is therefore formulated in the following way:

(V) if x is a commodity and the changes of supply and demand are equal to zero, and the economy which produces x does not exchange commerce with foreign countries, then the price of the commodity x depends in a linear way on the value of the product.

I n s h o r t :

(V) T(x) A W(x) = 0 A F(x) = 0 -~ F(x) =f(V(x)).

The law of value defined in the above way is assumed in two volumes of Capital. It establishes the prices of commodities for a closed economy with a permanent market balance (demand always matching supply). Real economies, as is well known, do not meet these conditions (i. e. the assumptions (4) and (2)). Therefore Marx lifts the assumption which postulates market balance in the third volume of Capital:

"For the market price of identical commodities, each, however, produced under different individual circumstances, to correspond to the market value and not to deviate from it either by rising above or falling below it, it is necessary that the pressure exerted by different sellers upon one another be sufficient to bring enough commodities to market to fill the social requirements ( . . . ) . Should the mass of products exceed this demand, the commodities would have to be sold below their market value; and, conversely, above the market value if the mass of products were not large enough to meet the demand" (Marx, 1, vol. III, part 1, pp. 192-193). Thus "the supply and demand regulate the market price, deviations of the market price from the market value" (ibidem p. 193). By formulating the theorem stating that " the market value ( . . . ) forms the center of fluctuations from market prices" (ibidem p. 193). Marx states that:

(V') T(x) A W(x) = 0 A F(x) 4:0 -,- P(x) = f(V(x)) + B(F(x))

144 L e s z e k N o w a k

where B stands for a class of functions which meet the following conditions:

a. B(F(x)) = 0, if F(x) = 0, i.e. D(x) = S(x) b. B(F(x)) > 0, if F(x) > O, i. e. D(x) > S(x) c. B(F(x)) < 0, if F(x) < O, i. e. O(x) < S(x).

The taw of value (V) is corrected thus in "Capital" (with respect to the assumptions which have been deleted in the present paper for the sake of brevity) eleven times (Nowak, 1, or, in a brief form, 2, 3)1. Each time Marx lifts an unrealistic assumption introduced before and modifies a consequent of the respective theorem: in the above case he had lifted the condition (1) and modified the consequent of the law (V), thus obtaining more realistic theorem, closer to real economy -- V'.

Let us examine Marx's method of inquiry more closely with the help of this simplified example. I. He introduces some assumptions, of which he knows a priori to be false in reality, i. e. he introduces the assumption that the demand and supply of any commodity are balanced all the time, in spite of the contrary being the case with any commodity -- changes of demand and supply are an ordinary phenomenon in free competition economy. II. With the above assumptions in mind he suggests an explanatory dependence, which reveals what the phenomena in question depend on: with an assumption that demand matches supply (i. e. F -~ 0) and that economy does not have foreign commerce (i. e. W-----0), etc. the prices should depend in a linear way on the values of commodities. The law has the following form: if A then B, and we know from the beginning that A does not hold in reality. III . These counterfactual assumptions are then lifted and the law (or, more exactly, the dependence which occurs in the consequent) is corrected correspondingly. The theorems which come closer and closer to reality are thus obtained, and they speak of the conditions which come closer to the empirical ones. Thus the theorem V', which speaks of a closed economy but allows for market imbalance, is closer to reality than the law V which speaks of a closed economy with market balance of supply and demand. V refers to the idealized conditions which differ from the real ones in two respects, while V' refers to the idealized conditions, too, except that the latter are less abstract since they differ from reality in one respect alone.

b. Introductory comparative analysis We have claimed above that the reconstruction of the Marxian cogni-

tive inquiry will be interesting, i. e. it is a starting point for the construction of the marxist methodology, only in case if Marx turns out to be a "strange case". I t seems that the above instance demonstrates this strange-

1 F o r a r e c o n s t r u c t i o n w h i c h d i f f e r s i n d e t a i l s - - see B a l i c k i (1).

On Some In terpre ta t ion of the Marxist Methodology 145

ness. A common sense concept of science cherishes an idea that whatever one may say about science, at least that is certain: science describes the reality we live in. But the theorem (V) does not describe the phenomenon of making the prices, since the latter, as we know from the empirical world, occurs in the situation of a permanent imbalance of supply and demand (and in economies which vigorously pursue commercial exchange). And Marx does not only formulate the law (V) but calls it the basic law for the capitalist economy!

However, it is possible that the Marxian proceeding is paradoxical from the viewpoint of common sense only, that it is not in the least surprising from the point of view of a modern methodology of science, which is quite refined with respect to its technical level.

Let us therefore examine the positivist definition of a law: "for an unrestricted universal to be called a law it is a plausible requirement that the evidence for it is not known to coincide with its scope of prediction" (Nagel, 1, p. 63). The evidence for the law is made of known facts fulfilling the consequent and antecedent of the law, the scope of prediction of the law is made of all the facts falling under its consequent and antecedent (ibidem). Applying Nagel's requirement to the law of value (V) we shall get the answer that the set of facts which fall under the antecedent and the consequent of the law (V) is empty:

{xlT(x) A W(x) = 0 A F(x) = 0 ~ P(x) = f ( V ( x ) ) } = ¢ ;

and the more so for the set of known facts which fall under this law. The evidence (in Nagel's sense) for the law (V) not only fails to be the subset of its scope of prediction, but is identical to it -- for both sets are empty. The law of value is not the law at all in Nagel's sense (or, more generally, in the positivist sense).

Let us therefore recall hypothetism. The law of science is physically necessary for Popper, i. e. it holds true in all the worlds, which, if they differ from our world at all, they do so only with respect to the initial conditions (Popper, 1, p. 433). The initial conditions of a general sentence (x)(A(x) -~B(x)) are A(a), (Ab) . . . . where a, b are actual objects. The above sentence is the law in Popper's sense if it holds true in every world which differs from ours at most in initial conditions, but does not differ in fulfilling the consequent. The condition B(x) is therefore valid in our world and in every other world which differs from ours only in initial conditions. But the law of value (V) does not fall even under this more subtle scheme. The dependence (1) from the consequent of the law of value (V) is not fulfilled in our world, for in our world the prices do not depend on value alone; they depend, for instance, on the changes of supply and demand (cf. theorem V'). In short, the law (V), to use Pop- per's words, is fulfilled in the world which differs from ours in its homo- logical structure. That is why Marx never uses the law (V) for a direct explanation of empirical phenomena, but develops it, establishes (V') on the basis of (V), and the former is fulfilled in the world which is homo-

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logically closer to ours. Therefore the law of value (V) is not the law in Popper's sense, either.

To sum it up. Marx conducts an inquiry in a way which is not only incompatible with a common view of science, but also in a way which is incompatible with the claims of the modern philosophy of science: the law of value (V) put forward as one of the main laws of Capital is neither the law in the positivist sense, nor the law in the hypotheticist sense. Both these influential tendencies of today fail to validate the scientific proceedings of Marx. Marx follows another route -- the laws he formulates are not laws in the sense of the other schools. I have just demonstrated this with respect to one instance. Now, let us have a few arguments in support of the thesis tha t the making of a theory of value is a typical instance of Marxian cognitive activity.

c. Further instances of the Marxian scientific procedures

Let us consider another basic theory of Capital, the theory of reproduction. This one is also based on numerous unrealistic assumptions of which only two shall be mentioned. Marx assumes that :

(5) the values of commodities are constant in the economy x, i. e. Val(x) =const. He writes: "we assume here ( . . . ) that no revolutionary changes in the values of the components of production capital occur" (Marx, 1, vol. II, p. 414), since these changes are generally "interferences, which can be understood only if they are considered as deviations from the unchanged value relations" (ibidem, p. 415, Marx's own stress). Intro- ducing the theory of a simple reproduction, Marx assumes that :

(6) accumulation in the economy x equals zero, i. e. Ma(x) = 0. He writes: "Simple reproduction in an unchanged scale is an abstraction in so far that ( . . . ) it can not be assumed that no accumulation might occur in the capitalist conditions i. e. that there could be no widened reproduction" (ibidem, p. 416). Therefore well known Marxian schemes of simple reproduction hold true only when these two conditions (we assume there are two of them for the sake of simplicity, actually there are at least seven of them in Capital, cf. Nowak, 4) are met. They assume the form of the theorems:

(R1) C(x) A Val(x) = const A M,(x) = 0 ~ Pl(x) = Cl(x) + + Vx(x) + Ms(x)

(R2) G(x) A Val(x) = const A M,~(x) = 0 --,- P=(x) = C~(x) + + V~(x) + M2(x)

where the condition "'G(x)" is read as: x is an economy, P is a global product, C is a constant capital, V -- variable one, M -- surplus value; the indexes 1, 2, demonstrate the relativization to the first and second sector of economy -- P1 is the product of the first sector, etc. From these two theses Marx draws his well known condition of balance for a simple

On Some Interpretat ion of the Marxist Methodology 147

reproduction, which also holds true with the assumptions (5) and (6). In a reconstruction it looks like a consequence of the these (R1) and (R2) of the following form:

(E) G(x) A Val(x) = const A Ma(x) = 0 -~ C2(x) : VI(x) + MI(x)

The passage to the schemes of enlarged reproduction is performed in the same way as the passage from the law of value (V) to the theorem which accounts for changes in balance of supply and demand (V'). Marx lifts an assumption (6) and he assumes realistically that economy x does accumulate, i. e. utilizes a part of surplus value for an increase of the means of production (M c) and for an employment of more labor force (MY):

0 < i a ( X ) : Me(x) + MY(x).

Finally, the schemes of simple reproduction (R 1) and (R 9.) (strictly speaking -- their consequents) gain the corrections and the schemes of enlarged reproduction are obtained:

(R~) G(x) A Val(x) : const /~ Ma(x) > 0 ~ P1(x) : Cl(x) + + Vl(x) + Ml(x) + Me(x) + M~(x)

(R6) G(x) A Val(x) : const A M~(x) > 0 ~ P2(x) : Ca(x) + + V2(x) + M2(x) + M[(x) + M~(x).

It is clear that the theorem (R~-) which accounts for accumulation is related to the theorem Rl which abstracts from an accumulation in the same way as the theorem (V') accounting for the changes of supply and demand is related to the law of value (V) abstracting from these changes of supply and demand. From the theses (R~) and (R~) the condition of balance for enlarged reproduction follows:

e (E') G(x) A Val (x) = const A Ma(x) > 0 -*- C2(x) + M~(x) : = Vl(x) + M~(x) + M~(x).

I t can be seen that Marx, when constructing the theory of reproduction, followed the same method he employed in constructing the theory of value: 1. he introduced unrealistic assumptions, 2. he established the basic laws with these assumptions in mind, 3. he modified these laws lifting successively these assumptions -- he was bringing the laws closer to reality.

I t cannot be the work of an accident" the Marxian way of proceeding is the same all the time -- in order to explain the phenomena he introduces the counterfactual assumptions, establishes the laws with their help, then corrects these laws lifting the assumptions and successively bringing the laws closer to reality. The methodological analyses of other instances fully confirm that. The theory of the classes by Marx is based on more than twenty unrealistic assumptions (Nowak, 5, pp. 5-46) and is composed of a number of "models" (the systems of theorems) based on

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the same assumptions -- like (R1) and (R~) or (R1) and (Rs) of which only four are included in these fragments of Capital which Marx managed to write (Jasifiska, Nowak, 1, pp. 141--169). The theory of socio-economic formation is also based on some unrealistic assumptions, which are then lifted, and the connection of the relations of production to the productive forces, base to superstructure being to consciousness, are made more complex (Nowak, 7). Things look very much alike with respect to the theory of the ratio of surplus value (Nowak, 8, pp. 71--76), the theory of the falling rate of profit (Nowak, 1, pp. 200--206) and other Marxian theories. Engels's theory of the development of the family is also of the same methodological nature (Burbelka, 1). The same also refers to Le- nin's theory of the growth of the capitalist market (Lawniczak, 1). Looking from this viewpoint on the subsequent works by marxists it also reveals that they have been employing, in a far less conscious and clear way than was the case with the author of Caflital, analogical procedure; this was the case with Kautsky (Farmus, 1) and Krzywicki (Kla- witer, 1, pp. 86--92) who at tempted the development of the marxist theory of social consciousness as determined by being.

To sum it up: the scientific procedure which consists of: 1. introducing unrealistic assumptions, 2. establishing the laws which are valid with these assumptions, 3. lifting these assumptions and simultaneous correction of the starting laws, is a characteristic cognitive procedure employed in marxism, at least in the classical writings of marxism.

This mode of proceeding is incompatible both with the positivist and hypotheticist methodology. Not only because the laws of value, reproduction, class division, etc. are not laws in the positivist or hypotheticist sense, but also because they cannot be laws within the latter doctrines even if their representatives modified their definitions so that these theorems could be called laws after all. For -- let us say -- the law of value (V) cannot be inductively justified. Particular cases of the law V:

T(a) A W(a) = 0 A _F(a) = 0 P(a) = f ( V ( a ) )

do not justify inductively the law (V) for ttlis simple reason that they contain (on a second and third position) evidently false components. To put it simply: how can we inductively justify (i. e. by way of observing real cases) the law which speaks of ideal closed economy, in which a permanent market balance does persist ? For similar reasons the law (V) cannot b e tested by means of the method of criticism of hypotheses designed by Propper. The method assumes deduction of observational sentences, which either confirm or falsify validity of hypotheses. But the theorems which follow from (V) are valid with the same counterfactual assumptions which hold the thesis (V) up. Analogically -- from (R1) and (Rz) (and some tacit premises) the thesis E follows, but it holds true with the same counterfactual assumptions (5) and (6) which support both these theorems. And observational sentences cannot, of course, be based on any

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counterfactual assumptions; each observable object is a real object, anyway.

The question arises whether this serious contradiction between the Marxian method and the modern methodological concepts is not by any coincidence an argument against the former. In order to decide this question we have to refer to the proceedings of the developed empirical sciences. It can be said that if Marx proceeds in a way which differs from the predictions of the present methodology, so much the worse for Marx. However, if it turns out that the physicists proceed as Marx did, then methodological theses of positivism and hypotheticism will be falsified. Before we start discussing this, a conceptualization of the Marxian cognitive procedure is necessary.

d. The method of idealization and concretization

Let us call the following sentential function an idealizing assumption:

(7) p(x) = 0

if for each real object a : p ( a ) = 0 . Of course, the growth of the factor p can be considered as a separate factor, hence the formula "p(x) = const." and "Ap(x) = 0" can be considered equivalent. The idealizational theorem shall be a general sentence of the following form:

(s) G(x) A pl (x) = 0 A . . . A p -l(x) = 0 A p (x) = 0 --, F(x) = f (H(x ) )

where G(x) are realistic assumptions, i. e. the ones which determine the universe of the discourse, while pi(x)----0 is an idealizing condition. The idealizing theorem determines what happens in idealized conditions in which idealizing assumptions are fulfilled: in a dosed economy with an ideally balanced market, in a capitalist economy, where the capitalists do not accumulate, in a society composed of just two antagonistic classes, etc. In order to pass from the idealized conditions to the conditions less idealized, and closer to the real ones, one should lift the assumption pk(x) ----0, i. e. replace it with a realistic condition pk(x) 4= 0 and to introduce a correction into a consequent in order to determine the influence of the factor p~ on the magnitude F. The operation is concretizing theorem (8) and its result is a concretization of this theorem (with respect to the functions g, h) :

(9) G(x) A p l (x ) = 0 A . . . p z - l ( x ) = 0 A p~(x) 4= 0 -~ F(x) = = fg - l (H(x ) , pk(x)) = g[fk(H(x)), h(p~(x))].

Concretizing may proceed until we obtain in a border case a factual theorem 2, i. e. the theorem with no idealizing assumptions:

More precise definitions of these concepts shall be provided later on.

150 Leszek Nowak

(10) G(x) A #l(x) = 0 A . . . A P~-l(x) = 0 A p~(x) = O -~ F(x) = = fg_~(H(x), !bg(x), pg-l(x)) = = n[fg- l (H(x) , j~(x)), m(p,-z(x))]

( l l) G(x) /~ pl(X) = 0 /~ . . . /~ j~g(x) = 0 -~ F(x) = fo (H(x ) , fig(x), . . . . , # l ( x ) ) = s [ f l ( H ( x ) , g(x) . . . . .

Comparing the above schemes with the Marxian instances we see that Marx proceeded in the following way: 1. he was introducing the idealizing assumptions, 2. he was establishing idealizing laws, 3. he was gradually concretizing or approximating these laws.

The assumptions (2), (4) or (5), (6) are the instances of idealizing assumptions which make idealizational laws valid -- the law of value (V) or the schemes of reproduction (R1), (R~). The theorems (V') or (R1), (R6) are the concretization of these laws, closer to the empirical world, but still idealizational. We can obtain factual theorems from them either by way of further concretization or by way of approximation. If the method determined above as the stages 1--3 is to be called the method of idealization and concretization, then we may briefly say that the peculiarity of the Marxian scientific proceeding is the employment of the method of idealization and concretization. The method corresponds to what is being defined as the method of abstraction and concretization in the marxist literature. However, as a rule, the method is conceived of in quite a different way: "abstraction consists of induction. The starting point is ( . . . ) a comparative observation of an actual economic process in different historical conditions. ( . . . ) (Finally) that results in ( . . . ) formulation of the abstract economic categories, theoretical models and their corresponding laws and theories. All this happens by means of inductive reasoning" (Lange, 1, p. 176--177, Rozental, 1, p. 495). The abstraction conceived of in the above way is not idealization. An interpretation of the method of abstraction and concretization as a method of induction and deduction of the detailed theses (ex. observational ones) from the inductive generalizations (ex. Lange, 1, Rozental, 1, Cornforth, 1) leads to the conclusion that the method of Marx coincided with the one of J. S. 1~{i11. With the above approach in mind, no chance is seen of the marxist methodology being capable of independent claim -- it happens to repeat the positivist methodology in its early form, far from the subtlety and penetrating insights of the present positivist propositions (for more -- see Nowak, 3, pp. 25--29).

e. The method of idealization and concretization in empirical sciences

We may now at tempt an answer to the question whether the method of idealization and concretization is employed only in marxism. We can quote instances which point out that the method of idealization and

On Some In te rp re ta t ion of the Marxist Methodology 151

concretization appeared in modern physics with Galileo (Nowak, 2, p. 5, Such, 1), and in biology with Darwin (Lastowski, 1), in linguistics with Chomsky (Nowak, 9). From this moment on the method becomes a reign- ing method of these sciences. Each physical law turns out, upon a closer examination, to be an idealizational theorem which is then concretized and approximated. For instance, the second law of Newton is being established for inertial systems and refers to the motion of material points in these systems. Hence a reconstruction of this law presents it as an idealizational theorem:

(12) O(x) A U(u) A x is placed within u A W(x) = 0 A Z(u) --~ 0 -,- F(x) = m(x)a(x)

where "0" , "U" are read as "is physical object", "is a physical system", W -- is size, Z -- the resultant of external forces, F is the force applied to the body x, m -- its mass, a -- its acceleration. What the physicists call a second law of motion of Newton for noninertial systems (the theorem which accounts for two additional forces of inertia: Fun and Foot) turns out to be a concretization of the law for inertial systems (12)

(13) O(x) /\ U(u) A x is placed within u A W(x) ~ 0 A Z(u) 4 :0 --*- F(x) = m(x)a(x) + Fu~,(x) + Feor(X).

Also far more complex sequences: the idealizational law and its concretizations, commonly appear in physics (Nowak, 1, 2, 8, Such 1, No- wakowa, 1, 2, 3, Krajewski, 1, Siemianowski, 1). The method of idealization and concretization occurs in physics and astronomy in a pure form. In other branches of science it appears in less clear-cut forms, but it is equally common. The same holds true for the present economy, both the marxist and non-marxist one, (Nowak, 10, Balicki, 1, 2, Kasznia, 1), in psychology (Brzezifiski, 1), sociology (Tuchafiska, 1, Jasifiska, Nowak, 1) and methodology itself (Kmita, 1, Nowak, 8), and even in such branches as art history (Lawnicak, 1), economic history (Topolski, 1), pedagogics (Muszyfiski, 1, Kozowna, 1)or jurisprudence (Nowak, 11, 12). In classical humanities the method of idealization occurs as the method of rational- ization developed by J. Kmita as the method of the humanist interpretation (Kmita, 2, 3): it turns out that the principle of rationality on which the humanist interpretation is based is a particular case of an idealizational theorem (Nowak, 13, Kmita, 1 and 4). In practical sciences (engineering, medicine, etc.) the method of idealization leads to the formulation of the optimalizational theorems, i. e. the theorems of the form of (8) which determine what the border intensity of the magnitude F depends on, and F is not just a magnitude then, but a value as well 3 (technical, economic, moral, etc.). Here is an example of an optimalizational theorem:

A factor can coincice wi th a value - - see Nowak, 14.

152 Leszek Nowak

(14) p(x) A R(x) = 0 A g(x) = const -,- Lmaz(X) - - g(x)

where p(x) stands for x being a missile fired from a gun, R -- air resistance, g -- earthly acceleration, Lmax -- maximal length, v0 -- starting velocity of a missile. Concretization of the optimalizational theorem means accounting for additional factors which are to be considered if we undertake any actions aiming at a realization of a respective value (ex. construction a gun with the longest possible range).

The method of idealization and concretization turns out therefore to be the basic method of, presumably, all empirical sciences, both natural and humanist, both basic and applied.

2. THE ESSENTIALIST ASSUMPTIONS OF THE METHOD OF IDEALIZATION AND CONCRETIZATION

a. Modern methodology and the problem of idealization

The universality of employing the method of idealization in empirical sciences is a shock: it is one of the few things which is common to a physicist who speaks of a motion of material point and to a lawyr who assumes that a legislator is perfec L I t is equally shocking to discover that the present methodology which has subtle positivist technical methods and profound philosophical ideas in a hypothetical version has practically ignored the problems of idealization. Not because the adherents of these schools fail to notice the simple fact that the physicists refer to perfectly rigid bodies, etc. 4, but because they fail to account for this fact while discussing actual methodological problems. They do not draw any consequences from this fact -- i. e. they fail to understand it.

For instance, a simple model of explanation is considered (for the sake of simplicity let us limit ourselves to an explanation of the facts by the laws and not laws by the taws):

(x)(A(x) - , B(x)) A(a)

B(a) not noticing that the above applies to the factual theorems alone (the second premise is always false for idealizational iheorems), i. e. the ones which occur as derivatives of idealizational laws in the advanced sciences. And how does one explain with the help of idealizational laws ?

It is said that scientific theories are deductive systems, i. e. that they include a distinguished subset of axioms and their further logical c0nse- quences. In fact real theories constructed by the physicists Or economists (Nowak, 8) are composed of a series of models which include the theorems holding with the same set of idealizing assumptions; the connections

4 Kotarbinska (1), and my reply (15).

On Some IrLterpretation of the Marxist Methodology 153

between these models are established by the relation of concretization. The problem of the connection between theoretical and observational

terms is discussed and the requirements are constantly liberalized as far as the logical power of this bond is concerned. However, the problem of the idealizational nature of theoretical terms is never raised. For instance how can one establish the meaning relation between observational terms and the term "perfectly black body' ? For instance: a model example of an operational concept could be found, according to P. W. Bridgman (1, p. 28) in Einstein's concept of contemporaneity. But, according to Ein- stein himself, the concept of contemporaneity is related to the inertial system (Einstein, 1, p. 37); and an inertial system is composed of the bodies which are not subjected to any external forces, hence the principle of inertia holds inside them. Therefore a complete form of the definition of contemporaneity is the following one: if P1 and P2 are points in an inertial system and they are distant in space and respective events E1 and E2 occur in them, then these events are contemporary if and only if the clocks in P1 and P2 tell the same time of the occurrence of E1 and E2 and they are synchronized with light signals determined by tile equation: t 2 : t t + ( t 3 - - t l ) / 2 ) (where tl is the moment a signal leaves P1, t2 is the moment a signal is reflected in P2, t3 -- when tile signal returns to P1). Therefore the concept of contemporaneity is introduced with the help of the idealizing assumption about an inertial nature of the respective system. And this is enough to maintain that it is not an operational concept, since the definitions which introduce these concept assume the following form: if we perform an operation A on an object x, then x has a property Q always and only if we obtain the result B (Prze- tecki, 1, p. 109). But it is impossible to perform any operation on the objects which are within an inertial system . . .

The discussion on justification is usually performed with a tacit assumption that the laws of science are factual theorems -- the pattern is usually a sentence "every raven is black" which does not occur in science at all, and not an instance like tile law of value, the law of free fall, the law of gravitation, the laws of natural selection, etc. But we may predict a priori that accounts for the fact that the laws of science are idealizational would bear heavily upon the problems of confirmation. The measure of confirmation usually put forward generally assumes a probability of respective theorems. The probability of idealizational theorems is the same for all of them -- it is equal to zero: the set {x[ G(x) A ~ l(x) : 0 A . . . A:h~(x) =0}, is an empty set.

The problems of idealization are also ignored with respect to an important question of the principles of the growth of knowledge -- both among the followers and opponents of the principle of correspondence (Nowakowa, 1, 2, and 3). The former compare the successive laws of science and present them as factual theorems, ex. :

(15) F ----- m • a

154 Leszek Nowak

~Yb~ (16) F = V; x2

C2

and conclude that the second is more general than the first one. The latter claim that the meaning of the terms in the later theory changes, and they fail to notice that it means an approval of what they combat -- of cumula- tivism; if F from (16) means something else than F from (15), then one may safely at tach (16) to (15) instead of stating that a new theory is incompatible with an older one. If we account for the fact that both these theorems are idealizational, then the situation changes. First of all (15) has to be presented in a more complete version:

(17) O(x) A U(u) A x is placed within u A W(x) .= 0 A Z(u) = 0 --,- -..- F(x) =- m(x)a(x).

A change in a theory of relativity which interests us at this junction consists of an awareness that an assumption that light velocity is infinite, accepted previously as a description of the facts, is not true. I t turned out that light velocity is constant, and presently the assumption about the infinite light velocity can occur only as an idealizing assumption. And if this additional assumption is accepted then the dependence (15) actually holds. Hence the equivalent of the thesis (17) within a particular theory of relativity is the following theorem:

(18) O(x) A U(u) A x is placed within u A W(x) ---- 0 A Z(u) -= 0 A A 1/c = 0 -,- F(x) = m(x)a(x).

The thesis mentioned above has a relativist correction introduced into itself:

(19) O(x) A U(u) A x is placed within u A W(x) = 0 A Z(u) = 0 A

m(x)a(x) A c = cons t . - , - F ( x ) - ]/1 v (x)

g e 2

The approach which accounts for the fact that idealizational laws are at stake results in a different approach towards the relations between successive theories (for more see -- Nowakowa, 1, and 5). Successive laws are not increasingly more general (ibidem), nor has one to assume that the meaning of theoretical terms changes -- from the fact that F depends additionally on velocity according to the present knowledge it does not follow that the meaning of the term F had changed: what did change was our knowledge about the determinants of the factor F.

I think that even these brief and superficial remarks are enough to demonstrate that contemporary methodology ignores, generally speaking,

O n Some I n t e r p r e t a t i o n of t h e Marx i s t Me thodo logy 155

the problem of idealization 5. In order to answer the question why this is the case another question has to be answered first: why does this problem reveal itself in the Marxian methodological remarks, unsyste- matic and vague as t h e y are? To put it short: why does the Marxian philosophy undertake the problems of idealization ?

b. Essentialism and phenomenalism I think that an answer to this question is related to the ontological

assumptions of marxism. As I have tried to justify with the help of the sources elsewhere (Nowak, 19), Marx can be ascribed the following ontological concepts.

Let us assume that a set of factors is given 6. Let us consider an arbitrary factor F. We shall accept the following primary concept: an expression " ( . . . ) influences ( . . . ) stronger than (. . .)". Of the relation S (to be a more influential factor for F than . . . ) let us assume that it is a antisymmetric and transitive relation in the set of the factors. Let us define the relation E of being a factor which influences F in the same way (of equi-significance for F): xEy if and only if it is neither the case that xSy nor ySx. The relation E is equivalence in the set of the factors. We are therefore distinguishing the classes A, B . . . . N in this set; these are classes of factors which are equally significant for F, i. e. such that all factors linked with the relation E to any distinguished element of this class belong there. This family of the sets can be ordered completely with respect to the following relation: X S ' Y if and only if every factor from X precedes with respect to S every factor from Y. Let us assume that this relation allows for an ordering of the family of the classes A, B . . . . , N in this way: A, B . . . . N. This sequence is called an essential sequence for the factor F.

The factors from the class A are the main factors for F, the others are minor factors for it.

Let us assume, for the sake of simplicity, that these sets have one element each: A = {H}, B = {pk} . . . . , N = {p 1}. The system of factors:

SF: (k) H ( k - 1) H, . . . . . . . . . .

(1) n ,p~ . . . . . p2 (0) H, . . . . . p l

is called an essential structure of the factor F. It is made of a number of (k + 1) levels of significance from the zero (surface) to the k (internal) one.

5 T h e p r o b l e m s h a v e been ra ised a t t i m e s b u t t h e i n t e n t i o n s were to s u b j e c t t h e m to t r ad i t iona l ones, which resu l ted in ser ious lack of consequence . See Nowak , 16, 17.

s T h e concep t of t h e fac tor c a n be defined wi th t h e he lp of o rd ina ry se t t h e o r y no t ions - - ex. Ajdukiewicz , 1.

156 Leszek Nowak

An analysis of Capital demonstrates, (Nowak, 19) that the Marxian idea of a regularity is explicated by a following definition: a regularity for the factor F is the function f~ of the following form: F =fk(H), if p 1 = 0 and . . . and ~bk = 0. The firstform of manifestation of this regularity with respect to the functions g, h, is the function fk-1 of the following form:

F = fk- l (H, p~), if p l = 0 . . . . and J~k-1 = 0 and pk ----- 0 where

fk-1(H, p~) = g(f~(H), h(p~)) ;

the function h is the correctional function which determines the influence of the minor factor Pk, while g is the directional function which determines the kind of "superposition" of a correction and regularity. Analogically we may derive further forms of manifestation of a regularity. The sequence ( f ~ , f k - 1 , . . . , f l , f o ) , where f~ is a regularity of the factor F, and the successive dependencies are its forms of manifestation (until the last, surface form) is called the nomological sequence of the factor F. And the system of dependencies:

NF: (k) f~ (k - - 1) fk, g, h ° , ° . , . . ° * .

(1) f~, g, h . . . . , n, m (0) fk, g, h . . . . . n, m, s, t

is a nomologicat structure of the factor F. 7 Between the nomological sequence and a nomological structure there is of course such a connection that :

f k-l(H, fl~) = g(#(H), h(.pk) ), . . . , f l(H, fib . . . . . Pz) = ---- n[fg.(H, p~, . . . , p~), m(pp)],fo(H, p~ . . . . . pl) = = s [ f l ( H , p k . . . . , p2) , t ( p l ) ] .

If we identify a phenomenon, roughly speaking, with the system (F, a), such that F assumes certain intensity for a, (i. e. F(a )=n , for certain values of F, in border cases n = 1 or 0), then we may say that the essence of this phenomenon is that F depends in an f~ way on the factor H, which is main for F. The essence of the phenomena of the (F, a) type is therefore determined by the main factor and a regularity of the magnitude F. The appearance of the phenomena of the (F, a) type is that F depends in an r way on its minor factor p, (i = 1 . . . . . k). An appearance of the phenomenon is therefore determined by the minor factors and by correctional functions for respective magnitudes.

After designing this conceptual framework, in which it can be shown, as I have pointed out, that certain principal ideas of the marxist ontology are explicated, we can start distinguishing between two principal onto-

7 I am correcting the concept of nomological structure iatroduced by Nowokowa (6).

On Some Interpretat ion of the Marxist Methodology 157

logical theses which are of methodological significance. The thesis of phenomenalism, according to which the distinction between the essence and appearance is senseless or subjective (individually -- it expresses only our interests, species -- wise -- expresses biological interests of the hu- mans) can be briefly expressed in the following way:

(f) the essential structure of every factor is a degenerated one, i. e. it consists of one level only.

The thesis of essentialism can be expressed in the following way: (e) the essential structure of every factor is a real structure, i. e. it consists of at least two levels.

According to the thesis ( f ) i n the scheme SF, k = 0 for every F, while according to the thesis (e),/~ > 0. This reconstruction seems to be valid in as much as it conceives of a primary concept "S" in a way which is ob- jective (it is relativized to the factor, not to any questions or needs). Moreover, if an essential structure SF consists of one level, then the distinction between main and minor factors is meaningless indeed, hence the distinction between the essence and the appearance vanishes.

c. Idealizational and factual 8 conce#tion of science The relation between the thesis of essentialism (e) and the necessity of

applying the method of idealization and concretization is the following one. If one believes that the phenomena are subjected to the differentiated influence of the main and minor factors, if one accepts the thesis (e), then one puts forward the hypotheses about which factors are main, which are minor, and the ones considered minor (rightly or wrongly) are eliminated, i. e. idealizing assumptions are introduced, which allow for an abstraction from these factors. One does not abstract from the factors considered main ones. These are accounted for in the starting hypothesis which determines the form of the bond, which occurs between the factor under investigation and the main one, viewed in the absence of the minor ones. Since the minor factors are also significant for the magnitude under investigation, i. e. they influence it, one does not abstract from the derivative factors once and for all. Having established a project of the law with idealizing assumptions accepted and having ignored these factors, i. e. having constructed idealizational thesis, an investigator starts to lift these assumptions introducing the corrections to the dependence in the consequent of this hypothesis. In a word, he gradually concretizes it. If corrections are too weak or if the idealizational theorem itself assures a sufficient approximation to the results of experience, the process of concretizing is broken, and an approximation of this theorem is established.

Hence, if the thesis of essentialism (e) is assumed, i. e. if we assume that all phenomena are differentiated into essence and appearance, then the

8 The term "'factual" is being used to mean "non-idealizational" exclusively, not "syathet ic" .

158 Leszek 51owak

method of idealization and concretization turns out to be a natural method of cognition. What matters is to "dissect it into componential influences", distinguish the strongest influence, and to "put them together" again. If the above reconstruction is right (the distinction of the main and minor factors is correct, the determination of the componential functions, both regularities and derivations, is proper), then the result is what experience provided us at tile beginning, but this time tile phenomenon will be theoretically understood. Simply: as the Marxian formula has it, from the actual to the abstract, and from the abstract to the "appriopriated actual".

If the thesis of phenomenalism (f) is assumed, then a phenomenon presents itself as undifferentiated with respect to significance, and it calls not for an idealizational reconstruction which pretends to reflect its deep level, and to reach finally the surface level, but it calls for a description. The description can be performed only as a generalization of the phenomenon - then the only theoretical problem is the one of representative- ness, i. e. whether it is confirmed in all the other cases of the phenomenon of this type. The problem of an induction and of its validity turns out to be the principal one. The description can be done indirectly, the descriptions of some phenomena are deduced from the descriptions of the others; it does not mat ter whether the reasons are deduced from empirical data, what matters is that the descriptions predicted on their basis are not falsified. The first solution expresses the formula of positivism, the second -- of hypotheticism. \Vhat both these tendencies have in common is the assumption of phenomenalism which generates a factual conception of science, -- and there is no place for idealization in this conception. The laws of science are factual statements; explanation occurs by means of factual statements, the theory is a set of factual statements constituted by the relation of consequence, scientific concepts are all introduced with realistic assumptions, the only problem is tile question of the connections between theoretical (non-observational) concepts and the observational ones; the links between successive theories are the links between different factual theories.

In these points the common features of tile positivist and hypotheticist conception of science coincide. In spite of serious differences between them, both assume the thesis of ontological phenomenalism, which generates a factual conception of science. In Marx's philosophy, however, there are, if I am not wrong, the ideas which reject what is common to both tendencies; namely the phenomenotogical thesis and the factual conception of science. The thesis of phenomenalism is abandoned for the thesis of essentialism and a factual vision of science is replaced with an idealizational one.

A most surprising fact is explained therewith, namely that the most commonly employed scientific procedure, which appears from physics to theory of literature (and within this spectrum both induction and the criticism of hypotheses disappear), remained unnoticed by very sophisti-

Oa Some Interpretation of the Marxist Methodology t59

cated methodological systems, and that it was noticed in modest, unsyste- matic, and sometimes very vague remarks of the author, who treated methodology as we see it nowadays as a margin of his occupations. A phenomenalist philosophy assumed both by positivism and hypothetism made it impossible to recognize a scientific procedure which assumed different, contrary philosophy. That is a well known phenomenon, (Kuhn, 1): whatever contradicts the accepted theoretical assumptions remains unnoticed for it is conceptualized in light of contrary assumptions.

3. IDEALIZATIONAL CONCEPT OF SCIENCE: PRELIMINARY ASSUMPTIONS

a. Essential structure of a scientific cognition So far, we have noticed that (1) Marx employed a definite cognitive

procedure which he defined as a method of abstraction and concretization, (2) the above method has not been recognized by contemporary methodological systems, for it is based on different ontological assumptions from the ones they have employed. It can therefore be supposed that if the above method was made the starting point of a construction of methodological system, then there would be a chance for such a system to represent one of the permissible interpretations of the marxist methodology, and to pretend, once it is developed to a sufficient degree, to a systematic explanation of the phenomena encountered in a scientific cognition.

Within a scientific cognition the role of the factors is played by cognitive procedures (they can be considered a kind of dychotomic factors). The problem arises, as to which should be thought of as the main ones, and which as the minor ones. The follower of the thesis of essentialism (e) has no doubts with respect to that, if the principal feature of reality is that it is differentiated with respect to significance (each phenomenon contains an essence and an appearance), then the principal cognitive method has to be the method of idealization and concretization, and all other methods, ex. the experiments, axiomatic method, modelling, etc. are minor ones. The thesis of essentialism refers therefore to this singular case of a scientific cognition, too; the method of idealization and concretization is its essence, the others are appearance, which must be accounted for, but no sooner than in the course of concretization. The scientific cognition is the only phenomenon which is able to reflect other phenomena: the essence of scientific cognition is what makes it able to reflect the essences of other phenomena -- the method of idealization and concretization.

b. Philoso#hical assur~J~tions of scientific researches The science which assumes essentialism and aims towards an expla-

nation of the phenomena of F type must start with the reconstruction of

160 Leszek Nowak

the essential structure for the phenomena of this type. The criteria of essentiality are the relations C~s~ such that it is accepted that the factor A remains in the relation C~s~ to the factor B with respect to F if and only if a researcher thiates that the factor A precedes the factor B with respect to F as far as significance S is concerned. These are mostly empirical criteria, ex. different kinds of statistical tests (Brzezifiski, Nowak, 1, Brze- zifiski, 1, 2). What matters is reducible to the theorem that these criteria are always employed within the framework of definite philosophical assumptions: it happens in some branches of science that the philosophical assumptions alone decide whether something is considered as a main or minor factor.

The philosophical doctrine assumed by an investigator generates some j~rinci2bles of essential stratification, i. e. the theorems which determine the type of main factors for a magnitude of a given kind (or, generally, the type of significant factors for magnitudes of this kind!. The doctrine generates the 2brinciples of ontic bonds which say what type of regularities (or, generally, dependencies), act between the classes of factors distin- gnished by the principles of essential stratification. Altogether, the system of the principles of essential stratification and of the principles of ontic bonds based on the former, generated by a given philosophical doctrine, is called an ontological 2berspective (see Nowak, 2, 20). The example of argument about the principle of essential stratification i the controversy between the individualism of subjectivist economy and a holism of the marxist economy. The former assumes that the main factors of economic phenomena are the characteristics of the features of economic agents of their aims, means they have at their disposal, distinguished relations between them: that is why "the instances of decisions made by an individual are best for the clearest and strongest formulation of the basic principles of an economic theory" (Samuelson, 1, p. 647). The marxists start with an analysis of the process of production in which the representatives of two antagonistic classes take part (capitalist and worker, feudal lord and a serf peasant, etc.), equipped with global characteristics, proper to the classes represented by these theoretical constructs. The argument is about the main factor for the economic phenomena: are they general, constant features and relations between individuals, or features and relations between the classes (represented by the collective subjects of Capital), which change from formation to formation, and are historical by nature? The instance of an argument about the principle of ontic bonds is the controversy between Einstein and the makers of the Copen- hagen interpretation of quantum mechanics. The principle of determinism defended by Einstein can be understood as the principle of ontic bonds: for every physical magnitude there is a system of physical magnitudes which determines the former in all univocal way. If such a system is pointed out, and it allows but for a statistical determination, it means that not all essential factors have been found, that there are "hidden parameters", which, if accounted for, allow for a construction of the determinist theory.


Ontological perspective is therefore, as can be noticed, characteristic for a given scientific school or tendency. Within ontological perspective one tries to employ the criteria of significance and to reconstruct the essential structures for given magnitudes. The system of factors considered to be essential in different degrees by an investigator is the image of an essential structure of a given magnitude. If the factor considered to be tile main one is indeed the main factor for this magnitude, then the image O(SF) is basically similar to the structure SF; otherwise it is basically different from SF. If the essential structure SF has the following form:

H H,

then the

H H, H,

P basically similar image is, for instance:

q

q,P Ontological perspective generates the families of the images of essential

structure, while the criteria of significance are applied to various alter- native elements of this family. For instance the follower of mechanicism does not dream of looking for the main factors for the physical magnitudes among the non-mechanical properties of the bodies, and the follower of linguistic structuralism does not think about the search for the determinants of language understanding among the inheritable rules of linguistic competence. Each of them works empirically in the area shaped by the ontological perspective he does not necessarily have to be aware of. Philosophy (metaphysics) not only enters science, but plays a principal role in it -- it determines the starting point of theory making. The investigators who assume the same ontological structure can construct different theories, but investigators who assume different perspectives must construct different theories.

c. Assumptions concerning an ideal researcher Several idealizing assumptions about the real research procedure will

now be made. Under assumption Z.1 a researcher in interested only in finding out on what the magnitude F depends; he is not interested in other magnitudes. The assumption Z.2 states that all adventitious factors are at work (i. e., take on values other than zero) whenever the principal factors is at work; hence, under the natural conditions, there is no situ~ ations in which F is subject to the working of H alone. Under Z.3, the researcher knows what effect all the adventitious factors p~ . . . . . P l have upon F, and under Z.4 (the assumption of the possibility of a perfect experiment) he is in a position experimentally to secure conditions in which all the adventitious magnitudes take on the zero value, while H takes on a value other than zero.

162 Leszek Nowak

4. THE MARXIAN MODEL OF AN EMPIRICAL SCIENCE (MODEL I)

a. Description of the model Model I consists of methodological hypotheses which state how the

ideal researcher, characterized by the assumptions Z. 1 to Z.4, carries out his fundamental research objectives: how he formulates laws, constructs theories, explains facts b y referring them to theories, and verifies his theories. That model is defined as Marxian, because the main ideas of all its component methodological hypotheses can be found in K. Marx methodological reflections contained in Capital.

b. Idealizational statements of the first kind The Marxian concept of a law of science is as follows: it is a true state-

ment about a certain regularity. Let us see now what type of statements corresponds to that concept of a law of science in Model I. Certain preliminary conventions must be adopted first. A realistic assumption is the light of the body of knowledge N is a sentential function z(x) = e, where z stands for a magnitude, and e is a numerical measure of that magnitude, such that it does follow from N that each object of the universe of discourse has the property z in the degree e. In particular, this schema covers qualitative sentential functions, in the case of which e is either 0 or 1, and z is a dichotomous magnitude. The said sentential function is an idealizing assumption in the light of N if and only if: (1) e is the minimum measure (e. g., zero) of z. (2) it follows from N that there is no object which has the property z in the degree e. By referring to these concepts we single out two kinds of universal statements, i. e., statements ill the form:

(1) zl(x) = e A . . . A zm(x) = e m --~ A(x) = f ( B l ( x ) , . . . , B~,(x))

Note that schema (1) covers the qualitative statements as degenerate cases of quantitative statements, when all the magnitudes occurring in (1) are dichotomous. Now, (1) is an idealizational statement of the first kind (in the light of a given body of knowledge) if some conditions in the antecedent of (1) are realistic and the remaining ones ore idealizing. If all conditions in the antecedent of (1) are realistic, then (1) is called a factual statement.

As an exemple of an idealizational statement of the first kind we can quote Clapeyren's law, usually formulated as pv = R T , where fl stands for preasure, v for volume, R for a gas constant, and T for temperature; the law is supposed to hold for ideal gases. In its fully reconstructed form that law might be writ ten thus:

(2) G(x) A vw(x) = 0 A pw(x) = 0 -,- fl(x) w(x) = RT(x).

where G(x) is the realistic assumption which states that x is a portion of gas, and the remaining two are idealizing conditions; the former states

On Some Interpretatio~a of the Marxist Methodology 163

that the dimensions of particles of that portion of gas x have zero values (i. e., those particles are material points), and the latter states that inter- actions between those particles also have zero values.

Now it is to be noted that no factual statement may be a law of science in the Marxian sense of the term, for such a statement refers to the surface level of significance of a given significance structure. And no lower levels by eliminating the adventitious factors one by one; this process of eli- mination consists in the adoption of idealizing assumptions. This shows that not all idealizational statements of the first kind are laws in the Marxian sense of the term. Those which include too few idealizing assumptions, and hence do not refer to the lowest level of significance, are not laws. Those idealizational statements of the first kind only which refer to the lowest level of the significance structure of the magnitude described in that statements can function as laws; hence, those only which are based on assumptions that eliminate all the factors which are adventitious for the magnitude in question. Such ideatizational statements of the first kind are called idealizationat taws of the first kind, provided that they are true descriptions of the respective regularities. Hence, under the assumptions concerning the significance structure of F, as adopted in Sec. 2, a corresponding idealizational law of the first kind has the form:

(3) G(x) A = d l A . . . A = F(x) - -

where G(x) is the abbreviations of the appropriate realistic assumptions, and the remaining assumptions ~b,(x) = d , are the idealizing conditions which ascribe to a magnitude :p, a minimum value d~ (e. g., zero).

Now in Model I we adopt thesis (A. I) : if Z. 1 to Z. 4 hold, then a universal statement is a law if and only if it is an idealizational law of the first kind. (A. I.) will be subject to modifications in other models.

c. A sim~le idealizational theory of the first kind

The concept of concretization is the methodological analogue of the ontological concept of a form of manifestation; likewise, the concept of a law is the methodological analogue of the ontological concept of a regularity. The concept of concretization may be explained as follows. Given an ideal~ational statement of the first kind:

(4) G(x) A pl (x) = dl A . . . A #re(x) = d m -* -,- A (x) = f (B l ( x ) . . . . . Bn(x)),

its concretization is

(5) e(x) A f91(x) = dl A . . . A ~m-l(x) = din-1 A 2bin(x) 4: d~ + -~ A (x) = g( f (Bl (x) . . . . . B•(x)), h(#m(x))).

The definitions adopted above show that if (4) is an idealizational law of the first kind, i. e., if it describes a regularity, then its concretization,

(5), describes the first kind, i. e., if it describes a regularity, then its concretization, (5), describes the first form of the manifestation of that

11"

164 Leszek Nowak

regularity. For instance, the concretization of (2) is Clapeyron's law with van der Walls's first correction:

(6) G(x) A Vw(X) = 0 A pw(x) 4 : 0 -,- (pw(X) + p(x)) v(x) = RT(x) .

and the concretization of (6) becomes van der Waals's law:

(7) G(x) A w(x) • 0 A pw( ) • 0 -~ (pw(x) + p(x)) (w(x) - - 4Vw(X)) = RT(x) .

Now a simple idealizational theory of the first kind concerned with a factor F is a sequence of theorems T ~, T ~-1, . . . , T 1, T o which are linked by the concretization relation wkere T~ is an idealizational law of the first kind, and T O is a factual statement; the factor F is the magnitude which is described in each of these theorems. An example is provided by the Marxian theory of prices as formulated in Capital.

This kind of theories is the only form of scientific theories which the ideal researcher constructs within Model I. He starts from an idealizational s tatement which he assumes to describe a regularity and then he proceeds to concretize that s tatement in order to discover the successive forms of the manifestation of the regularity involved. He thus obtains a sequence of increasingly realistic statements, which sequence, he believes, shows the regularity in question and its successive forms of manifestation up to the surface form. This is so because, under assumption Z. 3, the ideal researcher is in a position to concretize the initial statement with respect to all the idealizing assumptions made in that initial statement. This yields the thesis (B. I) : if Z. 1 to Z. 4 hold, then a set of universal statements is a scientific theory if and only if it is a simple idealizational theory of the first kind.

The present authors believes that the problem of a realistic interpretation of idealizational statements, can be resolved rather easily. Note that the concept of representation of regularities, even though it assumes that a given significance structure is proper, does not assume that a s tatement which represents a regularity must be satisfied non-vacuously. In other words, a statement which represents a regularity may (and even must) be an idealizational statement. Now, researchers strive not only for the formulation of statements that would be satisfied nonvacuously, but also, and even above all, for the establishment of regularities. Such a regularity holds between the factor F and its principal factor H (and that factor only). But both F and H do occur in fact, and since this is so, then there is in fact a relationship (function) f~ such that F in an fk- transformation of the principal magnitude H. And this is precisely what is stated in the consequent of the idealizational law (4). I t is true that F is affected not b y H alone, but also by numerous secondary factor p~, . . . . p 1. This is why the results of observations or measurements of F always lead us to the conclusion that there is no f~-relationship between F and its determinants. But formula (4) does not state in the least that F is fk-dependent on all those factors which effect it in some way. I t merely


states that F is f~-dependent on one of its determinants, namely on H, and this may be true. Nor do the results of observations and or measurements refute that, as we are never in a position to eliminate all secondary factors, even if an experiment is carried out with utmost precision. We can find out whether, in the world we are concerned with, F is Fk-dependent on H only is an indirect way, namely by gradually introducing secondary factors and by making sure whether we can in this way arrive an agreement with observational data.

Thus, idealizational statements may be referred to facts in the sense that we may see if their consequents represent regularities. We could find that out directly (that is, without any need to resort to concretizations) only if we could carry out perfect experiments, i. e., such that in each experiments, i. e., such that in each experiment each secondary factor would have the zero value. It would then turn out whether a given idealizational statement represents a regularity, i. e., the dependence of a specified magnitude on (and only on) its principal factor(s). But our impossibility of making sure about that (in view of the impossibility of carrying out a perfect experiment) does not authorize us to project that statement onto facts. Yet it may be so that a given idealizational statement represents a regularity, even though we can find that out in an indirect way only, namely be resorting to concretization.

d. The Marxian conce~bt of ex2blanation K. Marx linked explanation with the following important idea: to

explain a phenomenon is the same as to show how it is related to its essence. In methodological terms: to explain an observation is the same as to refer to that law of science from which the observed fact results.

This idea may be formulated as the following thesis (C. I): if Z. 1 to Z. 4 hold, then explanation follows the schema:

where the sequence T x . . . . . T O is a simple idealizational theory of the first kind, --] is the concretizational relation, -~L is the relation of logical consequence, P stands for the initial conditions of the factual statement TO, E is the explanandum. Hence, to explain is the same as to point to the principal factor and then add to them successively the various adventitious factors until the full determination of a given phenomenon, to which it is subject at the surface level, is described. Explanations in Ca#ital follows that schema: for instance, when explaining price formation Marx starts from the law of value endowed with numerous idealizing assumptions and then proceeds to concretize it in ten steps by introducing successively the laws of market value, production prices, etc.

Note that Marxian historicism may be interpreted as a meritorial rule of explanation which imposes extra-formal conditions upon the premisses of explanation. Ontological historicism states that the significance struc-

166 Leszek Nowak

ture of the same factors is different in different social formations. Method- ological historicism states that an idealization theory of a given factor must be different for different social formations, for if the significance structure varies according to a formation (this applies in particular to the principal factors), then idealizations must be carried out by constructing different theories for different social formations.

Note also that this approach enables us to advance certain suggestions connected with much discussed methodological issues. First, an important difference between explanation and prediction is revealed. We can predict even by referring to ordinary factual statements (e. g., empirical generalizations) and appropriate initial conditions. On the contrary, if we inter- pret the concept of explanation as Marx did, then we cannot explain by using factual statements alone and without pointing to the idealizational law of which that statement is a concretization. Secondly, we can now better understand why researchers strive to formulate simple theorems. We say that a universal theorem t is simpler than a universal theorem t' if the predicate which occurs in the consequent of t has fewer arguments than the predicate in the consequent of t' has. This shows that an idealizational law is simpler than any of its concretizations. There is nothing strange in this fact as such a law describes the simplest level of the significance structure, which has the smallest number of factors (the principal factors only). As can be seen, the methodological concept of simplicity, as defined above, corresponds to the ontological one. This observation points to the cognitive reasons of seeking simple theorems, for the discovery of a theorem that is simpler than a given theorem makes us suppose that the new theorem describes factors which are more significant than those described by the earlier one, and that the earlier theorem will prove merely a concretization of the new one. Hence the search for simpler theorems is a manifestation of the fact that researchers strive for ever deeper explanations (in the Marxian sense of the term).

e. Experimental verification Under the assumption Z. 4 a researcher can provide conditions in which

adventitious factors do not work, even though the principal factors do. This satisfies the initial conditions of the idealizational statements formulated by the researcher, who can deduce what the observable consequences would be and see whether they really take place in the course of such an perfect experiment. If they do not, then he rejects, once and for all, the idealizational s tatement he is verifying (on the condition that he accepts the premisses assumed). Such a verification by an perfect experimental is an idealization of actual experimental verification in science: we cannot obtain an ideal vacuum, hence we produce a "possibly ideal" vacuum and find out whether idealizational statements are then approximately satisfied. Hence (D. I) : if Z. 1 do Z. 4 hold, then idealizational statements are verified by perfect experiments.

On Some Interpreta*iort of the Marxist Methodology 1{37

5. MODELLING (MODEL ii)

a. Removal of Z. 1 Let us remove the assumption Z. 1 and assume realistically that a

researcher is interested in finding out on what numerous factors F1, . . . . Fw depend. This realistic assumption will be denoted by R. 1. The adoption of the realistic condition R. 1 in place of the idealizing condition Z. 1 makes him consider two facts, which did not occur in the simplified picture of science in Model I, but do occur in actual research. This refers to logical relationships among statements made at the same level of abstraction (i. e., about the same idealizing assumptions) and analogies between statements about various assumptions of the same kind.

b. Theory as a sequence of theoretical models

The researcher under consideration now resorts to a less abstract procedure and considers groups of "dependent variables". I t turns out that he need not formulate a separate theorem for each factor, but can deduce an idealizational statement about the magnitude he is interested in from those which have been formulated and verified earlier (and which he accordingly holds to be scientific laws). He thus constructs a complex idealizational theory of the first kind of the factor F. That theory is a sequence of theoretical models, that is, pairs (Z~, T ~) . . . . . (Z 1, T1), (Z0, TO), which satisfies the following conditions: (1) Z* is the set of idealizational statements of the first kind, each based on the same i idealizing assumptions which are logically independent of each other: T* is an idealizational statement of the first kind, based on the same i assumptions, which follows from Z* and describes the dependance of F ; (2) Z ~ is the set of idealizational laws of the first kind; (3) Z* is the union of a non- empty set R t and a set N f, (4) for every statement t in R* there is a t' in R*+I such that t is its concretization; (5) N* contains those statements which describe the dependence of those adventitious factors which are taken into account after the removal of the i + 1-ste idealizing assumption (for i----0 . . . . . k). Z* thus stands for the assumptions of the i-th theoretical model. T* is the resolution of that model, and elements of N* are additional assumptions.

As an example of a theory of this type let us consider the multiplier theory of economic growth (Klein, 1, pp. 360--3). It will be shown here already in its reconstructed form. The theory consists of two models, a simple and an expanded one. Symbolism: Ec = the set of economic systems, F = imports, E ---- exports, Y ---- national product, C = con- sumption, I ---- investments, Co, i, n, m ---- constants. Consider a very simple form of that theory, when if is based on a single idealizing assumption only:

(8) Ee(x) A F(x) - - E(x) ---- 0 -~ C(x) = Co + m Y ( x ) . (9) Ec(x) A F(x) - - E(x) ---- 0 -*- Y(x) = C(x) + I(x). Now (8) and (9) yield

168 Leszek hTowak

I l - - m - - l ( x ) + (10) Ec(x) A F ( x ) - - E ( x ) = O - ~ Y ( x ) - - 1 - - m Co

On removing the idealizing assumption we obtain an expanded model for an open economic system:

(11) Ec(x) A F ( x ) - - E ( x ) 4~ 0-*-C(x) = Co + m Y ( x ) .

(12) Ec(x) A F(x) - - E(x) 4 : 0 -~ Y(x ) = C(x) + I(x) + E(x) - - F(x).

(13) Ec(x) A F(x) - - E(x) 4 : 0 -~ F(x) = io + nY(x ) .

These statements yield 1

(14) Ec(x) A F(x) - - E(x) 4= 0 -~ Y(x) - - 1 - - m + n I(x) +

Co E(x) io + 1 - - m + n + 1 - - m + n l - - m + n "

It can easily be seen that (11) and (12) are, respectively, concretizations of (8) and (9), with (11) being a degenerate concretization of (8), since the removal of an idealizing assumption is not accompanied by a correction of the subsequent (the correction is vacuous). And (13) is a new theorem which takes into account the adventitious factor introduced at a lower level of abstraction.

Thus we see that the multiplier theory of economic growth (in its simplified form analysed here) is a complex ideatizational theory of the first kind constructed of two models: (Z 1, (10)), (Z °, (13)), where Z 1 ----RI= {(8),(9)}, Z ° = R ° + N ° = { ( l l ) , (12)} +{(13)}. Thus, in Model II we have (B.II) : if R.1 and Z.2 to Z.4 hold, than a set of universal statements is a scientific theory if and only if it is a complex idealization theory of the first kind.

e. A formal model of an idealizational theory

Given two universal statement in the form:

(15) zl(x) = el/ . . . A z . ( x ) = e . A ( x ) = f ( B l ( x ) . . . .

(16) sl(x) = cl A . . . A Sr(X) = cr -~ C(x) = f (Dl (x ) . . . . . D~(x)), they are said to be formally analogical relative to a formal formula:

(17) a = f (b l . . . . . b2o)

if the numerical variables a, b, range over the sets of numbers which are, respectively, both the sets of value of A, B, and the sets of values of C, D, (for i = 1 . . . . . ~b). If (15) is an idealizational statement, we say that (16), which may then be either idealizationat or factual, formal models (15). Thus, for instance, Coulomb's law formally models Newton's law of gravitation under the formal formula: a=b,b ' /c~; the idealizing assumptions of both laws are different, but their consequents fall under the same formula.

On Some Ilxterpretation of the Marxist Methodology 169

A formal model of the first order of a theory (Z ~, Tk) , . . . , (Z °, TO) is a theory (S% L n) . . . . . (S o, LO) which satisfies the following conditions: (1) there is a one~to-one correspondence between every theorem t in Z ~ and a theorem t' in S% t' being formally analogical to t: (2) there is in S n-1 a theorem which is not formally analogical to any theorem in Z k-1. Note that it follows from (1) that T ~ in formally analogical to L ~. Hence, if at one time the solution T ~ of the assumptions Z ~ is unknown, then if we know the solution L n of the assumptions S% we can find the theorem T k, which must be formally analogical to L n. But it follows from (2) that the possibilities of making use of a formal model of the first order end at this point: the analogy does not extend to first order concretizations, as not all concretizations of theorems which are elements of S are formally analogical to concretizations of theorems which are elements of Z~. It is otherwise in the case a formal model of the second order: all theorems which are elements of Z ~-1. By analogy, we could introduce the concepts of formal models of higher orders. Obviously, the higher the order of a formal model of a given theory, the greater its cognitive significance. For if the formal analogy of the assumptions which occur in the initial models is inherited by remote concretizations, then it is possible to find formally analogical solutions of the successive models.

d. A simulation model Two universal statements, t and t', will be called dual if they are for-

mally analogical and if t is true if and only if t' is true. Given an idealizational statements t, let a factual statement t' be dual to t. In such a case t' is termed a nominal simulation model of t, and the state of things described by t' is termed a real simulation model of t. In particular, a real simulation model may be produced by a researcher; an experiment which consists in producing a real simulation model of an idealizational statement is termed a model ext~eriment. By finding a real simulation model of an idealizational statement t we can verify that statement: the researcher watches that real model and finds out whether the factual statement t' (a nominal simulation model of t) is satisfied and concludes the logical value of the statement t which is being verified. Hence, within Model II we have (D.II): if R.1 and Z.2 to Z.4 hold then idealizational statement of the first kind ate verified by a perfect experiment or by observation of their real simulation models.

e. Other statements in Model I I As we have seen, two statements which occur in Model I have been

concretized in Model II, for in the latter, the structure of theories and the procedure of verifying those statement which aspire to the status of scientific laws are different from their analogues in Model I. Statement (C.1) has also been slightly modified: in Model II, where complex ideali-

170 Leszek Nowak

zational theories are constructed, links of the chain of explanations can be taken from the various theoretical models which combine to form such a complex theory. The explanation schema based on (C.I) remains the same: (C.II) states that if R. 1 and Z.2 to Z.4, then explanation follows the schema:

T ~ -~ . . . -~ T t -~ TO A p -~ L E.

where Tk . . . . ,T O are, respectively, in the successive theoretical models (Z*, L~) , . . . ,(Z 0, L0) of a complex idealizational theory of the first kind. On the contrary, if we disregard the removal of the assumption Z.1 in the antecedent, (A.I) is taken over by Model II unchanged, for in that model the conditions of establishing scientific laws do not change.

6. VARIATIONS OF IDEALIZATIONS (MODEL 11I)

a. Removal of the assumption Z.2

Let us now remove the assumption Z.2. We thus realistically admit that it happens that principal factors are at work with sone adventitious factors only, or even without any adventitious factors at all (condition R.2).

b. Idealizational statements of the second and the third kind

The condition: z(x)-----e is called a quasi-idealizing assumibtion in the light of the body of knowledge N if it follows from that knowledge that for every y in a proper subset K of the universe of discourse U: z(y) = e, and that for eve ryy in the remaining part of U(i. e., in the set U - - K z(y) 4= e.) For instance, the condition which states that the difference between demand and supply equals zero is a quasi-idealizing assumption, for some commodities may (which, it is true, does not occur frequently) be in a state of a market equilibrium. In the above definition, the set K is the range of realization of a given quasi-idealizing assumption, while the set U - - K is the range of idealization of that assumption.

A universal s tatement which in its antecedent has realistic, idealizing and quasi-idealizing assumptions is termed an idealizational statement of the second kind (in the light of a given body of knowledge); if the repertory of those assumptions is limited to realistic and quasi-idealizing ones, then such a statement is of the third kind. We can accordingly single out idealizational laws of the second and the third kind: they include all those assumptions which are necessary to eliminate those adventitious factors which sometimes do not co-occur with the principal ones. Hence (A.II) becomes concretized in Model I I I : (A.III) says that if R.1, R.2, and Z.3 to Z.4 hold, then a universal statement is a scientific law if and only of it is an idealizational law (of the first, second, or third kind).

On Some Interpretation of the-Marxist Methodology 171

c. Idealizational theories of the second and the third kind

Quasi-idealizing assumptions in science are removed in a somewhat different way than idealizing assumptions are. This can best be shown in the case of an idealizational statement of the third kind: (18) G(x) A jb(x) = d + A(x) = f (B l (x ) . . . . . B~(x)). Let the actual range of the realization of the quasi-idealizing assumption ";b(x) = d " be denoted by K: hence the range of the idealization of that assumption is the set G - - K . Let also the following statements be true:

(19) Z(x) - x ~ K,

(20) Z ' ( x ) - x e G - - K .

Now the removal of the quasi-idealizing assumption yields two statements:

(21) (a) e(x) A Z ( x ) -~ A(x) = f(B1(x) . . . . . Bn(x)). (b) G(x) AZ ' ( x ) ~ A(x) = g( f (Bl (x) . . . . . Bn(x)), h(jb(x))).

Statement (21b) is a limited concretization of (18); statement (21a) is a degenerate limited concretization of (18). When a quasi-idealizing assumption is removed, a given statement is modified only as far as its idealization is concerned; when it comes to the realization of that assumption the said statement remains unchanged.

By removing the idealizing and the quasi-idealizing assumption of his idealizational statements of the second kind a researcher constructs a coml~lex idealizational theory of the second kind. Such a theory also is a sequence of theoretical models (Z k, L k) . . . . . (ZL Lg), (Zg -1, Lg -1) . . . . . (ZO, L0). Its idealizational part (Zk, L ~) . . . . . (ZL Lg) has the structure of an idealizational theory of the first kind. Its quasi-idealizational ~art (Zg-1, Lg-1) . . . . , (ZO L o) has a similar structure except for the fact that it is organized not by the concretization relation, but by the relation of limited concretization. Hence every statement in a given model has a pair of statements assigned to it in the lower model: a limited concretization and degenerate limited concretization. A com~blex idealizational theory of the third kind consists of the quasi-idealizational part only.

We thus have (B . I I I ) : if R.1 and R.2 and Z.3 to Z.4 hold. then the set of idealizational statements is a scientific theory if and only if it is a complex idealizational theory (of the first, second, or third kind).

d. Other theorems in Model I I I

Note that the explanation schema becomes modified, too: we have ( c . I I I ) which says that if R.1, R.2, and Z.3 to Z.5 hold, then explanation follows the schema:

T~ =i . . . . i T ° A P "~ LE.

where the statements T ~ . . . , T o are in the successive theoretical models of a complex idealizational theory (of the first, second, or third kind).

172 Leszek Nowak

The symbol " = l " stands for the relation of concretization or the relation of limited concretization.

Idealizational statement of the first two kinds are verified like statements of the first kind in Model II , that is, by a perfect experiment or by observation of their real simulation model. Idealizational statements of the third kind can be verified simply by observation of those objects which are in the common part of the scopes of realization of all assumptions or by an ordinary experiment carried out on those objects (i.e., by a change in the natural conditions in which those objects are) (cf. D.III).

7. APPROXIMATION (MODEL IV)

a. Removal of assumption Z.3 We have so far assumed that a researcher knows what effect the

adventitious factors have upon the factor studied and that he accordingly has no doubts as to how to concretize the initial idealizational statements. Self-evidently, this condition is not always met. We therefore adopt the realistic assumption R.3 which states that the reasearcher in question knows how some of the adventitious factors work, but does not know how the remaining ones do. I t follows therefrom that the researcher knows how to concretize his initial statements with respect to a number of modelling assumptions (whether idealizing or quasi-idealizing), but cannot do that with respect to the remaining modelling assumptions. We also remove the assumption Z.4 and replace it by the realistic condition which states that the researcher in some cases succeeds in minimiz- ing the effect of adventitious factors upon the magnitude he studies, but is never in a position to reduce the effect of all those factors to the zero level (assumption R.4).

b. Approximation statements Given an idealizational statement of the first kind:

(22) G(x) A / 9 1 ( x ) = d l A . . . A.pk(x) = d k ~ A ( x ) - . ~ = f(Bl(x) . . . . . B,~(x))

the factual statement:

(23) G(x) A bl(X) a l A . . . A p(x) -*-A(x)Tf(Bl(x), . . . . B,,(@

is called an approximation statement of the first kind with respect to (22). Note that in (23) (i) a, is a number in the set of values of the magnitude jO, other than d,, (ii)e-----k(la 1--dl l , ' " , ] ara-dm l), where at 4 = p,, and k is a function such that the less the difference la~--d,I for the constant remaining differences of this type, the less k( lal- -dl 1 . . . . . I am--dmD, (iii) N>~s


where N is a constant adopted by the researcher. The function k is the criterion of approximation, and the constant N (which the researcher usually wants to have "sufficiently small") is the threshold of approximation. Now (23) states roughly that the closer the real conditions come to the ideal conditions decribed in the antecedent of the idealizational statement (22), the closer the value of the magnitude A under consideration comes tof(Bl(x) . . . . . Bn(x));in any case the difference between the two cannot exceed the threshold of approximation N, adopted by the researcher in advance.

We can analogously introduce approximation statements of the second and third kind; the only difference would be that when removing the quasi-idealizing assumption p,(x) =d, we would replace it by the condition pi(x) <~af, which would refer to the scope of idealization of that quasi-idealizing assumption.

c. An approximation theory Under assumption R.3 a researcher concretizes his initial statements

with respect to the working of those adventitious factors which he knows how to take into account, and then applies the approximation procedure: he summarily takes into consideration the working of all the remaining factors; in doing so he merely sees to it that the discrepancy between his results and the empirical data should not exceed a certain admissible measure. The structure of an approximation theory is therefore as follows: it is a sequence of theoretical model (Zk,L k) . . . . . (ZI,LO, (Z °, L °) where the sequence (Z ~, L k) . . . . . (Z i, L~) has the structure of an idealizational theory (of one of the three kinds), and the model (Z °, L °) includes the approximations (of the appropriate kind) of the approximation statements which are in the model (Z*, Lt). Hence (B.III) now becomes (B,IV), which says that if R.1 to R.4 hold, then a set of universal statements is a scientific theory if and only if it is an approximation theory.

d. Verification of an approximation theory The researcher in question used so far definitively to reject his ideali-

zational hypotheses if he obtained (e.g., as a result of a perfect experiment) some evidence against them. Now that assumption Z.3 has been removed the situation has changed. In order to describe it let us refer to a pair of Marxian concepts: a fact which prima facie refutes a statement, and a fact which really refutes a statement. Now, a fact which really refutes a statement (22) is a fact which refutes its approximation (23), but does not refute a statement in the form:

(24) G(x) A p l (x ) < al A . . . A pj(x) < aj A pj+~(x) , dj+~ A • . . A pro(x) 4: dra -~A(x) 7g(B~(x) . . . . . Bn(x) ,pm(x) , ...,p~+l(x)).

174 Leszek Nowak

(24) is an approximation of a concretization:

(2s) G(x) A p i (x ) = dl A . . . A p (x) = dj A pj+ (x) # dj+ A . . . /~ pro(x) 4: dm -*- A(x) = g ( B l ( x ) , . . . , B n ( x ) ,

p (x) . . . . .

of (22). In other words, it is a fact which negates the approximation of the idealization statement (22), but does not negate the approximation of a concretization of that statement. A fact which really refutes statement (22) not only negates the approximation of that statement, but also the approximation of its every concretization. Thus a fact which pr ima facie refutes an idealizational statement does so only apparently, because the discrepancies between the empirical data and the approximation of that statement can be explained by the working of disregarded adventitious factors. Such a fact does not prove that a given idealization statement is false. It merely shows that the statement may not be approximated yet, because discrepancies between that statement and the empirical data are too great as t he disregarded adventitious factors work too strongly. This is why a realistically minded researcher does not reject an idealizational statement merely because he has come across a fact which refutes it, but only When it turns out that the fact really refutes that statement.

This is why in Model IV we have the theorem (D.IV): if R.1 to R.4 hold, then idealizational statements are verified by observations in- tended to show whether there are facts which really refute those statements (under natural or experimental conditions or in a simulation model).

e. Other theorems in Model I V Theorem (A.III) remains unchanged in Model IV: since no factual

statement is a law in the Marxian sense of the term, hence an approximation statement is not a law either. Thus the set of laws remains unchanged in Model IV. But the theorem on explanation becomes modified. (C.IV) states that if R. 1 to R.4 hold, then explanation follows the schema:

T ~ =J . . . . I T , ~ TO 2\ P - ~ L E.

where '"-I" stands for the relation of approximation, and T • . . . . . TL T O are elements of the successive model of an approximation theory.

f . Conclusion The researcher as described in Model IV is still a very abstract concept,

since the analyses carried out in the present paper tacitly adopted a number of modelling assumptions, which have not been listed here. Removal of those numerous modelling assumptions would make the very simplified description of science, as given in Model IV, much more realistic which is done in m y book (19).


8. COI~'CLUDING REMARKS

a. The structure of a cognitive process

According to the traditional marxist formulae, the cognitive process occurs in two stages: I. "From the actual to the abstract" (abstraction) II. ,,From the abstract to the (understood) actual" (concretization). I t follows from that, with the interpretation of the marxist abstraction as idealization, that the process of arriving at the formulation of an idealizational law and the process of concretization of this law (strict or approximate) are two inseparable aspects of this cognitive process. They are inseparable, for idealization (the formulation of an idealizational law) is incorrect without concretization -- the error of reification is then committed, (see -- Nowak, 8), and concretization is impossible without idealization: concretization is an operation on an idealizational theorem of a given level, and it leads towards the idealizational level of a lower rank (in a border case -- to the zero level, i.e. to the factual theorem).

Starting with this idea we can present a more adequate model of the structure of a cognitive process, which observes the unity of the context of discovery and of the context of justification, (I and II).

AI. An investigator assumes a given ontological perspective, which is made of stratificational principles saying what kind of factors are essential (especially main factors) for the factors under investigation, and of the principles of ontic bonds, which say what types of dependencies occur between the factors which belong to the distinguished, (by the principles of the first kind) classes. The principles of the former kind determine the class of images of essential structure of the investigated magnitude, the principles of the second kind determine the class of dependencies which may be the case. For instance, a mechanicism is made of the following principle of stratification (among the others); for any magnitude the essential factors are the ones which characterize the state of molecules composing the bodies defined by this magnitude, and of t h e following principle of ontic bonds; any dependencies which hold between any magnitude and its essential factors consist of either attraction or repulsion between the bodies characterized by these magnitudes. According to that, the imagination of the 18th century physicist did not include the possibility of investigating the larger wholes and not the fragments of investigated bodies.

II. An investigator conducts empirical inquiry on what magnitudes influence the one he investigates, and which of them influence it stronger, which weaker (on empirical procedures applied in these kinds of analyses - - see Brzeziliski, 1, Brzeziliski, Nowak 1). The above empirical research is always carried out within an accepted ontological perspective -- the only magnitudes distinguished as essential are the ones admitted by the stratificational principles. Other magnitudes are unnoticed in a sense; if experience brings them out by accident, they are interpreted on the

176 Leszek Nowak

basis of accepted stratificational principles in a manner which the next epoch shall certainly consider "strange". Empirical research has to result in a selection of one image among the class of the images of essential structures, namely, the one which comes closest to the structure itself. If stratificational principles determine -- for the magnitude F -- a class K of the images of essential structure for this magnitude, then the role of empirical research is to distinguish one image in this class 0(SF), of which an investigator thinks that it coincides with the structure SF or at least that it differs from the structure only in minor factors.

III . Once the image of essential structure for a given magnitude has been established, when we know what factors are essential for the magnitude and which are main and minor ones, an investigator starts determining the dependence which holds between the distinguished magnitude and its main factors. The principles of ontic bonds define the type of this dependence (its "nature") -- that it can be reduced to attraction or repulsion, or that it is univocal, etc., and empirical research aims at select- ing one which actually occurs from this class -- univocal choice is never possible, and one can often determine empiricMly only distant consequences of this looked for dependence, and indirectly infer about its course. The dependence considered to be a regularity by an investigator (it holds between a given magnitude and its main factors) and described in a law which ignores in the precedent M1 the minor circumstances, while determining in the consequent the way in which an investigated magnitude depends on the main factors. The law is then concretized -- on the one hand the accepted principles of ontic bonds determine what type of dependencies are successive forms of the manifestation of a regularity, on the other hand empirical research defines (with above restrictions) the form of correctionM functions, pointing out how minor factors influence the magnitude in question. That is how a theory is established -- the law and a sequence of its succesive concretizations.

BIV. Next a theory is tested -- observational consequences are infered from it and one finds out whether they are the case or not. If not, the investigators conclude that -- if observation is credible -- the dependence provided by the final concretization has been established incorrectly. They suggest a new form of correctional function (ex. they organize new experiments which have to establish the influence of the minor factor upon the magnitude in question) or directional one, changing therewith the form of a dependence which candidates to the role of the ultimate form of manifestation of the regularity. If the agreement with the results of experiments is finally obtained, the theory suggested by our scientist shall be accepted not only by himself, but also by the others. If no agreement with empirical data is obtained, tile a t tempts at revision and corrections go on. So tile form of dependence is being changed, and a new one is given in the pre-ultimate coneretization of an idealizational law, then a new concretization is performed (i.e. a new ultimate concretization of the law) and they are confronted with experience. If agreement

On Some Interpre ta t ion of the Marxist Methodology 177

results, the modified project is accepted in a scientific group, if not -- the form of dependence is revised in successive theorems which make the theory in question. Finally, the dependence proposed in a law is revised, i.e. the one whose author thought it to be a regularity. After correcting this dependence, (ex. after assuming another mathematical function in a thesis which is a candidate for a law) successive concretizations follow until the ultimate concretization is obtained, and from which the next observational predictions are infered. If they agree with actual data, then the modified project of the first investigator is accepted, if not, further reaching revision is necessary.

V. The investigators who control the project (which may happen right after it is proposed, or years later, when it functions in science) come to conclusion that the incompatibility with experience results from deeper sources: from an improper image of an essential structure of a definite magnitude. First they t ry to change the repertory of minor factors. For instance, they discover new minor factors, so they abstract former theorems of the theory even further (they attach new idealizational assumptions) and lift these assumptions by way of concretization. Hence, a new version of the basic theory corresponds basically to the older one -- a regularity is upheld (with an increased number of idealizing assumptions) and it is modified with respect to an increased number of minor factors (Nowakowa, 1). A new ultimate concretization obtained in this way is then tested. I n case the results are positive, a new theory which basically corresponds to the old one is accepted in a scientific community (although it had previously been rejected). In case the results are nega- tive, the revision goes further -- the repertory of the main factors changes (the perception of "essence" changes compared to the primary project). A new image of essential structure is established, basically different from the previous one (i. e. with a different set of main factors), but all the former significant factors are still viewed as such. A new law is established and the new concretizations obtained; a new theory is derived and it corresponds derivatively to the old one (Nowak, 21) -- some correctional functions which appear in the concretizations of the new theory are identical to some dependencies which occur in the former theory's dependencies. And this theory, which corresponds derivatively to the older one, is tested again. If it fails, the way towards further modifications is blocked in principle -- the project turns out to be a "dead end" street since even far reaching modifications (the ones which correspond derivatively) fail. A scientific group waits for new projects then, and they become material for modifications according to the same scheme: first one changes the form of dependencies in concretizations, then in the law', then one revises the repertory of the minor factors, obtaining a theory which corresponds basically to the older one, finally, the repertory of the main factors is changed and a derivatively corresponding theory is obtained.

VI. If a number of projects based on the same ontological perspective

t2

178 Leszek Nowak

turns out to be "barren" in the above sense, i.e. none of successive modifications, (which may take years), does not result in compatibility with experiments, a belief grows in a scientific group that former theories proved to be incompatible with experience not by accident (in spite of their makers' conviction that the compatibility does occur), and that it was not a coincidence that all modifications have been rejected after some time. Responsibility for that is slowly heaped on the mistaken ontological perspective assumed by all the projects which result in successive corrections of the growing size (from the change of correctional function to the revision of the main factors). A conviction becomes widespread that the accepted ontological perspective (which, by the way, science becomes aware of no sooner than now), is a wrong one, and calls for replacement. This is a period when outstanding specialists start engaging in philosophical discussions. What happens is either that ontological perspectives drawn by philosophy are utilized, or new perspectives are created within sience itself, ex. one proposes a theory which assumes an ontological perspective different from the previous one.

I t should be added that ontological perspectives are being changed -- at least in social sciences -- not only according to the above process, i.e. as a result of incompatibility with empirical data. Ontological perspectives are generally value-judgements. I t is possible, for magnitudes are values at times, essential structures -- axiological structures (Nowak, 22). In the sex cases, ontological perspectives are at the same time axiological perspectives of definite social categories (ex. classes or parts of classes). Therefore, a change of social structure (ex. a passage from one formation to the other) is linked to the change in social consciousness, in axiological perspectives in general, and that calls for a change of ontological perspective, too, (ibidem). For instance, the rise of the oppressed class as the "class for itself" linked to the acceptance of a radical axiological perspective (which poses new values which were not respected in social or- ganization so far) results in the ontological perspective of a dialectical kind (which proposes the change-bearing factors as the main ones, since the essence of the world is considered to be found in what decides about its changeability, not stability). That is how the changes of social structure result -- at least in social sciences -- in the change of ontological perspective. The scheme can be illustrated with the following table :(s. P. 179) The symbol " ~ " stands for the relation of general generating which established the class of the images of essential structure for the magnitude in question; the principles of ontic bonds determine the class of dependencies. The symbol" - - . -~" stands for the relation of particular generating-- experience which points out which actual image or actual dependence is a proper one. Finally, the symbol"-~" stands for relation of controlling or testing, and the number at the arrow points out the position of modi- fying procedures in a series which a scientific group shall launch with respect to the controlled theory. It may happen that a theory is accepted at once, and new experimental data are found later on, which gradually


I

!

I

7~ I /

I -?; I I i I I I_

/ stratification ~ principles I I

' I t 1 !

Social structure]

O O 0

ontic bonds ] principles -t

ontological perspective

| I

repertory of the main factors

I

! ! ! ! ! ! ! ! I i i

idealiza- l • tional law

t

I I

| t

F . . . . . ~ |

I i !

! I

, , ( - ~

I

! t [ e x p e r i e n c e ] |

1 ' • 1

shall result in increasingly far reaching concretizations; it may also happen that a theory shall be accepted after some modifications of the lower rank (ex. the form of some concretizational dependencies changes), and that further corrections will become necessary after some time, when new data are discovered.

b. Metamethodologieal remarks The above conception of science, outlined very roughly, pretends to be

just one of a number of possible starting points in the reconstruction of scientific procedures of the makers of marxism and to reconstruct a

12"

1 8 0 L e s z e k Blowak

cognitive procedure of modern science. I t calls for constant renewal and refreshment from both these points of view, and it actually is constantly modifiedg, i.e. when we observe that it is inadequate for some reason, additional idealizing assumptions are introduced, which abstract from the circumstances responsible for the inadequacy of this concept, then the assumption is lifted by way of concretization and the deviation from the original concept is explained therewith. 10 The sequence of models which make a given version of the concept gains another model, more realistic, for it accounts for some minor procedures of a scientific inquiry and at the same time it shows how these procedures modify the ones determined by earlier models, primarily the main device -- the method of idealization and concretization.

Finally, a more general remark. A characteristic feature of almost all contemporary methodological schools is the incompatibility between the image of science it represents and itself. According to inductionism sciences have to observe and generalize observations, while no one seriously claims that this is what a methodologist does; his raw material is composed of the texts,which are not only to be observed, but understood as well. Interpretation, however, is a theoretical procedure, a non- observational one (Kmita, 3). According to instrumentalism empirical sciences construct a theory as pure calculus, which does not say anything about the world, but establishes links between observables -- why no one would claim that theoretical theses of instrumentalists themselves (ex. that one explains wi th the help of Hempel's model, that scientific theories are deductive systems, etc.) play instrumental roles alone, and do not represent the structure of real cognitive processes and their products. Finally, according to hypotheticism empirical sciences apply the method of the criticism of hypotheses, but methodology, as the author of The logic of scientific discovery has put it, should determine vague "conventions" of a scientific conduct. In a word: the inductionist view is not itself the product of induction, the intrumentalist view does not have only instrumental value, the concept of hypotheticism is not itself the result of application of the method of hypotheses critisism. The idealizational conception of science, however, can be described, roughly outlined as it is , as a kind of idealizational theory11 -- methodology employs the same cognitive method which the sciences described by it have employed before. I t can be supposed that liberating methodology from the status of science based on who-knows-what principles is in itself an argument for the correctness of an idealizatinola conception of science. And indirectly: for validity of Marx's methodological ideas which the above conception wants to develop.

9 Cf. Brzezinski , 2, P a t r y a s , 1. 10 See - - Brzez ins td e t al., L 11 W h a t m a t t e r s is t h e k i n d of idea l iza t ional t h e o r y ecnoun t e r ed in t h e h u m a n i t i e s

( a n d m e t h o d o l o g y does be long to t h e h u m a n i t i e s ) - - N o w a k 8.


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Adresse des Autors :

Prof. Dr. Leszek Nowak, 60-247 Poznarl , Cybulskiego 13, Polska

on some interpretation of the marxist methodology

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