Quantity and Quality 8 (1974) 107-120 0 Elsevier Scientific Publishing Company - Printed in The Netherlands

VALUE, IDEALIZATION, VALUATION

LESZEK NOWAK Poznan/ University, Poland

1. Unitary formulas in Marxist dialectics

In Marxist dialectics the set of theses includes formulas which state the unity of two different spheres of phenomena, e.g., the unity of language and thought, the unity of content and form, etc.; they are usually termed unitary formulas. Their underlying idea seems to be that these different spheres of phenomena are subject to the same laws. Thus, the laws of language are at the same time the laws of thought (the unity of language and thought), the laws which govern the representing structure of a work of art have their semantic analogues in the laws which govern the represented structure (the unity of content and form), and so forth.

The present paper is intended to substantiate two other unitary for- mulas, namely those which link the sphere of the phenomena studied in axiology with that which is studied in Marxist ontology (the formula of the unity of being and duty) and with that which is studied in Marxist epistemology (the formula on the unity of cognition and valua- tion). l

2. Value and magnitude

The initial concept is that of preference. We shall be concerned, however, not with the preferences of a given individual, but with the preferences of a“socia1 subject” who expresses a standard of,valuation (with respect to his external world) that is fixed in a given social group (a class, section of a class, or - in the limiting case - society as a whole). The preference ascribed to that social subject is not any average of the preferences which the various individuals have, but a preference which accounts for the fact that that social agent’s actions are necessary for his group holding in the social structure the position it actually holds. In this interpretation, the capitalist as described in Capital is such

’ The paper contains the main ideas of Nowak’s book (1974a).

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a social subject. He has only one preference, namely the maximization of profit. Marx ascribed it to him not because most capitalists are guided by such a preference (it being well known that no real capitalist is guided in his actions by a single preference only), but because the maximization of profit by the individual capitalists is necessary for that class to be dominant.

We shall not, however, concentrate on these semantic conditions imposed upon the concept of preference since they are not essential for the problems with which the present paper is concerned. Moreover, certain formal conditions, too, are imposed upon the concept of prefer- ence. Preference is a relation defined on the set W of states of things; it is -also an antisymmetric and transitive relation:Hence, if a state of things p is preferred to a state of things 4, then it is not true that q is preferred to p; and if a state of things is preferred to a second one, and the second one, to a third one, then the first one is preferred to the third one.

The concept of preference is used in the following definition of the relation of being equivaluable: p and q are equivaluable if and only if it is not true that p is preferred to q and it is not true that q is preferred to p. This relation is reflexive (every state of things is equivaluable to itself), symmetric (if a state of things is equivaluable to another, then the latter is equivaluable to the former), and transitive. It is thus an equivalence relation which partitions the set W of states of things into the classes 2, Z’, Z”, . . . of pairwise equivaluable states of things. Each of these classes contains equivaluable states of things (i.e., equivaluable for a given person) ; further, no two states of things contained in differ- ent classes are equivaluable, but one is always preferred to the other.

We now define the concept of general preference. Now, a class 2 is generally preferred (by a given social subject) to a class 2’ if and only if, for every p in 2 and for every q in Z’, p is preferred (by that agent) to q. The relation of general preference is antisymmetric, transitive, and connected (i.e., out of any two classes of equivaluable states of things one class is preferred to the other, or vice versa). Thus this relation orders the set of the classes of equivaluable states of things, i.e., it enables us to arrange that set as a sequence in which each class has its definite place.

Now that set of the classes of equivaluable states of things is a value (for a given social subject) if and only if it is ordered by the relation of general preference (characteristic of that subject). These classes of equivaluable states of things are cases of value. All values are, as it seems, opposition-based families of sets of states of things, i.e., such which contain both a maximum and a minimum under the relation that

orders a given family. In other words, a value is a set V/‘= {Z,,,, Z, . . . . Z’, .Zmin } such that Z,,, and Zmin are, respectively, the set of those states of things which are maximally preferred and the set of those which are minimally preferred (by a given social subject). We assume that between the maximum case Z,,, and the minimum case Zmin of a given value there is an indifferent case Zind , which contains those states of things which are axiologically neutral. 2 Every positive case of a given value, i.e., every set of the states of things in a given value, which precedes (under the relation of general preference) its indifferent case will be termed a good. Every negative case, i.e., a set of the states of things which is preceded (under that relation) by the indifferent case of that value will be termed an evil. The structure of a value V may be represented thus: I’= {Z,,,, Z, . . . . Z’, Zind , Z”, . . . . Zmin},) where Z max , . . . . Z’ are goods, and Z”, . . . . Zmin are evils.

Compare now the above construction of the concept of value with the usual construction of the concept of magnitude (factor).

Given a set U objects and a precedence relation R defined on that set and asstl‘;:,:d to be antisymmetric and transitive, we define the undistin- guishak i I; 7 relation thus: two objects are undistinguishable if and only if it is not true that one of them precedes the other under R and it is not true that the latter precedes the former under R. If we assume that the relation of undistinguishability is transitive, then we can prove that it is an equivalence relation, which thus partitions the set U into classes of objects which are pairwise undistinguishable under R.

We now define the relation of general precedence, which holds be- tween a class Z of (pairwise undistinguishable) objects and a class Z’ of (pairwise undistinguishable) objects if and only if every element of Z precedes every element of Z’ under R. The relation of general prece- dence is antisymmetric, transitive, and connected, and hence it enables us to order the said classes of objects which are pairwise undistinguish- able (under R). A family of such classes is a magnitude (factor) if and only if it is ordered by such a relation of general precedence.

When we compare this construction of the concept of magnitude (factor) with the construction of the concept of value we see a com- plete formal analogy between the two: the process of construction is precisely the same at each step. In other words, we might say that the ontological structure of value and that of magnitude (factor) are the same.

3. Axiological structure and significance structure

The social subject under consideration is marked by a number of

2 Those states of affairs can be considered as tautological. (I owe this remark to J. Kmita.)

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preferences, and not by a single one. This is why a number of values may be ascribed to him. Now when we evaluate a state of things, then in the set of all values we single out those which are important (signifi- cant, relevant) for that state of things, and then a hierarchy is estab- lished even among those important values. Some values are singled out as the fundamental ones, which must unconditionally be taken into consideration when a given case is being evaluated, whereas others are treated as secondary ones, which can merely modify or complete the evaluation based on the fundamental values. Thus, for instance, when we evaluate physicians, we take the effectiveness of their treatment to be the fundamental value. That evaluation may also be modified from the point of view of such values as approach to the patient, etc., so as to become a joint evaluation on which the decision which physician to choose can be based.

In other words, in a moral or aesthetic discourse some criteria of domination of values are assumed. What these criteria are is an empiri- cal issue which will be disregarded here. The important point is that there aye some criteria which enable us to accept universally that in the evaluation of physicians the value of the effectiveness of treatment dominates the value of the good approach to the patient, and that in the evaluation of students the value of intelligence dominates the value of sociability.

Let us accordingly assume that the critera of the domination of values have been fixed empirically for a given social subject (while they may be different for other social subjects). Let us also assume that in evaluating the states of things of type K the social subject under con- sideration holds the values V, S,, . . . . S, to be important; and that these values are such that V dominates S,, S dominates S,-, , etc. The axio- logical structure of the states of things of type K for the social subject under consideration becomes the following table of values:

(k) V (k-1) V, S, . . . . . . . . . . . . . . . . . . (1) K s,, . . . . s, (0) v, s,, . ., s,, s,

which includes the zero, first, etc., levels of domination. The zero level will be called the surface level, because it includes all those values which the subject holds to be important for the cases of type K. The kth level will be called the internal level, because it includes only the fundamen- tal value V; the agent disregards here all the secondary values Sk, . . . . S, and thus assumes counterfactually that the state of things being evalu-

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ated is axiologically neutral from the point of view of those secondary values, i.e., that it forms an indifferent case of those values. Obviously, there may be more fundamental values (equivalent to one another, that is, such that one does not dominate the other); likewise, at a given level there may be more pairwise equivalent secondary values.

Example. S. Morawski (1964, p. 330) has adopted a “system of criteria for the evaluation” of works of art, in which we can see a special case of the axiological structure in the sense defined above. That system includes artistic criteria: the constitutive value of a work of art, its novelty, and its originality, and extra-artistic ones, such as moral, political, and the like. The former are the dominant ones: “There is no reason to reject an extra-artistic evaluation of works of art. The art theorist may only demand that the division into these two different types of criteria of evaluation be respected, and that a given critic should always realize which criteria he uses. There is also no doubt that the art theorist will argue, not without justification, for the appli- cation to works of art of those criteria which are proper to it, that is, artistic ones.” Artistic values are here explicitly treated as dominant over extra-artistic ones, and priority is given to an evaluation based on artistic values, extra-artistic ones being disregarded. Among the latter Morawski gives the pride of place to “such an ideological qualification which results from the mimetic tissue of the work;” he emphasizes that “those ideological elements which are mainly connected with the mi- metic transformation of reality in art may play a considerable role in the scaling of works of art.” The other extra-artistic criterion which he seems to place at the same level is “the evaluation of a work of art from the point of view of disalienation.” He gives a lower status to the other two criteria: an ideological qualification “of works of art which disre- gards the artistic structure of a given work, its inner elements, and their mutual relationships” and the criterion of comprehensibility of art.

Thus, the fundamental values, in the axiological structure which Morawski adopts for the works of art, are: the constitutive values of a given work (k), its novelty (n), and its originality (0). The extra-artistic values are treated as secondary; among them we find those on the higher level: the ideological values of the artistic structure of a given work (m), and disahenation (d), and those on the lower level: the ideological expression which disregards the artistic structure of a given work (m’) and comprehensibility (z). Hence the axiological structure of a work of art, as adopted by Morawski, is this:

k, a, 0, k n, 0, m, d, k, n, o, m, d, m! z.

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Here again, we can see a strict analogy between this axiological struc- ture and the fundamental concepts of ontology. As the present writer strove to demonstrate in Nowak (1974b), in Marxist ontology the basic concept is that of the significant 4 structure of a given factor (magni- tude). Assume namely that the significant magnitude for a magnitude F (i.e., those magnitudes which affect F) are H,pk, . . . p1 . But the magni- tudes which are elements of that set are marked by a certain hierarchy: some of them are more significant for F than the others are (i.e., they affect F more than the others do). Assume that H is more significant for F than pk is, that pk is more significant for F than pk-1 is, etc. The table of magnitudes

(k) H (k-1) K pk . . . . . . . . . . . . . . . . . (0) H pk,....’ P1

is the significance structure of the magnitude F, consisting of the zero (surface), first, . . . . kth (inner) level of significance, where H is the fundamental factor (there may, of course, be more than one fundamen- tal factor), and pk ,...., p1 are secondary factors.

As can be seen, the concept of axiological structure if formally fully analogical to that of significance structure. As we shall soon see, the construction of the significance structure is a tacit assumption which underlies all cognition, and the construction of the axiological structure is in the same way a tacit assumption which underlies all valuation.

4. The system of values and the system of factors

In an axiological (ethical, aesthetic, etc.) discourse we assume certain general rules which state which kinds of values are to be placed above values of other kinds (e.g., spiritual values above utilitarian values, etc.). Such rules apply not to any specified values, but to classes of values. They will be termed here the principles of axiological stratification: they state that every value of a given class dominates every value of some other class.

Example. Scheler adopted the following “criteria which enable us to prefer certain values to others: values seem to be high in proportion to their permanence, to their being indivisible in their extensiveness, to the satisfaction they give, and in inverse proportion to their being based on other values and being experienced because of a specified position of the person who experiences them and gives his preference to them”

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(Trebicki, 1972, p. 52). It is obvious that his “criteria” are principles of axiological stratification that make it possible to compare entire classes of values.

The principles of axiological stratification determine the relation of general domination. It will be said that a class of values X generally dominates a class of values Y if and only if every value S in X domi- nates every value S’ in Y. The relation of general equiposition between the classes X and Y of values holds if neither class dominates the other. This is an equivalence relation which enables us to partition the set of values held by a given agent into families of generally equipositioned classes. This gives the following family of classes which will be called a system of values:

I. x, ) . ..) x,, II. Y,) . ..) Y,, . . . . . . . . . . . . . . . . . . . . . . N.Z,, . . . . Z,,

where the classes of values at one level (i.e., the classesXt , . . . . X,) are generally equipositioned, and the relation of general domination holds between classes at different levels. The values included in the first-level class will be called primary values. If 12 equalled I and the set X, contains one value only, a system contains only one primary value.

An assumed system of values (adopted tacitly or postulated by a doctrine) serves as the basis for the determination of axiological struc- ture for the evaluation of certain states of things. It does not, however, predetermine the form of given structures: it is always so, that a class of axiological structures is admitted in a given system; yet certain types of axiological structures are not admitted in a given system. This is illus- trated by the following example. Let a system of value be in the form:

where X1 = {S}, Y, = {,S’), Y, = {S”, S”‘>. Assume that the values S, S’, S” are held to be important for a certain state of things. Now this system does not admit the axiological structure:

(1) S’, (0) S’, s, S”.

But this system leaves a certain freedom, since the following class of axiological structure is admitted:

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(1) s> (2) x (2) x (0) s, S’, S”, (1) s, S’, (1) s, S”,

(0) s, S’, S”, (0) s, S”, S’. This is so because the condition imposed by the structure of the system of values under consideration is that the set Y, is generally equiposi- tioned with the set Y,, and this condition is met both if S’ and S” are equipositioned and if one dominates the other.

Example. In Max Scheler’s ethics the following system of values is assumed (which is constructed in accordance with the principles of axio- logical stratification as mentioned in the previous example):

I. value of the sacred, II. spiritual values, III. vital values, IV. hedonistic values.

Like in the previous cases, the concept of system of values has its analogue in cognitive processes: it is tacitly assumed in science that there are specified principles of stratification of significance, which determine which kind of factors are more significant (for all the mag- nitudes under consideration in a given domain) than factors of other kinds. These principles enable us to define the relation of “being gener- ally more significant than” which holds between classes of magnitudes and which, like in the case of the principles of axiological stratification, determines a system of factors:

I. A 1, .a*> A,, II. B 1, . . . . B,, . . . . . . . . . . . . . . . . . . . . . . N. Ml , . . . . M,,

where the classes at one and the same level (e.g., A r , . . , A, ) contain equi- significant factors, and classes at a higher level contain factors which are more significant than those which are contained in classes at a lower level.

A given system of factors, as determined by the set of principles of significance stratification (principles fixed in a given philosophical doc- trine or applied spontaneously in a philosophical system tacitly adopted by researchers) serves as the basis for defining significance structures for magnitudes under consideration. But it does not define them un- ambiguously, and admits whole classes of them. Its role is the same as that of a system of values: it eliminates certain types of significance structures. In this way a given system of factors admits certain kinds of

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explanation and eliminates other kinds, in the same way as a system of values admits certain kinds of valuation and eliminates other kinds. This is the group of problems to be discussed now.

5. Valuation and explanation

As agreed upon above, a value is a family of sets of states of things. A certain symbolism will now be adopted. Let So stand for an indifferent case of a value S. Above So we have goods, to be symbolized as s’ r ,S+ 2 , -*-> Smax , where s+ i stands for the ith good in the value S beginning with the neutral value SO, Below So we have evils, S- 1, S- 2, . . . . Smifi , where S- ’ stands for the ith evil in the value S beginning with the neutral value So _

A term which valuates positively (negatively) denotes a good (an evil) in a given value (in the system held by a given social subject). A state- ment in the form “every F is G”, where at least the term G valuates, will be called a general evaluation (by a given social subject). A state- ment in the form “a is F”‘, where F valuates, is a singular evaluation (by a given social subject).

Note that the restriction to a social subject is essential as it enables us to make a distinction between evaluations and statements that express individual emotions and/or likes and dislikes.

Suppose now that a given social subject has to evaluate a given state of things p. of type K, for which he has fixed the following axiological structure:

. . . . . . . . . . K s,, . ..I s,, Now, the term evaluation standard will be applied to a general evalu-

ation in the form: (1) if p E Sy and . . . and p E SE, then if p E K,- then p E V+i, where V+i

stands for the ith good or the ith evil in the value V. Thus an evaluation standard includes counterfactual assumptions which state that the state of things p is axiologically neutral from the point of view of the second- ary values Sk, . . . . S, . Yet, since p is of the type K, then it follows from the very concept of axiological structure for the case K that p is good or evil from the point of view of those values; hence the said assump- tions have the status of simplifying assumptions. Thus the evaluation standard shows the evaluation of a state of things p of the type K only and

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exclusively from the point of view of the fundamental value(s); the secondary values are disregarded for the time being.

The evaluation standard which takes into account only the funda- mental values for a given case once being fixed, the social subject suc- cessively corrects his basic evaluation by taking into account the succes- sive secondary values which occur at lower levels of the given axiologi- cal structure. In an ideal case, he would arrive, on having made all the corrections, at the comprehensive evaluation, that is a general evalua- tion that takes into account all the values in the given axiological struc- ture.

Consider now a very simple case. Let the axiological structure for a state of things of a type K be in the form:

(1) v, (0) v, s.

Now the social agent in question at first disregards the fact that the state of things p. in K is a good (or an evil) in terms of the secondary value S and adopts the evaluation standard:

(2)ifpeSO.thenifpe K, thenpe YcJ.

Next, that standard, which was adopted for the inner level of the struc- ture under consideration, is modified by him: he does so by taking into account the secondary value S, as a result of which he adopts the comprehensive evaluation:

(3) ifp E Pi, then if p E K, then p E y*(iJi),

where f is a function defined on the values V and S, which assigns to each pair of cases of the values V and S a case of the value V. The evaluation described under (3) is a modification of (2): it classes states of things of type K as f(j,i), that is, that good or evil in terms of V, whereas previously (when the secondary value S was disregarded) those states of things were classed, under the standard (2), as the ith good or evil in terms of V. It may occur that fl,i) = 0, so that the state of things which was at first evaluated as good or evil, comes to be evaluated as neutral when the secondary value is taken into account. Thus, when the simplifying assumption that ascribes to the state of things of type K a neutral position in terms of the secondary value S is removed, then the social subject in question realistically takes into account their actual position in terms of that value; he namely assumes that they are the ith good (or evil) in terms of that value. This results in a changed classifica- tion of the state of things p in terms of the fundamental value V: it is located on the scale of that value according to two factors: the differ-

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ence between the new and old classification in terms of the secondary value S (i.e., the difference between its real and neutral position), and the old classification in terms of the fundamental value I’, i.e., the classification based on the evaluation standard (2); this is why that now position is defined as fG,i).

In this case, the schema of strict evaluation is as follows:

1. if p e SO, then if p E K, then p E V’i, 2. if p E Ski, then if p E K, then p E V*f(isi), 3. p. E S’i and p. E K,

4. pee v+f(iJi),

where p. is a given state of things that is subject to evaluation. Strict evaluation thus begins with the adoption of an evaluation standard which disregards the secondary values, and takes into account the fun- damental values only; that standard is then modified a number of times: the social subject in question does so by taking into account all secondary values and thus arriving at a comprehensive evaluation, on the strength of which he adopts singular evaluation that apply to a given state of things which is subject to evaluation.

It is self-evident that the process described above is an idealization of the evaluation processes as they actually take place. Except for the few cases of evaluation in science (linked with optimization issues in practi- cal disciplines) those modifying functions (e.g., f in the schema above) are not defined at all. The above idealization may be justified by the fact that it points to the “pure form” of the basic characteristics of evaluation as it takes place actually, and hence that idealization is a good starting point for the reconstruction of those schemata of evalua- tion which are used more universally. Such a more universal schema is that of approximate evaluation which, in the case of the simplest axio- logical structure outlined above, is as follows:

1. ifp ESO, then ifp e K, thenp e V’i, 2. if p E Ski, then if p E K, then p E V’+i, 3.p, eS*iandp E K,

4. p. E Pi,

where v+i stands for that class of the cases of the value V, which “come sufficiently close” to the case V+i. Which cases of a given value “come sufficiently close” to a given is an open issue, in the same way as it remains undefined which cases of black colour “come sufficiently close” to ideal black; in certain cases there are “zones of vagueness” which only an (arbitrary) decision may eliminate.

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Thus, the general schema of evaluation is such in which the initial evaluation standard is subject to certain modifications and in which finally an approximation is used:

where Ln stands for the initial evaluation standard that disregards yz secondary values, Lnwl to Li are its modifications, Lo is an approxima- tion of the evaluation Li, P are the initial conditions of the evaluation Lo, and J is the final singular evaluation: > stands for the relation of modification, and >, for that of approximation.

For lack of space it would be difficult to compare here, in detail, the above model of evaluation and the Marxian model of explanation (cf. Nowak, 1971, p. 337). We shall therefore confine ourselves to some remarks. First, the concept of evaluation standard is a strict analogue of the concept of idealizational law; an idealizational law states that a given magnitude depends exclusively on those factors which are funda- mental for it, and disregards all secondary factors; the evaluation stand- ard likewise refers exclusively to those values which are fundamental for a given case and disregards all secondary values. Secondly, the con- cept of modification corresponds to that of concretization, and the concept of approximation plays the same role in both cases. Thirdly, the formal version of the model of evaluation as outlined above is strictly analogous to the formal version of the Marxian model of expla- nation:

Tk i Tk- 1 -i . . . i P’--iT” Ap+ E,

where Tk is the initial idealizational statement that disregards k second- ary factors, Tk- 1 to Tj are its concretizations, To is an approximation of Ti, P are the initial conditions of To, and K is the explanandum; further, 4 stands for the relation of concretization, and -I, for that of approximation.

6. Ontology, epistemology and axiology in the Marxist theory

The results obtained so far might be summed up thus. The ontologi- cal description of reality, as assumed in the Marxist theory, determines the way of explaining that reality by reference to idealizations that enable us to acquire the knowledge of the latent essence of phenomena, and by reference to concretizations, which enable us to find out the forms in which that essence of reality manifests itself. We have seen that the ontological description of value is quite analogous to what has

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just been said, and that it also determines the very way of valuation; to put it more precisely, the axiological structures of the cases under consideration determine the schemata of the valuation of those cases. It has also turned out that the schemata of valuation and explanation are fully analogical. This seems to indicate that the two unitary formulas adopted in Marxian dialectics, namely that on the unity of existence and obligation and that on the unity of cognition and valuation, are true.

It may be added, as a concluding remark, that these statements yield a simple answer to the question: what role is being played by valuation in the humanities and the social sciences? Now in some cases magni- tudes are values (e.g., balanced economic growth is not merely an eco- nomic magnitude, but also a social value), and significance structures are axiological structures. In such cases, the valuation made by a re- searcher helps him construct certain significance structures and, as it were, prompt him when he is to find out what is fundamental and what is secondary in the sphere of facts, what may be disregarded, and what ought be taken into account.It thus indirectly affects the form of his scientific theories. Since the valuations made by a researcher bear speci- fied reIations to the social status of the group which he represents, we can indirectly point to the relationships that link the social status of the group of which a researcher is a theoretical representative, and the significance assumptions included in the theories he formulates.

References

Morawski, S. (1964). “Criteria of Evaluation of a Work of Art.’ (in Polish), Studio Estetyczne, t. IV.

Nowak, L. (1971). “The Problem of Explanation in Marx’s Capital.” Quality and Quantity, v: 2.

Nowak, L. (1974a). Foundations of the Marxist Axiology (in Polish, in press). Nowak, L. (1974b). The Principle of theMarxist Philosophy of Scienc_e (in Polish, in press). Trebicki, S. (1972).Max Scheler’s Ethics (in Polish). Warsaw, 1972.

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