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Leszek Nowak and the idealizational approach to science.

"All science would be superfluous if the outward appearance and the essence of things directly coincided."

Karl Marx

1. Abstraction or Idealization?

In general, especially in the epistemological and philosophical fields, abstraction has been considered the main theoretical practice of science; but in reality scientists use the method of Idealization. The philosophers of science and epistemologists who put in evidence systematically for the first time this theoretical practice were the main members of the so-called Poznan School. The method of Idealization is maybe the main contribute to science given by the Poznan School and by its founder, that's to say, Leszek Nowak (but it's possible to find some anticipations of this method in the most important works of the Lvov-Warsaw School members (1)).

The epistemological meditations of the Poznan School philosophers renewed the scientific debate concerning not only the Marxism (from one side petrified by the soviet dogmatism and from the other side "humanized" by the western Marxists), but even the modern epistemology. In fact, the modern epistemology was living a period of crisis if we turn our look to the Received View (2) and to the Popperian program.

The consequence of this situation was, especially for the philosophers of science, to find different ways, rethinking the traditional image of science and its main theoretical statements, accepted both from Popperism and from its most radical enemies. (3) By the way, after this period of crisis the Poznan School's meditations came out with all its originality and logic-formal power, so that we can call this period a real epistemological revolution. (4)

The starting point of the Poznan School's meditations is both simple and innovative; there's a big difference between abstraction and idealization, in fact is the last to be the core of the scientific method and not the former. In summary, there is a substantial difference between abstraction and idealization that Nowak finds in Marx's Capital; in effect, Marx in his works used the term "abstraction", but not in the classic meaning, but in the Nowak's meaning. In this case, Nowak interprets the Marxian abstraction as an Idealizational approach to science, in order to distinguish it from the classic empiricist way of using abstraction.

This difference is explained by Nowak in the following way:
   A scientific law is basically a deformation of phenomena. It
   resembles much more the logical structure of a caricature than that
   of the generalization of facts. The crucial point for a proper
   understanding of the Idealizational procedure is that it differs
   fundamentally from that of abstraction [...]. Abstraction, i.e. the
   omitting of properties, leads from individuals to sets of
   individuals (and from sets of individuals to families of sets,
   etc.). Idealization does not do this. Omission of the dimensions of
   physical bodies does not yield any set of physical bodies but the
   mass-point. Abstraction is generalization. Idealization is not. (5)


But what is the role of Idealization in the scientific practice? Its role consists in separating the essence from the appearance of the phenomenon. Nowak, in this case, talks about five paradigms of idealization:

1. The neo-Duhemian paradigm. "Idealization is basically a method of transforming raw data;"

2. The neo-Weberian paradigm. "Idealization is basically a method of constructing scientific notions. Having a certain typology in mind, one may identify its extreme member. If the member is an empty set, it is termed an ideal type and the notion attached to it is labelled idealization. It is particular notions, or their definitions, that exemplify idealizations in science;"

3. The neo-Leibnizian paradigm. "Idealization is a deliberate falsity which never attempts to be more than truthlike. An Idealizational statement is a special type of counterfactual which has to do with what goes on at possible worlds given by antecedent of that statement. The smallest is the distance between the intended possible world of the kind and the actual world, the truer the counterfactual is;"

4. The neo-Millian paradigm. "No mathematical structure fits any piece of reality with full precision, there is always discrepancy between a mathematical formalism and reality we want to describe with the theory. Idealization is a means to fill the gap;"

5. The neo-Hegelian paradigm. It consists in "focusing on what is essential in a phenomenon and in separating the essence from the appearance of the phenomenon." (6)

Let's try to analyze, for instance, the law of free fall presented by Galileo that way:
   The spaces described by a body falling from the rest with a
   uniformly accelerated motion are to each other as the squares of
   the time-intervals employed in traversing these distances. (7)


So, Galilei states, a "motion is said to be [...] uniformly accelerated when, starting from the rest, its momentum receives equal increments in equal times." (8)

In this case the formula is the following:

S= [gt.sup.2]/2

where s equals to the distance covered by a falling body, g it's the earth's gravitation (that's to say 9,80 m/[s.sup.2]) and t instead is the time of free fall. This law, obviously, doesn't describe a real motion, but an ideal one, obtained by operating counterfactual statements on some factors that have real influences on bodies. So, we can formulate the formula this way:

if R(x) = 0 and g = const, [right arrow] S = [gt.sup.2]/2

In this transcription of the law we can notice how the resistance of the air on body x, R(x), equals to zero and the earth's gravitation is constant, where we know that in reality things are different. Even though these two conditions are implicitly given, it means that to state this law Galileo had to ignore one aspect of reality and later he equalled it to zero. So, Galileo substituted, to the real situation, an ideal situation obtained through an aware deformation of what is effectively given. That's the reason why every law introduces counterfactual statements to describe, that way, not reality in its phenomenal manifestation, but how it should be if some of its real conditions were ignored.

To explain that, Leszek Nowak applies an efficacious comparison between science and caricature, because, according to him, both science and arts use the same procedure of deformation in order to catch the essential aspects of reality:
   Let us see what a cartoonist does: he leaves out some details of
   the person presented, thus stressing what he considers important.
   That is, he employs the method of exaggeration: he does not present
   everything but distorts a person or a situation by neglecting some
   features he thinks minor ones. Science, as we have seen, in fact
   does the same. When a physicist constructs the concept of a
   material point, he does not present physical objects but distorts
   them--he assumes that they have zero dimensions and focuses on
   other properties of these bodies (e.g. mass) which he considers
   more essential for physical magnitudes he investigates. In short:
   science consists in the same method we find in caricature. There
   is, obviously, some difference: caricature does not apply
   concretization; it does not cover the distance between the
   prolonged nose of a man, through a middle sized one, to the
   portrait with an ordinary nose in the centre of the man's face.
   Nevertheless, it is a deviation from the same standard: in order to
   say the truth about a fact it should not be presented as
   common-sense used to say, but distorted. And doing this, both
   science and caricature achieve, or at least are able to achieve,
   the truth. The problem arises as to what kind of truth is arrived
   at by them. (9)


So, arts and science apply to reality the same procedure of deformation in order to catch what is more essential in a given phenomena, ergo the truth of an artistic work doesn't consist in a faithful representation but in a proper deformation and scientific truth does the same. (10)

But idealization needs another fundamental procedure that Nowak calls concretization, but before to explain this procedure it's necessary to understand what is an idealizing assumption; it consists in the following propositional function:

[1] p(x) = 0

If and only if 0 denotes the minimum value of magnitude p and it holds for any real object x, (R)x.

Thus, an Idealizational statement will be a general proposition with the following form:

[2] ([T.sup.k]) G(x) [conjunction] [p.sub.1] (x) = 0 [conjunction] ... [conjunction] [p.sub.k-1] (x) = 0 a [p.sub.k] (x) = 0 [right arrow] fx) = f (H(x))

Where G(x) is a realistic statement, while [p.sub.i](x) = 0 is a generic idealizing condition. In this case, ([T.sup.k]) determines how a given magnitude depends on another one in idealizing conditions in which the given idealizing conditions are satisfied: we have examples of idealizing assumptions in Marx's Capital, where Marx used to talk about a society characterized by only two social classes (capitalists and workers), while we know (and Marx too) these are not the only existing classes.

Even though an Idealizational statement describes an ideal state and not a real one, it's possible anyway to pass from idealized conditions to less idealized conditions, closer to reality through the procedure of concretization. According to Nowak, to do that we must delete the assumption [p.sub.k](x) = 0, introducing the realistic condition [p.sub.k] [not equal to] 0. That way, we can concretize the formula [2] and its result is what Nowak calls concretization (11) of the statement ([T.sup.k]):

[3] ([T.sup.k-1]) G(x) [conjunction] [p.sub.1](x) = 0 [conjunction] ... [conjunction] [p.sub.k-1](x) = 0 [conjunction] [p.sub.k](x) [not equal to] 0 [right arrow] F(x) =

= [f.sub.k-1](H(x), [p.sub.k](x)) = G[[f.sub.k](H(x)), h([p.sub.k](x))]

Obviously, we can concretize further this formula until we obtain, at limit, a factual statement, that's to say, a statement containing no idealizing assumptions:

[4] ([T.sup.k-2]) G(x) [conjunction] [p.sub.1](x) [not equal to] 0 [conjunction] ... [conjunction] [p.sub.k-1](x) [not equal to] 0 [conjunction] [p.sub.k](x) [not equal to] 0 [right arrow] F(x) =

= [f.sub.k-2](H(x), [p.sub.k](x)), [p.sub.k-1](x)) = n[[f.sub.k-1](H(x)), ([p.sub.k](x))] m[p.sub.k-1](x)]

[5] ([T.sup.0]) G(x) [conjunction] [p.sub.1](x) [not equal to] 0 [conjunction] ... [conjunction] [p.sub.k](x) [not equal to] 0 [right arrow] F(x) =

= [f.sub0](H(x), [p.sub.k](x)), [p.sub.1](x)) = s[[f.sub.1](H(x)), ([p.sub.2](x))], t[p.sub.1](x)]

Nowak, basing his analysis on [4] and [5], states that Marxian methodology consists in the following passages:

* He introduces idealizing conditions;

* He states idealizing laws;

* He gradually concretizes and approximates these laws.

So, the Marxian procedure of Capital falls under the general scheme of the method of idealization and concretization. Anyway, Marx was not the only one who applied the Idealizational approach to science, because it has been applied by empirical sciences since its origins, even if not always with the necessary methodological awareness.

2. From Archimedes to Galileo: Examples of Idealization in Natural Sciences

As Jan Such stated, "Archimedes was probably the first scientist who was aware of applying the Idealizational method in the natural sciences." (12) That's why Jan Such considers Archimedes the real pioneer of contemporary science instead of Aristotle. In effect, his physics was based on common experience while Archimedes understood perfectly the contradiction existing between "common experience" and "idealizing assumptions."

Jan Such considers the second outstanding representative of Idealizational approach to science the astronomer Eratosthenes:
   He [Eratosthenes] was the first to correctly calculate the Earth's
   circumference. As the basis, he assumed the angular difference in
   the angles under which the sun rays fall on the Earth's surface in
   Alexandria and Syene and he accepted an idealizing assumption that
   the sun rays falling on different spots of the Earth's surface
   (their latitude notwithstanding) were perfectly parallel to each
   other. Thus, physics (statics) and astronomy were the first natural
   sciences in which the Ancient scientists successfully applied the
   method of idealization. (13)


As we can see, physics and astronomy were the first natural sciences to which the ancient scientists like Archimedes and Eratosthenes applied successfully the method of idealization. (14)

But it's thanks to Galileo that idealization has been applied with a more mature methodological awareness. In fact in this case Nowak applies a differentiation between the period of immature science and the period of theoretical science. In the first period science applies the induction as the fundamental scientific practice, while in the second period science applies the method of idealization. Further, Nowak states that three stages can be distinguished in the development of knowledge:

1. the pre-scientific stage, in which there exists no epistemological principle of a transformation of earlier theories into later one;

2. the stage of immature science with the principle of dialectical refutation;

3. the stage of mature science with the principle of dialectical correspondence. (15)

There's a kind of dichotomist image of the historical development of scientific method, divided into the Empirical period and the Idealizational period; between the two we have a kind of methodological breakdown, like the ones operated by Galileo in physics, by Marx in political economy and by Darwin in biology.

Our senses reveal us the false image of the world, because the phenomenon we see are the result of both what is essential and what is less essential; the aim of science is to reveal how these phenomena depend on the most important factors. That's what Galileo did when he tried to explain the nature of motion opposed to the Aristotelian theory of motion. In fact, Aristotle used to state that we have two types of motion: natural and forced.

So, according to the common observation of the moving objects, there are two factors that influence movement of bodies, that's to say, external forces and resistance of the environment. But, Nowak says, "the question of how objects behave when there is no resistance was never answered by Aristotle, for 'first it should be made clear what a vacuum between the moving bodies is. Since for that matter it has never been noticed within this world' (Aristotle, Phys., 216b)." (16)

Instead, Galileo knew very well that the vacuum cannot be perceived, but nonetheless he asked himself a question which was senseless in Aristotle's physics:
   how will 'the perfect round ball move on the plane which is
   smoothly levelled in order to eliminate all external and accidental
   obstacles" upon an assumption that the "resistance arising when the
   ball makes its way and all other obstacles that could arise' are
   not considered at all? (17)


Galileo answered to this apparently senseless question postulating that:

1. the rolling ball is perfectly round;

2. the plane is ideally smooth;

3. the plane is perfectly spherical;

4. the resistance of the environment = 0.

Thanks to these idealizing assumptions, Galileo formulated his famous law of inertia, applied to an obvious ideal case that doesn't exist in reality but idealization, I said previously, differs from abstraction just because the former refers to ideal terms that allowed us to overcome the abyss existing between essence and appearance.

So, according to Nowak,
   The Galilean breakthrough consisted then in system of
   systematically imagining what a given phenomenon would be like if
   the factors considered to be secondary did not act upon this
   phenomenon at all. And that is what was typical for the innovation
   Galileo brought into the body of methods applied in the natural
   sciences. Galileo systematically applied the method of
   idealization. And that was the real meaning of the revolution in
   the natural sciences which was named after him. (18)


That's the reason why Galileo turned his look to the great Aristotle's antagonist, that's to say Plato. At the base of this Galilean choice there was the impossibility, postulated by Aristotle, of applying geometry to physics, while Galileo wrote that nature is written just in a mathematical language. (19) But why Plato then? Because according to the platonic point of view, geometry is a science of ideal models and that's why Galileo applied to his method the platonic point of view. (20)

Anyway, in history of science there are cases of scientists and philosophers who applied idealization without a mature methodological awareness, sometimes because of the Aristotelian legacy or because of a wrong use of abstraction. In effect, some members of the Poznan School demonstrated how idealization has been applied in linguistic by Noam Chomsky (21) and by Darwin in biology. (22)

Even though Idealizational laws, and its concretizations, are so common in physics, anyway they can be found also in economy (23) (see the methodological reconstruction of Marx's ideas made by Nowak), in psychology, (24) sociology, (25) history of arts, methodology, pedagogy, law (26) and so on. It's easy, that way, to realize that Idealizational laws are the fundamental types of law formulated in physics and Nowak, in order to demonstrate that, makes some examples of Idealizational laws of physics like the law of inertia, the law of free fall, Boyle-Mariotte and Gay-Lussac's laws (for perfect gases), the Ostrogradski-Gauss's formula, Ohm's law and so on.

Let' see, for instance, the Clapeyron's law:

[6] pv = NT

where p stands for the pressure of a portion of a gas, v stands for its volume, T for the temperature and N for the gas constant. In this case the full formulation is the following:

[7] (x) (p(x)v(x) = NT(x)).

The statement [7] it's valid only for ideal gases not for real ones just because ideal gases are characterized by these two properties: "their particles are material points, and there are no interactions between those particles, so that the inner pressure of those gases equals zero." (27)

That's the reason why physicists in this case apply two idealizing assumptions:

[8] p1: pw(x) = 0

p2: vw(x) = 0

The first idealizing assumption states that the inner pressure of gas particles x = 0 and the second one that the proper volume of gas particles x = 0; so, Clapeyron's law is an idealizing law.

Unfortunately, a lot of scientists and philosophers of science cannot catch the Idealizational nature of scientific theories, because of a wrong conception of abstraction or because of an indifference towards idealization. This fallacy existing, for instance, in the neo-positivism, has been explained by Nowak comparing idealization with the main epistemological trends like neo-positivism.

3. Idealization vs. Contemporary Epistemology

Idealizational Theory of Science has never been considered by contemporary epistemology even though, recently, important philosophers of science like Nancy Cartwright take into account this new approach both for its originality and important epistemological status. (28)

First of all, Nowak criticizes neo-positivism just because it has never taken into account idealization not allowing, that way, <<the procedure which is basic for empirical sciences in the Marxian model of science>>. (29)

The most representative example of this neo-positivist aspect can be found in Carnap's extreme positivism, (30) that "was originally linked to subjectivism conceiving of observational sentences to which all the other statements are to be reduced as sentences about sense data"; (31) but this kind of reductionism is not able to explain ideal concepts. Nevertheless Carnap applies Idealizational laws directly to real objects and we know, if Nowak's interpretation is correct, that we cannot apply Idealizational statements to reality without the procedure of concretization. In fact, according to the neo-positivists there's no Idealizational law in science but only factual statements, mortifying, that way, the necessity of theoretical terms; in effect, Nowak demonstrated that it's impossible to justify the postulations of classic mechanics or the statements of thermodynamics through the inductive generalization. So, what's the difference between theoretical terms and observational terms? Hempel, for instance, tried to face this problem with a formulation known as the "theoretician's dilemma". According to Hempel, the aim of a scientific theory is to "systematize the experience data, i.e. finding out the relations of consequences between observational sentences"; (32) but, that way, we need necessarily the theoretical terms because in order to do that we must refer to non-observational objects.

Hempel was aware of that but he was sure, nonetheless, that the theoretical terms are unnecessary (and Craig too). (33) In short, there's no place for the Idealizational approach to science in the positivist model, even if we have to say that Hempel distinguished two kinds of idealization, the intuitive one and the theoretical one (without explaining, anyway, the concept of idealization in itself). According to Nowak the first one is legitimate from a cognitive point of view (especially for human sciences) while the theoretical ones, Hempel states, are ex definitione:
   particular cases of the theorems which are described as factual
   ones. This condition allows us to assume that "theoretical
   idealizations" meet the conditions imposed by the positivist
   philosophy of science as well as all the other types of theorem.
   Although they are not directly confirmable on the basis of
   experience, as logical consequences of the theorems which are, they
   (indirectly) are, also, empirically confirmable. (34)


But theoretical idealization doesn't correspond to Nowak's idealizations for two reasons: Hempel's idealization is not an Idealizational law, but the consequent of an Idealizational law, just because theoretical idealization doesn't have the conditional form.

Let's see the law for perfect gases:

if [o.sub.w] (x)=0 [conjunction] [p.sub.w](x) = 0 [right arrow] [T(x) = cost [right arrow] p(x)v(x) = cost]

where [o.sub.w], [p.sub.w], T, p, v are the proper volume of the molecules (portion of a gas), the internal pressure, the temperature and the volume of a portion of gas.

The form of this law is doubly conditional in which the first premise is characterized by two idealizing assumptions; instead, in Hempel's view, the law assumes the following form:

T(x) = cost [right arrow] p(x)v(x) = cost.

The consequence of this difference is that Idealizational laws, according to Hempel, are analytical statements while in Nowak's view they are synthetic; so, the Idealizational law and the theoretical law are not equivalent and that's the second reason why theoretical idealization doesn't correspond to Nowak's idealization.

Through Idealizational theory of science Nowak criticizes the almost universally accepted model of explanation, that's to say the Hempel-Oppenheim's D-N model of explanation.35 Before to do that, I think it's better to explain the D-N model and after that compare it with the Marxian model of explanation (accepted by Nowak in the light of the idealizational approach to science).

Let's analyze this scheme:

[L.sub.1], [L.sub.2], ..., [L.sub.r]

[C.sub.1], [C.sub.2], ..., [C.sub.k]

E

In this scheme the premises [L.sub.1], [L.sub.2], ..., [L.sub.r] are general laws, while [C.sub.1], [C.sub.2], ..., [C.sub.k] are statements which describes the initial conditions of the general laws ([L.sub.1], [L.sub.2], ..., [L.sub.r] together with [C.sub.1], [C.sub.2], ..., [C.sub.k] is the Explanans). In this model E, the explanandum, is the statement that must be explained and it follows logically from the premises (that have to be true). Nowak, comparing the D-N model with the Marxian one, finds the first fallacy living inside the D-N model, the fallacy deriving by the use of factual laws (it's easy to understand Hempel's reasons if we turn back our look to his position towards Idealizational laws). Nowak explains the D-N model that way:
   [...] the laws which occur in it are not idealizing laws [in
   Nowak's view], and moreover they are not "theoretical
   idealizations" as understood by Hempel. For should a "theoretical
   idealization" I imply any statement E, that fact could be accepted
   as an explanation of E only on the condition that also accepted is
   a factual statement F of which the statement I is a special case.
   (36)


In these given conditions, E follows from the factual statement F, so the explanation scheme should have the following form:

F [right arrow] E.

But that way, idealizations cannot play any role in the explanation and they are "superfluous from the point of view of the explanation procedure, and hence are superfluous in science." (37)

Nowak puts in evidence the sterility of the D-N model analyzing the Gay-Lussac's law.

In the handbooks of physics, in general, we can find this law in the following form:

p = cost [right arrow] [v.sub.t] = [v.sub.0] (1 + [[gamma].sup.t]),

where p is the pressure of a given amount of a gas, [v.sub.t] is the volume of that amount of the gas at the moment t, [v.sub.0] is its volume with a temperature = 0 and [gamma] is a constant.

The physicians state that this law is satisfied only by perfect gases, and that's why Nowak writes the formula that way:

[v.sub.w](x) = 0 [conjunction] [p.sub.w](x) = 0 [right arrow] [p(x) = cost [right arrow] [v.sub.t](x) = [v.sub.0](x) (1+[gamma]t(x))]

where [v.sub.w] is the volume of the particles of the amount of the gas while [p.sub.w] is its inner pressure. This law satisfies both the two conditions that we have in the antecedent, that's to say perfect gases, but in this case the law doesn't satisfy the Hempel's view of law of science. So, this Idealizational law cannot explain the behaviour of real gases just because, as we have seen, Idealizational laws cannot directly explain the behaviour of real objects. Now, if we apply D-N model to the explanation of particular facts we obtain the following scheme:

(1) (x) A(x) [right arrow] B(x)

(2) A(a)

(3) B(a)

In the light of the Idealizational theory of science "premise (2) in the explanans would always, i.e., for any real object a be false. Hence Idealizational laws cannot in fact explain actual phenomena in Hempel's sense of explanation." (38) Anyway, the epistemological conception of the Received View is characterized by an instrumentalist point of view just because, according to it, scientific theories have no cognitive status while in the realist conception of science things are different:
   [...] for someone who thinks scientific theories have different
   aims, especially for someone who would like to see a scientific
   theory as a somehow independent source of information about
   objective regularities, there does not arise a theoretician's
   dilemma at all, the theoretician's dilemma is formulated with an
   assumption of an instrumentalist concept of scientific theory; for
   a realist in treating a cognitive status of scientific theories
   there is here no dilemma. (39)


4. Popper--An Unconscious Marxist?

As we have seen, Idealizational theory of science has never been taken into account by Neopositivism, especially for its instrumental conception of science. Anyway, and this is in a class by itself, even one of the most deadly enemies of Neopositivism, (40) that's to say Popper, about idealization expressed some thoughts about this approach very similar to the positivist ones. In fact, Popper never talked about idealization and when he has to do with idealization he managed its statements as they were factual ones. (41) But sometimes Popper, especially when he talks about social sciences, refers to the idealizing assumption that "men" act "rationally." This principle of rationality is called by Popper "logic of situation;" according to him this principle can have an approximate value, but it's very far from any scientific strictness (and it can be used only in social sciences). (42)

These Popperian scientific deficiencies, especially regarding the scarce and non-existing role of idealization in science, has been summarized by Nowak that way:
   [...] even if the interpretation of the humanities is ascribed to
   Popper according to which its methodological peculiarity consists
   of the employment of idealization--conceived of as the assumption
   of rationality, for Popper does not mention another kind of
   idealization in the humanities--we have to say that this has not
   been made comparable with the whole Popperian model of science. For
   instance the author fails to explain in what sense the assumption
   of rationality can be falsified. Thus one fails to decide such an
   elementary--from the viewpoint of the author of The Logic of
   Scientific Discovery--question as the one about the assumption of
   rationality: does it belong to science as a valid component, or is
   it a metaphysical insertion? (43)


Otherwise, Popper doesn't realize that the Keplerian law he refers about in his Logic, (44) is an Idealizational one. But this confusion, in my opinion, drives from the Popperian statement according to which "all universais are dispositional;" (45) but dispositional terms exclude Idealizational concepts just because "no Idealizational term is dispositional, then Idealizational terms and laws are inadmissible in the Popperian model of empirical sciences" (Nowak, 1980, p. 73).

Anyway, the inauspicious consequences of the Popperian misunderstanding of idealization will bring Popper to a systematic incomprehension of both essentialism and Marxism, but in reality, from a particular point of view, Popper was an unconscious Marxist.

The Popperian critiques to the Marxian historicism, according to him deriving from Hegel, are based on the tacit assumption according to which historicism wants to provide a complete explanation of history in causal terms. To historicism is linked even Max Weber's position, who applied idealization extending it from natural sciences (as Galileo did) to social sciences. But Popper rejects every attempt of causal historical explanation in causal terms because, according to him, history lacks the essential requirement of science tout court, that's to say the existence of universal laws. In fact, according to Popper an historian doesn't aim to the discovery of universal laws, at the opposite historians base their analysis on inductive generalizations. Such a generalization erects these unrepeatable facts to objective laws and this is, in Popper's view, false and outlawed.

Nevertheless, Popper makes a lot of systematic mistakes concerning the understanding of Marxism, first of all because he assimilated Marxism, considered a kind of fatalism, to completely different conceptions like the ones of Turgot, Spencer, Condorcet, Comte, and so on; (46) secondly because through his critiques to essentialism he finished to consider Marxism a teleological thought, misunderstanding completely, that way, the Marxian methodology of Capital.

Popper's reflections about historicism can be found in his Poverty of Historicism, a set of articles appeared on the journal Economica between 1944 and 1945, and later published as a volume. (47) Popper criticizes essentialism (an important component of the Poznan School) because it aims to an ultimate explanation that doesn't admit any further explanation (things are different with the Popperian's modified essentialism). That's why Popper considers essentialism unacceptable:
   Essentialism is, I believe, untenable. It implies the idea of an
   ultimate explanation, for an essentialist explanation is neither in
   need of, nor capable of, further explanation. (If it is in the
   nature of a body to attract others, then there is no need to ask
   for an explanation of this fact, and no possibility of finding such
   an explanation) Yet we know, at least since Einstein, that
   explanation may be pushed, unexpectedly, further and further. (48)


That's why Popper denies every epistemological value to essentialism; anyway, he's wrong in two points: the first consists in the absoluteness of his judgment, because the essentialism he criticizes is not the only one (as we will see); secondly he's wrong when he attributes to Marx the essentialism by him criticized.

In fact, Marxian idealization requires essentialist assumptions about the world, but Marx doesn't mean that these assumptions want to reach the ultimate essence not furthermore extendable. A famous Marxian claim is the following: "all science would be superfluous if the outward appearance and the essence of things directly coincided." (49) This Marxian claim, according to Popper, is nothing but "pure essentialism." (50) But it couldn't be different if we turn our look to the Popperian views on essentialism.

But Marxian essentialism really corresponds to the Popperian one? The answer, obviously, is not affirmative just because Marxian essentialism is based on idealizing assumption that Popper can't understand. In fact, idealization "makes possible the discovery the essence of facts of a given type, i. e., revealing the influence principal factors have upon the magnitude under investigation" (Nowak 1980, p. 102). But to clarify how is that possible, we must introduce the notions of ontological perspective, image of the essential structure, essential structure and levels of significance. In doing that we must come back to the difference between abstraction and idealization, specifying that "abstraction leaves unchanged the discourse the scientific theory refers to, classifying only the individuals by procedures of linguistic type." (51) So, individuals are "given with all their properties: we have only, by the method of comparison and inductive generalization, to classify them in homogeneous sets including identical properties present in more individuals or, at limit, in everyone." (52) About idealization, things are different, in fact thanks to this approach we can restructure not only the universe's individuals, but we have even their "ontological transformation and the building of an ontological different universe diverse from the one we started from." (53)

Let us suppose that an ideal researcher is making use of idealization; once he determined the type of domain he's interested to, he aims to discover what factors are essential for a given magnitude. He will take into account the type of magnitudes that, in principle, can influence the one he's interested to. To this regard, we will consider all the factors that influence a given magnitude F and that are necessary for its explanation.

After doing so, we have to arrange this set, called by Nowak, "space of the essential magnitudes" for F, depending on the capacity their elements have to influence the magnitude F.

Let us suppose that this set "is composed by k+1 elements: H, ..., [p.sub.k], ..., [p.sub.1], where H is the main factor for F and the others, called collateral factors, are less essential." So, now we have an essential structure of the factor F of the following form:

Sf: (k) H

(k-1) H, [p.sub.k]

...

(1) H, [p.sub.k], ..., [p.sub.2]

(0) H, [p.sub.k], ..., [p.sub.2], [p.sub.1]

In this case factor F depends, in some way, on each sequence of the mentioned factors to k, k-1, ., 0 level of essence of this structure. The dependence [f.sub.k] of the magnitude F from the main factor H, is an internal dependence or, in other terms, a regularity. So, the dependence [f.sub.k-1] is the first form of manifestation of a regularity f by the functions g, h, when we have (H, [p.sub.k]) = g[[f.sub.k](H), h([p.sub.k])].

As we can see, there's a big difference between Popperian essentialism and the one postulated by the Poznan School. In fact, from one side we have the scientist's hypothesis, with which he can ideate an image of the essential structure; further, he will try, by the procedures of approximation and concretization, to see to what extent this image corresponds to the effective essential structure.

This is a clear case of realism hidden to Popper. He criticized the methodological assumption of Marxian Capital considering them false because based of ideal assumptions. For instance, Popper interpreted Marxian theory of value --considered by Nowak a paradigmatic example of Idealizational approach to science--as an essentialist or metaphysical one, (54) and according to him this law "shows clearly enough the influence of Platonic Idealism with its distinction between a hidden essential or true reality, and an accidental or delusive appearance." (55)

What Popper doesn't catch, is the ideal model present in Marxian Capital, and this is true not only regarding the theory of value, for the perfect concurrency, and so on; these are theories all based on idealizing assumptions and on the necessary procedure of concretization (as widely demonstrated by the Poznan School literature).

This Popperian incapacity to understand the peculiarity of Marxian method, will bring Popper to interpret Marxian theories with the pejorative name of "prophecy;" that way, Popper made a confusion between ideal models and factual situations.

So, the mortification of idealization made by Popper doesn't help him to comprehend the real nature of the Idealizational approach used by Marx in his Capital; that's why Popper stated that Marxian philosophy "was influenced by ancient distinction between 'reality' and 'appearance', and by the corresponding distinction between what is 'essential' and what is 'accidental.'"56

An example of the non-scientific value attributed by Popper to idealization can be found in that Popperian quotation:
   The opposition between legal and the social system is most clearly
   developed in Capital. In one of its theoretical parts [...] Marx
   approaches the analysis of the capitalist economic system by using
   the simplifying and idealizing assumption that the legal system is
   perfect in every respect. Freedom, equality before the law,
   justice, are all assumed to be guaranteed to everybody. (57)


Obviously, Popper considers this Marxian analysis false just because referred to an ideal situation; that's why Popper stated, also, that the Marxian idea "of a free market is paradoxical." (58)

Well, the weaker aspect of Popperian reflections about Marxism consists on the repudiation of idealization, considered by Popper non-scientific. But why, then, Nowak appreciated Popperian hypotheticism claiming the debt that idealization has toward it? The reason is too simple: Nowak evaluates positively the coherent Popperian anti-inductivism:
   Experience does not constitute the issue of the theory, but its
   criterion of the choice among theoretical proposals our imagination
   is able to create. In this the Idealizational theory of science is
   indebted to Popper's hypotheticism, differing from it in the
   definition of the aim of science (reconstruct the essence of
   phenomena) and of the main means to employ (the deformation through
   idealizing them). (59)


In fact, Popper, coherently with his hypotheticism, used to admit the existence of the objective knowledge, but avoiding to postulate a kind of absolute knowledge of the laws of nature by the man; just because "we search for truth, but we may not know when we have found it [...] and that, though there are no general criteria by which we can recognize truth [...] there are criteria of progress towards the truth." (60)

Though Nowak clarified the difference between Popperian hypotheticism and Idealizational theory of science, we must claim the almost perfect concordance between this particular Popperian epistemological aspect and the Engelsian and Leninian ones.

Let us see what Lenin wrote in his Materialism and Empiriocriticism:
   Human thought then by its nature is capable of giving, and does
   give, absolute truth, which is compounded of a sum-total of
   relative truths. Each step in the development of science adds new
   grains to the sum of absolute truth, but the limits of the truth of
   each scientific proposition are relative, now expanding, now
   shrinking with the growth of knowledge. [...] From the standpoint
   of modern materialism i.e., Marxism, the limits of approximation of
   our knowledge to objective, absolute truth are historically
   conditional, but the existence of such truth is unconditional, and
   the fact that we are approaching nearer to it is also
   unconditional. The contours of the picture are historically
   conditional, but the fact that this picture depicts an objectively
   existing model is unconditional. When and under what circumstances
   we reached, in our knowledge of the essential nature of things, the
   discovery of alizarin in coal tar or the discovery of electrons in
   the atom is historically conditional; but that every such discovery
   is an advance of 'absolutely objective knowledge' is unconditional.
   In a word, every ideology is historically conditional, but it is
   unconditionally true that to every scientific ideology (as
   distinct, for instance, from religious ideology), there corresponds
   an objective truth, absolute nature. [...] The materialist
   dialectics of Marx and Engels certainly does contain relativism,
   but is not reducible to relativism, that is, it recognizes the
   relativity of all our knowledge, not in the sense of denying
   objective truth, but in the sense that the limits of approximation
   of our knowledge to this truth are historically conditional. (61)


But the epistemological analogies between Popper and Marxism are not present only in Lenin's works. If we go backwards, we can find some anticipations of the Popperian hypotheticism in Engels' Dialectics of Nature:
   The form of development of natural science, in so far as it thinks,
   is the hypothesis. A new fact is observed which makes impossible
   the previous method of explaining the facts belonging to the same
   group. From this moment onwards new methods of explanation are
   required--at first based on only a limited number of facts and
   observations. Further observational material weeds out these
   hypotheses, doing away with some and correcting others, until
   finally the law is established in a pure form. If one should wait
   until the material for a law was in a pure form, it would mean
   suspending the process of thought in investigation until then and,
   if only for this, reason, the law would never come into being. (62)


Comparing Lenin's and Engels' quotations with the Popperian ones, we can notice that the first two used to claim, from an epistemological point of view, a materialistic-dialectical gnoseology in substance congruent with the Popperian one: this gnoseology doesn't restrict itself to state that "every our knowledge--in particular the scientific one--is relative and then perpetually changeable," because next to this thesis there's another one assuming that "our knowledge gives us the chance to reach reality effectively, even if without knowing it absolutely, so that it makes sense talking about knowledges 'more true' than other ones." (63)

These epistemological aspects, reclaimed and defended strenuously by Popper, are present in the Marxian thought and they were claimed much before the Popperian hypotheticism; so it's very weird that Popper used to consider Marxism as a metaphysic and non-scientific theory just because not subjected to falsificationism (64)!

5. Conclusions

As we have seen, Idealizational approach to science developed by Nowak corresponds to the real way science works. Fortunately, neo-positivism is dead but some of its fallacies still continue to remain in scientific research and science debates, like the reductionist approach. Reductionism contains some limitations that science nowadays must overcome, if it wishes to conform to a holistic and Idealizational approach to science. Another fallacy is the perfect ideal of absolute objectivity. This image of science, obviously, has never corresponded to the real science because, as I said previously, science is an idealization of reality; when a scientist tries to investigate a phenomenon, he applies idealizations that simplify reality. Thanks to this methodology we can face the complexity of phenomenon and of reality. This idea of science, states Coniglione (2009: 32): "inevitably impoverishes reality, but [...] it gives us the chance to work with choice criteria consciously placed within some limits of approximation and of accuracy that every scientific theory--not a mere prophecy or mystic knowledge--is aware that it possesses." Thanks to this Idealizational approach, science loses the dogma of objectivity, because we are aware that scientists do not aim so much to give us a representation of what the world is, but rather as approximate an image of it as possible. As the great physicist Feynman (2002: 153) stated: "The scientist lives with ignorance, doubt, and uncertainty everyday and this is, in my opinion, a fundamental experience. [...] Scientific knowledge is a set of statements with a variable degree of certainty; we are not completely sure of some of them, other statements are almost certain but none of them is absolutely certain."

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NOTES

(1.) About this "School" see Wolenski (1989); Coniglione (1993, 2005, 2007); Jadacki (1994); Szaniawski (1989) and Rieser (1960).

(2.) This term has been introduced by Hilary Putnam in (1962). For a critique of the Received View analyzed in the light of the Idealizational approach to science see Suppe (1972).

(3.) See Coniglione (2004b).

(4.) See Harre (1970)

(5.) Nowak (1992), 10-11.

(6.) Nowak (2000d), 109-110.

(7.) Galilei (1963), 167.

(8.) Ibid., 162.

(9.) Nowak (1980), 134. About the analogy between science and caricature postulated by Nowak see also I. Nowakowa-L. Nowak (200), 9-14.

(10.) See I. Nowakowa-L. Nowak, (1978), 211.

(11.) About the procedures of idealization and concretization see: Nowak (1972), 533-548; Nowak (1975b), Nowak (1990), Nowak (1975a), 23-26. About this topic see also: Tuchanska (1977), 213-234; Palubicka (1976), 89-100; Batog (1976), 101106; ZieMska (1976), 108-114; Patryas (1975), 83-85; Nowakowa (1975), 75-80; Brzezinski (1975), 43-58; Kmita (1991), 147-161; Klawiter (1975), 13-28; Krajewski (1977), 323-339 and Brzechczyn (2009), 137-157.

(12.) Such (2004), 11.

(13.) Ibid., 12.

(14.) For an analysis of idealization in physics and in science in general see Barr (1974, 1971); Lind (1993); Schwartz (1978) and Jones-Cartwright (2005).

(15.) See Nowak (2000c), 425.

(16.) Nowak (2000b), 18.

(17.) Galilei (1962), 155.

(18.) Nowak (2000b), 21.

(19.) "La Filosofia e scritta in questo grandissimo libro, che continuamente ci sta aperto innanzi agli occhi (io dico l'Universo) ma non si puo intendere, se prima non s'impara a intender la lingua, e conoscer i caratteri, ne' quali e scritto. Esso e scritto in lingua matematica [...]" (Galilei (1811), 229). [Philosophy is written in this gigantic book [...] I mean the Universe, but we cannot comprehend it if before we don't learn its language [...]. The Universe is written in a mathematical language].

(20.) About the Galilean Platonism see F. Coniglione (2004a).

(21.) See Nowak (2000a, 2004).

(22.) About this aspect of Darwin's biology see Lastowski (1977, 1982).

(23.) On Idealizational procedures applied in economy see Hamminga-De Marchi (1994); Nowak (1988) and Hunt (2001).

(24.) See Brzezinski (1976, 1997).

(25.) See Tuchanska (1975).

(26.) See Nowak (1969, 1973b).

(27.) Nowak (1972), 536-537.

(28.) About the study of idealization in important philosophers of science see: Cartwright (1983, 1989); Cohen (1991); Dilworth (1990); Hamminga (1989); Laymon (1982, 1985); Ludwig (1981); Niiniluoto (1986); Suppe (1989); Liu (1999, 2004a, 2004b); Adams (1982); Niaz (1999).

(29.) Nowak (1980), 56.

(30.) See Carnap (1968).

(31.) Nowak (1980), 54.

(32.) Ibid., 63.

(33.) Craig (1953), 30-32.

(34.) Hempel (1952), 81.

(35.) See Hempel-Oppenheim (1958), 135-175.

(36.) Nowak (1974b), 17.

(37.) Ibidem.

(38.) Nowak (1980), 69.

(39.) Ibid., 63.

(40.) About anti-positivism in contemporary philosophy see Giedymin (1975), 275-301.

(41.) See Coniglione (1981), 40-U.

(42.) See Popper (1975), 121-122.

(43.) Nowak (1980), 73. About Popper as a critic of historicism see Nowak (1974a), 43-47.

(44.) See Popper (1970), 131.

(45.) Popper (1972b), 204.

(46.) About the Popperian misunderstanding of Marxian historicism see Topolski (1975), 211-217.

(47.) See Popper (1944a, 1944b, 1945).

(48.) Popper (1972a), 299.

(49.) Marx (1973), 228.

(50.) Popper (1962), 347.

(51.) Coniglione (2002), 264.

(52.) Ibid., 264-265.

(53.) Ibid., 265.

(54.) Popper (1962), 174.

(55.) Ibid., 177.

(56.) Ibid., 107.

(57.) Ibid., 123.

(58.) Ibid., 348.

(59.) Nowak (1983), 10.

(60.) Popper (1972c), 387-388.

(61.) Lenin (2004), 149-151.

(62.) Engels (1974), 522.

(63.) Geymonat (1972), 33-34.

(64.) About the "poverty" of the Popperian falsificationism see Barbagallo (1995), 55-60.

GIACOMO BORBONE

giacomoborbone@yahoo.it

University of Catania
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