The main problem of the present book is to conceptualize the rule of correspondence of scientific laws and theories in terms of the idealizational approach to science. The conception was presented in L. Nowak’s The Structure of Idealization (Dordrecht/Boston: Kluwer, 1980), its developments may be found in numerous papers by various authors, notably J. Brzezinski, A. Klawiter, A. Kupracz, K. Lastowski, M. Paprzycki, K. Paprzycka, W. Patryas, R. Zielinska and others, published mainly in the book series Poznan Studies in the Philosophy of the Sciences and the Humanities (Amsterdam/Atlanta: Rodopi), vols. 1,1 (1975), 2,3 (1976), 8 (1985), 16-17 (1990), 25 (1992).

On this approach, a scientific theory is basically a deformation of phenomena. It resembles much more the logical structure of caricature than that of the inductivist generalization, or hypotheticist reconstruction, of empirical data. The scientific method as seen from the standpoint which is presupposed here can be summarized as follows. The pure abstract of a given type of phenomena is formed by depriving them of some of their features, those which are considered to be secondary. What remains still contains merely the essential magnitudes of the empirical original. If some simple formulae stating relations among them (idealizational laws) are true, it is for the ideal types alone. The idealizational statement is concretized by gradually admitting the previously neglected secondary properties and modifying its formula. The laws become more and more complicated and therefore ever closer to the empirical reality. And also the body of them in subsequent increasingly realistic models becomes larger and larger. This procedure continues until the most realistic model becomes a sufficient approximation of a given system. Whether this is the case, or not, only experience can decide. The simplest idealizational sequence T would have the following form:

(t) (x) If G(x) & p(x) = 0 & q(x) = 0 then F(x) = f(H(x))
(t1) (x) If G(x) & p(x) /= 0 & q(x) = 0 then F(x) = g(H(x), p(x))
(t2) (x) If G(x) & p(x) /= 0 & q(x) /= 0 then F(x) = h(H(x), p(x), q(x))

where (t2) is less and less abstract and, if true, more and more realistic at the same time. (‘G‘ stands for the so-called realistic condition, delimiting the domain of the theory, H is the principal factor influencing the investigated magnitude F, p and q are secondary factors).

The book attempts to reconstruct the principle of correspondence between scientific laws and theories in terms of the idealizational conception of science, thereby extending that conception to cover the dynamics of idealizations.

The starting point (CHAPTER I) is an analysis of the main conceptions of the principle of correspondence known from the methodological literature: implicational (Woodger, Nagel), explanational (Kemeny-Oppenheim), approximativist (Schaffner, Moulines). It is argued that all these reconstructions neglect the idealizational nature of scientific laws; this holds also for the nihilist approach to the correspondence principle (Kuhn, Feyerabend).

CHAPTER II finds a natural explication of the principle of correspondence in terms of the idealizational approach to science. Its main idea is that the falsification of a given idealizational law forces a scientist to abstract from the source of deviation by introducing an explicit idealizing condition, and then to remove the condition by concretizing the formula of the law. Assume (t2) has been falsified; this testifies indirectly to the falsity of the initial idealizational law (t). When the source of the deviations, say factor r, is identified, it must be abstracted from in order to preserve the old formula of (t):

(t‘) (x) If G(x) & p(x) = 0 & q(x) = 0 & r(x) = 0 then F(x) = f(H(x))

In science, however, it is possible to abstract from the sources of deviations only on the condition that it will be shown how this very factor which is responsible for the deviations influences the given magnitude. In other words, a scientist’s entitlement to abstraction carries with it the commitment to concretization:

(t1) (x) If G(x) & p(x) = 0 & q(x) = 0 & r(x) = 0 then F(x) = g(H(x), p(x))
(t2) (x) If G(x) & p(x) /= 0 & q(x) = 0 & r(x) = 0 then F(x) = h(H(x), p(x), q(x))
(t3) (x) If G(x) & p(x) /= 0 & q(x) /= 0 & r(x) /= 0 then F(x) = k(H(x), p(x), q(x), r(x))

In this way the old theory T has been replaced by the new one T‘, i.e. (t‘)-(t3) which is to be accepted provided that the facts that have falsified its predecessor can now be explained on the ground of the new, more complex, statement (t3). The relation which holds between T‘ and T is termed dialectical correspondence.

CHAPTER III takes examples from physics to illustrate how the proposed explication works. CHAPTERS IV-VI attempt to extent this simple solution to the level of scientific theories of increasing complexity and to adjust it to the more and more realistic conceptions of the method of idealization recently proposed within the idealizational approach to science. CHAPTERS VII-VIII discuss various traditional methodological problems — among them, the evolution of scientific concepts, reduction, induction, correction of data, multiplicity of the notions of approximation, etc. — attempting to conceptualize them in terms of the proposed approach.