20th WCP:

If the 17th century could be considered the century of the reformation of science, the present century is one of counterreformation in every sense of the word. Ever since the turn of the century, the same ideology has been in existence: titanic efforts to complete the development of the science whose foundation was laid in the 17th and 18th centuries and outright failures followed by the reconstruction of the foundation. There are many exemples, some of them very striking: Hilbert's formalisation program and Godel's incompleteness theorem in mathematics, Charlier's theory of a hierarchic universe and Fridman's theory of the evolutionary universe in cosmology, Newton's mechanics and relativistic and quantum mechanics in physics, and finally, the logical program of the Vienna circle and epistemological anarchism in methodology.

Our task is to reveal the essence of the turning points in 20th centuries science history and to try to determine at least the general outlines, if not the cause, of the new type of rationality that is succeeding (or has already succeeded) the old one. Needless to say, we are obviously unable to embrace all branches of knowledge ; therefore, we will confine ourselves to the history of cosmology, or rather to its three paradigms that successively prevailed in this century : Newtonian, Fridman's and inflationary. By outlining the problem, we have defined the way of its solution from clarifying changes in the value orientations, ideals and norms of scientific research to their possible generalization.

There are numerous studies devoted to the revolutionary changes in the physicogeometric conceptions of the universe. Yet, what has happened in cosmology over the past 10-15 years makes it possible to again look at the first revolution and analyze the epistemological guidelines predominant it at the beginning of the century.

As is well known, at the turn of the century, cosmology was not yet completely mature science. This was largely due to the fact that general knowledge of the stellar field was incorporated into astronomy as one of its subdivisions. Having no subject matter of its own (there existed merely a general tradition of the new European cosmogonies from Kant, Herschel,Laplace to Schmidt), cosmology could not claim a description of the universe as a whole because it was not sufficiently clear what a whole was.

The mentality formed during the 19th century, with its fluctuations between the recognition of the infinity of the universe, on the one hand, and a desire to reveal changes in this infinity, on the other (a typical illustration is the attempt to solve the problem of the thermal death of the universe, which will never come precisely to the infinity of latter), gave rise to difficulties in assuming the form of two cosmological paradoxes-photometric (Olbers,1826)and gravitational (Seeliger,1895). This made it necessary to give more attention to the problem of the static-immobile (hence, non evolutionary) character of both the entire universe and infinite space. But even such assumptions as the absorption of light by interstellar accumulations of matter,etc. could not solve the problem because Seeliger's paradox was based on the following irreconcilable contradiction arising from Newton's law of gravity : applied to the infinite universe, this law leads to a universal collapse . if we assume that matter spread across the universe is infinite.

Thus, by the mid-19th century, it was realized that the universe cannot be simultaneously represented as immobile, whole, and infinite. Such a viewpoint is beginning way (so far only in the form of the presented paradoxes) to a new belief: the universe cannot be infinite if it is a whole.

That was the shaky construction of infinite space that Charlier tried to save in the early 20th century, by assumption that "the density of stars diminishes the further one moves into space" and that "although matter in the universe is infinite, its mean density approaches zero in proportion to the penetration into space" (Charlier [1914], p.5). This proposition does not arise out of Newton's gravitation theory. Therefore, it is ad hoc assumption intended to save from the gravitation paradox not only Newton's law but also, as it appears after many years , the entire paradigm of knowledge called Newtonian, which actually goes back to Campanella, More, and the whole tradition viewing the universe and space as the receptacle and tool of God.

In other words, within Newton's cosmological paradigm, based on the law of universal gravitation, what evolves is not the universe as a whole, and what would be defined today as the universe as a whole does not evolve. Consequently, the universe as a whole is immobile. These conclusions, as mentioned before, were reached through cosmology in the 20th century. Fifteen years after Charlier's hierarchic hypothesis, Fridman presented his work On the Curvature of Space, where the picture of the world, not only physical but also epistemological, underwent qualitative changes that may be reduced to the following :

All the matter and radiation filling the universe are included in Einstein's field equation. In other words a cosmological theory proper describing and explaining the universe as a whole was produced for the first time.

The universe as a whole began to be considered boundless but not infinite because the question as to what lies beyond it is meaningless in the terms of the relativistic cosmology.

Fridman's paradigm introduced the concept of the evolution of the universe as a whole, i.e., of a qualitative change of its characteristics in the course of time, which, in turn, gave rise to the problem of the beginning of the evolution (birth) of the universe and its end (death) defined physically as a problem of singularity or a special point.

The problem of singularity raised for the first time in a purely cosmological aspect the problem of a fact unobservable in principle by virtue of, first, its unique nature ( this universe is born only once) and, second, its scope and parameters (r ~ 10⁹⁴ g/cm³ , l = ^-33 cm),

which are incompatible not only with the possibility of the of the observer's existence. The birth and death of the universe take place without witnesses.

Until the 20th century,experience and theory marched in step with each other. In Fridman's paradigm, we can see that the observation of the early states of the universe does not depend directly on equipment resolution, for the two above-mentioned reasons. There emerges an epistemological abyss.

Finally, an awareness of the existence in the past of a fact, unobservable in principle, raised the problem of the validity of indirect confirmations of theoretical predictions of cosmology by experience . For example, the receding of galaxies, discovered by Hubble in 1928 in analyzing the displacement of their spectral lines, and the discovery of the 2.7 K° background radiation in 1964-1965 by Penzias and Wilson are not phenomena of singularity itself but merely their effect from which we draw conclusions about the cause.

Far-reaching mathematization of the physicogeometric theory of the universe placed theoretical predictions far ahead not only of their empirical confirmation, which is self-explanatory, but also of the entire empirical range of scientific knowledge, a feature by no means typical of Galilean-type science.

Fridman's cosmology, perhaps for the first time since Greek philosophy and protoscience, raised the question as to why the universe is made this way and not differently, thus going beyond the traditional question of the previous centuries: How is the universe made? After posing this question, however, it actually stopped because it was unable to answer itself in a satisfactory manner, i.e., to explain why the universe as a whole has a baryon asymmetry, why space is three-dimensional and time one-dimensional, why locally the universe looks flat, and many other things. This fact, as well as the fact that some problems (for instance, of singularity) cannot be solved in satisfactorily within Fridman,s paradigm, led to the second revolution this century of the cosmological views of the universe.

The beginning of the second revolution of scientific cosmology is associated with the development and construction of the inflationary scenarios of the universe, based on De-Sitter's so-called empty models. Let us first examine the epistemological changes that have stimulated and continue to stimulate, in our view, the emergence of a new type of scientific rationality.

The class of objects covered by the concept of the universe as a whole is substantially expanding ; the observable area (1028 cm) is becoming local. This leads to a number of consequences.

First, there are now doubts about the validity of extrapolating the properties of the observable area to those unobservable in principle, whereas previously, doubts used to arise about the validity of extrapolating macro physical (terrestrial) properties of space and time to the large-scale structure of the universe.

Second, inflationary cosmology solves the majority of the problems in the Fridman's theory (Flatness, horizon, three-dimensionality, etc.). At what price, however, from the standpoint of epistemological ideals of modern European science, does it to do? Its theoretical basis is expanding so quickly that Einstein's picture of the physical world is already becoming classical, and, as its new physicotheoretical foundations, it uses successively the theory of the supergravitation and the theory of superstrings describing such physical objects and properties of space-time as are in most cases transcendental to the terrestrial world and cannot be revealed by observation in the foreseeable future or cannot be revealed at all.

Third, Fridman's paradigm questioned the validity of mediated empirical observations, while the inflationary paradigm suggested that the observations or experimental confirmations of many of the facts it predicts are meaningless. Let us cite just a few examples. In the inflationary theory, the walls (heterogeneties) of a domain have dimensions on the order of (10¹⁰)⁷ - (10¹⁰)14 cm, exceeding the observable area (10²⁸ cm) an untold number of times! The inflationary theory also recognizes the existence of a causal horizon of a multifactor nature: no signal can be received from a source beyond the light horizon; different domains have, in general, a different signature of space-time in whose totality our four-dimensional continent is a particular case.

Fourth, the transparency of the boundary between physics (the theory of elementary particles) and cosmology, incipient in Fridman's paradigm, has practically become complete.According to A. D.Linde, contemporary theories of elementary particles pass, above all, a test for their cosmological value (Linde [1990]).

Recognizing two facts-that empirical experience acquires a subordinate role as purely local (i.e., everything denoted by the this concept operates only within a very narrow range by modern standards-from post-Planck dimensions to those exceeding the observable part of the universe ) and that experience is now beginning to be treatedas primarily theoretical (i.e., not transcending the realm of intelligent examination-qewria)-enables us to reinterpret this concept . A newly, theoretically discovered object will be interpreted in a system of other less abstract, theoretical objects, including purely empirical,verifiable, or falsifiable ones within a local realm. This is where the principle of complementation and mutual matching of different objects comes in . Local experience may be totally absent. It is not difficult to see a parallel to such an interpretation in Platonic and Pythagorean tradition.

In my opinion, the Pythagorean conception of the Cosmos-Universe anticipated many ideas of presentday cosmology. It anticipated them in the sense that fire-hearth-Hestia is that "center" from which the fiery inflation of the Universe proceeds. But even in presentday scientific descriptions, it cannot be "shown", since, apart from this Universe, which prescribes the scale of reference, there is no other in whose coordinates such a center could be singled out. As early as the very beginning of the epoch of the construction of inflationary scenarios (in the 1970-1980s), the absence of a basis for recognizing a reference system in its classical neo-European meaning evoked strong criticism and reproaches of a "lack of realism" leveled at the approaches proposed by A.Guth, A. Albrecht, P.Steinhard, A.Linde, and others for the very reason that it was "empty" space that was inflated (Dymnikova [1986]). Up to now the presence of a material substance-whether a material body or a physical field-was considered essential in physics and cosmology for establishing a reference system. The fact is that the process of inflation is associated with the scalar field j , although other fields may firure in some scenarios. The substantive ( meaningful) site of the " Pythagorean fire" in inflationary scenarios is the energy of vacuum whose density is negative, which is expressed by the Gleener equation of state P = - r. A significant feature of negative energy density is the fact that , when accumulated by a field, it is converted to thermal energy with the subsequent birth of matter.

And today, recognizing that we live in a spherical world (domain), we should be able to determine its geometric center, which however, need to coincide with the genetic center-the point 10-33 cm in radius where inflation began. The power of the heating of the scalar field j-the genetic origin of the Universe-can be likened only to the Pythagorean fire.

If we have correctly diagnosed the trend of the evolution of theoretical knowledge, it is safe to say that the new ideals of rationality are essentially the revival of the old ones established long ago in antiquity (Pavlenko [1997], p. 202-209). We have thus witnesses e new epistemological turn toward the Pythagorean-Platonic origins of European science and philosophy. And there is reason to hope that new frontiers will be reached along this road in understanding the structure of the Universe. At any rate, historical "statistics" show: every return of cosmology to the Pythagorean principles of explaining the universe signified a breakthrough in understanding its structure and, conversely, a departure from principles that brought stagnation upon cosmology.