The article is a continuation of the paper Aristotle's Idea of Motion in „Roczniki Filozoficzne”, vol. 17 (1969), no. 3. Aristotle and Thomas Aquinas stressed several times the significance of a principle of motion: „anything that moves is moved by something else”. This is a metaphysical principle resulting from a principle of compatibility. The author polemizes with these who question the universality of a principle of motion, referring usually to contemporary physical theories. In Poland K. Kłósak and T. Wojciechowski: 1. postulate revision of Aristotle’s definition of motion, 2. they restrict a range of a principle of motion, 3.they accept a possibility of self-activating in microcosmos phenomena, for instance, dying-out of radioactive substances.The author polemizes with the mentioned above authors pointing out a constant validity of Aristotle’s and St Thomas’ principle of motion. Some Thomists (S. Ziemiański) hold that the defence of a principle of motion should be undertaken first of all in philosophy. The author, referring to the texts of Aristotle and Thomas Aquinas, shows the everlasting significance of this principle in the field of philosophy as well as in natural science. This also was the method of St Thomas who, in Contra Gentiles, proved the universality of a principle of motion on the basis of metaphysical arguments (theory of act and potentiality) and physical ones.The author, referring to contemporary physicists (E. Fermie, A. Haas, J. Chojnacki) points out hat they do not promulgate the idea of self-activating in the strict sense. This idea is not even proved by radioactivity phenomenon, for instance, emission of alpha, beta, gamma rays is entirely spontaneous because there exist such external factors as cosmic radiation or interatomic transformation which initiate this phenomenon, Physical law of inertia also agrees with the metaphysical principle of motion — still valid in macrocosmos and microcosmos.

There is tendency in cosmogony to call evolutionary changes such qualitative changes which are directional and irreversible. The problem of evolution of individual celestial bodies has to be distinguished from that of the evolution of the Universe considered as a whole. In the latter problem cosmogony is inseparable from cosmology. In both problems the accepted philosophical attitude plays a crucial role. Facts proving the existence of the cosmic evolution can be classifiexl as follows: 1 — distributed in time direct observations of evolution, 2 — data about motions of celestial bodies, 3 — comparison of various objects Which can be suspected of being of the same kind but in various stages of evolution, 4 — observations of regions of space in various distances which consequently — because of the finite speed of light — are of various age, 5 — taking use of relationships between megacosmical and microcosmical constants. Only data under 2, 4 and 5 can give evidence of the evolution of the Universe as a whole. No uniform, consistent picture of the cosmic evolution exists at present.

The present paper aims at stressing these aspects in special theory of relativity which are concerned with a relative character of space and time, that is, it attempts to examine the sense of the theorem which speaks that time and space are relative.In Einstein’s theory there are relative and absolute quantities. Stability of velocity of light belongs to absolute quantities (laws of nature), and space, time, motion, mass belong to relative ones. The notion of simultaneity is not of absolute character, either. While stating that space and time are . relative we suggest that (a) measurements of these quantities are relative because they depend on reference frame in which they are done, (b) measurements of time imply measurements of space.Space and time cannot be treated separately. Space-time event has a physical meaning and we assign to it four numbers: three space coordinates and one time coordinate.Though the results of time and space measurements are relative, laws of nature remain absolute being constant relations between physical quantities. Special theory of relativity, through relativity of measurements comes to formulate absolute regularities and thereby to describe physical real world independently from cognitive subject.

J. A. Wheeler made an attempt to reformulate the boundary condition problem in General Relativity. According to him Mach’s Principle has to be understood as a selection rule of these solutions which are consistent with the boundary conditions of certain type. Yet, one must remember that the a priori assumed boundary conditions for the field equations appear to be an absolute, and therefore anti- -Machian, element of the theory. Also well known theorems about the singularities in General Relativity strongly point against the possibility of Wheeler’s programme realization.

The paper presents a certain fragment of the recently carried discussion which deals with one of the aspects of a theoretical explanation of reduction. The very notion of reduction is introduced here in the contextual way and is applied mainly to physical theories. Formal and factual conditions were exposed to a detailed analysis along with assuming an attitude towards some reservations set up against them. A special stress was put upon these conditions which are especially important as regards intertheoretical deductive explanations as well as on meaning elements of the term „reduction”. In the final part of the paper an attempt was made to group different approaches to reduction.

The author of the paper has discussed notion of infinity in Aristotle and Bolzano wfhioh serves as a basis for the adoption of the two following theorems: infinite seiis exist in potentiality (Aristotle), infinite sets exist in actuality (Bolzano). Aristotle understands an infinite set as the one to which a new element may be continually assorted from the outside. That whidh has already nothing outside is finite and complete. Therefore, infinity — as seen by Aristotle — is associated with potentiality. So it is not suprising that he comes to the acceptance of potential existence in infinity. On the other hand, Bolzano sees an infinite set as the one which is greater than any other finite set. In other words, according to Bolzano set is infinite when it has proper subset equinumerous with it. He holds that infinite sets exist in the domain of potential beings as well as in the domain of real world. This is, of course, a question of adtual existence in the Aristotelian terminology.A notion of set is commonly used in contemporary mathematics. The problem arises whether it refers to Arisltotle’s notion of set or to Bolzano’s. Bringing arguments of the axiomatic system of Zermelo-Fraenkel type the author has shown that one deals here with the continuation of Bolzano’s conception. For in the mentioned above axiomatic system the existence of at least one infinite set is clearly postulated. Whereas this axiomatic system does not distinguish different kinds of existence. In that respect it is uniform and thereby agrees with Bolzano’s conception. So, contemporary mathematics would declare for Bolzano’s idea of notion of set.It can be noticed that this briefly discussed above fact may serve as an example of a constant progress in science. In this case it would consist in the abandonment of Ariistoltle’idea and the introduction of Bolzano’s, in coming from Sta- girite’s conception to that of Bolzano.In contemporary mathematics one more interesting phenomenon can be also observed. Namely, cathegory theory still requires a broader notion than Bolzano’s notion of seit. This broader notion is a notion of class. Every set is a class. But hot every class ils a set. For instance cathegory is mostly not a set but it is a class. It seems that in this enlarging of a notion of set to a notion of class one can see the next step in progress of science made in this interesting field.Thus a question arises whether this doming from Aristotle’s notion of set to Bolzano’s and from the latter to a notion of class one should not regard as successive stages of a constant progress of science.

In biology motion has been studied from the point of view of kinematics. Therefore there came to develop such branches as morphology of organs of motion, physiology of muscles, nerves and bones and also biochemistry of concomitant procesises of motion. The author examines this problem from the point of view of evolutionary biophysics. The starting point chosen here is bioelectronics on a semiconductive characterization of proteins and nucleic acids as well as their piezoelectric properties. It also refers to animal tissues connected with motion (muscular, nervous, osseous) and to plant tissues.On a certain stage of the biophysical evolution piezoelectric properties of organic compounds were produced and then developed further in a tissue structure. Foundations of motion can be already noticed in the molecular dimensions of proteins, DNA and RNA and also of some saccharides in the form of electrostric- tion. Moreover, one has to take into account: termostriction (pyroelectric properties), magneto- and magnetochemistriction, or mechanoChemical processes. The basis phenomena would be quantum ones summing up in tissue — mainly in muscular and nervous tissue and less in osseous one. The biological system examined in the aspect of the evolution of motion serves as a good example of transition from quantum state to mactroquantization.The quantum background of the action of muscles, nerves and bones does not only result from their semiconducting properties but also from microstructures confirmed by electro-microscopy. Structures show evidence of various optical and electrical properties. However, quantum results can be noticed in the slight luminescence of an active muscle or nerve. The action of muscles and nerves seems to be the molsit probable in its electronic aspects as the voltage-current situation in a junction p-n which was stated by Basset and Becker for a bone and recently for a nerve, too.Formation of a phononic wave is the „left side” of striction in piezoelectric systems. Living object is a generator of its own mechanical information, because a phononic wave is a shifting alternate phase of kinetic and potential energy. And the latter causes the release of charges in piezoelectric proteins in phases of compression and decompression. Thus any mechanical information from the environment and the one received as a result of active or passive motion (in higher plants) is a form of electronic disorders of the system. If we consider mean bioelectronic states to be physical plasma we can easily examine some general energetical changes in any living system. And so, a phononic wave connects mechanical energy with electrical one, chemi-dal energy with magnetic one, motion with electromagnetics. The biological system does not work on the base of a thermic machine. Motion is first of all an electronic process and thereby is connected with metabolism. Motion, working on a „quantum” principle, is a mobilizing factor of the system. Life had inserted quantum phenomena of striction characteristic for protein ferroeleotrios between chemical processes of anabolism and those of catabolism. Motion is a basic life phenomenon and contributes to general metabolism of the biological system. Moreover, motion is a basic factor in ithe evolution of life.

The experiments were carried to examine the influence of light and mercuric ions on green plants. The introductory experiments covered only the observation of dynamics of growth, vegetative propagation and morphology of shoot limbs of Lemna perpusilla Torrey, graft 6609. The influence of mercuric ions on the plant organism during their direct effect and after effect was analysed. The amount of plants and limlbis were estimated as well as dry mass, colour and shape of shoot limbs of cilia. Mercuric ions were administered in the form of molar solution of corrosive sublimate in distilled water. The final concentration of corrosive sublimate in plant cultures varied from 1 X 10-4 M/l to 1 X 10-9 M/l.It was found that: 1 — influence of mercuric ions on cilia depends upon their concentration and upon light conditions.2 — light has a great influence on the increase of toxicity of mercury for green plants.3 — plants activate their effective mechanism of protection only in light against the penetration of a poison into living cells.

In the present paper the problem of finding numbers x of n-digits satisfying the congruence: x2 — kx = 0 (mod.10n) was solved; where k = integer, n = 1, 2, 3... and even a more general congruence x2 — kx = 0 (mod. gn).Three cases were examined: 1) k = 1; 2) k= -1; 3) |k|>1. Thus the paper consists of three parts. In part I the first case k = 1 was analysed. This problem in such a form was first introduced by P. Tedenat in 1814. It was solved in this paper by means of three methods: a) the method of recurring sequences, b) the method of continued fractions, c) the method of .power sequences. The author also gives ways to calculate x in the case of any numbers of digits; effectively numbers of x are given for n = 21, whereas E. Lucas gave them only for n = 10.In part II the author analyses the so far unexamined case no. 2: k= -1. The above mentioned methods a), b), c) all apply to this case. Case no. 2 is the parallel case no. 1.In part III the author examines case no. 3, which has not been also treated by other authors, namely | k | > 1. It represents a generalization of the two former cases and can be easily reduced to them by means of a substitution.Laisit of ail the author generalizes the given problem for the congruence x2 — ax + c=0 (mod. 10n) in the case, when A = a2 — 4c = m2 and m = integer.