Two opposite streams

We discern in human culture three main spheres of cognition: science, philosophy, religion (not to say especially about art). The first two form a domain of our activity. In religion man is more receptive. So, science and philosophy express together one stream in culture, religion does the second one. Let’s discuss these spheres more thoroughly.

Science

Saying about modern science we mean the so called exact sciences, having precision and measurement as their characteristic features. Science gives mathematical description of fragments of reality to be checked then in experiment. “To check in experiment” means that we compare the values of parameters pre–dicted by a theory with the values obtained in experiment. “Obtain values in experiment” means we have to measure them. Natural sciences are unthinkable without measurement. This is a characteristic feature of modern science. In Galileo’s works[1] we see how insistently he seeks to find a connection of parameters (e.g. in the law of movement). This connection is always a function. It is interesting that in mathematics they give the definition of function and begin to study them systematically in XVII century as well[2], in the time of emergence of modern science. This calculus of functions – Differential and Integral Calculus – becomes main theoretical tool of new science.

The seeking of mathematical exactitude depends on the tie of modern science with technics. Modern science, the one of Galileo, Descartes, Huygens, emerged both in heads of philosophers and mathematicians and in mechanical workshops. To build a machine it is necessary to know exact dimensions. To make a gear, launch an artificial satellite, make a chemical reaction to run in the right direction, one has to know to calculate exactly them. Scientific synthesis is always a concordance of quantities. So, a truth of thing and its determination are sought by science as a determination of quantity. Reduction of all the variety of experience to quantity was one of the main task of modern science from the very beginning. Pioneers of XVII century’s science tried to resolve this problem by different ways. Thanks his metaphysics Descartes reduces physics to geometry and the last, by the method of analytical geometry to arithmetic, i.e. to calculations. Galileo tried by his sophisticated dialectics to refute Plato’s thesis about matter’s inability to embody exact geometrical forms. In his turn, Leibniz’ phenomenological rethinking of space and time helped substantially to the progress of mathematical physics. The parallel development of new branches of mathematics – theory of differential equations, theory of complex functions, etc. - more and more strengthens authority of mathematical science and gradually accustoms to see in it a paradigm of science in general. “In every learning about nature there is as much science in strict sense as it has mathematics” (I.Kant)[3].

Physical science of Antiquity and Middle Ages was of other kind. Measurement and qualitative characteristics were not main method and task of cognition. Science of Antiquity considered that one can measure only that what can embody exact mathematical forms. This was valid only for so called “supralunar sphere” of fifth element (“quinta essentia” of Aristotle) and, generally speaking, for astronomy, laws of motion of celestial bodies. But “sublunar world”, terrestrial things in particular, was in principle indescribable in the language of mathematics. Just because matter can’t exactly embody ideal forms. So Aristotle’s physics has qualitative language. To understand a movement here means to interpret it in terms of Aristotle’s four causes: formal, material, efficient and final ones. Physics of Aristotle considered movement, so to say, “in its genetic wholeness”, in its tie with the whole order of Cosmos. The modern science is interested more by process of movement, its phenomenal side, its parts, including infinitesimal ones and this is studied by quantitative methods. Notwithstanding the metaphysical pathos of modern science’s fathers – Galileo, Descartes, Leibniz, Newton – ontological questions gradually moved away in the background. History of science shows a play of different scientific paradigms – atomism, ether, energitism – but none can pretend to express the deepest level of reality. Science doesn’t reach the ultimate reality. That what science really can is more or less reliable mathematical description of human experience. This “more or less” is a matter of principle. In spite of pathos of exactitude in exact sciences we, strictly speaking, can say definitely about no scientific theory whether it is true or not. Experimental justification of a scientific theory gives closeness of the predicted values to ones of experiment only in the limits of error of experiment. It means two different scientific theories giving predictions that differ from experimental results not more than experiment’s error, are not discernable by our method. But these theories can give good approximations of experimental data for the space and time acheavable for us and, at the same time, completely different values for the great time and space. Because that it is not logically correct to deduce from “justified” scientific theories any ontological statements or just long – term predictions (e.g., like theory of the so called “heat death” of Universe, so hotly discussed on the border of XIX – XX centuries). Paradoxically, the program to obtain an exact quantitative description in exact sciences has its boundary in the scientific method itself.

Modern science had the difficulties to realize the program “to give exact mathematical description to all the existing” in notion of number itself, too. Science (and philosophy) of Antiquity saying “number” means only integer. Greek science uses intensively the notion of the ratio of integers, as well, but nowise considers it as a number (as we do today using rational numbers). Having discovered the fact of incommensurability, e.g. of a square’s diagonal with its side, Greeks refused Pythagoras’ ideology “all is a number” or, in more liberal form, “all can be measured”. There is an incommensurability in the world, a continuous value, continuum can’t be as a whole described through numerical correlations. So science of Antiquity approved the dualistic paradigm as a philosophical base of its considerations: side by side with the measurable, there is an other principle in the world, the ir – rational… But modern science pretends to measure all and with any precision. Is it possible however ? To discuss this one needs more fundamental language than a scientific one, namely philosophical language.

Philosophy

Immediately philosophy wants to put in order our cognition, elucidate and define what do we mean saying: I know, it’s evident, it’s proved, it’s possible (or not) etc. Deepening the discussion about scientific knowledge we come naturally to philosophy. Thus, we say about measurement as a characteristic feature of modern science. But what does it mean “to measure” ? What does exactly mean “size of a thing” ? What is a “boundary of a thing” ? Measurement turn out to be a deep philosophical problem touching fundamental questions. Not to “get stuck” in these questions science has to respond to them more or less conditionally and conventionally. In philosophy one meets these questions “face to face”. Most of them has no final response, nevertheless philosophy teaches us two things: 1) not to accept wrong responses for the true ones, resist to the “idols of truth”; 2) to state the value, in a sense, of the epistemological depth of the problem to resolve.

To begin discussion about measurement better may be from the question: Is really all measurable ? Can one measure freedom, beauty, love ? We say: “He loves her so much”. Does really one means here a qualitative aspect ? Could we really compensate by money the “moral damage” ? All these questions are very complicated ones. It is important to stress that they interpret most of the measurements used in natural sciences, e.g. measurements of colour, heat, brightness etc. in no natural sense, but quite the contrary, in very conditional one, that demands special philosophical theories. Usually it’s theory dividing things qualities on two parts: primary (space, form, movement) and secondary ones (colour, temperature, taste, smell etc.) and a reduction of the latter to the former. The question about the validity of this theory, being discussed from XVII century, is very complicated one not only for physics, physiology, psychology but for philosophy as well. What do we measure, hence, depends on what a physical, - and metaphysical ! – hypothesis have we accepted. Nature is describable from different points of view, complementary one to another, and a possible completeness of its description is always an unattainable ideal of science…

The question “What do we measure ?” has another philosophical side. What do we really have in our experience: either a result of interaction of things with our organs of perceptions (reinforced by experimental technics) i.e. phenomena, or reality itself of things, i.e. things as they exist in themselves. What do we really cognize ? In history of philosophy both points of view were deeply elaborated. If we adopt that only phenomena are given, it raises many new questions: What is this “phenomenological space” where features of things are presented ? What it depends on ? How is possible, then, the thought about “thing itself” ? Thus Leibniz’, Kant’s, Husserl’s philosophical systems emerge. If otherwise we adopt that reality itself is given us in experiment then other questions arise: What is the human ability to touch that ‘what really is” ? What is a character of that reality ? What is our place in it ? Responses may be rather different. Thus, Plato taught that true reality is a “world of ideas” and things are only imperfect embodiment of those. For Aristotle an essence of thing is this concrete thing, as a definite unity of form and matter. Modernity gives its own responses on this question. For Descartes all existing can be reduced to two essences: res extensa and res cogitans. All the nature, except man, should be reduced with help of mathematics, practically, to geometrical constructions. For Leibniz all Universum consists out of monads, ideal principles, having perceptions and will. In accordance with what kind of metaphysics we adopt, we’ll interpret differently our cognition and science.

There is one more philosophical topic growing necessarily from discussions about measurement. I told that Antiquity’s science recognized as a number only integers. We added to them rational and irrational numbers. So for us, contrary to Greek mathematics, every segment can be measured by a unit of length. They used this considerations already from XVII century but it’s curious that strict theory of real numbers was build only by the end of XIX century (Dedekind, Weierstrass, Cantor). It is significant that these theories use substantially actual infinity. But long time ago the question of principle was put: Is it logically correct to use actual infinity ? All our experience is finite and much more: Greek science already understood that using of actual infinity implicates unsolvable contradictions, aporia (famous Zeno’s paradoxes: the Dichotomy, the Achilles, the Arrow). In mathematical theory of actual infinite sets ( the sets theory), built by the end of XIX century, similar paradoxes and aporia were found as well (Russel’s paradox, the notion “set of all the sets”, discussions concerning the axiom of choice etc.) The opponents of actual infinity told: we can’t imagine infinity, we have no right to use it in science. The proponents argued: we can’t imaging many things, e.g. big numbers, “thousand”, “million”, but as a matter of fact yet they exist… Also an actual infinity exists: without any doubt, you know, God, an Infinite Reason sees all the infinite set of numbers as a whole. This curious argument for justification of his theory of infinity G.Cantor used too, quoting St.Augustine[4]. It is significant that science in its development comes to necessity to see things sub specie aeternitatis, from God’s point of view. This is not yet “God of Abraham, Isaac and Jacob”, but only “God of philosophers and scientists”, World Reason, Logos, ruling the world, a completeness of all the natural laws. Notwithstanding that scientist doesn’t need “a hypothesis of God” it is important that seeking a completeness of logical conditions[5] of scientific knowledge, he comes to questions: “What is an essence of the Law ruling the world?” and “Does a Law – giver exist ?” We see that our knowledge in science and philosophy depends of our world – outlook orientation, expressed either in some regulative principles or rightly in theology. The last is a base of data’s interpretations and just through this base religion and worldoutlook influence science. Not only our understanding of nature, but our perception of it and, hence, sense of art depend on our worldoutlook orientation, too.

Generally speaking philosophy seeks to see a sense of cognition more strictly. This strictness of thought is a striving to represent every object of thought against a background of infinitely different opportunities of the other, the strictly outlined “logical contour” of this object to appear in all its definiteness and specificity. These two features contain a kind of canon for philosophy: to seek for strictness of definition and, at the same time, to understand all the boundlessness of the possible. Philosophy remains always “in the middle”: knowing neither its origins nor its ends… As if philosophy follows Pascal’s maxim: “The greatness of man is in keeping to the middle”[6].

Religion

(Eastern Christianity point of view)

Not all in culture and life is confined to the “daylight consciousness”. Science and philosophy are only islands of the more or less understandable, rationalized in boundless ocean of life. There are places in life for the miraculous, dark, for miracle… There is a sphere of the mystic: surmises, concurrences,

illuminations, missings… It is very difficult to rationalize them. The mystic has a characteristic feature differing it from science and philosophy. The latter necessary “work” in the situation of a logical boundary between subject and object, the cognizing principle (organ, ability, method) and ob – jectum being cognized. Mysticism says insistently about overcoming of subject – object division, about “direct entry” in object…

There are different kinds of mysticism: aesthetic, hedonistic, intellectual, social, national… Christian mysticism is characterized by an experience of brotherhood with the others in Christ, when Christians feel themselves as members of mystical Christ Body, His Church. From all the sphere of the mystical religion is distinguished by two characteristic features:

1. The Irrational, superrational God, the completeness of Wisdom, Power and Holiness appears as a Person, the personal meeting with God occurs;

2. God reveal us Himself, the meeting with God is an event to decide by God. We can only search after God, strive for this personal meeting, but the result depends, at the end, on God’s will only. Jesus Christ says to his apostles: “You didn’t choose me, but I chose you and appointed you that you should go and bear fruit and that your fruit should abide…”(Jn.15:16). Science and philosophy are human reason attempts to interpret reality. Activity is here on the side of man. In religion activity is on the side of Godhead. Certainly our understanding of revelation depends on our expectations, our scientific, philosophical and cultural vocabulary: our theology is influenced by our understanding of world. But nevertheless, activity in religion is on God’s side: if He needs, God can make “the very stones would cry out” (Lk.19:40).

Reality that is higher than human one is revealed us in religious experience… Man’s part here is a humble searching of this revelation. Humility turns out to be a necessary point of intercourse with God, with the Sacred: “Then He said [to Moses from the burning bush], “Do not come near; put off your shoes from your feet, for the place on which you are standing is holy ground” (Ex.3:5). “God opposes to the proud, but gives grace to the humble” (Jas.4:6), teaches us the Holy Scripture. Humility of man’s heart, crying for his sins is a genuine sacrifice to God: “The sacrifice acceptable to God is a broken spirit; a broken and contrite heart, o God, thou wilt not despise” (Ps.51, 17). Having been vocated to be God’s children, Christians should in their faith and gentleness be spiritually like children, too: “Truly, I say to you, unless you turn and become like children, you will never enter the kindom of heaven” (Mt.18:3).

There is a characteristic distinction between religion and science and philosophy. The latter are always some theories, as a logical (or mathematical) schemes of reality. Religion in its kernel is a reality itself ! Not only the reality enlightened, participating to sense, but the one identical with sense. Not just reality – in – itself, but the one giving sense and being, enlightening and blessing to all in the world – the Sacred. Religion in this sense goes in no theory. Certainly, there is Christian theology (theo – logy). But theology is only a rational projection of living religious experience. In history, theology was a rational reaction on deviations in religious life. Religious dogmata mark only the boundaries dividing the Truth from delusion. But Truth itself one perceives superrationally, it is ontological… In culture man creates never new being, he does only its symbols: painting, musical piece, scientific or philosophical theories. Christianity in its kernel is a life itself, a true life, where being and sense coincide; it is reducible to no theory. This supreme life can be grasped only by faith as a highest synthesis[7] of human abilities and one perceives it more and more to the extent of theosis, the graceful transfiguration of human nature by God’s energies…

So, we see two main opposite streams in culture: upwords – from the unknown to knowledge, from darkness to light, from man to God; and downwords – from God to man, from Heaven to Earth, maintaining order and peace, giving light, commandments, faith and hope. It is their fragile balance that culture consists of.