The speed of light, according to Newton, depends from speed of source of light, according to Einstein - not. And so on. This phenomenon is used by the fallibilists and first of all Popper to substantiate assertion that any theory is fallible in principle. The obstacle, that new fundamental theory correspond to set of facts, describing by previous theory plus non-described by previous leads us to next phenomenon: Some concrete set of facts in field, which some theory pretends to describe, potentially countless due to potential countless ness of virtual experiments giving new facts , but actually always limited, can be covered by conclusions of different theories based on different sets of axioms with different concepts.
Notably that some representatives of natural sciences also share this position, and in real science we can meet theories built in accordance with this scheme. Parting science completely from reality, it was not difficult to the social post positivists to come to belief that science is depended from social factor According to Kuhn, Einstein made space and time absolute, due to reading Marx. Now I will explain my point of view on the problem in interest. I named my position new rationalism, opposing it as to the classic rationalism of above-mentioned absolutists of science, so and mainly to dominating up today wave of relativists of science.
This general method, opposite to the assertion of Kuhn, gives common language to scientists - representatives of different paradigms, and permits them to reach based agreement which theories to accept and which to roll out. The last only shows limits of the truth ness workability of this theory. My point of view on the problem being considering is based on my theory of cognition 8 , from which followed the general method of substantiation 9, 10, In real science this method exists as stereotype of natural-scientific conscience, like the grammar of usual language exists in it before it grammar will be described.
The method appeared gradually in process of the evolution of the natural science and had largely taken shape in the classic mechanics of Newton-Lagrange. The general method of substantiation consists of next three points: 1 Introducing, building of concepts.
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Simultaneously fundamental postulate axioms , concerning these concepts, are formulating. Relation between our concepts and reality, which they describe, is a corner stone of my theory of cognition and basis to answer all the questions at the beginning of the article. That is why I want to consider it here intently. First of all, opposite to ideas of the analytics and the post positivists, which concentrated on words and tried, or to achieve single meaning of them, or to prove impossibility of that and to deduce from that all kind of relativity of knowledge, not words but concepts are fundamental elements of cognition.
But concepts, although they are expressed in science usually but not necessarily by means of words, as I will show, may be determined single meaning. That is why in vain the analytics tried to achieve single meaning of words and the conclusions of the relativists, based on absent of this single meaning are wrong.
Why concepts, not words, are fundamental elements of cognition? Because, as historically so morphologically, concepts appeared before language. In morphologic development child occupies concepts before he knows to speak. He doesn't realize even that he sees various colors. He only receives different perceptions from different colors and the same perceptions from the same colors. On base of similar and different visual perceptions, with help of perceptions from other receptors for example tactile ones , accompanied by moving activity, he forms in mind, firstly subconsciously, and after that consciously, but not yet on linguistic level, the primordial concepts of objects and phenomena, which Piajet 12 named image-etalons.
They are really concepts, because with help of them comparing with them , child makes identification of new objects. In that manner, he without knowing words differs an apple from a ball with the same dimensions and color. Therefore he already has the concept of apple and with help of it he separates the set of apples from multitude of other objects. By analogy it is easy to see that high animals also possess some concepts in form of image-etalons.
From that it is followed, that historically, during the evolution, predecessors of the human been had possessed concepts before language appeared. Even scientist firstly subconsciously feels some common property in objects or phenomena in field of his interest, after that he recognizes this property, and only after that he finds words to define this property.
Three Paradigms of Reality: From Homer to Einstein
When words are only means to transfer information in general and concepts in particular, from one to others. The means, which are very efficient, universal, but still not only possible and even not always the most efficient. Drafts, schemes, formulas and algorithms are much more efficient, each in its field, than words. But since language played so exceptional role in evolution of the human been and its cognition, and deluge of words in our time of mass-media simply pours over individual, fetishisation of language is happened in philosophy not only of the positivists and the post positivists, but in such branches as the hermeneutics, the communicative philosophy, the theory of discourse and so on.
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In the same time science, first of all the natural science due to its origin never fetishisated language, but with more or less degree of conscience always operated with concepts, not with words. More of that, science, overcoming no single meaning of words with help of which it up today usually formulated definitions of its concepts , aids to single meaning of concepts and achieves it practically, using the general methods of substantiation how it does that, will be clear further. Because also at pre-scientific stage the evolution developed in such a way, that concepts become more precise single meaning.
That is expected, if we take into account that evolution of cognition is a part of the general evolution of human been.
Cognition is form of adaptation to environment and the richer cognition knowledge of some community is, the more this community is adapted to environment. But human community accumulates knowledge by means of transfer of information from one to others. The less the transfer is accurate, the less useful it is. This evolution was going in such a way.
For example, one can consider concrete plant as a tree, and another - as bushes, and so on. At early science stage further growth of strictness of concepts goes on due to adding enumeration of properties qualities of objects to words-denominations.
For instance: deer is animal, mammal, herbivorous and so on. The last was achieved only with adopting the general method of substantiations, in which to determine concept - means to enumerate its properties, to introduce measure of each from these properties and to indicate exactly quantity all of these properties.
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For instance, the axiomatic method of definition also is single meaning one and, by the way, they are following one from another. More exactly there are no objects in reality, which exactly correspond to nominal or other kind single meaning definition. Suppose we define straight line as a curve with curvature constant equal to 0. To such a definition no one concrete object of reality corresponds absolutely. For example, rays of light distort in field of gravitation of big masses but since field of gravitation is unequal in vicinity of any point of space, rays, absolutely complying with the above definition, are absent.
In real science not always we meet nominal or axiomatic definitions of concepts, but imperative of science - the demand of single meaning ness of definition in possible measure, is obvious. Also not always we see admissible deviation in science practice, but reason for that is deviation of objects from nominal definition in such sciences like physics are usually negligible.
The next point of the general method of substantiation is building of conclusions. As to single meaning ness of conclusions it is easy to see difference in this aspect between physics, which is an etalon of rational science, and, let say, astrology, which also pretends to be science, but it is not. All engineers, using physics formulas to solve concrete task, will receive the same result. In the same time astrologic forecasts given by various astrologists in the same case will differ each other. Single meaning ness of conclusions and retaining sense of concepts are provided and guaranteed only by using the general method of substantiation.
According to the general method, building theory, deducing conclusions from initial postulates, must be axiomatically. Because in axiomatic theory set of axioms not only determines completely concepts but also in such a theory we can substitute axioms by some conclusions and such rebuilt theory preserves all the conclusions unchanged.
As it is known, we can change the fifth axiom of the planimetry of Euclid with the theorem about sum of angles of a triangle and to retain all other theorems. Also we can substitute the second law of Newton by the conclusion of his theory about quantity of movement with the same result.
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But if conclusions can become axioms and axioms determines concepts including their sense, therefore sense of concepts stay unchangeable from beginning till end of the theory. I must accentuate, that no other method of conclusions' constructing, for example, genetic or constructive one, does possess this quality. It is pertinent to mark here, that not all the scientific theories up today have been built axiomatically, especially pure axiomatically.
And secondly, there are philosophers, which affirm impossibility in principle of axiomatic rebuilding any rich enough scientific theory. As concerns the first I must accentuate, that the general method of substantiation is used at the stage of substantiation. But this stage is preceded by stage of genesis of theory, in which not only the genetic method of constructing of conclusions, but even pure intuition, fantasy and other things, which blend science with art are permitted and useful.
When substantiation the general method of substantiation separate science from art and non-science generally. Also, remember, that the general method of substantiation is an idealization of real practice of substantiation in science. Pure axiomatic constructing not always has place even in phase of substantiation, but in these cases no formal axiomatic, namely deductive expanding of theory has place in rational science.
As example of works in which impossibility of axiomatic rebuilding of any theory is affirmed, I can give the book of Styopin But he forgets, that Gilbert had accomplished axiomatically the geometry of Euclid. Basic element of the axiomatic method is a concept. Concept fixes only those properties of objects, which determined by axioms. It is very valuable heuristics property at genetic stage, but it destroys deductive ness of constructing and single meaning ness of conclusions and therefore must be eliminated at stage of substantiation.