The Search for Physics. Infinity.

About 300 years Physics was combination of mathematics, philosophy and experiments with observations. In modern time it is easy to see domination of mathematics over all other, and the fall of importance of experiments and observations from main role to auxiliary role, especially, to role of experiments to prove “experimentally” that 2 + 2 = 5. Herewith mathematics mutates from logic to powerful symbolism where can be accepted any concept, notion, axiom, by man wishes. Doctor philosophy from 1957, Princeton University, Steven Weinberg, in his book “Dreams of a Final Theory: The Search for the Fundamental Laws of Nature (1993)”, had written chapter VII “AGAINST PHILOSOPHY”, to prove “the unreasonable ineffectiveness of philosophy.” In chapter VI “BEAUTIFUL THEORIES” he provides point of view of Eugene Wigner, that mathematics has “unreasonable effectiveness”. The mathematician and historian of mathematics - Morris Kline, had shown the illogical development of mathematics in his book “Mathematics. The Loss of Certainty”, 1980. But in 1985, Morris Kline had done illogical step in his book “Mathematics and The Search for Knowledge”: he tried to show a “truth” of illogical mathematics by a “useful” and “fruitfulness” application of mathematics in physics. This work was done as attempting to move in logical direction from physics point of view, first of all, discussed the initial notions, and specially, notion of infinity. All facts and knowledge about inconsistency of infinity used in this work were and are well known, and were and are ignoring from logic point of view. Inconsistency of notion of infinity well knows more than 2500 years. Usage an inconsistence notion in logical reasoning is logical mistake. But per Hermann Weyl, mathematics is science about infinity, per David Gilbert, usage infinity in set theory is mathematical paradise. Well known that mathematics pretends on status of the most logical science, and even more, per Emmanuel Kant, “In any particular theory there is only as much real science as there is mathematics.” Usage notion of infinity in mathematics, and usage mathematics in physics raises a question: when does mathematics itself become a science, and what is the science? The worth of mathematics consists in its deductive nature, and this means that “in mathematics there is only as much real science as there is logic”, and this formula applicable to science too. There is problem with logic too – man is so weak to follow logic, and man feels himself so powerful to modify logic per his wishes. Man prefers beauty and intuition, but not logic, and most of all man loves paradoxes. Smart man prefers point of view well known authority, especially authority which sits on the money. Well known that a reference to authority, and to tradition, is logical fallacy of argumentation. In this work reference to authority will use to show this renown of facts, concepts, and notions – but not to argue its correctness or truth. Objectives this book is attempting to follow logic way in physics, first of all, and in mathematics as tool for physics. There are many historians of mathematics, but one of them – Morris Kline – shown illogical development of mathematics. Illogicality of mathematics was found in paradoxes followed from its axioms, but inconsistency of mathematics begins in so called “undefined notion” and in axioms itself, axiom which used undefined notion. It is vicious circle – attempt “solve” paradox without analyzing of undefined notion and axiom itself. Understanding inconsistency of used notion and axiom follows to conclusion that we have approximate model or theory which has limited features for extrapolation and interpolation. Using terms “undefined notion” and “axiom” implies accepting those terms without analyzing them for inconsistency, but we should do that because all notions have its base - our experience, direct or indirect, implicit or explicit, for who believe it or not, - and our sense and even mathematical intuition can make mistakes. Main idea this book is attempting to show problem in mathematics and, especially in physics, - wrong way of usage a symbolic theory: Start from real object and/or phenomenon; Make abstraction and express it in symbolic form; Do idealization with inconsistency; Inconsistency of ideal abstract form assigns to real object; Relation to the start real object is used as argument of existence of the ideal object; Transfer to physics a math method to create abstract object by declaration properties this object, and then “create new” real object; “Discover” in experiment the real object which is necessary to “solve” the inconsistency of the ideal abstraction. It is old known problem, which is completely ignoring in physics. From time of the Aristotle’s Physics the second reborn of physics was made by Galileo and Newton per combination of mathematics, natural philosophy and experiments with observations. Long time of usage symbols in math and physics brought to us habit to correspond notion and real object or phenomenon. Next step per habit follows creation new notion and the faith that real object, which correspond to this new notion, should exist. Lack of reflection in math show us that mathematicians “invented” methods to hide – not solve – this problem. There are: acceptance so called “undefined” notions, axiomatic method, acceptance conflicting sets of axioms, and so on. Lack of reflection in physics brings the complete faith to math, loosing physical objects, transfer a inconsistency of man’s theory to reality, declaration and the faith that Nature follows the math laws, experimental confirmation of existence of a non-existent. This work is attempting to separate the abstract symbol world from reality, the faith from logics, the science from religion activity – it is, in short words, meaning of The Search For Physics, and Infinity is “undefined” notion which is used in mathematics and physics.