Modern positivism...expresses criticism against the naïve use of certain terms... by the general postulate that the question whether a given sentence… - Werner Heisenberg

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Modern positivism...expresses criticism against the naïve use of certain terms... by the general postulate that the question whether a given sentence has any meaning... should always be thoroughly and critically examined. This... is derived from mathematical logic. The procedure of natural science is pictured as an attachment of symbols to the phenomena. The symbols can, as in mathematics, be combined according to certain rules... However, a combination of symbols that does not comply with the rules is not wrong but conveys no meaning.
The obvious difficulty in this argument is the lack of any general criterion as to when a sentence should be considered meaningless. A definite decision is possible only when the sentence belongs to a closed system of concepts and axioms, which in the development of natural science will be rather the exception than the rule. In some case the conjecture that a certain sentence is meaningless has historically led to important progress... new connections which would have been impossible if the sentence had a meaning. An example... sentence: "In which orbit does the electron move around the nucleus?" But generally the positivistic scheme taken from mathematical logic is too narrow in a description of nature which necessarily uses words and concepts that are only vaguely defined.

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About Werner Heisenberg

Werner Karl Heisenberg (5 December 1901 – 1 February 1976) was a German theoretical physicist, one of the main pioneers of the theory of quantum mechanics, and a principal scientist in the Nazi nuclear weapons program during World War II. He published his Umdeutung paper in 1925, a major reinterpretation of old quantum theory. In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, his matrix formulation of quantum mechanics was substantially elaborated. He is known for the uncertainty principle, which he published in 1927. Heisenberg was awarded the 1932 Nobel Prize in Physics "for the creation of quantum mechanics".

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Native Name: Werner Karl Heisenberg
Alternative Names: Heisenberg Werner K. Heisenberg
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Additional quotes by Werner Heisenberg

"Any concepts or words which have been formed in the past through the interplay between the world and ourselves are not really sharply defined with respect to their meaning: that is to say, we do not know exactly how far they will help us in finding our way in the world. We often know that they can be applied to a wide range of inner or outer experience, but we practically never know precisely the limits of their applicability. This is true even of the simplest and most general concepts like "existence" and "space and time". Therefore, it will never be possible by pure reason to arrive at some absolute truth.
The concepts may, however, be sharply defined with regard to their connections. This is actually the fact when the concepts become part of a system of axioms and definitions which can be expressed consistently by a mathematical scheme. Such a group of connected concepts may be applicable to a wide field of experience and will help us to find our way in this field. But the limits of the applicability will in general not be known, at least not completely."

But the resemblance of the modern views to those of Plato and the Pythagoreans can be carried somewhat further. The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" is a sentence attributed to Pythagoras. The only mathematical forms available at that time were such geometric forms as the regular solids or the triangles which form their surface. In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms but of a much more complicated nature.

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