Werner Heisenberg: Use

“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.”

Werner Heisenberg

Physics and Philosophy (1958)
Context: 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.

World , Way , Past , Help

“Of course, we all know that our own reality depends on the structure of our consciousness; we can objectify no more than a small part of our world. But even when we try to probe into the subjective realm, we cannot ignore the central order…In the final analysis, the central order, or 'the one' as it used to be called and with which we commune in the language of religion, must win out.”

Werner Heisenberg

Werner Heisenberg as quoted in Quirks of the Quantum Mind, p. 175, ICRL Press, ISBN 1936033062

World , Religion , Communication , Reality

“If nature leads us to mathematical forms of great simplicity and beauty”

Werner Heisenberg

Conversation with Einstein, as quoted in Bittersweet Destiny: The Stormy Evolution of Human Behavior by Del Thiessen
Context: If nature leads us to mathematical forms of great simplicity and beauty—by forms I am referring to coherent systems of hypothesis, axioms, etc.—to forms that no one has previously encountered, we cannot help thinking that they are "true," that they reveal a genuine feature of nature... You must have felt this too: The almost frightening simplicity and wholeness of relationships which nature suddenly spreads out before us and for which none of us was in the least prepared.

Beauty , Mathematics , Nature

“Can nature possibly be so absurd as it seemed to us in these atomic experiments?”

Werner Heisenberg

Physics and Philosophy (1958)
Context: I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?

Nature

“Quantum theory provides us with a striking illustration of the fact that we can fully understand a connection though we can only speak of it in images and parables.”

Werner Heisenberg book The Part and The Whole

Die Quantentheorie ist so ein wunderbares Beispiel dafür, daß man einen Sachverhalt in völliger Klarheit verstanden haben kann und gleichzeitig doch weiß, daß man nur in Bildern und Gleichnissen von ihm reden kann.
Der Teil und das Ganze. Gespräche im Umkreis der Atomphysik (1969); also in "Kein Chaos, aus dem nicht wieder Ordnung würde", Die Zeit No. 34 (22 August 1969) http://www.zeit.de/1969/34/kein-chaos-aus-dem-nicht-wieder-ordnung-wuerde/komplettansicht; as translated in Physics and Beyond : Encounters and Conversation (1971)

Understanding

“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?"”

Werner Heisenberg

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.
Physics and Philosophy (1958)

Mathematics , Question , Nature , Decision