Cautious deliberation based on purely rational arguments can save us from many errors and dangers. ...But ...there will always be a fundamental complementarity between deliberation and decision. ...The decision finally... pushing away all the arguments... The decision may be the result of deliberation, but it is... complementary... it excludes deliberation. Even the most important decisions... contain this inevitable element of irrationality. ...[I]t cannot be avoided that some real or apparent truth form the basis of life; and this fact should be acknowledged with regard to those groups... whose basis is different from our own.

[E]ven in the most precise part of science, in mathematics, we cannot avoid using concepts that involve contradictions. ...[I]t is well known that the concept of infinity leads to contradictions... but it would be practically impossible to construct... mathematics without this concept.

[F]rom all that has been said about modern science... modern physics is just one... but... characteristic, part of a general historical process... toward a unification and a widening of our... world. This... would... lead to a diminution of... cultural and political tensions that create the great danger... But... forces in the existing cultural communities... try to ensure for their traditional values the largest... role in the final state of unification... and thereby adds to the instability of the transient state. Modern physics... shows that the use of arms... would be disastrous, and... through it openness for all... concepts it raises the hope that in the final state of unification many different cultural traditions may live together and... combine different human endeavors into a new... balance between thought and deed, between activity and meditation.

"[The probability wave] meant a tendency for something. It was a quantitative version of the old concept of "potentia" in Aristoelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality."

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In a darkened world no longer illuminated by the light of this center [God], technical advances are scarcely more than despairing attempts to make Hell a more agreeable place to live in. This must be particularly emphasized against those who think that by spreading the civilization of science and technology even to the uttermost ends of the earth, they can furnish all the essential preconditions for a golden age. One cannot escape the Devil so easily as that.

I am firmly convinced that we must never judge political movements by their aims, no matter how loudly proclaimed or how sincerely upheld, but only by the means they use to realize these aims.

In the philosophy of Democritus the atoms are eternal and indestructible units of matter, they can never be transformed into each other. With regard to this question modern physics takes a definite stand against the materialism of Democritus and for Plato and the Pythagoreans. The elementary particles are certainly not eternal and indestructible units of matter, they can actually be transformed into each other. As a matter of fact, if two such particles, moving through space with a very high kinetic energy, collide, then many new elementary particles may be created from the available energy and the old particles may have disappeared in the collision. Such events have been frequently observed and offer the best proof that all particles are made of the same substance: energy.

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.

"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."

The way in which the convergent mathematical schemes did not fulfill the requirements of relativity and quantum theory was... interesting. ...[O]ne scheme ...interpreted in terms of actual events in space and time, led to a...time reversal... The physicists are convinced... that the processes... do not occur in nature... if... separated by measurable distance in space and time. ...If we assume that the laws of nature do contain a third universal constant... of the order of 10<sup>-13</sup> cm, then... our usual concepts... apply only to regions in space and time that are large compared to the universal constant. We should... be prepared for phenomena of a qualitatively new character when we... approach regions... smaller than the nuclear radii. The phenomenon of time reversal... might therefore belong to these smallest regions.

The existing scientific concepts cover always only a very limited part of reality,
and the other part that has not yet been understood is infinite. Whenever we
proceed from the known into the unknown we may hope to understand, but we
may have to learn at the same time a new meaning of the word ‘understanding’.

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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. It may be that these forms also cover our subjective relationship to nature, that they reflect elements of our own thought economy. But the mere fact that we could never have arrived at these forms by ourselves, that they were revealed to us by nature, suggests strongly that they must be part of reality itself, not just of our thoughts about reality. ... 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.