II 183
Logic/mathematics/Genz: the statements of logic are also based on physics. Every piece of evidence is a physical process. Therefore, it is physics that says what can and cannot be proven.
Unity of Sciences/Genz: we achieve the unity of science more easily if mathematics and logic thus also become empirical sciences.
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Science.
II 209
Logic/Genz: logic is among other things also a consequence of the laws of nature. It is limited by physics.
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Natural laws.
II 217
Logic/Physics/Genz: For example, "the smallest number that can only be determined by more than thirteen words": leads to a relationship between logic and physics.
This sentence consists of thirteen words. I. e. there is the number, but it cannot be calculated.
There must be numbers that need more than thirteen words because otherwise it would be possible to express infinite numbers by finite many characters in finite many places.
Incalculability/non-calculability/non-calculable/calculability/Genz: if there are any numbers that can be defined by 13 words, then even a smallest number. However, this can only be defined by exactly 13 words. Therefore, it is unpredictable.
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Incalculability.
Incalculability/non-calculability/non-calculable/calculability/Chaitin/Genz: if a physical theory provided the statement that a pole is an incalculable number of centimetres long, (i. e. that a natural law would produce this) we would have to change our concept of calculability. This would make an incalculable number measurable.
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Gregory Chaitin.
Incalculability/non-calculability/non-calculable/calculability/Genz: for proof that a number cannot be calculated, its definition by an impracticable rule is not sufficient. For example "the smallest number that can only be determined by more than thirteen words": e.g. we define a number called NOPE.
II 218
Definition NOPE/Genz: the smallest number that can only be determined by more than thirteen words minus the smallest number that can only be determined by more than thirteen words
N.B.: the rule is impracticable, but we still know that NOPE = 0!
II 301
Logic/quantum mechanics/Genz: in order to achieve logical consistency for quantum mechanics, assumptions about nature, which we tend to take for granted, had to be banned from their system.
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Quantum mechanics.
