|Logic: logic is the doctrine of the admissibility or inadmissibility of relations between statements and thus the validity of the compositions of these statements. In particular, the question is whether conclusions can be obtained from certain presuppositions such as premises or antecedents. Logical formulas are not interpreted at first. Only the interpretation, i. e. the insertion of values, e.g. objects instead of the free variables, makes the question of their truth meaningful._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Books on Amazon
Logic/Mathematics/Genz: their statements 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 this more easily if mathematics and logic thus also become empirical sciences.
Logic/Genz: is among other things also a consequence of the laws of nature. It is limited by physics.
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.
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.
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": For example, we define a number called NOPE.
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!
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._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Gedankenexperimente Weinheim 1999
Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002