|Completeness, philosophy: A) Systems are complete, if all valid statements are provable. B) The question of the completeness of a description is always concerned with specific purposes of this description within the framework of a theory which applies to the described objects. It is a peculiarity in the case of particle physics that the complete description of elementary particles does not allow the differentiation of other particles of the same type. See also incompleteness, determinateness, determination, distinction, indistinguishability._____________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.|
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Mazes/Poundstone: anticipate the basic problem of inference, namely the question of how to recognize a paradox - (NP-complete) - "rule of law": is overcome by islands, therefore inefficient - Solution: Tremaux: thread, at a dead end return to the last node - also mark dead ends - two breadcrumbs mark old dead ends - at old node choose a path that was not chosen before - I 259 results in first exploring remote areas I 267 "Problem of the longest path": is there an easy way? - Trying does not lead directly to the shortest one - no intelligent algorithm available
NP-Complete/Poundstone: the answers are easy to verify! - E.g. maze: the right way may only be two nodes away, but you had to try out many combinations - I 282 prove that NP problems cannot be solved with a computer
Combination/Permutation/Combinatorics: P: polynomial function: n² - E.g. puzzle with 5000 parts. solvable - NP: exponential function. 2n. E.g. Maze with 5000 paths - unsolvable - in general: difficult to solve - NP: "non-deterministically polynomial-temporally complete" - I 276 so far no evidence that NP problems cannot be solved in polynomial time - but no empirical evidence - process of logical inferences itself an NP problem - our conclusions about the world are limited - I 281 the chain end, the very basis of our knowledge, can be recognized in polynomial time and checked for contradictions - (list - but not walkable as a maze)_____________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.
I W. Poundstone Im Labyrinth des Denkens, Reinbek 1995