Economics Dictionary of ArgumentsHome
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| Monotony: Monotony in mathematics refers to the behavior of a function as its input changes. A function is said to be monotonic if its output either always increases or always decreases as its input increases. See also Functions._____________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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Gerhard Schurz on Monotony - Dictionary of Arguments
I 55 Def Monotony/Schurz: A valid conclusion from premises P1...Pn to the conclusion K is called monotonic, gdw. if it remains valid even after adding arbitrary further premises. (New information does not change anything. All deductive inferences are monotonic, i.e. they satisfy the monotonicity rule: P1,..,Pn/K is valid >for any Q/P1...Pn/K is valid. >Validity, >Conclusions, >Logic, >Inference. Uncertain inferences: are not monotone. Notation: monotone inferences: "/" Non-monotonic: "II". Non-monotonic inferences: Here we are not talking about validity but correctness. A correct non-monotonic inference can become incorrect by new information. Even if the truth of the previous premises is not affected. A black swan does not make the previous observations of white swans wrong. So it always has only provisional validity. Non-monotonicity/probability theory: The probabilistic reason of non-monotonicity is: From the fact that the conditional probability of A under the assumption ("premise") B is high, it does not always follow that also the probability of A under the assumption of B plus a further assumption C is high. >Conditional probability, >Probability, >Bayesianism. I 154 Non-monotonic/single case probability/statistical/Schurz difference to strict (non-statistical) hypotheses: (when explaining single cases): Non-statistical: the conclusion Ka of a deductive inference with true premises (x)(Ax > Kx) and Aa may be split off at any time. I 155 One may infer the truth of the conclusion from the truth of the premises without knowing what else is true. Against: statistich: Bsp from the premise p(Kx I Ax) = 90 % and Aa, however, one may conclude Ga with subjective belief probability of 0.9 only if the condition of the closest reference class is guaranteed. The antecedent information A must include all statistically relevant information about a. >Hypotheses, >Probability, >Probability theory, >Verification, >Relevance._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
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