## Economics Dictionary of ArgumentsHome | |||

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Probability: Probability is a measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty. See also Knowledge, Certainty, Likelihood, Chance, Probability theory, Probability distribution, Probability 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. | |||

Author | Concept | Summary/Quotes | Sources |
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Gerhard Schurz on Probability - Dictionary of Arguments Def Conditional probability/Schurz: the probability of A assuming that B exists: P( A I B) = p(A u B)/p(B). (pB) must be >0. B: conditional event, antecedent. A: conditional event, consequent. In the statistical case, p(A I B) coincides with the rel.frequ. of A in the finite set of all B's. Or with the limit of rel.frequ. in an infinite random sequence of B's. >Bayesianism. Non-monotonicity/non-monotonic/conditional probability /Schurz: conditional probabilities are non-monotonic: i.e. from p(A I B) = high does not follow that p(A I B u C) = high. >Monotony. Objective probability /type/predicate/Schurz: statistical probabilities always refer to a repeatable event type, expressed in a predicate or an open formula. Subjective probability: refers to an event token, expressed in a sentence. E.g. that it will rain tomorrow: tomorrow exists only once. >Subjective probability. Subjective/objective/probability /Reichenbach: Principle for the transfer from objective to subjective probability: I 101 Principle of narrowest reference class/Reichenbach: the subjective probability of a token Fa is determined as the (estimated) conditional probability p(Fx I Rx) of the corresponding type Fx, in the narrowest reference class Rx, where a is known to lie. (i.e. that Ra holds). E.g. Whether a person with certain characteristics follows a certain career path. These characteristics act as the closest reference class. Ex Weather development: closest reference class, the development of the last days. Total date/carnap: principle of: for confirmation, total knowledge. Subjective probability: main founders: Bayes, Ramsey, de Finetti. Logical probability theory/Carnap: many authors Vs. Mathematical probability theory/Schurz: ignores the difference subjective/objective probability, because the statistical laws are the same. I 102 Disjunctivity/ probability: objective. The extension of A u B is empty subjective: A u B is not made true by any admitted (extensional) interpretation of the language. Probability/axioms/Schurz: A1: for all A: p(A) > 0. (Non-negativity). A2: p(A v ~A) = 1. (Normalization to 1) A3: for disjoint A, B: p(A v B) = p(A) + p(B) (finite additivity). I.e. for disjoint events the probabilities add up. Def Probabilistic independence/Schurz: probabilistically independent are two events A, B. gdw. p(A u B) = p(A) times p(B) . Probabilistically dependent: if P(A I B) is not equal to p(A). >Conditional probability, >Subjective probability. I 109 Def exhaustive/exhaustive/Schurz: a) objective probability: a formula A with n free variables is called exhaustive, gdw. the extension of A comprises the set of all n tuples of individuals b) subjective: gdw. the set of all models making A true (=extensional interpretations) coincides with the set of all models of the language considered possible. I 110 Def Partition/Schurz: exhaustive disjunction. >Probability theory. _____________ 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 |

> Counter arguments against **Schurz**

> Counter arguments in relation to **Probability**