# Economics Dictionary of Arguments

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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.
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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

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.

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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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> Counter arguments in relation to Probability