Philosophy Lexicon of Arguments

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Probability conditional: is the linkage of antecedence and consequence, in which the probability of the antecedence being true has an effect on the truth value of the consequence.

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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V 133f
Conditional/Probability/Lewis: thesis: the probability of conditionals is the conditional probability. - (VsStalnaker) - Logical form: P(A->C) and P(C I A) - But not for the truth-functional conditional >(horseshoe). - Because here they are only sometimes equal. - Therefore, the indicative conditional is not truth-functional. - We call it probability conditional. - Problem: then the probability of conditionals would hint at the relation of probability of non-conditionals. - That would be incorrect. - Solution: assertibility is not possible with not absolute probability in the case of the indicative conditionals.
V 135
Conditionalisation/Lewis/(s): E.g. conditionalisation on B: P(A) becomes P(A I B) the probability A given B.
V 135f
Probability conditional/prob cond/Lewis: here the probability of the antecedent must be positive. - A probability conditional applies to a class of probability functions - universal probability conditional: applies to all probability functions (Vs).
V 137
Right: C and ~ C can have both positive values: E.g. C: even number, A: 6 appears. - Then AC and A~C are both positive probabilities. - Important argument: A and C are independent of each other. - General: several assumptions can have any positive probability if they are incompatible in pairs. - The language must be strong enough to express this. - Otherwise it allows universal probability conditionals that are wrong.
V 139
Indicative conditional/Probability/Conditional probability/Lewis: because some probability functions that represent possible belief systems are not trivial - (i.e. assigns positive probability values to more than two incompatible options). - The indicative conditional is not probability conditional for all possible subjective probability functions. - But that does not mean that there is a guaranteed conditionalised probability for all possible subjective probability functions. - I.e. the assertibility of the indicative conditional is not compatible with absolute probability.
V 139
Assertibility is normally associated with probability, because speakers are usually sincere. - But not with indicative conditionals. - Indicative conditional: has no truth value at all, no truth conditions and therefore no probability for truth.
V 144
Conditional/Probability/Lewis/(s): the probability of conditionals is measurable - antecedent and consequent must be probabilistically independent. - Then e.g. if each has 0.9, then the whole thing has 0.912.
V 148
Probability/conditional/Lewis: a) picture: the picture is created by shifting the original probability of every world W to WA, the nearest possible worlds - (Picture here: sum of the worlds with A(= 1) or non-A(= 0) - This is the minimum revision (no unprovoked shift). - In contrast, the reverse: b) conditionalisation: it does not distort the profile of probability relations (equality and inequality of sentences that imply A). - Both methods should achieve the same.

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.

D. Lewis
Die Identität von Körper und Geist Frankfurt 1989

D. Lewis
Konventionen Berlin 1975

D. Lewis
Philosophical Papers Bd I New York Oxford 1983

D. Lewis
Philosophical Papers Bd II New York Oxford 1986

LwCl I
Cl. I. Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991

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Ed. Martin Schulz, access date 2017-11-21