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Full Idea
Lewis was first to prove this remarkable result: there is no proposition A*B such that, in all probability distributions, p(A*B) = pA(B) [second A a subscript]. A conditional probability does not measure the probability of the truth of any proposition.
Gist of Idea
A conditional probability does not measure the probability of the truth of any proposition
Source
report of David Lewis (Probabilities of Conditionals [1976]) by Dorothy Edgington - Conditionals (Stanf) 3.1
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.14
A Reaction
The equation says the probability of the combination of A and B is not always the same as the probability of B given A. Bennett refers to this as 'The Equation' in the theory of conditionals. Edgington says a conditional is a supposition and a judgement.
| 7803 | Modal logic began with translation difficulties for 'If...then' [Lewis,CI, by Girle] |
| 14286 | In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker] |
| 14283 | A conditional probability does not measure the probability of the truth of any proposition [Lewis, by Edgington] |
| 13768 | Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington] |
| 13853 | It is a mistake to think that conditionals are statements about how the world is [Edgington] |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| 14623 | Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |