The Ramsey Test
The evaluation of a counterfactual conditional can be done, according to the Ramsey test, to the hypothetical addition of to the set of current beliefs followed by a check for the truth of . If is the set of beliefs currently held, the Ramsey test is formalized by the following correspondence:
- if and only if
If the considered language of the formulae representing beliefs is propositional, the Ramsey test gives a consistent definition for counterfactual conditionals in terms of a belief revision operator. However, if the language of formulae representing beliefs itself includes the counterfactual conditional connective, the Ramsey test leads to the Gardnefors triviality result: there is no non-trivial revision operator that satisfies both the AGM postulates for revision and the condition of the Ramsey test. This result holds in the assumption that counterfactual formulae like can be present in belief bases and revising formulae. Several solutions to this problem have been proposed.
Read more about this topic: Belief Revision
Famous quotes containing the word test:
“Utopias are presented for our inspection as a critique of the human state. If they are to be treated as anything but trivial exercises of the imagination. I suggest there is a simple test we can apply.... We must forget the whole paraphernalia of social description, demonstration, expostulation, approbation, condemnation. We have to say to ourselves, “How would I myself live in this proposed society? How long would it be before I went stark staring mad?””
—William Golding (b. 1911)