Table 2.
The main bases for probabilistic theories, and whether (+) or not (-) they and the model theory account correctly for phenomena concerning conditionals. All theoretical bases in the table accept the Equation that p(if A then C) = p(C|A) as a norm
| 1. Predicts conjunctive errors in estimates of the Equation |
2. Has an algorithm simulating mental processes | 3. Applies to creation of permissions and obligations | 4. Free of the ‘paradox’ that truth of if A then C implies A |
5. Predicts inferences of the sort: If A or B then it follows that A |
6. Predicts subadditive JPDs | 7. Predicts explanations in defeasible reasoning |
8. Has no automatic elicitation of probability |
|
|---|---|---|---|---|---|---|---|---|
| Ramsey’s test | +* | - | - | + | - | - | - | + |
| Partial truth table | - | - | - | - | - | - | - | + |
| Jeffrey table for probabilities | - | - | - | + | - | - | - | - |
| Adams’ probabilistic logic | - | - | - | - | - | - | - | - |
| de Finetti’s coherence and system P | - | - | - | - | - | - | + | - |
| Model theory of default possibilities | + | + | + | + | + | + | + | + |