| This is a file in the archives of the Stanford Encyclopedia of Philosophy. |
Proof. (Cubitt and Sugden 2003)
| 1. | Ri A | (from RCI1 and the assumption that A holds) | |
| 2. | A indi Rj A | (from RCI2) | |
| 3. | i reasons faultlessly | (assumption) | |
| 4. | A indi (j reasons faultlessly) | (from RCI3) | |
| 5. | A indi x | (from RCI3) | |
| 6. | Ri x | (from 1 and 5, using CS1) | |
| 7. | Bi x | (from 3, 6, and the definition of "faultless reasoning") | |
| 8. | Ri (A indi x) | (from 5, using RCI4) | |
| 9. | A indi (Rj x) | (from 2 and 8, using CS5) | |
| 10. | A indi (Ri x ∧ (j reasons faultlessly)) | (from 4 and 9, using CS3) | |
| 11. | (Rj x ∧ (j reasons faultlessly)) entails Bj x | (from definition of "faultless reasoning") | |
| 12. | A indi Bj x | (from 1 and 11, using CS1) | |
| 13. | Ri Bj x | (from 1 and 12, using CS1) | |
| 14. | Bi Bj x | (from 3, 13, and the definition of "faultless reasoning") | |
| 15. | Ri (A indj Bk x) | (from 12, using RCI4) | |
| 16. | A indi (Rj Bk x) | (from 2 and 15, using C5) |
And so on, for all i, j, k, etc. in P. Lines 7, 14, 7n (n > 2) establish the theorem.
| Peter Vanderschraaf peterv@cyrus.andrew.cmu.edu | Giacomo Sillari Carnegie Mellon University gsillari@andrew.cmu.edu |