RIK SENGUPTA Professor Delia Fara PHI 201 Homework 5 LPL 6.17 Fitch won’t let me perform the last step (8). This is because in this step we are using step 5, a step that occurs within an earlier subproof. But the statement of step 5, namely Dodec(b), had been proven on the basis of the assumption we used for THAT particular subproof, an assumption that was only temporary. This assumption is no longer in force at step 8, because the subproof in which it was valid has ended a number of steps ago. Once we end a subproof, we cannot cite a particular line within that subproof anywhere else in the proof, we have to cite the whole subproof itself. So we cannot assume step 5 anywhere other than only that particular subproof – and thus it cannot be assumed true in step 8. The conclusion is not a consequence of the premises, because of the following counterexample: consider a world in which there are three elements a, b, and c. Here, a is a tetrahedron, b and c are large cubes. So the premise is true, because Tet(a) /\ Large(c), but the conclusion is obviously false. LPL 7.23
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This note was uploaded on 05/03/2010 for the course PHI 201 at Princeton.