PHL 410 Textbook Exercise 6.7.1
Symbolize each argument using the letters suggested. Construct formal deductions for the valid arguments below. Each of these can also be proven using the method of truth-trees.
1. If it is not the case that if all Republicans are conservative, then the Democrats will lose, then a better disaster plan can be developed. A better disaster plan cannot be developed and the Democrats will not lose. So, it is not the case that all Republicans are conservative. (R: All Republicans are conservative. D: The Democrats will lose. B: A better disaster plan can be developed.)
2. Everyone can tell right from wrong. But if moral judgment is a personal matter, then there is no moral law. Of course, there is a moral law, if J. S. Mill was correct. If everyone can tell right from wrong, then Mill was correct. Therefore, moral judgment is not a personal matter. (E: Everyone can tell right from wrong. P: Moral judgment is a personal matter. L: There is a moral law. M: Mill was correct.)