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Unformatted text preview: Homework # 6 RIK SENGUPTA Professor Delia Graff Fara EXERCISE 9.11 2. I t would not be possible. If 3 were t rue, then every object in the world would be a tetrahedron and small, i.e. the world would consist entirely of small tetrahedra. But then sentence 4 would have to be t rue, because whenever x would be a tetrahedron (which is all the time), it would also have to be small (which is also all the time). The limiting case where the world is empty is also easily dealt with, because in this case 3 and 4 are both t rue. 3. I t would not be possible. If 1 were t rue, then there would exist a large dodecahedron in the world. Let’s say 2 is false. Then, there is no object in the world that is large when it is a dodecahedron. But there already is a large dodecahedron in the world. So sentence 2 cannot be false when 1 is t rue. So when 1 is t rue, 2 would have to be t rue as well. The limiting case does not arise here, because the truth of sentence 1 ensures that the world is not empty....
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- Polyhedron, Claire, Platonic solid, Rue