10. Since "All Greeks are human" goes over into logical notation as "Vx (Gx-Hx)." it is tempting ...
10. Since "All Greeks are human" goes over into logical notation as "Vx (Gx-Hx)." it is tempting to imagine that "Some Greeks are human" goes over as b instead of as a. (a) 3x (Gx & Hx) (b) 3x (Gx-Hx) To see why a is the right translation, work out the trees for the in ferences from a to b and b to a, and think about the counterexamples, i.e., cases in which b is true but a is false. (Draw circle diagrams.) Would you say that any of those are cases in which some G's are H's?
10. Since "All Greeks are human" goes over into logical notation as "Vx (Gx-Hx)." it is tempting to imagine that "Some Greeks are human" goes over as b instead of as a. (a) 3x (Gx & Hx) (b) 3x (Gx-Hx) To see why a is the right translation, work out the trees for the in ferences from a to b and b to a, and think about the counterexamples, i.e., cases in which b is true but a is false. (Draw circle diagrams.) Would you say that any of those are cases in which some G's are H's?