From jjllambias@xxxxxxx.xxxx Tue Oct 19 06:42:31 1999 X-Digest-Num: 260 Message-ID: <44114.260.1391.959273825@eGroups.com> Date: Tue, 19 Oct 1999 06:42:31 PDT From: "Jorge Llambias" The meaning of "ci gerku cu batci re nanmu" is taken to mean >"each of three dogs bite two men", leaving the number of men not >necessarily 2 but any value between and including 2 and 6. The >result is that the 2 is taken less literally than the 3 because it is >declared later. I wouldn't say less literally. What happens is that the 2 has in this case a narrower scope than the 3, because it is declared later. Number quantifiers can be understood in terms of the more basic existential and universal quantifiers. For example, 2x: F(x) could be rewritten as Ex Ey: x<>y & F(x) & F(y). This expansion will always involve both existential and universal quantifiers (here the universal is in the form of &). The order in which these quantifiers appear is what determines their scope. There are many ways in which 3x 2y F(x,y) could have been given meaning. The one chosen is to take it as 3x G(x), where G(x) = 2y F(x,y), and there we can see why the scope of the second quantifier is narrower. The way you propose would involve having a separate expansion for the quantification (3x 2y) that could not be reduced to the single variable case. co'o mi'e xorxes