SPECIAL PROBLEMS IN SYMBOLIZATION

The templates previously given for statements calling for multiple quantifiers and two-place predicates need to be used with a certain amount of caution. Look at these two arguments.

Use this code.
Fx: x is a novel
Gx: x is literate
Hx: x is interesting
Fxy: x likes y
a: Alice
b: Ted
(1) Alice likes novels. If Alice likes novels then she is literate. Therefore, Alice is literate.
(Ex)(Fx&Fax), (x)(Fax->Ga) |- Ga

(2) Alice likes novels. All novels are interesting. Therefore, Alice likes things that are interesting.
(Ex)(Fx&Fax), (x)(Fx->Hx), |- (Ex)(Hx&Fax)

In both cases we are assuming that there really are novels for Alice to like, and so we do not use a hypothetical expression and a universal quantifier. If we did we would find ourselves with an invalid pattern, yet the natural language argument certainly does appear valid (and we could have used a single predicate to describe Alice as a novel-liking individual).

Contrast this with an argument such as the following (adding Jx to our code to represent English majors):
English majors like novels. Anyone who likes novels is literate. Therefore, English majors are literate.
(x)[Jx->(y)(Fy->Fxy)], (x)(y)[(Fy&Fxy)->Gx] |- (x)(Jx->Gx)
Here there is no problem with validity, and the derivation can be worked through by beginning with the hypothesis Ja.

In the same way, we would express the idea that Alice likes (all) English majors with a universal quantifier if we were then to go on and identify Ted as an English major and conclude that Alice likes Ted.
(x)(Jx->Fax), Jb |- Fab
The working rule, then, is to consider the context of a statement carefully.

Other examples:
Men and women are both students. We would restate this as a disjunction (men or women).
Students are anxious. We would use a universal quantifier, since this is intended as a blanket statement.
Students work at the pizza parlor. We would use an existential quantifier, since obviously we are not speaking of all students.