Predicate logic translation
I've requested for info from someone who's been helpful in the past, but bring it here for further support.
My issue in predicate logic is concerned with English - translation. I understand that when translating occurs, an individual is ascribed a predicate, the former denoted by an individual constant and the latter by a predicate constant. I also am aware to an "extent", the usage of variables that represent individuals in the monadic aspect. However, specifically, my problem lies with general sentences and how variables are assigned to expressions that subsequently fit into polyadic relational predicates (2 place, etc.) What exactly does it mean for a general sentence (a sentence not denoting a subject with a singular term) to say something about a quantity of something, and to what scope is that quantity extended, in terms of the English sentence saying so?
EX 1: "Dave is good" could be translated as "Gd". I know this.
EX 2: All men are good" could be translated as "(x)(Mx-->Gx)". I know this too, and looking at "men" as a class of individuals, I understand that the quantifier in relation to men is mentioning every individual within it.
--HERE'S THE PROBLEM--
EX 3:
a) "All women admire cats"
and
b) "All women love to dance"
3.a How are both general subjects "women" and "cats" different than if we used instead "Melissa" and "Mr. Pebbles"? Are we using the universal quantifier in the general sentence to state that "all of something" RELATES TO "all of something?" And is the term "cats" implicitly universal VS if we had instead added "some" cats? Also, when relating a subject to something else, does it necessary have to be a SET or CLASS OF INDIVIDUALS? Such as (x) RELATION(class,class). If so, how is this SET distinguished when using class terms not as obvious such as the aforementioned? (<-more about this below)
3.b. My confusion lies in how to pick out whether "love to" is a 2_place predicate or not. I'm not even sure if "dance" can be an entity to be used IF "love to" is by itself relational, as they may be dependent on each other to be only a monadic predicate, and I can't imagine "dance" itself representing individuals.
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It seemed like I kinda knew the answer, but thought more into and dun confused mahself:P
