Now suppose we want to say that Dick is Jane's brother (which would give us the same information as saying that Jane is Dick's sister). We would use both names: Bdj (we predicate of Dick that he is a brother with respect to Jane) or Sjd (we predicate of Jane that she is a sister with respect to Dick), and we could make everything come together by also saying Bdj <-> Sjd.
By convention, the letters used for the predicates are not assumed to represent the same person or thing when we move from one-place to two-place predicates. We could easily have the sentence "If Dick is a bachelor then he is Jane's brother" and let it be Bd -> Bdj.
There is no limit to how many names we want to string together. "Ted is a bachelor who lives in Los Angeles with Dick" might come out Btld, but again we have to keep in mind conventional rules do not allow for shortening a wff so as to have it be an inference from a longer wff. Even if it is obvious that Ted is a bachelor, we could not derive Bt from Btld. (Some may note that PLN does permit this, but PLN declares a code in advance that already makes this easier to work with.)
One reminder: ordinarily the small letters
represent the names of individual persons, but already we are extending
it to the names of places and there is no reason we could not go further
and refer to particular books or movies.
Here are some more examples of what we may
do (using the first letters for our names):
Los Angeles is larger than San Francisco.
Lls
San Francisco is not larger than Chicago.
~Lsc
"Gone with the Wind" sold more tickets than
"Citizen Kane" but it was not a better movie. Sgc
& ~Bgc
Again, a very important point is that even when we know that relationships are reciprocal (as when we can express the relationship of a brother and sister or compare the size of cities), this must be explicitly stated in our wff's if there is going to be any use made of such an idea. This is certainly one reason that even very simple statements can turn into quite awkward expressions.
Thought problem:
"Dick is Jane's brother, and Ted lives with
Dick, so Ted lives with Jane's brother." We can symbolize the
premises easily enough. What is the problem in symbolizing the conclusion?