6.  SYMBOLIZATION TO EXPRESS RELATIONSHIPS

Up to now we have looked at expressions in which the letter indicating a characteristic is followed by a single name--what are called monadic predicates.  We can also have what are called polyadic (many-place) predicates, expressions that are more complicated but allow us to express relationships.  For instance, to express the idea that Bob and Carol are friends we could write Fbc, with F carrying the idea that person b is a friend of person c.  We could also have something like Fbcd to "translate" the thought that Bob finds Carol in Dallas so that F now expresses the relationship of person b finding person c in city d.  In these different situations the letter F does indicate distinct predicates, even though there could be an expression that uses both at the same time, as in Fbc -> Fbcd ("IF Bob and Carol are friends, then Bob will find Carol in Dallas").
How complicated could this become?  For practical purposes we would have little reason to use anything more than a two-place predicate.  As we will see later, the main use of these is to "translate" sentences such as the following: "every English major reads some novels."  In an argument with this premise and the additional premise that Al reads no novels at all, we would see it following that Al could not be an English major.


We also use quantifiers with these new expressions, but we increase the number of variables in play  For instance,  (x)(Ey)Fxy could express the idea that everyone is someone's friend while (Ex)(y)Fxy could express the idea that there is someone who is everyone's friend.  (The order of the quantifiers does not matter, but the order of the variables does matter.)

Please note that a more complete development of how we work with these kinds of expressions will come later in the course.  This section is just to get you started.
EXERCISES (ON YOUR OWN)

Symbolize the following sentences.

1.  Alice likes Ted but she does not like Carol.
2.  Everyone likes Alice.
3.  Alice likes everyone.
4.  Some individuals like everyone.
5.  There are individuals who do not like anyone.


Go to the answer key