LESSON 11 -- Two-Place Predicates

Assignment 11

So far we have been working just with expressions in which we talk about only one individual at a time.  We can also be talking about the relationships between individuals.  Let's say we know that Al and Bob are friends.  We can symbolize this as Fab.  We can work with this wff just as we would with Fa or Fb, but what we have to watch out for is that we do not assume that Fab in any way implies Fa.  Each variable has its own meaning in symbolic logic, even if in our natural language one idea implies the other.

When we have two-place predicates we also can have quantifiers for each.  Here are some examples.

Everybody is friendly to Al.  Ax(Fxa)
Al is friendly to everybody.  Ax(Fax)
There is someone who is friendly to everybody.   ExAy(Fxy)
Everybody is friendly to somebody.  AxEy(Fxy)

In working with these expressions, though, you will need to use different variables (x and y, for instance), and you will need to be very careful about the new name rule in instantiating them.

Read more about these two-place or dyadic predicates  and also about multiple quantifiers before going on to the assignment, which is an exercise in symbolization and derivation.  For the derivations, remember that you must instantiate (remove the quantifier) from the left inward, but you could generalize (put in the quantifier) in any order building out to the left.

At this point we need to note that we could very well have valid argument forms for which a consistency tree is useless.  This is because of the new name rule, and it is explained on a page about decidability.  For this course, I will not ask you to test such forms.

Go on to assignment 11.