Chapter Nine, Tutorial Three
Complex Names (a.k.a. "functions")

English allows complex names. For example, one may say

(*) George's father is a former US president.

Here the phrase "George's father" acts as a name. In chapters six and seven, we called this a definite description, (it's equivalent to "the father of George") and symbolized it with a PL name.

For example, given the symbolization key:

g: George W. Bush
f: George's father
Px: x is a former US president

We would have symbolize (*) simply as:

(*)'s symbolization:        Pf

There's nothing really wrong with this. But we might still want to do better: The English (*), but not the PL symbolization, explicitly requires a relationship between the referent of 'f' and 'g' (father to son).

There are lots of other examples of complex names in English. All with the same problem of PL symbolization. For examples:

7+3
H20

But all we can do to represent these is something like:

s: the sum of 7 and 3
h: H20

In both cases, the PL symbolization gives up information about relationships between objects named in the English. To see how to do better, think about the following:

Let's look for a HINT about how we will represent these complex names. In each case described, a complex name determines its referent given the inputs of the referents of simpler names. In mathematics, we call such dependence a ...

1. function
2. sum
3. divisor
4. ultrafilter