PHIL 210 Lecture Notes - Lecture 3: Infix Notation, Arity

• School: McGill University
• Department: Philosophy
• Course: PHIL 210
• Professor: Michael Hallett

Document Summary

In our language so far, we have names/constants and predicates/relations. But in addition to referring directly using a name, we frequently refer to objects indirectly, by using the names of other things. You could not say (cid:494)the parent of max(cid:495) because max has more than one parent. Again we can use the same terminology which we had with relations; we speak of the arity of the function symbol, i. e. , how many places *** usual sense. mother(max), father(max) father(mother(max)), mother(mother(max)) The advantage of functions is that they can be combined and iterated indefinitely. A standard example of a 2-place function with which you(cid:495)re all familiar is ordinary. Clearly, we can have 2-place functions as well, or 3-place, 4-place, and so on. addition in arithmetic: What we have done by applying function symbols in effect is to broaden the category of names: So we can certainly correctly say ge = mae. But we can also say correctly: (cid:494)george eliot(cid:495) is a name.