Chapter Six, Tutorial One
This chapter introduces "predicate logic" or "PL". With predicate logic, we will greatly increase the expressive power of our language and so significantly enhance our logic. PL is a sophisticated logic compared to SL. Happily, the new language gains its power with only a few additions to the lexicon. Most things we do in this chapter, indeed in all the remaining chapters, will remind you of SL.
To get a very general idea of what we will add, recall that SL treats whole sentences and their truth functional compounds: it is the logic of compound sentences. So, in SL we can represent "Agnes will attend law school but not everyone will" as, say,
PL goes beyond SL by analyzing not only the compound structure of a molecular sentence, but also gets at the structure of the atomic components. For instance, the component
Agnes will attend law school
attributes a property (law school attendance) to someone (Agnes). Just symbolizing this component as 'A' leaves these particulars out. We can do better by including names (like "Agnes") and predicates (like "will attend law school") in our new language PL.
Everyone will attend law school
can only be symbolized as an atomic sentence of SL, perhaps as 'E'. But the English sentence includes a quantity term "everyone" in its subject. We'll call this quantity term a "quantifier". In PL, we will add quantifiers in addition to names and predicates. With only these three additions, our language will be much more powerful, powerful enough to represent a significant fragment of a natural language (like English).
For example, reconsider the English sentence
Agnes will attend law school but not everyone will.
One consequence of this last statement is ...