Chapter 11 presents an introduction to quantification theory, which offers a powerful method for dealing with deductive arguments whose constituents are not compoundwhich means that their validity depends on the inner logical structure of their propositions. The chapter introduces a new notation and a new concept: the propositional function.
After reading this chapter, you should be able to:
- Understand the concept of a propositional function, and how a proposition may be obtained from a propositional function by instantiation.
- Obtain propositions from propositional functions by means of generalization.
- Use the universal quantifier (x) and the existential quantifier (õx).
- Apply the four additional rules of inference: UI, UG, EI, and EG (universal instantiation and generalization, and existential instantiation and generalization).
- Use the method of refutation by logical analogy to prove the invalidity of arguments involving quantifiers.
- Symbolize and evaluate asyllogistic arguments (those not reducible to A, E, I, and O propositions, or singular propositions).