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 Quantification Theory Objectives

Chapter 11 presents an introduction to quantification theory, which offers a powerful method for dealing with deductive arguments whose constituents are not compound—which 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:

1. Understand the concept of a propositional function, and how a proposition may be obtained from a propositional function by instantiation.
2. Obtain propositions from propositional functions by means of generalization.
3. Use the universal quantifier (x) and the existential quantifier (õx).
4. Apply the four additional rules of inference: UI, UG, EI, and EG (universal instantiation and generalization, and existential instantiation and generalization).
5. Use the method of refutation by logical analogy to prove the invalidity of arguments involving quantifiers.
6. Symbolize and evaluate asyllogistic arguments (those not reducible to A, E, I, and O propositions, or singular propositions).

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