Chapter 9 presents the fundamental concepts of modern symbolic logic. Since the analysis and appraisal of arguments is made difficult by the peculiarities of language, the system of modern symbolic logic was set up to be independent of language. Using a system of artificial symbols, modern symbolic logic attempts to move the analysis of argument directly to the issue of validity, bypassing the vagaries of any specific language.
After reading this chapter, you should be able to:
- Use the special symbols: the dot, wedge, horseshoe, curl, and three bars (, , , , ).
- Understand how these symbols are used to express negation, conjunction, disjunction, material implication, and material equivalence.
- Use truth tables to test the validity of argument forms.
- Deal with statement forms, including tautologous, contradictory, and contingent forms.
- Use logical equivalence and De Morgan's theorems, as well as the principle of double negation.
- Understand why the paradoxes of material implication are not really paradoxes after all.
- Discuss the proper place of identity, non-contradiction, and excluded middle in logic.