Logical Implication and Validity

Recall that logic is about general criteria and methods of correct reasoning expressed in arguments. When used to analyze arguments that have already been constructed, logic is being used critically. When used to create new arguments logic is being used constructively. The next chapter describes some methods for using logic constructively. This chapter describes some methods for using logic critically. After studying it you should be able to:

• 1. Explain what it means for an argument to be valid.

• 2. Describe the relations among true premises, true conclusions, validity, and soundness. Give examples of arguments having various logical characteristics and explain why certain combinations of those characteristics are impossible.

• 3. Explain the difference between formal and informal methods of showing validity.

• 4. Use informal methods to determine whether simple arguments are valid or invalid and explain your conclusions.

• 5. Use the truth table test to investigate the validity of arguments.

• 6. Use reasoning based on quantifiers and interpretations of wffs to investigate the validity of arguments.