Section 3.4: The Nature of Proof

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3.4 Outline

  1. Introduction
    1. theorem
    2. syllogism
  2. Direct reasoning
    1. definition
    2. modus ponens
    3. law of detachment
    4. assuming the antecedent
  3. Indirect reasoning
    1. definition
    2. modus tollens
    3. denying the consequent
  4. Transitive reasoning
    1. definition
    2. formulate a conclusion
  5. Logical proof
  6. Fallacies
    1. fallacy of the converse
      1. also called fallacy of assuming the consequent
      2. counterexample
    2. fallacy of the inverse
      1. also called fallacy of assuming the consequent
      2. counterexample
    3. fallacy of the inverse
      1. fallacy of the antecedent
      2. test validity
    4. false chain pattern

3.4 Essential Ideas

There are three types of syllogisms considered in the text:

3.2.5

These forms can be mixed together in a single problem.

In addition there are three common logical fallacies considered:

Remember this forms are NOT valid:

3.2.6