Deductive Reasoning

1
Deductive Reasoning

• Mathematical Certainty

2
Characteristics

• offers two or more assertions that lead
  automatically to a conclusion
• can be phrased as "syllogisms," in which the
  premises lead inexorably to the conclusion
• Premise All dogs have four legs.
• Premise Rover is a dog,
• Conclusion Rover has four legs.
• Deductive Reasoning begins with generalizations

3
Characteristics Structure

• a deductive argument has three parts
• a major premise, a statement of general truth
  dealing with categories rather than individual
  examples
• a minor premise, a statement of particular truth
  dealing with a specific instance governed by the
  major premise
• and a conclusion, the statement derived from the
  minor premises relationship to the major premise.

4
Characteristics Structure, cont.

• Major premise
• All men are mortal
• Politicians are crooks
• Telemarketers are obnoxious
• Major premises are composed of two parts
• The Antecedent (or Subject -- see underlined)
• The Consequent (or predicate not underlined)

5
Characteristics Structure, cont.

• Minor premise
• Socrates is a man
• Newt Gingrich is a politician
• The guy on the phone at dinnertime is a
  telemarketer.
• Note that the minor premise deals with a part of
  the major premise

6
Characteristics Structure, cont.

• Conclusion (therefore . . .)
• Socrates is mortal
• Newt Gingrich is a crook
• The guy on the phone at dinnertime is obnoxious.
• Note that the relationship between major and
  minor premises dictates the concl.

7
Characteristics Types of Relationships

• Affirming the antecedent
• Minor premise equates something to the
  antecedent
• All blonds (ant.) are fun. Chris is a blonde.
  Chris is fun.
• Great literature (ant.) improves your life. Gone
  with the Wind is great literature. Gone with the
  Wind will improve your life.

8
Characteristics Types of Relationships, cont.

• Denying the consequent
• Minor premise equates the negative to the
  consequent
• All blonds are fun (cons.). Chris is not fun.
  Chris is not blond
• Great literature improves your life (cons.).
  Gone with the Wind will not improve your life.
  Gone with the Wind is not great literature.
• These are the only sound relationships.

9
Characteristics soundness

• Deductive arguments are not spoken of as "true"
  or "false," but as "sound" or "unsound."
• a sound argument is one in which the premises
  guarantee the conclusions an unsound argument is
  one in which the premises do not guarantee the
  conclusions
• a deduction can be completely true, yet unsound.
  It can also be sound, yet demonstrably untrue

10
Characteristics Soundness examples

• All Southern presidents in the 20th century were
  Baptists.
• Jimmy Carter was a Baptist.
• Jimmy Carter was a Southern president in the 20th
  century.
• (True but unsound)
• All Southern presidents in the 20th century were
  Republicans.
• Jimmy Carter was a Southern president in the 20th
  century.
• Jimmy Carter was a Republican.
• (Sound but untrue)