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Syllogisms
Types of Syllogisms

Categorical Syllogism – deals with categories and whether or not things belong in certain categories

Disjunctive Syllogism – involves a choice and contains an either/or statement

           Either Tom is a cat, or he is on a mat.
           Tom is not a cat.
           Therefore, Tom is on a mat.

Hypothetical Syllogism – created through a chain. When the chain is created properly, the syllogism
is said to be valid. The chain is made of one or various if/then statements.

           ex. If you make lots of money, you will be happy.
           You make lots of money.
           Therefore, you are happy.

           If you sit down to rest, you will have energy.
           If you have energy, you will go for a run.
           Therefore, if you sit down you will go for a run
    Recall:
                                        The Major Premise of a syllogism contains the
    Major premise                       predicate of the conclusion and the middle
    Minor premise                       term. The Minor Premise contains the subject
    Conclusion                          of the conclusion and the middle term.



     Figure of the Syllogism
                                           predicate term
          middle term

                                                        middle term
subject term       All cats are on mats.
                   Garfield is a cat.
                   Therefore, Garfield is on a mat.


                         subject term               predicate term
                                  Figure 1      Figure 2      Figure 3     Figure 4

        Major premise             M-P           P-M           M-P          P-M

        Minor premise             S-M           S-M           M-S          M-S

        Conclusion                S-P           S-P           P-S          P-S



 All dogs are cats                                                    All dogs are cats
 Some mice are dogs                                                   Some dogs are mice
 Therefore, some mice are cats                                        Therefore, some mice are cats

 All mammals are animals                                              All mammals are animals
 Some ‘things with four legs’ are mammals                             Some mammals are ‘things with four legs’
 Therefore, some ‘things with four legs’ are animals                  Therefore, some ‘things with four legs’ are animals
Types of Syllogisms

The types of syllogisms (we have already seen these) are referred to with the vowels A, E, I, and O.

      A–      Universal affirmative      All A’s are B’s
      E–      Universal negative         No A’s are B’s
      I–      Particular affirmative     Some A’s are B’s
      O–      Particular negative        Some A’s are not B’s

So we can refer to a specific type with a specific figure in the following manner:

      AAA-1

We have already seen many examples of this syllogism.

      All philosophers are Greek.
      All people with beards are philosophers.
      Therefore, all people with beards are Greek.
Rules of the syllogism

1)   There are only three terms in a syllogism (by definition).
2)   The middle term is not in the conclusion (by definition).
3)   The quantity of a term cannot become greater in the conclusion.
4)   The middle term must be universally quantified in at least one premise.
5)   At least one premise must be affirmative.
6)   If one premise is negative, the conclusion is negative.
7)   If both premises are affirmative, the conclusion is affirmative.
8)   At least one premise must be universal.
9)   If one premise is particular, the conclusion is particular.
Venn Diagrams

Venn diagrams can be used to test or show the validity of a syllogism. These can be used in
two different ways.

           All men are mortal.
           Socrates is a man.
           Therefore, Socrates is mortal.
Examples: Identify the type, the figure, and use a Venn diagram to show the argument.



All cats are on mats.
All mice are on mats.
Therefore, all cats are mice.



No cats are on mats.
Jill is not a cat.
Therefore, Jill is on a mat.



All dogs have fur.
Some dogs have fleas.
Therefore, some things with fur have fleas.

				
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