Chapter 5: Categorical Syllogisms (Symbolic Logic)

categorical syllogisms

categorical arguments with TWO premises that mention THREE different classes

256

How many possible syllogisms?

standard form (categorical syllogisms)

 when each term appears exactly TWICE in the syllogism (the middle term ONCE in EACH PREMISE), the premise with the MAJOR term listed first, and each statement is an A, E, I, or O statement

major term

the predicate term of the argument’s conclusion in a categorical syllogism

major premise

• the premise that contains the major term

  • Always the FIRST PREMISE when written in STANDARD FORM

minor term

the subject term of the argument’s conclusion in a categorical syllogism

minor premise

•  the premise that contains the minor term

  • Always the SECOND PREMISE when written in STANDARD FORM

middle term

• term that appears in BOTH PREMISES, but NOT in the CONCLUSION

  • Can be the subject or predicate of either premise!

mood

the letter-type of the statements in a categorical syllogism (A, E, I, or O)

figure

the placement of the MIDDLE TERM in EACH PREMISE

figure 1

1. All M are P

2. All S are M

figure 1 (explanation)

• Middle term in subject position in the major premise

• Middle term in predicate position in the minor premise

figure 2

1. All P are M

2. All S are M

figure 2 (explanation)

Middle term in predicate position in BOTH premises

figure 3

1. All M are P

2. All M are S

figure 3 (explanation)

Middle term in subject position in BOTH premises

figure 4

1. All P are M

2. All M are S

figure 4 (explanation)

• Middle Term in predicate position in the major premise

• Middle Term in subject position in the minor premise

• Have exactly THREE statements (TWO premises, ONE conclusion)

• Have exactly THREE classes mentioned

  • Each class must be mentioned exactly TWICE

• Have the Major Premise listed FIRST

• Have the Middle Term appear ONCE in EACH PREMISE and NOT APPEAR in the CONCLUSION

• Have each statement be a STANDARD-FORM categorical statement (A, E, I, or O)

Standard-form categorical syllogisms must: