Categorical Syllogisms, Chapter 9

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CATEGORICAL SYLLOGISMS
A SYLLOGISM: A ONE STEP
ARGUMENT WITH 2 PREMISES,
WHICH ARE DEPENDENT, AND 1
CONCLUSION.
A CATEGORICAL SYLLOGISM
SIMPLY USES CATEGORICAL
PROPOSITIONS IN PREMISES AND
CONCLUSION
CATEGORICAL SYLLOGISMS
 1. ALL WHALES ARE MAMMALS.
 2. ALL MAMMALS ARE ANIMALS THAT
BREATHE BY MEANS OF LUNGS.
 3. ALL WHALES ARE ANIMALS THAT
BREATHE BY MEANS OF LUNGS.
 COMPONENTS OF CATEGORICAL
SYLLOGISMS
CATEGORICAL SYLLOGISMS
 MAJOR TERM: OCCURS IN PREDICATE OF
CONCLUSION (P)
 MAJOR PREMISE: PREMISE IN WHICH
MAJOR TERM APPEARS
 MINOR TERM: OCCURS IN THE SUBJECT OF
THE CONCLUSION. (S)
 MINOR PREMISE: PREMISE IN WHICH MINOR
TERM APPEARS.
 MIDDLE TERM: TERM WHICH APPEARS IN
EACH PREMISE BUT NOT IN CONCLUSION.
CATEGORICAL SYLLOGISMS





THE FUNCTION OF THE MIDDLE TERM:
THIS TERM WILL BE NAMED M.
IT MEDIATES OR CONNECTS S AND P.
MOOD OF CATEGORICAL SYLLOGISMS:
REFERS TO ORDER OF TYPES OF
PROPOSITIONS IN THE SYLLOGISM.
 WHALE ARGUMENT AGAIN. AAA
CATEGORICAL SYLLOGISMS
 FIGURE OF A CATEGORICAL
SYLLOGISM:
 REFERS TO THE POSITION OF THE
MIDDLE TERM IN THE PREMISES.
 ONLY 4 MOODS, SEE P. 236. YOU NEED
TO COMMIT THIS TO MEMORY.
CATEGORICAL SYLLOGISMS
 STANDARD FORM: WHEN SYLLOGISMS
APPEAR IN ORDINARY LANGUAGE
CONTEXTS WE NEED TO PUT THEM
INTO STANDARD FORM.
 STRATEGY: (EACH SYLLOGISM HAS
THREE LINES WHICH CORRESPOND TO
EACH PROPOSITION.)







CATEGORICAL SYLLOGISMS
1. PUT PROPOSITIONS INTO STANDARD
FORM (CHAPTER 8)
2. IDENTIFY THE CONCLUSION. WRITE IT
DOWN AND PUT A NUMBER 3 BEFORE IT.
3. IDENTIFY S AND P AND WRITE THEM
DOWN TO THE SIDE.
4. IDENTIFY MIDDLE TERM AND WRITE IT
DOWN AT SIDE.
5. FIND PREMISE WITH MAJOR TERM AND
WRITE IT ON LINE 1.
6. FIND PREMISE WITH MINOR TERM AND
WRITE IT ON LINE 2.
P.QUIZ 9.1. P. 238.
CATEGORICAL SYLLOGISMS
 SEE PRACTICE QUIZ EXAMPLE ON
WEB.
 VALIDITY OF CATEGORICAL
SYLLOGISMS
 VALIDITY: NECESSITY: ALL OR NONE
 IN TOTAL 256 FORMS OF CATEGORICAL
SYLLOGISMS.
TESTING FOR VALIDITY
 RULES AND VENN DIAGRAMS. PLEASE
EXCLUDE CANCELLATION METHOD
 GOAL: TO UTILIZE BOTH TO UNDERSTAND
WHY SOME SYLLOGISMS ARE VALID AND
OTHERS ARE NOT.
 RULES: 5 TOTAL AND ALL NEED TO BE
SATISFIED FOR SYLLOGISM TO BE VALID.
 2 RELATED TO DISTRIBUTION
 2 RELATED TO NEGATIVITY
 1 RELATED TO MODERN SQUARE OF
OPPOSITION
TESTING FOR VALIDITY
 RULE 1: THE MIDDLE TERM MUST BE
DISTRIBUTED IN AT LEAST ONE PREMISE.
 (FALLACY OF UNDISTRIBUTED MIDDLE)
 RULE 2: IF EITHER TERM IS DISTRIBUTED IN
THE CONCLUSION, IT MUST BE DISTRIBUTED
IN THE PREMISE IN WHICH IT APPEARS.
 EXAMINE CONCLUSION!
 ILLICIT MINOR OR MAJOR
 RULE 3: NO VALID SYLLOGISM CAN HAVE
TWO NEGATIVE PREMISES.
 TWO NEGATIVES DO NOT ADD UP TO
ANYTHING.
TESTING FOR VALIDITY
 RULE 4: IF EITHER PREMISE IS NEGATIVE,
THE CONCLUSION MUST BE NEGATIVE. IF
THE CONCLUSION IS NEGATIVE, ONE
PREMISE MUST BE NEGATIVE. (CONVERSE)
 RULE 5: IF THE CONCLUSION IS
PARTICULAR, ONE PREMISE MUST BE
PARTICULAR. (CANNOT INFER A
PARTICULAR FROM TWO UNIVERSAL
PREMISES: CANNOT DRAW THE
SUBALTERNATES)
ENTHYMEMES
 CATEGORICAL SYLLOGISMS WITH
IMPLIED PREMISE.
 P.QUIZ 9.3. P. 242.
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