CATEGORICAL CATEGORICAL PROPOSITIONS, CHP. 8 PROPOSITIONS, CHP. 8 DEDUCTIVE LOGIC VS INDUCTIVE LOGIC DEDUCTIVE LOGIC VS INDUCTIVE LOGIC ONE CENTRAL PURPOSE: UNDERSTANDING ONE CENTRAL PURPOSE: UNDERSTANDING CATEGORICAL SYLLOGISMS AS THE CATEGORICAL SYLLOGISMS AS THE BUILDING BLOCKS OF CATEGORICAL BUILDING BLOCKS OF CATEGORICAL SYLLOGISMS SYLLOGISMS DEFINITION: A DECLARATIVE SENTENCE DEFINITION: A DECLARATIVE SENTENCE IN WHICH SUBJECT TERM AND PREDICATE IN WHICH SUBJECT TERM AND PREDICATE TERM ARE RELATED AS CATEGORIES TERM ARE RELATED AS CATEGORIES
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CATEGORICAL PROPOSITIONS, CHP. 8 DEDUCTIVE LOGIC VS INDUCTIVE LOGIC ONE CENTRAL PURPOSE: UNDERSTANDING CATEGORICAL SYLLOGISMS AS THE BUILDING BLOCKS OF.
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DEDUCTIVE LOGIC VS INDUCTIVE LOGICDEDUCTIVE LOGIC VS INDUCTIVE LOGIC
ONE CENTRAL PURPOSE: ONE CENTRAL PURPOSE: UNDERSTANDING CATEGORICAL UNDERSTANDING CATEGORICAL SYLLOGISMS AS THE BUILDING BLOCKS SYLLOGISMS AS THE BUILDING BLOCKS OF CATEGORICAL SYLLOGISMSOF CATEGORICAL SYLLOGISMS
DEFINITION: A DECLARATIVE SENTENCE DEFINITION: A DECLARATIVE SENTENCE IN WHICH SUBJECT TERM AND PREDICATE IN WHICH SUBJECT TERM AND PREDICATE TERM ARE RELATED AS CATEGORIESTERM ARE RELATED AS CATEGORIES
CATEGORIES: CLASSES OF CATEGORIES: CLASSES OF THINGSTHINGS
E.G. WHALES ARE MAMMALSE.G. WHALES ARE MAMMALS S V S V PP SUBJECT, VERB AND PREDICATESUBJECT, VERB AND PREDICATE
5 COMPONENTS OR ATTRIBUTES OF 5 COMPONENTS OR ATTRIBUTES OF CAT. PROPSCAT. PROPS
EACH PROPOSITION HASEACH PROPOSITION HAS…… QUANTITY: PARTICULAR OR QUANTITY: PARTICULAR OR
UNIVERSALUNIVERSAL AND…AND… QUALITY: AFFIRMATIVE OR NEGATIVEQUALITY: AFFIRMATIVE OR NEGATIVE E.G. SOME WHALES ARE MAMMALS E.G. SOME WHALES ARE MAMMALS
(PARTICULAR AFFIRMATIVE)(PARTICULAR AFFIRMATIVE) E.G. ALL WHALES ARE MAMMALS E.G. ALL WHALES ARE MAMMALS
(UNIVERSAL AFFIRMATIVE)(UNIVERSAL AFFIRMATIVE)
THERE ARE 4 STANDARD THERE ARE 4 STANDARD CATEGORICAL PROPOSITIONS.CATEGORICAL PROPOSITIONS. A: UNIVERSAL AFFIRMATIVEA: UNIVERSAL AFFIRMATIVE E: UNIVERSAL NEGATIVEE: UNIVERSAL NEGATIVE I: PARTICULAR AFFIRMATIVEI: PARTICULAR AFFIRMATIVE O: PARTICULAR NEGATIVEO: PARTICULAR NEGATIVE P.QUIZ 8.1. P. 198.P.QUIZ 8.1. P. 198.
STANDARD STANDARD FORM/TRANSLATING INTO FORM/TRANSLATING INTO
STANDARD FORMSTANDARD FORM GOAL: TO PUT INTO S V P FORM AND RELATE GOAL: TO PUT INTO S V P FORM AND RELATE
TERMS AS CATEGORIES OF THINGSTERMS AS CATEGORIES OF THINGS SOME CHALLENGES:SOME CHALLENGES: 1. SUBJECT AND PREDICATE ARE SWITCHED1. SUBJECT AND PREDICATE ARE SWITCHED E.G. “TENDER IS THE NIGHT.”E.G. “TENDER IS THE NIGHT.” 2. SUBJECT IS SPLIT IN TWO2. SUBJECT IS SPLIT IN TWO E.G. “NO CODE HAS BEEN MADE THAT CANNOT BE E.G. “NO CODE HAS BEEN MADE THAT CANNOT BE
BROKEN”BROKEN” STANDARD FORM: NO CODE THAT CANNOT BE STANDARD FORM: NO CODE THAT CANNOT BE
BROKEN IS A THING THAT HAS BEEN MADEBROKEN IS A THING THAT HAS BEEN MADE
STANDARD FORM, CONT.STANDARD FORM, CONT.
3. SINGULAR TERMS3. SINGULAR TERMS E.G. E.G. “TOM IS A GOOD BASKETBALL “TOM IS A GOOD BASKETBALL
PLAYER.”PLAYER.” ““NEW YORK IS A LARGE CITY.”NEW YORK IS A LARGE CITY.” 4. NON-STANDARD QUANTIFIERS. 4. NON-STANDARD QUANTIFIERS. ““EVERY,” “EVERYTHING,” “NOTHING,” EVERY,” “EVERYTHING,” “NOTHING,”
“NONE.”“NONE.” E.G. “OBJECTS HEAVIER THAN AIR MUST E.G. “OBJECTS HEAVIER THAN AIR MUST
FALL WHEN UNSUPPORTED.”FALL WHEN UNSUPPORTED.”
STANDARD FORM, CONT.STANDARD FORM, CONT.
SPECIAL PROBLEM: ALL S IS NOT PSPECIAL PROBLEM: ALL S IS NOT P E.G. ALL POLITICIANS ARE NOT E.G. ALL POLITICIANS ARE NOT
CRIMINALSCRIMINALS RULE OF THUMB: IN MOST CASES, RULE OF THUMB: IN MOST CASES,
TRANSLATE UNIVERSAL NEGATIVE TRANSLATE UNIVERSAL NEGATIVE AS AS NO S IS PNO S IS P
P.QUIZ 8.2. P. 202.P.QUIZ 8.2. P. 202.
CLASSICAL SQUARE OF CLASSICAL SQUARE OF OPPOSITIONOPPOSITION
DESCRIBES RELATIONSHIP BETWEEN DESCRIBES RELATIONSHIP BETWEEN CATEGORICAL PROPOSITIONSCATEGORICAL PROPOSITIONS
PURPOSE: TO BECOME FAMILIAR WITH PURPOSE: TO BECOME FAMILIAR WITH TRUTH VALUES OF PROPOSITIONS AND TRUTH VALUES OF PROPOSITIONS AND MAKING INFERENCESMAKING INFERENCES
CONTRARIES: IF A IS TRUE, E MUST BE CONTRARIES: IF A IS TRUE, E MUST BE FALSE.FALSE.
IF E IS TRUE, A MUST BE FALSEIF E IS TRUE, A MUST BE FALSE A AND E CANNOT BE TRUE AT THE SAME A AND E CANNOT BE TRUE AT THE SAME
TIME BUT CAN BE BOTH FALSE.TIME BUT CAN BE BOTH FALSE.
E.G. A: ALL BREAD IS NUTRITIOUSE.G. A: ALL BREAD IS NUTRITIOUS E: NO BREAD IS NUTRITIOUSE: NO BREAD IS NUTRITIOUS CONTRADICTORIES: SIMPLE: IF ANY CONTRADICTORIES: SIMPLE: IF ANY
ONE PROPOSITION IS TRUE, THE ONE PROPOSITION IS TRUE, THE OTHER MUST BE FALSE AND VICE OTHER MUST BE FALSE AND VICE VERSA.VERSA.
ISSUE OF INDETERMINATE TRUTH.ISSUE OF INDETERMINATE TRUTH. P.QUIZ 8.3. P. 207.P.QUIZ 8.3. P. 207.
EXISTENTIAL IMPORT AND THE EXISTENTIAL IMPORT AND THE MODERN SQUARE OF MODERN SQUARE OF
OPPOSITION.OPPOSITION. A DILEMMA: NOT STRESSED TOO MUCHA DILEMMA: NOT STRESSED TOO MUCH THE ISSUE: SOME UNIVERSAL THE ISSUE: SOME UNIVERSAL
PROPOSITIONS ARE OF SUCH A NATURE PROPOSITIONS ARE OF SUCH A NATURE THAT WE CANNOT DRAW THE THAT WE CANNOT DRAW THE SUBALTERNATE, OR THE PARTICULAR.SUBALTERNATE, OR THE PARTICULAR.
OR, PARTICULAR PROPOSITIONS, LIKE I, OR, PARTICULAR PROPOSITIONS, LIKE I, ENTAIL THAT THE SUBJECT OR CONCEPT ENTAIL THAT THE SUBJECT OR CONCEPT IS SOMETHING EXISTING.IS SOMETHING EXISTING.
EXISTENTIAL SQUARE CONT.EXISTENTIAL SQUARE CONT.
E.G. ALL UNICORNS HAVE HORNS (A E.G. ALL UNICORNS HAVE HORNS (A FORM)FORM)
SOME UNICORNS HAVE HORNS (I)SOME UNICORNS HAVE HORNS (I) WHICH UNICORNS HAVE HORNS?WHICH UNICORNS HAVE HORNS? WHEN A PROPOSITION HAS WHEN A PROPOSITION HAS
EXISTENTIAL IMPORT:EXISTENTIAL IMPORT: WHEN ITS TRUTH DEPENDS UPON WHEN ITS TRUTH DEPENDS UPON
THE EXISTENCE OF S AND/OR P, THE EXISTENCE OF S AND/OR P, SUBJECT OR PREDICATE.SUBJECT OR PREDICATE.
EXISTENTIAL IMPORT CONT.EXISTENTIAL IMPORT CONT.
ALL PARTICULAR STATEMENTS DO HAVE ALL PARTICULAR STATEMENTS DO HAVE EXISTENTIAL IMPORT.EXISTENTIAL IMPORT.
BUT…BUT… E.G. ALL STUDENTS WHO MISS THREE OR E.G. ALL STUDENTS WHO MISS THREE OR
MORE CLASSES WILL FAIL THE COURSE. MORE CLASSES WILL FAIL THE COURSE. (A)(A)
SOME STUDENTS WHO MISS THREE SOME STUDENTS WHO MISS THREE OR MORE CLASSES WILL FAIL THE OR MORE CLASSES WILL FAIL THE COURSE. (I)COURSE. (I)
CONTRADICTORIESCONTRADICTORIES
DISTRIBUTIONDISTRIBUTION
AN ATTRIBUTE OF TERMS, NOT THE AN ATTRIBUTE OF TERMS, NOT THE PROPOSITIONS.PROPOSITIONS.
THE CONCEPT: WHETHER WE KNOW THE THE CONCEPT: WHETHER WE KNOW THE EXTENT OF THE CLASS OR CATEGORY OR EXTENT OF THE CLASS OR CATEGORY OR NOT.NOT.
RULE OF THUMB: IF WE KNOW THE RULE OF THUMB: IF WE KNOW THE EXTENT OF THE CLASS OR CATEGORY, EXTENT OF THE CLASS OR CATEGORY, POSITIVELY OR NEGATIVELY, THEN WE POSITIVELY OR NEGATIVELY, THEN WE CAN SAY THE TERM IS DISTRIBUTED. IF CAN SAY THE TERM IS DISTRIBUTED. IF NOT, IT IS UNDISTRIBUTED.NOT, IT IS UNDISTRIBUTED.
CHART ON DISTRIBUTIONCHART ON DISTRIBUTION
Proposition Proposition TypeType
SubjectSubject PredicatePredicate
AA DD UU
EE DD DD
II UU UU
OO UU DD
IMMEDIATE INFERENCES. IMMEDIATE INFERENCES. ALSO CALLED LOGICAL ALSO CALLED LOGICAL
OPERATIONS.OPERATIONS. THE IDEA: TAKING OUR FOUR THE IDEA: TAKING OUR FOUR
STANDARD FORM CATEGORICAL STANDARD FORM CATEGORICAL PROPOSITIONS AND SUBMITTING PROPOSITIONS AND SUBMITTING THEM TO A VARIETY OF OPERATIONS.THEM TO A VARIETY OF OPERATIONS.
ONE OF OUR PURPOSES: TO LEARN ONE OF OUR PURPOSES: TO LEARN BASIC INFERENCE AND DETERMINE BASIC INFERENCE AND DETERMINE WHETHER THE CHANGED WHETHER THE CHANGED PROPOSITION FOLLOWS, IS TRUE OR PROPOSITION FOLLOWS, IS TRUE OR LEGITIMATE (EQUIVALENT)LEGITIMATE (EQUIVALENT)
COMPLEMENTS ARE NOT OPPOSITES! COMPLEMENTS ARE NOT OPPOSITES! THEY REFER TO THE CLASS OF THEY REFER TO THE CLASS OF EVERYTHING NOT S OR NOT P.EVERYTHING NOT S OR NOT P.
QUIZ 8.7. P. 218.QUIZ 8.7. P. 218. CONTRAPOSITIVECONTRAPOSITIVE 2 CHANGES.2 CHANGES. SWITCHING SUBJECT AND PREDICATE SWITCHING SUBJECT AND PREDICATE
(CONVERSION)(CONVERSION) REPLACING BOTH TERMS WITH THEIR REPLACING BOTH TERMS WITH THEIR