CATEGORICAL PROPOSITIONS, CHP. 8 DEDUCTIVE LOGIC VS INDUCTIVE LOGIC ONE CENTRAL PURPOSE: UNDERSTANDING CATEGORICAL SYLLOGISMS AS THE BUILDING BLOCKS OF

CATEGORICAL CATEGORICAL PROPOSITIONS, CHP. 8PROPOSITIONS, CHP. 8

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

1. SUBJECT, 2. PREDICATE, 3. 1. SUBJECT, 2. PREDICATE, 3. COPULA, 4. QUANTITY, 5. QUALITY.COPULA, 4. QUANTITY, 5. QUALITY.

QUANTITY AND QUALITYQUANTITY AND QUALITY

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

LOGICAL RELATIONSHIPS:LOGICAL RELATIONSHIPS: CONTRARIESCONTRARIES CONTRADICTORIESCONTRADICTORIES SUBALTERNATESSUBALTERNATES SUBCONTRARIESSUBCONTRARIES

AKA: BASIC INFERENCESAKA: BASIC INFERENCES

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.

LOGICAL RELATIONSHIPS, LOGICAL RELATIONSHIPS, CONT.CONT.

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.

SUBALTERNATES: SUBALTERNATES: SUBCONTRARIES:SUBCONTRARIES:

LOGICAL RELATIONSHIPS, LOGICAL RELATIONSHIPS, CONT.CONT.

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)

IMMEDIATE INFERENCES, IMMEDIATE INFERENCES, CONT.CONT.

CONVERSION, THE CONVERSE.CONVERSION, THE CONVERSE. SWITCHING SUBJECT AND SWITCHING SUBJECT AND

PREDICATE.PREDICATE. E.G. SOME ENGLISHMEN ARE E.G. SOME ENGLISHMEN ARE

SCOTCH DRINKERS.SCOTCH DRINKERS. THE CONVERSE: SOME SCOTCH THE CONVERSE: SOME SCOTCH

DRINKERS ARE ENGLISHMEN.DRINKERS ARE ENGLISHMEN. THIS FOLLOWS.THIS FOLLOWS. EQUIVALENCE AND LEGITIMACYEQUIVALENCE AND LEGITIMACY


E PROPOSITION: NO WOMEN HAVE E PROPOSITION: NO WOMEN HAVE BEEN U.S. PRESIDENTS.BEEN U.S. PRESIDENTS.

CONVERSE: NO U.S. PRESIDENTS CONVERSE: NO U.S. PRESIDENTS HAVE BEEN WOMEN.HAVE BEEN WOMEN.

FOR BOTH I AND E PROPOSITIONS, FOR BOTH I AND E PROPOSITIONS, THE CONVERSE FOLLOWS.THE CONVERSE FOLLOWS.


A FORM: ALL PICKPOCKETS ARE A FORM: ALL PICKPOCKETS ARE CRIMINALS.CRIMINALS.

CONVERSE: ALL CRIMINALS ARE CONVERSE: ALL CRIMINALS ARE PICKPOCKETS.PICKPOCKETS.

O FORM: SOME HUMAN BEINGS ARE NOT O FORM: SOME HUMAN BEINGS ARE NOT AMERICANS.AMERICANS.

CONVERSE: SOME AMERICANS ARE NOT CONVERSE: SOME AMERICANS ARE NOT HUMAN BEINGS.HUMAN BEINGS.

FOR BOTH, A AND O, CONVERSION IS NOT FOR BOTH, A AND O, CONVERSION IS NOT LEGITIMATE.LEGITIMATE.

P.QUIZ, 8.6. P. 215.P.QUIZ, 8.6. P. 215.


OBVERSION: ALL OBVERSION IS OBVERSION: ALL OBVERSION IS LEGITIMATE!LEGITIMATE!

BASICALLY, DRAWING THE COMPLEMENT BASICALLY, DRAWING THE COMPLEMENT OF THE CLASS.OF THE CLASS.

2 CHANGES:2 CHANGES: 1. REPLACE THE PREDICATE TERM WITH 1. REPLACE THE PREDICATE TERM WITH

ITS COMPLEMENTITS COMPLEMENT 2. CHANGE THE QUALITY OF THE 2. CHANGE THE QUALITY OF THE

PROPOSITIONPROPOSITION SEE CHART P. 216.SEE CHART P. 216.


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

COMPLEMENTSCOMPLEMENTS


STRUCTURE: ALL S IS P BECOMES ALL STRUCTURE: ALL S IS P BECOMES ALL NON-P ARE NON-S.NON-P ARE NON-S.

CONTRAPOSITIVE OF A IS ALWAYS CONTRAPOSITIVE OF A IS ALWAYS LEGITIMATELEGITIMATE

IS NOT LEGITIMATE FOR I OR E IS NOT LEGITIMATE FOR I OR E PROPOSITIONS.PROPOSITIONS.

E.G. NO PRIMATE IS AN AQUATIC ANIMALE.G. NO PRIMATE IS AN AQUATIC ANIMAL CONTRAPOSITIVE: NO NON-AQUATIC CONTRAPOSITIVE: NO NON-AQUATIC

ANIMAL IS A NON-PRIMATE.ANIMAL IS A NON-PRIMATE. COWS ARE NON AQUATIC ANIMALS THAT COWS ARE NON AQUATIC ANIMALS THAT

ARE NON-PRIMATES.ARE NON-PRIMATES.


EQUIVALENCE!!!EQUIVALENCE!!! DO NOT WORRY ABOUT VENN DO NOT WORRY ABOUT VENN

DIAGRAMS TO TEST THIS.DIAGRAMS TO TEST THIS. OUR PURPOSES: WE USE THE OUR PURPOSES: WE USE THE

OBVERSION OF THE A PROPOSITION OBVERSION OF THE A PROPOSITION TO CAPTURE THE A FORM IN VENN TO CAPTURE THE A FORM IN VENN DIAGRAMS.DIAGRAMS.

P. QUIZ 8.8, 220P. QUIZ 8.8, 220

VENN DIAGRAMS OF VENN DIAGRAMS OF CATEGORICAL PROPOSITIONSCATEGORICAL PROPOSITIONS

A: A:


E: E:


I:I:


O:O:

Documents

CATEGORICAL PROPOSITIONS, CHP. 8 DEDUCTIVE LOGIC VS INDUCTIVE LOGIC ONE CENTRAL PURPOSE: UNDERSTANDING CATEGORICAL SYLLOGISMS AS THE BUILDING BLOCKS OF