CATEGORICAL
PROPOSITIONS, CHP. 8
DEDUCTIVE LOGIC VS INDUCTIVE LOGIC
ONE CENTRAL PURPOSE:
UNDERSTANDING CATEGORICAL
SYLLOGISMS AS THE BUILDING BLOCKS
OF CATEGORICAL SYLLOGISMS
DEFINITION: A DECLARATIVE SENTENCE
IN WHICH SUBJECT TERM AND PREDICATE
TERM ARE RELATED AS CATEGORIES
CATEGORIES: CLASSES OF
THINGS
 E.G.
WHALES ARE MAMMALS

S
V
P
 SUBJECT, VERB AND PREDICATE
5
COMPONENTS OR ATTRIBUTES OF
CAT. PROPS
 1. SUBJECT, 2. PREDICATE, 3.
COPULA, 4. QUANTITY, 5. QUALITY.
QUANTITY AND QUALITY
 EACH
PROPOSITION HAS…
 QUANTITY: PARTICULAR OR
UNIVERSAL
 AND…
 QUALITY: AFFIRMATIVE OR NEGATIVE
 E.G. SOME WHALES ARE MAMMALS
(PARTICULAR AFFIRMATIVE)
 E.G. ALL WHALES ARE MAMMALS
(UNIVERSAL AFFIRMATIVE)
THERE ARE 4 STANDARD
CATEGORICAL PROPOSITIONS.
 A:
UNIVERSAL AFFIRMATIVE
 E: UNIVERSAL NEGATIVE
 I: PARTICULAR AFFIRMATIVE
 O: PARTICULAR NEGATIVE
 P.QUIZ 8.1. P. 198.
STANDARD
FORM/TRANSLATING INTO
STANDARD FORM

GOAL: TO PUT INTO S V P FORM AND RELATE
TERMS AS CATEGORIES OF THINGS
 SOME CHALLENGES:
 1. SUBJECT AND PREDICATE ARE SWITCHED
 E.G. “TENDER IS THE NIGHT.”
 2. SUBJECT IS SPLIT IN TWO
 E.G. “NO CODE HAS BEEN MADE THAT CANNOT BE
BROKEN”
 STANDARD FORM: NO CODE THAT CANNOT BE
BROKEN IS A THING THAT HAS BEEN MADE
STANDARD FORM, CONT.






3. SINGULAR TERMS
E.G.
“TOM IS A GOOD BASKETBALL
PLAYER.”
“NEW YORK IS A LARGE CITY.”
4. NON-STANDARD QUANTIFIERS.
“EVERY,” “EVERYTHING,” “NOTHING,”
“NONE.”
E.G. “OBJECTS HEAVIER THAN AIR MUST
FALL WHEN UNSUPPORTED.”
STANDARD FORM, CONT.
 SPECIAL
PROBLEM: ALL S IS NOT P
 E.G. ALL POLITICIANS ARE NOT
CRIMINALS
 RULE OF THUMB: IN MOST CASES,
TRANSLATE UNIVERSAL NEGATIVE
AS NO S IS P
 P.QUIZ 8.2. P. 202.
CLASSICAL SQUARE OF
OPPOSITION
 DESCRIBES
RELATIONSHIP BETWEEN
CATEGORICAL PROPOSITIONS
 LOGICAL RELATIONSHIPS:
 CONTRARIES
 CONTRADICTORIES
 SUBALTERNATES
 SUBCONTRARIES
AKA: BASIC INFERENCES

PURPOSE: TO BECOME FAMILIAR WITH
TRUTH VALUES OF PROPOSITIONS AND
MAKING INFERENCES
 CONTRARIES: IF A IS TRUE, E MUST BE
FALSE.


IF E IS TRUE, A MUST BE FALSE
 A AND E CANNOT BE TRUE AT THE SAME
TIME BUT CAN BE BOTH FALSE.
LOGICAL RELATIONSHIPS,
CONT.
 E.G. A:
ALL BREAD IS NUTRITIOUS

E: NO BREAD IS NUTRITIOUS
 CONTRADICTORIES: SIMPLE: IF ANY
ONE PROPOSITION IS TRUE, THE
OTHER MUST BE FALSE AND VICE
VERSA.
 SUBALTERNATES:
 SUBCONTRARIES:
LOGICAL RELATIONSHIPS,
CONT.
 ISSUE
OF INDETERMINATE TRUTH.
 P.QUIZ 8.3. P. 207.
EXISTENTIAL IMPORT AND THE
MODERN SQUARE OF
OPPOSITION.

A DILEMMA: NOT STRESSED TOO MUCH
 THE ISSUE: SOME UNIVERSAL
PROPOSITIONS ARE OF SUCH A NATURE
THAT WE CANNOT DRAW THE
SUBALTERNATE, OR THE PARTICULAR.
 OR, PARTICULAR PROPOSITIONS, LIKE I,
ENTAIL THAT THE SUBJECT OR CONCEPT
IS SOMETHING EXISTING.
EXISTENTIAL SQUARE CONT.
 E.G.
ALL UNICORNS HAVE HORNS (A
FORM)
 SOME UNICORNS HAVE HORNS (I)
 WHICH UNICORNS HAVE HORNS?
 WHEN A PROPOSITION HAS
EXISTENTIAL IMPORT:
 WHEN ITS TRUTH DEPENDS UPON
THE EXISTENCE OF S AND/OR P,
SUBJECT OR PREDICATE.
EXISTENTIAL IMPORT CONT.





ALL PARTICULAR STATEMENTS DO HAVE
EXISTENTIAL IMPORT.
BUT…
E.G. ALL STUDENTS WHO MISS THREE OR
MORE CLASSES WILL FAIL THE COURSE.
(A)
SOME STUDENTS WHO MISS THREE
OR MORE CLASSES WILL FAIL THE
COURSE. (I)
CONTRADICTORIES
DISTRIBUTION

AN ATTRIBUTE OF TERMS, NOT THE
PROPOSITIONS.
 THE CONCEPT: WHETHER WE KNOW THE
EXTENT OF THE CLASS OR CATEGORY OR
NOT.
 RULE OF THUMB: IF WE KNOW THE
EXTENT OF THE CLASS OR CATEGORY,
POSITIVELY OR NEGATIVELY, THEN WE CAN
SAY THE TERM IS DISTRIBUTED. IF NOT, IT
IS UNDISTRIBUTED.
CHART ON DISTRIBUTION
Proposition
Type
A
Subject
Predicate
D
U
E
D
D
I
U
U
O
U
D
IMMEDIATE INFERENCES. ALSO
CALLED LOGICAL
OPERATIONS.
 THE
IDEA: TAKING OUR FOUR
STANDARD FORM CATEGORICAL
PROPOSITIONS AND SUBMITTING
THEM TO A VARIETY OF OPERATIONS.
 ONE OF OUR PURPOSES: TO LEARN
BASIC INFERENCE AND DETERMINE
WHETHER THE CHANGED
PROPOSITION FOLLOWS, IS TRUE OR
LEGITIMATE (EQUIVALENT)
IMMEDIATE INFERENCES, CONT.
 CONVERSION,
THE CONVERSE.
 SWITCHING SUBJECT AND
PREDICATE.
 E.G. SOME ENGLISHMEN ARE
SCOTCH DRINKERS.
 THE CONVERSE: SOME SCOTCH
DRINKERS ARE ENGLISHMEN.
 THIS FOLLOWS.
 EQUIVALENCE AND LEGITIMACY
IMMEDIATE INFERENCES, CONT.
E
PROPOSITION: NO WOMEN HAVE
BEEN U.S. PRESIDENTS.
 CONVERSE: NO U.S. PRESIDENTS
HAVE BEEN WOMEN.
 FOR BOTH I AND E PROPOSITIONS,
THE CONVERSE FOLLOWS.
IMMEDIATE INFERENCES, CONT.






A FORM: ALL PICKPOCKETS ARE
CRIMINALS.
CONVERSE: ALL CRIMINALS ARE
PICKPOCKETS.
O FORM: SOME HUMAN BEINGS ARE NOT
AMERICANS.
CONVERSE: SOME AMERICANS ARE NOT
HUMAN BEINGS.
FOR BOTH, A AND O, CONVERSION IS NOT
LEGITIMATE.
P.QUIZ, 8.6. P. 215.
IMMEDIATE INFERENCES, CONT.






OBVERSION: ALL OBVERSION IS
LEGITIMATE!
BASICALLY, DRAWING THE COMPLEMENT
OF THE CLASS.
2 CHANGES:
1. REPLACE THE PREDICATE TERM WITH
ITS COMPLEMENT
2. CHANGE THE QUALITY OF THE
PROPOSITION
SEE CHART P. 216.
IMMEDIATE INFERENCES, CONT.






COMPLEMENTS ARE NOT OPPOSITES!
THEY REFER TO THE CLASS OF
EVERYTHING NOT S OR NOT P.
QUIZ 8.7. P. 218.
CONTRAPOSITIVE
2 CHANGES.
SWITCHING SUBJECT AND PREDICATE
(CONVERSION)
REPLACING BOTH TERMS WITH THEIR
COMPLEMENTS
IMMEDIATE INFERENCES, CONT.






STRUCTURE: ALL S IS P BECOMES ALL
NON-P ARE NON-S.
CONTRAPOSITIVE OF A IS ALWAYS
LEGITIMATE
IS NOT LEGITIMATE FOR I OR E
PROPOSITIONS.
E.G. NO PRIMATE IS AN AQUATIC ANIMAL
CONTRAPOSITIVE: NO NON-AQUATIC
ANIMAL IS A NON-PRIMATE.
COWS ARE NON AQUATIC ANIMALS THAT
ARE NON-PRIMATES.
IMMEDIATE INFERENCES, CONT.
 EQUIVALENCE!!!
 DO
NOT WORRY ABOUT VENN
DIAGRAMS TO TEST THIS.
 OUR PURPOSES: WE USE THE
OBVERSION OF THE A PROPOSITION
TO CAPTURE THE A FORM IN VENN
DIAGRAMS.
 P. QUIZ 8.8, 220
VENN DIAGRAMS OF
CATEGORICAL PROPOSITIONS

A:
VENN DIAGRAMS OF
CATEGORICAL PROPOSITIONS

E:
VENN DIAGRAMS OF
CATEGORICAL PROPOSITIONS

I:
VENN DIAGRAMS OF
CATEGORICAL PROPOSITIONS

O: