These slides are of Logic made by Fatima

1. CategoricalCategorical
PropositionsPropositions

2. Presenter:Presenter:
Fatima IbrahimFatima Ibrahim
Supervised by:Supervised by:
Madam MehwishMadam Mehwish

3. What are categorical propositions?What are categorical propositions?
• Categorical propositions are statements that relate two differentCategorical propositions are statements that relate two different
classes of things.classes of things.
– Examples:Examples:
• Horror movies always have obvious endings.Horror movies always have obvious endings.
– All horror movies are included in the class of things that have obvious endings.All horror movies are included in the class of things that have obvious endings.
• Action movies are for movie buffs.Action movies are for movie buffs.
– The whole class of action movies is included in the class of people that are movieThe whole class of action movies is included in the class of people that are movie
buffs.buffs.
– Essentially, either all or part of the subject is included in all or part of theEssentially, either all or part of the subject is included in all or part of the
predicate.predicate.
• Standard formStandard form
– A proposition that expresses the relation between subject and predicateA proposition that expresses the relation between subject and predicate
with complete clarity.with complete clarity.

4. Four types of categorical propositionsFour types of categorical propositions
• Categorical propositions are in standard form only if they appear in the following way:Categorical propositions are in standard form only if they appear in the following way:
– All S are P.All S are P. All members IncludedAll members Included e.g: All spiders have 8 legs.e.g: All spiders have 8 legs.
– No S are P.No S are P. All members ExcludedAll members Excluded e.g: No dogs are fishe.g: No dogs are fish
– Some S are P. Some members Included e.g: Some human beings are astronautsSome S are P. Some members Included e.g: Some human beings are astronauts
– Some S are not P. Some members Excluded e.g: Some people are not banker robbers.Some S are not P. Some members Excluded e.g: Some people are not banker robbers.
– All S are not P isAll S are not P is notnot standard form since it can mean two different things:standard form since it can mean two different things:
• It can mean that “No S are P” or that “Some S are not P”.It can mean that “No S are P” or that “Some S are not P”.

5. • Some propositions are not in standard form when they don’t begin with theSome propositions are not in standard form when they don’t begin with the
words “all”, “no”, and “some”.words “all”, “no”, and “some”.
Example: The brown bear was eating fish.Example: The brown bear was eating fish.
• Categorical propositions are just specific forms of substitution instances.Categorical propositions are just specific forms of substitution instances.

6. Breaking down the standard formBreaking down the standard form
• Normal sentences have a subject and a predicate.Normal sentences have a subject and a predicate.
– Example: All bears are brown.Example: All bears are brown.
• Standard form categorical propositions break this down further, and haveStandard form categorical propositions break this down further, and have
four parts:four parts:
– QuantifierQuantifier
• Specify how much of the subject is included in the predicate.Specify how much of the subject is included in the predicate.
– All, some, and no.All, some, and no.
– Some means “at least one”.Some means “at least one”.
– Subject termSubject term
• Main subject word, identified without its quantifier.Main subject word, identified without its quantifier.
– CopulaCopula
• Word that links the subject term and the predicate term.Word that links the subject term and the predicate term.
– Are and are not.Are and are not.
– Predicate termPredicate term
• Main predicate word, identified without its copula.Main predicate word, identified without its copula.

7. Attributes of categorical propositionsAttributes of categorical propositions• QualityQuality
– Affirmative or negative, depending on whether it affirms or denies thatAffirmative or negative, depending on whether it affirms or denies that
the subject is included in the predicate.the subject is included in the predicate.
• All S are P = Affirmative qualityAll S are P = Affirmative quality
• Some S are P = Affirmative qualitySome S are P = Affirmative quality
• No S are P = Negative qualityNo S are P = Negative quality
• Some S are not P = Negative qualitySome S are not P = Negative quality

8. • QuantityQuantity
– Universal or particular, depending on whether a statement saysUniversal or particular, depending on whether a statement says
something aboutsomething about all or some thingsall or some things referenced by the subject.referenced by the subject.
• All S are P = Universal quantityAll S are P = Universal quantity
• No S are P = Universal quantityNo S are P = Universal quantity
• Some S are P = Particular quantitySome S are P = Particular quantity
• Some S are not P = Particular quantitySome S are not P = Particular quantity

9. Classifying the four propositionsClassifying the four propositions
• The four kinds of propositions are classified according to the firstThe four kinds of propositions are classified according to the first
four vowels in the alphabet.four vowels in the alphabet.
– A types – All S are P. (Universal affirmative)A types – All S are P. (Universal affirmative)
– E types – No S are P. (Universal negative)E types – No S are P. (Universal negative)
– I types – Some S are P. (Particular affirmative)I types – Some S are P. (Particular affirmative)
– O types – Some S are not P. (Particular negative)O types – Some S are not P. (Particular negative)

10. DistributionDistribution
• An attribute of the terms in a proposition (subject and predicate).An attribute of the terms in a proposition (subject and predicate).
• A term is distributed if it makes an assertion about every thing in theA term is distributed if it makes an assertion about every thing in the
class that it refers to.class that it refers to.
– All S are P. (S only is distributed)All S are P. (S only is distributed)
– No S are P (S and P are both distributed)No S are P (S and P are both distributed)
– Some S are P (Neither one are distributed)Some S are P (Neither one are distributed)
– Some S are not P (P only is distributed)Some S are not P (P only is distributed)
– Example:Example:
• All people are happy. (Everyone who is a person falls within the class ofAll people are happy. (Everyone who is a person falls within the class of
being happy).being happy).
• Some people are not happy. (The state of being happy is separate from theSome people are not happy. (The state of being happy is separate from the
one person we know who is not happy).one person we know who is not happy).

11. Main attributes of categorical propositionsMain attributes of categorical propositions
PropositionProposition Letter nameLetter name QuantityQuantity QualityQuality TermsTerms
distributeddistributed
All S are P.All S are P. AA UniversalUniversal AffirmativeAffirmative SS
No S are P.No S are P. EE UniversalUniversal NegativeNegative S and PS and P
Some S areSome S are
P.P.
II ParticularParticular AffirmativeAffirmative NeitherNeither
Some S areSome S are
not P.not P.
OO ParticularParticular NegativeNegative PP

12. S P
All S are P

13. S P
All S are not P

14. S P
Some S are P

15. S P
Some S are not P