CategoricaCategorical l

PropositionPropositionss

Presenter:Presenter:

Fatima IbrahimFatima Ibrahim

Supervised by:Supervised by:

Madam MehwishMadam Mehwish

What are What are categorical categorical propositions?propositions?• Categorical propositions are statements that relate two Categorical propositions are statements that relate two

different classes of things.different 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 All horror movies are included in the class of things that have obvious

endings.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 The whole class of action movies is included in the class of people that

are movie buffs.are movie buffs.

– Essentially, either all or part of the subject is included in all or Essentially, either all or part of the subject is included in all or part of the predicate.part of the predicate.

• Standard formStandard form– A proposition that expresses the relation between subject and A proposition that expresses the relation between subject and

predicate with complete clarity.predicate with complete clarity.

Four types of Four types of categorical categorical propositionspropositions• Categorical propositions are in standard form only if they appear in the Categorical propositions are in standard form only if they appear in the

following way:following way:– All S are P.All S are P. All members Included All members Included e.g: All spiders have e.g: All spiders have

8 legs.8 legs.– No S are P.No S are P. All members Excluded All members Excluded e.g: No dogs are fish e.g: No dogs are fish– Some S are P. Some members Included e.g: Some human beings are Some S are P. Some members Included e.g: Some human beings are

astronautsastronauts– Some S are not P. Some members Excluded e.g: Some people are not Some S are not P. Some members Excluded e.g: Some people are not

banker robbers.banker robbers.

– All S are not P is All 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”.

• Some propositions are not in standard form when they don’t begin with the Some 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.

Breaking down the Breaking down the standard formstandard 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 have Standard 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.

Attributes of Attributes of categorical categorical propositionspropositions

• QualityQuality

– Affirmative or negative, depending on whether it affirms or denies that Affirmative 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

• QuantityQuantity

– Universal or particular, depending on whether a statement says Universal or particular, depending on whether a statement says something about something 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

Classifying the Classifying the four propositionsfour propositions• The four kinds of propositions are classified according to The four kinds of propositions are classified according to

the first four vowels in the alphabet.the first 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)

DistributionDistribution• An attribute of the terms in a proposition (subject and An attribute of the terms in a proposition (subject and

predicate).predicate).• A term is distributed if it makes an assertion about every A term is distributed if it makes an assertion about every

thing in the class that it refers to.thing in the 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 All people are happy. (Everyone who is a person falls within the

class of being happy).class of being happy).• Some people are not happy. (The state of being happy is separate Some people are not happy. (The state of being happy is separate

from the one person we know who is not happy).from the one person we know who is not happy).

Main attributes of Main attributes of categorical categorical propositionspropositionsPropositionProposition Letter Letter

namenameQuantityQuantity QualityQuality Terms Terms

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 are Some S are P.P.

II ParticularParticular AffirmativeAffirmative NeitherNeither

Some S are Some S are not P.not P.

OO ParticularParticular NegativeNegative PP

S P

All S are P

S P

All S are not P

S P

Some S are P

S P

Some S are not P