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1. Subject Terms and Predicate Terms

A categorical proposition (or categorical statement) is a proposition that relates two classes or

categories. The two classes are denoted by the subject term and the predicate term. The subject

term is the term (i.e., noun or noun phrase) that appears in the subject position of a categorical

proposition. The predicate term is the term (i.e., noun or noun phrase) that appears in the predicate

position of a categorical proposition. The subject of a sentence is the object or objects about which a

claim is being made, and the predicate of a sentence is what is being claimed about that subject.

Every categorical proposition asserts that all or part of the class referred to by the subject term is

either included in or excluded from the class denoted by the predicate term.

Consider the following categorical propositions. For each categorical proposition, identify the subject

term and the predicate term.

Categorical Proposition:

Not all events in life are reasons to celebrate.

Subject Term: events

Predicate Term: reasons to celebrate

Categorical Proposition:

Some religious experiences are genuine mysteries.

Subject Term: religious experiences

Predicate Term: genuine mysteries

Categorical Proposition:

Hulk Hogan is a professional wrestler.

Subject Term: Hulk Hogan

Predicate Term: professional wrestler

Categorical Proposition:

All cacti are succulents.

Subject Term: cacti

Predicate Term: succulents

Categorical Proposition:

Subject Term: dedicated teachers

Predicate Term: people with selfish

ambitions

No dedicated teachers are people with selfish

ambitions.

Categorical Proposition:

Some cellular phones are digital music players.

Subject Term: cellular phones

Predicate Term: digital music players

Categorical Proposition:

Laptop computers are digital devices.

Subject Term: Laptop computers

Predicate Term: digital devices

Categorical Proposition:

Stepfathers are not biological parents.

Subject Term: Stepfathers

Predicate Term: biological parents

2. Standard Form

A categorical proposition is a standard-form categorical proposition if and only if it is a

substitution instance of one of the following four forms:

Standard Forms for Categorical Propositions

All S are P.

No S are P.

Some S are P.

Some S are not P.

Recall that a substitution instance involves the uniform replacement of letters in a form with content

words, which in a categorical proposition are terms (i.e., nouns or noun phrases). Since a categorical

proposition states that all or part of the class denoted by the subject term is either included in or

excluded from the predicate class, these four forms cover all of the possible relationships between two

classes or categories. There are, of course, other ways to express categorical propositions in ordinary

language, and later you will explore methods for transforming these other categorical expressions into

standard-form categorical propositions.

Indicate the subject term and predicate term for each given categorical proposition. Also determine

whether the statement is a substitution instance of one of the four standard forms just shown or

whether it is not a standard-form categorical proposition. (Remember that a standard-form categorical

proposition must be an exact substitution instance of one of the preceding forms.)

Categorical Proposition:

No modern political parties are organizations immune to

dissent.

Subject Term: modern political

parties

Predicate Term: organizations

immune to dissent.

Which of the following statements is true of this categorical proposition?

It is not a standard-form categorical proposition.

It is a standard-form categorical proposition because it is a substitution instance of this

form: No S are P.

It is a standard-form categorical proposition because it is a substitution instance of this form: All

S are P.

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are not P.

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are P.

Categorical Proposition:

All reputable biologists are proponents of

evolution.

Subject Term: reputable biologists

Predicate Term: proponents of

evolution.

Which of the following statements is true of this categorical proposition?

It is a standard-form categorical proposition because it is a substitution instance of this form: No

S are P.

It is a standard-form categorical proposition because it is a substitution instance of this

form: All S are P.

It is not a standard-form categorical proposition.

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are P.

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are not P.

Categorical Proposition:

Some valid arguments are not sound arguments.

Subject Term: valid arguments

Predicate Term: sound arguments

Which of the following statements is true of this categorical proposition?

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are P.

It is a standard-form categorical proposition because it is a substitution instance of this

form: Some S are not P.

It is a standard-form categorical proposition because it is a substitution instance of this form: All

S are P.

It is not a standard-form categorical proposition.

It is a standard-form categorical proposition because it is a substitution instance of this form: No

S are P.

Categorical Proposition:

Bottlenose dolphins are carnivorous marine

mammals.

Subject Term: Bottlenose dolphins

Predicate Term: carnivorous marine

mammals

Which of the following statements is true of this categorical proposition?

It is a standard-form categorical proposition because it is a substitution instance of this form: All

S are P.

It is not a standard-form categorical proposition.

It is a standard-form categorical proposition because it is a substitution instance of this form: No

S are P.

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are P.

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are not P.

Categorical Proposition:

No diesel electric locomotives are steam

locomotives.

Subject Term: diesel electric

locomotives

Predicate Term: steam locomotives.

Which of the following statements is true of this categorical proposition?

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are not P.

It is not a standard-form categorical proposition.

It is a standard-form categorical proposition because it is a substitution instance of this form: All

S are P.

It is a standard-form categorical proposition because it is a substitution instance of this

form: No S are P.

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are P.

Categorical Proposition:

Former presidents of the United States are living

ghosts of history.

Subject Term: Former presidents of the

United States

Predicate Term: living ghosts of history.

Which of the following statements is true of this categorical proposition?

It is a standard-form categorical proposition because it is a substitution instance of this form: All

S are P.

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are P.

It is not a standard-form categorical proposition.

It is a standard-form categorical proposition because it is a substitution instance of this form:

Some S are not P.

It is a standard-form categorical proposition because it is a substitution instance of this form: No

S are P.

3. Quantifiers 1

Quantifiers determine how much of the subject class is included in, or excluded from, the predicate

class. There are three quantifiers that are used in standard-form categorical propositions: the words

"all," "some," and "no." These quantifiers determine how much of the class denoted by the subject

term is being included in, or excluded from, the class denoted by the predicate term. The meaning of

"all" and the meaning of "no" are self-explanatory, but in logic the word "some" always means at

least one. Therefore, the meaning of the proposition that "some S are P" is that there is at least one

object in the class denoted by S that is also within the class denoted by P.

Each of the following statements is a standard-form categorical proposition. Identify the quantifier

used in each categorical proposition.

Example A

No residents of the state of Ohio are residents of the state of New Jersey.

What is the quantifier in this categorical proposition?

Are

Residents

All

New Jersey

No

Some

Residents of the state of Ohio

Example B

All people who are afraid of doctors are folks w...