Logic Cards 4

Front 1

What is a categorical proposition?

Back 1

A proposition that relates two classes or categories.

Front 2

How are the classes in questions denoted?

Back 2

By the subjective term and the predicate term.

The proposition asserts that either all or part of the class denoted by the subject term is included in or excluded from the class denoted by the predicate term.

e.g. Not all romances have a happy ending.

Front 3

What are the four types of categorical propositions?

Back 3

1. Those that assert that a whole S class is included in the P class.

2. Those that asser that part of the S class is included in the P class.

3. Those that assert that the whole S class is excluded from the P class.

4. Those that assert that part of the S class is excluded from the P class.

Front 4

A standard form categorical proposition
comes in the following four forms:

Back 4

All S are P.

No S are P.

Some S are P.

Some S are not P.

Front 5

Define quantifier and copula:

Back 5

Quantifier: The words "all", "no" and "some". They specify how much of the S class is included or excluded from the P class.

Copula: The words "are" and "are not". They link or "couple" the S term with the P term.

Front 6

Analyze this standard form categorical proposition:

All members of the AMA are people holding degrees from recognized academic institutions.

Back 6

Quantifier: all.

Subject term: members of the AMA

Copula: are

Predicate term: people holding degrees from recognized academic institutions.

Front 7

What is NOT a standard form?

Back 7

All S are not P.

Front 8

The quality of a categorical proposition is either:

Back 8

Affirmative (affirms class membership) or negative (denies class membership).

Front 9

The quantity of a categorical proposition is either:

Back 9

Universal (makes a claim about every member of a class) or particular (just some members).

Note: The statement "some S are P" does NOT imply that some S are not P and vice versa.

Front 10

The four kinds of categorical propositions and their letter designation:

Back 10

A: Universal affirmative.

E: Universal negative.

I: Particular affirmative.

O: Particular negative.

Front 11

Define distribution:

Back 11

An attribute of the terms (S and P) of propositions. A term is said to be distributed if the proposition makes an assertion about every member of the class denoted by the term; otherwise, it is undistributed.

Note: See paper cards!

Front 12

Unprepared Students Never Pass:

Any Student Earning B's Is Not On Probation:

Back 12

Universals distribute Subjects, Negatives distribute Predicates.

A statements distribute the Subject, E statements distribute Both terms, I statements distribute Neither term, and O statements distribute the Predicate.

Front 13

Boolean categorical proposition meanings:

Back 13

All S are P: No members of S are outside of P.

No S are P = No members of S are inside P.

Some S are P = At least one S exists, and that S is a P.

SOme S are not P = At least one A exists, and that S is not a P.

Note: Universal propositions imply nothing about the existence of the things denoted by S.

Front 14

What is a Venn Diagram?

Back 14

An arrangement of overlapping circles in which each circle represents the class denoted by a term in a categorical proposition.

Shading an area means that the shaded area is empty, and placing an X in an area means that at least one things exists in that area.

Note: See cards!

Front 15

Boolean categorical proposition meanings:

Back 15

All S are P: No members of S are outside of P.

No S are P = No members of S are inside P.

Some S are P = At least one S exists, and that S is a P.

SOme S are not P = At least one A exists, and that S is not a P.

Note: Universal propositions imply nothing about the existence of the things denoted by S.

Front 16

What is a Venn Diagram?

Back 16

An arrangement of overlapping circles in which each circle represents the class denoted by a term in a categorical proposition.

Shading an area means that the shaded area is empty, and placing an X in an area means that at least one things exists in that area.

Note: See cards!

Front 17

How to translate an ordinary language statement into a categorical form:

Back 17

Understand the meaning of the statement, then re-express it in a new statement that has a quantifier, subject term, copula, and predicate term.

Front 18

Terms Without Nouns:

Back 18

If a term consists of only an adjective, a plural noun or pronoun should be introduced.

e.g. Some roses are red.

Some roses are red flowers.

Front 19

Nonstandard Verbs:

Back 19

The only copulas allowed in standard form are "are" and "are not".

e.g. Some college students will become educated.

Some college students are people who will become educated.

Front 20

Singular Propositions:

Back 20

Makes an assertion about a specific person, place, thing, or time. Typically translated by means of a parameter.

A parameter is a phrase that, when introduced into a statement, affects the form but not the meaning.

e.g. George went home.

All people identical to George are people who went home.

NOTE: Parameters are not used when the term has a plural noun!

Front 21

Adverbs and Pronouns:

Back 21

Statements containing spacial adverbs may be translated in terms of places or times.

e.g. He always wears a suit to work.

All times he goes to work are times he wears a suit.

Statements containing pronouns such as "who", "whoever", "anyone", "what", "whatever", or "anything" may be translated in terms of people or things.

e.g. Whoever works hard will succeed.

All people who work hard are people who will succeed.

NOTE: For "W" words, the language following "W" goes into the subject term of the categorical proposition.

Front 22

Unexpressed Quantifiers:

Back 22

e.g. Emeralds are green gems.

All emeralds are green gems.

Front 23

Nonstandard Quantifiers:

Back 23

SEE TEXT p. 236

Front 24

Conditional Statements:

Back 24

p. 237