Module 4: Categorical Syllogisms

Categorical Proposition

A statement that asserts a relationship between classes or categories using a subject term and a predicate term. Example: 'All dogs are mammals.'

Categorical Syllogism

A deductive argument consisting of three categorical propositions: two premises and one conclusion, containing exactly three terms. Example: 'All mammals are warm-blooded…'

Major Term

The predicate of the conclusion in a categorical syllogism. Example: in a conclusion, mammals.

Minor Term

The subject of the conclusion in a categorical syllogism. Example: poodles.

Middle Term

The term appearing in both premises but not in the conclusion; it links the other terms. Example: dogs.

Major Premise

The premise containing the major term.

Minor Premise

The premise containing the minor term.

Standard-Form Categorical Syllogism

A categorical syllogism arranged in standard order.

Mood

The pattern of proposition types (A, E, I, O) in a syllogism.

Figure

The arrangement of the middle term within the premises.

First Figure

Middle term is subject of the major premise and predicate of the minor premise.

Second Figure

Middle term is the predicate in both premises.

Third Figure

Middle term is the subject in both premises.

Fourth Figure

Middle term is predicate of major premise and subject of minor premise.

Validity

An argument where it is impossible for the premises to be true and the conclusion false.

Invalidity

An argument that fails to guarantee its conclusion.

Venn Diagram

A diagram using overlapping circles to represent classes and test validity.

Class

A collection of things sharing a common characteristic.

Shading

Indicates a region contains no members.

X Marking

Indicates at least one member exists.

Existential Import

The assumption that a class actually contains at least one member.

Aristotelian Interpretation

Assumes universal statements have existential import.

Boolean Interpretation

Does not assume existential import for universal propositions.

Universal Proposition

A proposition about all members of a class.

Particular Proposition

A proposition about some members of a class.

Rule of the Middle Term

The middle term must be distributed at least once.

Undistributed Middle

Fallacy where the middle term is not distributed in either premise.

Rule of the Major Term

A distributed major term in the conclusion must be distributed in its premise.

Illicit Major

Fallacy where the major term is distributed only in the conclusion.

Rule of the Minor Term

A distributed minor term in the conclusion must be distributed in its premise.

Illicit Minor

Fallacy where the minor term is distributed only in the conclusion.

Rule Against Two Negative Premises

A valid syllogism cannot contain two negative premises.

Exclusive Premises Fallacy

Fallacy caused by two negative premises.

Rule Requiring a Negative Premise for a Negative Conclusion

A negative conclusion requires exactly one negative premise.

Affirmative Premises with Negative Conclusion

Fallacy of drawing a negative conclusion from affirmative premises.

Negative Premise with Affirmative Conclusion

Fallacy of drawing an affirmative conclusion from a negative premise.

Rule Against Two Particular Premises

A valid syllogism cannot have two particular premises.

Two Particular Premises Fallacy

Fallacy resulting from two particular premises.

Existential Fallacy

Drawing a particular conclusion from universal premises under Boolean interpretation.

Distribution

A term is distributed when it refers to all members of a class.

Reduction Technique

A method used to simplify an argument to its essential terms.

Synonymous Expressions

Different expressions with the same meaning.

Nonstandard Argument

An argument not initially in standard syllogistic form.

Ordinary Language Argument

An argument expressed in everyday language.

Translation

Converting ordinary language into standard-form categorical propositions.

Standardization

Rewriting an argument for formal logical analysis.

Categorical Translation Rules

Guidelines for converting statements into A, E, I, or O propositions.

Quantifier

A word such as all, no, some, many, most, few indicating quantity.

Enthymeme

An argument with a missing premise or conclusion.

Suppressed Premise

A premise that is not explicitly stated.

Suppressed Conclusion

A conclusion that is implied but not stated.

Reconstructing an Enthymeme

Supplying the missing premise or conclusion.

Sorites

A chain argument with more than two premises.

Categorical Sorites

A sorites composed entirely of categorical propositions.

Polysyllogism

A series of connected syllogisms.

Chain Reasoning

Reasoning linked through a sequence of logical steps.

Testing a Sorites

Examining component syllogisms to check validity.

Conclusion of a Sorites

The final statement reached from the chain of premises.