Traditional Square of Opposition Flashcards

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Questions and Answers

What does the Traditional Square of Opposition illustrate?

The relations between categorical propositions (correct)

Mathematical equations

Social interactions

Logical fallacies

What is a contradictory in the context of categorical propositions?

Opposite truth value

What does contrary mean in categorical logic?

At least one is false (not both true)

Define sub-contrary in categorical propositions.

At least one is true (not both false) Signup and view all the answers

What does sub-alternation describe?

Truth flows downward, falsity flows upward Signup and view all the answers

What is denoted by an A proposition?

Universally affirmative Signup and view all the answers

What does an E proposition represent?

Universal negative Signup and view all the answers

What does an I proposition denote?

Particular affirmative Signup and view all the answers

Define an O proposition.

Particular negative Signup and view all the answers

What is an illicit subcontrary?

A formal fallacy that occurs from incorrect application of subcontrary relation Signup and view all the answers

What does illicit contrary refer to?

Inferences based on incorrect application of the contrary relation Signup and view all the answers

What is illicit sub-alternation?

Inferences based on illicit application of sub-alternation Signup and view all the answers

Define existential fallacy from an Aristotelian perspective.

An existential fallacy occurs when conclusions are drawn from premises about non-existent things Signup and view all the answers

What does existential fallacy mean in the Boolean context?

Invalid argument due to lack of existential import Signup and view all the answers

What is meant by existential import?

Dependence on evidence for the existence of beings in categories Signup and view all the answers

What does conditionally valid mean in Aristotelian logic?

Validity depends on whether the subject term denotes existing things Signup and view all the answers

Is the phrase 'All A are B; therefore, it is false that no A are B' conditionally valid?

Yes, it follows the contrary relation Signup and view all the answers

Study Notes

Traditional Square of Opposition

A visual representation of relationships between four types of standard-form categorical propositions based on Aristotelian logic.

Types of Propositions

Contradictory: Propositions that have opposite truth values.
Contrary: At least one proposition is false, cannot both be true.
Sub-contrary: At least one proposition is true, cannot both be false.
Sub-alternation: Truth flows downward; if the universal is true, the particular is true. Inversely, falsity flows upward.

Proposition Denotations

A Proposition (Universal Affirmative): Distributed subject term; predicate term not distributed.
E Proposition (Universal Negative): Both subject and predicate terms are distributed.
I Proposition (Particular Affirmative): No distribution of terms.
O Proposition (Particular Negative): Predicate term is distributed.

Illicit Fallacies

Illicit Subcontrary: Formal fallacy when incorrect application leads to false conclusions about subcontrary relations.
Illicit Contrary: Formal fallacy arising from incorrect deductions based on contrary relations.
Illicit Sub-alternation: Incorrect application of sub-alternation results in faulty inferences.

Existential Fallacies

Existential Fallacy (Aristotelian): When conclusions improperly derived from premises about non-existent entities lead to errors.
Existential Fallacy (Boolean): Occurs when premises are interpreted without existential import leading to invalid arguments.

Existential Import

Refers to the requirement that a categorical proposition's truth depends on the existence of entities in its subject and predicate categories.

Conditional Validity

Inferences are conditionally valid when the subject term of a premise may not refer to existing entities. Validity remains uncertain based on existence.

Example of Conditional Validity

"All students who failed the exam are students on probation. Therefore, some students who failed the exam are students on probation." Validity depends on whether any students failed.

Analyzing Conditional Validity

The example "All A are B. Therefore, it is false that no A are B" demonstrates valid reasoning under contrary relations, affirming conditional validity.

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Description

Explore the Traditional Square of Opposition with these flashcards. Learn about the relationships between various categorical propositions based on Aristotelian logic. Perfect for students of logic and philosophy.