Questions and Answers
What does the Traditional Square of Opposition illustrate?
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.
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What does sub-alternation describe?
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What is denoted by an A proposition?
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What does an E proposition represent?
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What does an I proposition denote?
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Define an O proposition.
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What is an illicit subcontrary?
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What does illicit contrary refer to?
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What is illicit sub-alternation?
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Define existential fallacy from an Aristotelian perspective.
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What does existential fallacy mean in the Boolean context?
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What is meant by existential import?
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What does conditionally valid mean in Aristotelian logic?
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Is the phrase 'All A are B; therefore, it is false that no A are B' conditionally valid?
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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.
