contradictories

logic

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In logic, a contradiction occurs when two statements are opposed in both quantity and quality, meaning one is universal and the other particular, with one being an affirmation and the other a denial. For instance, "Every S is P" and "Some S is not P" are contradictories. A fundamental principle in logic, the law of contradiction, states that a thing cannot simultaneously be and not be of a specified kind or in a specified manner. This means that two contradictory statements cannot both be true; if one is true, the other must be false. Contradictions can also refer to a statement that asserts both the truth and falsity of something, or a situation where inherent factors are inconsistent. The study of logic, particularly formal logic, examines the validity of arguments and the relationships between propositions, ensuring that conclusions logically follow from premises without self-contradiction.1234

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contradictories and contraries
Two categorical propositions are contradictories if they are opposed in both quantity and quality; i.e., if one is universal (“every”) and the other particular (“some”) and one an affirmation and the other a denial. For example, “Every S is P” and “Some S is not P” are contradictories. Some…
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Two categorical propositions are contradictories if they are opposed in both quantity and quality; i.e., if one is universal (“every”) and the other particular (“some”) and one an affirmation and the other a denial. For example, “Every S is P” and “Some S is not P” are contradictories. Some…
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history of logic
Categorical forms
These Aristotle called contradictories. He had no special term for pairs related as forms I and O, although they were later called subcontraries. Subcontraries cannot be false together, although, as Aristotle remarked, they may be true together. The same holds for indefinite affirmatives and negatives, construed as equivalent…
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These Aristotle called contradictories. He had no special term for pairs related as forms I and O, although they were later called subcontraries. Subcontraries cannot be false together, although, as Aristotle remarked, they may be true together. The same holds for indefinite affirmatives and negatives, construed as equivalent…
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rationalism
Types and expressions of rationalism
…believed that the law of contradiction “A and not-A cannot coexist” holds for the real world, which means that every truth is consistent with every other; at the highest level, they have held that all facts go beyond consistency to a positive coherence; i.e., they are so bound up with…
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…believed that the law of contradiction “A and not-A cannot coexist” holds for the real world, which means that every truth is consistent with every other; at the highest level, they have held that all facts go beyond consistency to a positive coherence; i.e., they are so bound up with…
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