entailment

Meanings

• noun

  The relationship between two propositions such that the truth of one proposition logically implies the truth of the other.

  - "The statement 'all men are mortal' entails the statement 'Socrates is mortal'."
  - "The proposition 'it will rain' entails the proposition 'you should carry an umbrella'."

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Rhymes

Words rhyming with entailment
chalement , element , helament , mentalment

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Variants

List of all variants of entailment that leads to same result
entailment , entailments

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Etymology

origin and the way in which meanings have changed throughout history.

From Old French 'entailer', meaning 'to involve, to enchain'. The modern English word 'entailment' comes from the Middle English term 'entaille', meaning 'to bind or obligate'.

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Trivia

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1. The concept of entailment can be traced back to ancient Greek philosophy, particularly in the works of Aristotle and Plato.

2. Entailment is a key concept in modal logic, which is used to reason about necessity and possibility.

3. The relationship between entailment and implication is similar to the relationship between the subset and the superset in set theory.

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Related Concepts

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1. implication: Implication is a logical relationship between two propositions, where the truth of one proposition logically implies the truth of the other. However, unlike entailment, implication is not necessarily a strict logical relationship, as there may be possible worlds in which the implicant is true but the implicate is false. Entailment, on the other hand, is a stronger relationship, as the truth of the entailer guarantees the truth of the entailed proposition in all possible worlds.

2. consequence: A consequence is a logical or natural result of a given situation or action. While entailment refers to the logical relationship between two propositions, consequence can refer to a broader range of outcomes, including physical or natural effects.

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Culture

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The concept of entailment is fundamental in logic and mathematics, and is used to describe the relationship between propositions in formal systems. It has also been explored in various philosophical contexts, particularly in discussions of modal logic and the nature of necessity and possibility.

How to Memorize "entailment"

1. visualize
   

   - Imagine a chain of propositions, where each proposition is linked to the next by the relationship of entailment. The truth of each proposition in the chain implies the truth of the next, forming a logically consistent chain of reasoning.

2. associate
   

   - Associate the concept of entailment with the idea of a logical chain or a series of implications. Remember that entailment is a stronger relationship than implication, as it guarantees the truth of the entailed proposition in all possible worlds.

3. mnemonics
   

   - Use the mnemonic 'Every Implication Necessarily Has An Entailment' to remember the relationship between implication and entailment.

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