Concept

Monotonicity of entailment

Overview

Monotonicity of entailment is a property of many logical systems such that if a sentence follows deductively from a given set of sentences then it also follows deductively from any superset of those sentences. A corollary is that if a given argument is deductively valid, it cannot become invalid by the addition of extra premises.

Logical systems with this property are called monotonic logics in order to differentiate them from non-monotonic logics. Classical logic and intuitionistic logic are examples of monotonic logics.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

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1. When from a general proposition, not alone (for from a single proposition nothing can be concluded which is not involved in the terms), but by combining it with other propositions, we infer a proposition of the same degree of generality with itself, or a less general proposition, or a proposition merely individual, the process is Ratiocination. When, in short, the conclusion is more general than the largest of the…

   John Stuart Mill, A System of Logic

   States what Monotonicity of entailment is.

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2. Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.

   Alfred North Whitehead, Science and the modern world

   States what Monotonicity of entailment is.

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3. But although there may exist no contradiction in our judgement, it may nevertheless connect conceptions in such a manner that they do not correspond to the object, or without any grounds either à priori or à posteriori for arriving at such a judgement, and thus, without being self-contradictory, a judgement may nevertheless be either false or groundless. Now, the proposition: “No subject can have a predicate that…

   Immanuel Kant, The Critique of Pure Reason

   States what Monotonicity of entailment is.

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Related ideas

• Intuitionistic logic
• Relevance logic
• Validity (logic)
• Non-monotonic logic
• Classical logic
• Linear logic

Place in the tradition

Part of Affine logic.

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