Peter D. Klein, in the second edition of The Cambridge Dictionary of Philosophy, defines closure as follows:
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| - Peter D. Klein, in the second edition of The Cambridge Dictionary of Philosophy, defines closure as follows:
A set of objects, O, is said to exhibit closure or to be closed under a given operation, R, provided that for every object, x, if x is a member of O and x is R-related to any object, y, then y is a member of O. [links not in original]
In propositional logic, the set of all propositions exhibits deductive closure: if set O is the set of propositions, and operation R is logical entailment ("\vdash"), then provided that proposition p is a member of O and p is R-related to q (i.e., p \vdash q), q is also a member of O. In the philosophical branch of epistemology, many philosophers have and continue to debate whether particular subsets of propositions–especially ones ascribing knowledge or justification of a belief to a subject–are closed under deduction. (en)
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| - Peter D. Klein, in the second edition of The Cambridge Dictionary of Philosophy, defines closure as follows: (en)
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