“Fundamental Binary Relation in Logic: Inclusion”

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0.3 Relation of InclusionLike all deductive theories, the algebra of logic may be established on various systems of principles14; we shall choose the one which most nearly approaches the exposition of Schroder and current logical interpretation.See Huntington on, “Sets of Independent Postulates for the Algebra of Logic”, _Transactions of the Am. Math. Soc._, Vol. V, 1904, pp. 288-309. [Here he says: “Any set of consistent postulates would give rise to a corresponding algebra, viz., the totality of propositions which follow from these postulates by logical deductions. Every set of postulates should be free from redundances, in other words, the postulates of each set should be _independent_, no one of them deducible from the rest.”]The fundamental relation of this calculus is the binary (two-termed) relation which is called _inclusion_ (for classes), _subsumption_ (for concepts), or _implication_ (for propositions). We will adopt the first name as affecting alike the two logical interpretations, and we will represent this relation by the sign \(


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